A Survey of TDMA Scheduling Schemes in Wireless Multihop Networks

53

A Survey of TDMA Scheduling Schemes in WirelessMultihop Networks

AGGELIKI SGORA, VTT Technical Research Centre of FinlandDIMITRIOS J. VERGADOS, Norwegian University of Science and TechnologyDIMITRIOS D. VERGADOS, University of Piraeus

One of the major problems in wireless multihop networks is the scheduling of transmissions in a fair andefficient manner. Time Division Multiple Access (TDMA) seems to be one of the dominant solutions to achievethis goal since it is a simple scheme and can prolong the devices’ lifetime by allowing them to transmit onlya portion of the time during conversation. For that reason, several TDMA scheduling algorithms may befound in the literature. The scope of this article is to classify the existing TDMA scheduling algorithms basedon several factors, such as the entity that is scheduled, the network topology information that is needed toproduce or maintain the schedule, and the entity or entities that perform the computation that produces andmaintains the schedules, and to discuss the advantages and disadvantages of each category.

Categories and Subject Descriptors: C.2.1 [Computer-Communication Networks]: Network Architectureand Design-Wireless Communication

General Terms: Scheduling, Performance

Additional Key Words and Phrases: Time Division Multiple Access (TDMA), collision, wireless multihopnetworks

ACM Reference Format:Aggeliki Sgora, Dimitrios J. Vergados, and Dimitrios D. Vergados. 2015. A survey of TDMA schedulingschemes in wireless multihop networks. ACM Comput. Surv. 47, 3, Article 53 (April 2015), 39 pages.DOI: http://dx.doi.org/10.1145/2677955

1. INTRODUCTION

Wireless multihop networks (i.e., ad hoc, sensor, mesh networks) are formed by a setof nodes, in which each node has not only to transmit its own generated traffic, butalso to act as a relay, sending traffic on behalf of other nodes. Thus, the number oftransmissions of each node in comparison with those of a node in an infrastructure-based network is increased. Consequently, the interference caused by simultaneoustransmissions in these networks is also increased, and, therefore, efficient mediumaccess control is a necessity.

Since the most popular medium access control mechanism for ad hoc networks isthe IEEE 802.11 Distributed Coordination Function (DCF) [IEEE 1999], which usesthe Carrier Sense Multiple Access (CSMA), most of the research works on wirelessmultihop networks adopt it as the Medium Access Control (MAC) mechanism. However,

Authors’ addresses: A. Sgora, VTT Technical Research Centre of Finland, Kaitovayla 1, FI-90570 Oulu, Fin-land; email: [email protected]; D. J. Vergados, Department of Telematics, Norwegian University of Science andTechnology (NTNU), O.S. Bragstads plass 2B, N-7491, Trondheim, Norway; email: [email protected];D. D. Vergados, Department of Informatics, University of Piraeus, 80 Karaoli & Dimitriou St. GR-185 34,Piraeus, Greece; email: [email protected] to make digital or hard copies of part or all of this work for personal or classroom use is grantedwithout fee provided that copies are not made or distributed for profit or commercial advantage and thatcopies show this notice on the first page or initial screen of a display along with the full citation. Copyrights forcomponents of this work owned by others than ACM must be honored. Abstracting with credit is permitted.To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of thiswork in other works requires prior specific permission and/or a fee. Permissions may be requested fromPublications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212)869-0481, or [email protected]© 2015 ACM 0360-0300/2015/04-ART53 $15.00

DOI: http://dx.doi.org/10.1145/2677955

ACM Computing Surveys, Vol. 47, No. 3, Article 53, Publication date: April 2015.

http://dx.doi.org/10.1145/2677955

http://dx.doi.org/10.1145/2677955

53:2 A. Sgora et al.

Fig. 1. Example of primary and secondary collisions.

DCF has been shown to suffer from a fairness problem caused by the existence of hiddenterminals and exacerbated by the adopted binary exponential backoff algorithm toresolve contention [Xu and Saadawi 2001; Fang and Bensaou 2004]. Furthermore,the IEEE 802.11 DCF has numerous disadvantages, such as high overhead, increasedaccess delay, high jitter, and limited Quality of Service (QoS) capabilities [Vergadoset al. 2005].

For these reasons, some researchers have focused their attention on the Time Di-vision Multiple Access (TDMA) scheme since it is simpler and can prolong devices’lifetimes by allowing them to transmit only a portion of the time during conversation.In a TDMA system, time is divided into frames that consist of time slots. The numberof time slots in each TDMA frame is called the frame length. A time slot has a unittime length required for a packet to be transmitted between adjacent nodes. Whennodes are in close range, collisions may occur in case of simultaneous transmissions.Therefore, the use of TDMA as the MAC mechanism in wireless multihop networksrequires scheduling in order to avoid collisions.

The scope of this article is to provide a comprehensive state-of-the-art survey ofTDMA scheduling algorithms, to classify them, and to discuss them accordingly.

It should be noted that the problem of TDMA scheduling is a subset of the moregeneral wireless scheduling problem, where the outcome is a repeating cycle of slotassignments. The problem of wireless scheduling has been studied in the literature,and theoretical results have been obtained for the capacity of the system using greedymaximal scheduling [Joo et al. 2009] or longest queue first [Dimakis and Walrand2006] algorithms and for the stability of scheduling policies with respect to arrivaltraffic rates [Tassiulas and Ephremides 1992]. In this article, however, we focus ourattention on the problem of TDMA scheduling due to its popularity in wireless multihopnetworks (i.e., IEEE 802.16) and its ease of implementation.

2. TDMA SCHEDULING ALGORITHMS

During the communication between two nodes in a wireless TDMA network, two typesof collisions may occur: primary (explicit) or secondary (implicit) collisions (interferenceor conflict) [Fattah and Leung 2002]. A primary collision occurs when a node does morethan one thing in a single time slot (e.g., when a node transmitting in a given time slotis also receiving in the same time slot on the same channel; see Figure 1a). In thecase of a node equipped with multiple radio interfaces (assuming an omnidirectionalantenna), a primary collision will also occur whenever its radio interfaces operate onthe same channel at the same time [Gabale et al. 2013]. A secondary collision occurswhen a Mobile Station (MS) that receives a transmission intended for it is interferedby another transmission that is not intended for it [Ramanathan and Lloyd 1993](Figure 1b). Therefore, in order to avoid collisions, any two stations that may result ina collision must be scheduled to transmit at different time slots. However, even in thecase that primary and secondary collisions are avoided, legacy TDMA is very inefficientfrom the resource utilization point of view [Bjorklund et al. 2004].


A Survey of TDMA Scheduling Schemes in Wireless Multihop Networks 53:3

Table I. Scheduling Algorithms Categories

Criterion Basic Characteristics TypesScheduling Entity Links Link Scheduling

Nodes Node SchedulingNetwork Topology Knowledge Accurate Topology Information Topology-Dependent Scheduling

Independent of the Topology Topology-Transparent SchedulingSchedule Computing A Central Station Centralized Scheduling

Distributed among Nodes Distributed Scheduling

Spatial reuse will greatly improve system performance [Cai et al. 2003], and, forthat reason, the Spatial Reuse TDMA (STDMA) [Nelson and Kleinrock 1985] is usedin wireless multihop networks to achieve both high capacity and delay guaranteesbecause it allows a time slot to be shared by geographically separated radio units, sothat small interference is obtained [Gronkvist 2006].

The problem of assigning at least one transmission slot for all nodes in the networkwhile ensuring collision avoidance is called the Broadcast Scheduling Problem (BSP)and has been proved to be NP-complete [Ephremides and Truong 1990]. The mainobjectives of the BSP are the following [Chen et al. 2006]:

(1) minimize the total frame length and/or increase the network capacity,(2) maximize the number of simultaneous transmissions from noninterfering stations,

and(3) minimize the average packet delay.

To solve the BSP, several TDMA scheduling algorithms have been proposed in theliterature that may be classified based on several factors, such as the entity that isscheduled, the network topology information that is needed to produce or maintain theschedule, and the entity or entities that perform the computation for producing andmaintaining the schedules, as depicted in Table I.

First, depending on the entity that is scheduled, the TDMA scheduling algorithmscan be distinguished into link (or point-to-point) and node scheduling (or activation)[Ephremides and Truong 1990]. In a node schedule, the scheduled entities are the sta-tions themselves, and, therefore, each node’s transmission must be received collision-free by all of its neighbors [Ephremides and Truong 1990]. On the other hand, in alink schedule, the links between the stations are scheduled. The transmission of a nodethat is intended for a particular neighbor is required to be without collisions at thisreceiver [Han et al. 2006].

In addition, TDMA scheduling algorithms can also be classified into topology-dependent and topology-transparent (or independent or code-based [Amouris 2001]algorithms. Topology-dependent TDMA scheduling algorithms require some a prioriknowledge of the network topology (topology information). Therefore, in these algo-rithms, when the topology changes, the previous schedules expire and new schedulesshould be generated [Cai et al. 2003]. On the other hand, in topology-transparentTDMA scheduling algorithms, collisions may occur while no topology information isused [Sun et al. 2008]. Thus, they are fully distributed and less complex than thetopology-dependent algorithms [Xu et al. 2011].

TDMA scheduling algorithms can also be classified into centralized and distributedones, depending on which node the computation for creating and maintaining theschedules is performed. In the centralized approaches, there is an entity, a “controller,”that performs the computation for producing and maintaining the schedules; in thedistributed ones, the computing is distributed among the nodes.

In addition to the pure MAC-layer TDMA solutions, there are also cross-layer so-lutions that either use other layers to obtain better schedules or try to include in the



Fig. 2. TDMA scheduling algorithms.

Fig. 3. TDMA scheduling methods categorization.

initial BSP other constraints, such as energy consumption. Cross-layer solutions can beused in several operations, such as environmental monitoring, topology control, powerefficiency, and joint routing and scheduling. Finally, in addition to the pure TDMA so-lutions, there are also hybrid solutions that combine TDMA with other protocols (e.g.,CSMA, etc.) in order to obtain the benefits of all the protocols combined.

Figure 2 depicts the classification used in this article. The following sections discussaspects concerning each category.

3. TDMA NODE SCHEDULING ALGORITHMS

In TDMA node scheduling, the entities that are scheduled are the nodes, so that eachnodes transmission may be received by all of its neighbors without interference. TheTDMA node scheduling algorithms can be further distinguished into centralized anddistributed. This section overviews, classifies, and discusses aspects concerning cen-tralized and distributed TDMA node scheduling algorithms.

3.0.1. Centralized TDMA Node Scheduling Algorithms. Several centralized TDMA node (orbroadcast) scheduling algorithms can be found in the literature. These algorithms canbe further divided into two categories: single-stage and two-stage approaches [Shi andWang 2005a].

The single-stage approach tries to find the optimal solution for the BSP in onestage. On the other hand, the two-stage approach aims to solve the BSP problem intwo separate stages: The first is to schedule transmissions of all nodes in a minimalTDMA length without any collisions; the second is to maximize the total collision-free transmissions in order to maximize channel utilization. Independently from theapproach followed (single- or two-stage), the centralized TDMA scheduling algorithmsuse several approaches (Figure 3) including greedy algorithms, Mean Field Annealing(MFA), tabu search, Genetic Algorithms (GAs), neural networks, graph coloring, andother mathematical approaches in order to solve the BSP.

Ephremides and Truong [1990] proved that the NP-complete problem of finding amaximum cardinality-independent set in a graph can be reduced to the problem of



finding a maximal broadcasting mode in a radio network. The authors also proposeda heuristic algorithm that tries to find the maximum cardinality-independent set in agraph that represents the wireless multihop network. However, this algorithm focusesonly on channel utilization optimization and does not consider the optimization of theframe length as well as the average packet delay [Chen et al. 2006].

Wang and Ansari [1997] proposed an approximation algorithm based on MFA tosolve the scheduling problem and achieve maximum channel utilization as well aslower delay. More specifically, the authors map the channel utilization to be maximizedand the interference-free constraints onto an energy function, and then the MFA pro-cedure is executed to search for the optimal solutions. Numerical results have shownthat the proposed algorithm is capable of finding the shortest interference-free frameschedule while it provides the maximum channel utilization. Moreover, in comparisonwiththe Ephremides and Truong’s [1990] algorithm, numerical results showed that theproposed algorithm achieves better performance in terms of time delay and channelutilization. However, the proposed algorithm has two drawbacks [Yeo et al. 2002]:

(1) It cannot efficiently minimize the frame length due to the possibility that a numberof additional time slots are needed (in case the initial frame length is set to thelower bound).

(2) There is no ideal method to determine the optimal parameters for the MFAprocedure.

Since simulated annealing is a time-consuming process [Chakraborty 2004], many re-search efforts were concentrated on GAs. More specifically, Ngo and Li [2003] proposeda centralized scheduling algorithm using a modified GA (MGA) called the genetic-fixalgorithm. The authors first formulate the broadcast scheduling problem as an uncon-strained optimization problem, and then the genetic-fix algorithm was used to obtain,within a reasonable time, a conflict-free broadcast assignment in which the framelength is close to minimum. The main advantage of this algorithm is that, at eachrepetition, the search space is reduced. Chakraborty [2004] showed that the standardgenetic algorithm performed poorly for large networks since its crossover and muta-tion operations create invalid members that flood the whole population, hindering theprogress of searching for valid solutions. To overcome this problem, he proposed theMGA algorithm, in which special crossover and mutation operations are defined, sothat that members of the population always remain valid solutions of the problem.

Gunasekaran et al. [2010] proposed the GACFS algorithm for Worldwide Interoper-ability for Microwave Access (WiMAX) networks, which tries to converge to the optimalvalue at a much faster rate than the classical GA algorithm. The novelty of the algo-rithm is that it considers two kinds of population: the Solution Population (SP) thatcontains all the candidate solutions, which represent the TDMA frames for the sched-ule, and the Test-case Population (TP) that contains a set of constraints and acts as testcases to the SP. These two populations act as competitors against each other and henceincrease the evolving rates. Simulation results showed that the proposed algorithmexceeds the MGA [Chakraborty 2004] and the Finite-State Machine-Based (FSMA)algorithm [Ahmad et al. 2008] in terms of throughput. The main drawback of the algo-rithm is that since each member of TP has to be compared with every member of SP, itrequires lots of comparisons and calculations, especially in cases where the populationsizes are huge [Arivudainambi and Rekha 2012].

In addition, in order to find less time-consuming algorithms, several solutions eitherbased on graph theory or in mathematics have been proposed. In many graph the-oretic approaches, restricted classes of graphs are also considered. More specifically,Ramanathan and Lloyd [1993] modeled packet radio networks using two restrictedclasses of graphs—trees and planar graphs—and then produced the broadcast TDMA



schedule by applying the graph coloring algorithm. Experimental results showed thatthe proposed algorithm uses on average roughly 10% fewer slots than Ephremides andTruong’s [1990] algorithm does.

Sen and Huson [1997] modeled packet radio networks as planar point graphs and ap-plied the coloring algorithm to find the broadcast TDMA schedule. However, restrictedclasses of graphs are suitable only for a few real-life network environments. Trees aretoo restrictive, but planar graphs are a reasonable model only when the transmissionrange is quite small, and disc and planar point graphs are only valid when there areno obstacles in the signal path (e.g., a building) [Ramanathan 1999]. Yeo et al. [2002]proposed a TDMA scheduling algorithm based on the Sequential Vertex Coloring (SVC)algorithm applied in an arbitrary graph network. Numerical results showed that SVCcan find near-optimal schedules and can achieve lesser or equal performance in termsof frame length and better performance in terms of throughput in comparison withWang and Ansari’s [1997] algorithm.

As an alternative approach to GAs, neural networks have been also used to solvethe BSP. More specifically, Takefuji et al. [1992] proposed a Maximum Neural Net-work (MNN) model that always guarantees a valid solution and greatly reduces thesearch space without the burden of parameter-tuning. Bi et al. [2005] added a nega-tive self-feedback to the MMN in order to prevent the network from getting stuck atlocal minima. Simulation results showed that the use of negative self-feedback to theMNN introduces richer and more flexible nonlinear dynamics and that the proposedalgorithm usually converges to a stable equilibrium point.

Funabiki and Kitamichi [1999] proposed a two-stage scheduling algorithm for packetradio networks. More specifically, the proposed algorithm uses a Gradual Neural Net-work (GNN) to find the minimal frame length in the first stage and a binary HopfieldNeural Network (HNN) to maximize the conflict-free transmission in the second stage.However, the main drawback of the algorithm is that HNN is easily trapped in localminima [Sun et al. 2010].

Shen and Wang [2008] proposed a Fuzzy Hopeld Neural Network (FHNN) clusteringtechnique to solve the BSP. Simulation results showed that the proposed algorithm hadsuperior ability to find a solution of the BSP in packet radio networks over the MFA[Wang and Ansari 1997], SVC [Yeo et al. 2002], HNN-GA [Salcedo-Sanz et al. 2003],and Shi and Wang [2005a] algorithms.

Shi and Wang [2005b] proposed a two-stage TDMA broadcast algorithm based on aGradual-Noisy Chaotic Neural Network (G-NCNN; i.e., a chaotic neural network witha stochastic nature). Simulation results showed that the proposed algorithm achievesbetter solutions than the MFA [Wang and Ansari 1997], SVC [Yeo et al. 2002], andFunabiki and Kitamichi [1999] algorithms with minimal average time delay and max-imal channel utilization.

To further improve the time needed to find the optimal solution for the BSP, severalhybrid algorithms that combine different heuristics have been proposed in the liter-ature. More specifically, Salcedo-Sanz et al. [2003] proposed a mixed neural-geneticalgorithm (the HNN-GA) as a solution to the broadcast problem. The algorithm is acombination of an HNN and a GA, which are used during the first and second stages,respectively. Simulation results showed that the proposed algorithm obtains optimalframe lengths and performs better in terms of throughput than the MFA [Wang andAnsari 1997] and SVC [Yeo et al. 2002] algorithms in several benchmark cases.

Shi and Wang [2005a] proposed a two-stage hybrid method (SVCNCNN) that com-bines the SVC) algorithm and an NCNN for the first and second stages, respectively.Also, the same authors in Shi and Wang [2005b] proposed another hybrid algorithm,BSC-NCNN, that combines a Backtracking Sequential Coloring (BSC) algorithm andan NCNN during the first and second stages, respectively. Unfortunately, the process



of finding the optimum choice of parameters takes long calculation time in both al-gorithms. In addition, this method easily converges to local optima [Shen and Wang2008].

Sun et al. [2010] proposed a two-stage Hysteretic NCNN algorithm (H-NCNN) forpacket radio networks. The novelty of the paper is the hysteretic function of the NCNNthat increases the effective convergence toward optimal or near-optimal solutions athigher noise levels. Simulation results showed that the proposed algorithm is morelikely to find optimal or near-optimal TDMA frame solutions than the MFA [Wangand Ansari 1997], SVC [Yeo et al. 2002], GAFCS [Gunasekaran et al. 2010], or FSMA[Ahmad et al. 2008] algorithms.

Peng et al. [2004] proposed a two-stage hybrid algorithm that combines tabu searchand a greedy algorithm during the first and second stages, respectively. The firststage guarantees a transmission time slot for each station, while the second stageattempts to maximize the throughput. Simulation results showed that, in compari-son with the HNN-GA [Salcedo-Sanz et al. 2003] algorithm, the proposed algorithmachieves slightly better performance in terms of channel utilization and equivalentperformance in packet delay. Xizheng and Yaonan [2008] proposed a two-stage hybridalgorithm, the FC-HNN. During the first stage, it uses a modified SVC algorithm toobtain a minimal TDMA frame length; in the second stage, the channel utilization ismaximized by using a fuzzy HNN. Simulation results showed that the proposed algo-rithm can achieve better performance, with shorter frame length and higher channelutilizing ratio, than the MFA [Wang and Ansari 1997], SVC [Yeo et al. 2002], and Shiand Wang [2005a] algorithms.

In addition to these attempts, several methods based on various mathematical the-ories can also be found in the literature. More specifically, Chen et al. [2006] trans-formed the BSP in a packet radio network into a Low-Density Parity Check (LDPC)-like problem using a factor graph. The optimal broadcast is obtained by applying thesum-product algorithm into the factor graph. Simulation results showed that the pro-posed algorithm performs better, especially in large networks, in comparison with theMFA [Wang and Ansari 1997] and HNN-GA [Salcedo-Sanz et al. 2003] algorithms interms of channel utilization and average packet delay.

Vergados et al. [2005] also proposed an algorithm for overcoming the NP-completeBSP in TDMA ad hoc networks, one based on an interference vector. Simulation re-sults showed that the proposed algorithm was superior to the MFA [Wang and Ansari1997] algorithm and equivalent to the HNN-GA [Salcedo-Sanz et al. 2003] algorithmfor most of the tested network topologies in terms of delay, throughput, and fairness.Furthermore, a modification of the previous algorithm was proposed by Sgora et al.[2008a] that achieves both efficiency and fairness. This is achieved by taking into con-sideration the communication requirements of the active flows of a wireless multihopnetwork during the scheduling process. Simulation results showed that the proposedalgorithm exhibits improved performance compared to the other solutions (MFA [Wangand Ansari 1997], HNN-GA [Salcedo-Sanz et al. 2003]) not only in terms of fairness,but also in terms of throughput.

Finally, Ahmad et al. [2008] transform the BSP as a Finite State Machine (FSM).More specifically, the authors define the maximal set of nodes that can be scheduled totransmit in a time slot without any collisions as maximal compatibles. A tight lowerbound derived from the set of maximal incompatibles forms the basis for derivingminimum frame length. The proposed algorithm (FSMA) applies a set of rules on themaximal compatibles in order to maximize utilization of slots. Experimental resultsshowed that the proposed algorithm exhibits improved performance in terms of delaythan the MFA [Wang and Ansari 1997], SVC [Yeo et al. 2002], HNN-GA [Salcedo-Sanzet al. 2003], and Funabiki and Kitamichi [1999] algorithms.



An overview of the basic characteristics, advantages, and disadvantages of the cen-tralized TDMA node scheduling algorithms referred to in this article is presentedin Table II. An overview of the centralized TDMA scheduling can also be found inCommander et al. [2004].

Since it is difficult to implement all the scheduling algorithms because limited in-formation concerning their implementation is available, we tried to summarize theirperformance in terms of frame length on the basis of the three common referencetopologies—a 15-node network (Figure 4a), a 30-node network (Figure 4b), and a 40-node network (Figure 4c)—used in these papers. Table III summarizes this comparison.

3.1. Distributed TDMA Node Scheduling Algorithms

In distributed TDMA node scheduling algorithms, the schedules are produced byusing only limited (local) knowledge of the topology. These algorithms can be fur-ther divided into topology-dependent (graph-based) and topology-transparent (code-based) approaches [Amouris 2001]. Topology-dependent approaches focus on finding aconflict-free schedule based on prior information about the network topology. Topology-transparent algorithms are independent of the specific topology and therefore immuneto nodal mobility. These algorithms can be further divided into deterministic and prob-abilistic, depending on the policy by which slots are allocated to nodes. In the deter-ministic policy, nodes are not allowed to access slots other than those assigned to them,whereas in the probabilistic policy, nodes are additionally allowed to access nonas-signed slots with some nonzero probability p.

3.1.1. Distributed Topology-Dependent TDMA Node Scheduling Algorithms. Distributedtopology-dependent node scheduling algorithms require nodes to have prior knowledgeabout the network (such as size and the node’s degree) [Zhu and Corson 2001b]. Thus,recomputation and information exchanges are required to maintain accurate networktopology information [Liu et al. 2012]. In these algorithms, transmission schedules canbe established by either dynamically exchanging and resolving time slot requests or byprearranging a timetable for each node based on the network topologies [Loscri 2007].

One of the first distributed topology-dependent TDMA node algorithms was pro-posed by Ephremides and Truong [1990] (denoted as E-T); it assumes that each MShas knowledge of connectivity only two hops away. By using this information, an initialskeleton schedule is produced. Then, every node broadcasts those columns of the skele-ton schedule that correspond to itself and to its one-hop neighbors. For the assignmentof nonreserved or blocked slots, a deterministic priority discipline is applied: The nodewith highest priority among the contenders starts first and utilizes the slot. All nodesthat perceive this use broadcast this event during their assigned skeleton slots. Thus,nodes with the highest priority status go ahead and utilize that same slot in the nextframe. However, this algorithm does not ensure fair slot assignments among all MSs,and it is not topology-transparent [Fattah and Leung 2002].

Vergados et al. [2006] proposed a deterministic distributed algorithm based onan interference vector, the Distributed Dynamic End-To-end Scheduling Algorithm(DDETSA), which invokes end-to-end reservations for all nodes in the path from thesource to the destination node. DDETSA provides a mechanism for adapting the num-ber of time slots that are allocated to each node according to the traffic that it is serving.This is done with an on-demand mechanism for slot allocation and deallocation. Thealgorithm assigns transmission slots to the nodes in the network by taking into con-sideration the collision avoidance requirements of the topology. Since this algorithmresponds to dynamic traffic requirements, it surpasses the performance of the staticMFA [Wang and Ansari 1997] and HNN-GA [Salcedo-Sanz et al. 2003] algorithms bothin terms of throughput and delay.



Table II. Broadcast Centralized Scheduling Algorithms Overview

Perf. MetricsRef. Method Thr. Fair. Del. Advantages Disadvantages[Ephremidesand Truong1990]

GrA - - - Simple. Suitable only for a few real-lifenetwork environments.

SVC-NCNN [Shiand Wang2005a]

GT andNN

- - � Decreased average timedelays.

1. Difficult to determine theoptimum choice of theparameters.

2. Optimizing slot utilizationand frame lengthseparately does not lead toa good solution with respectto both criteria.

MFA [Wang andAnsari 1997]

SA - - � Provides maximumchannel utilization.

1. Time-consuming process.2. There is no ideal method to

determine optimalparameters for the MFAprocedure.

SVC [Yeo et al.2002]

GT � - � Can find near-optimalsolutions in respect tosystem delay.

Long calculation time isneeded to determine theoptimum choice of theparameters.

MGA[Chakraborty2004]

GA � - - Generates a search spacewith valid solutions.

Optimizing slot utilization andframe length separatelydoes not lead to a goodsolution with respect toboth criteria.

GAFCS[Gunasekaranet al. 2010]

GA � - - The population evolves ata faster rate thanclassical GA algorithms.

Not suitable for densenetworks with heavy trafficload.

[Ngo and Li2003]

GA - - - At each repetition, thesearch space is reduced.


[Sen and Huson1997]

GT - - � Simple. Suitable only for a few worldnetwork environments.

MNN[Takefuji et al.1992]

NN - - � 1. Always guarantees validsolutions.

2. Reduces the searchspace without theburden of parametertuning.

Difficult to reach an optimumsolution due to the largercrossbar switch problems.

BSC-NCNN [Shiand Wang2005b]

GT andNN


1. Long calculation time isneeded to determine theoptimum choice of theparameters.


[Bi et al. 2005] NN - - - 1. Introduces richer andmore flexible nonlineardynamics.

2. Usually converges to astable equilibriumpoint.


(Continued)



Table II. Continued

Perf. MetricsRef. Method Thr. Fair. Del. Advantages Disadvantages[Funabiki andKitamichi 1999]

NN - - � Increases the likelihood ofconvergence to theglobal minimum.

1. Can be easily trapped inlocal minima.

2. Converges to infeasiblesolutions for its gradientdescent mechanism.

FHNN [Shenand Wang 2008]

NN - - � 1. Reduces the processingtime.

2. Increases theconvergence time to theBSP.


HNN-GA[Salcedo-Sanzet al. 2003]

GA andNN



G-NCNN [Shiand Wang2005c]

GT andNN

� - � Decreased average timedelays.

1. Long calculation time isneeded to determine theoptimum choice of theparameters.


H-NCNN [Sunet al. 2010]

NN - - � Increases the effectiveconvergence towardoptimal or near-optimalsolutions at highernoise levels.


TS-GR [Peng etal. 2004]

TS andGrA

� - � Simple. 1. Time-consuming process.2. Optimizing slot utilization

and frame lengthseparately does not lead toa good solution with respectto both criteria.

FC-HNN[Xizheng andYaonan2008]

GT andNN

- - � Short frame length. Optimizing slot utilization andframe length separatelydoes not lead to a goodsolution with respect toboth criteria.

[Vergados et al.2005]

O � � - Simple. A greedy approximation.

[Sgora et al.2008a]

O � � - Takes into considerationthe communicationrequirements of theactive flows.

Not suitable for networks withheavy load conditions.

FSMA [Ahmadet al. 2008]

O � - � 1. Explores complexsolution space insmallerCPU time.

2. Achieves minimumframe length and themaximum slotutilization in arelatively shorter time.

Does not take into accountQoS (bandwidth or delayrequirements) whendetermining the broadcastschedule.

Abbreviations used in this table: GrA, Greedy Algorithm; GT, Graph Theory; NN, Neural Networks; O, Other;GA, Genetic Algorithm.



Fig. 4. The network topologies used in the simulation studies: (a) Topology 1: a 15-node network,(b) topology 2: a 30-node network, and (c) topology 3: a 40-node network.

Table III. Comparison of Several TDMA Node Scheduling Algorithms Overview

Top

olog

yF

ram

ele

ngt

h(#

slot

s)

SV

C-N

CN

N

MF

A

SV

C

MG

A

GA

FC

S

Fu

nab

ikia

nd

Kit

amic

hi1

999

FH

NN

HN

CN

N

HN

NG

A

GH

NN

TS

GR

FC

-HN

N

Ver

gado

set

al.

2005

FS

MA

15 nodes 8 8 8 8 8 8 8 8 8 8 8 8 830 nodes 10 12 11 9 9 10 11 10 10 10 10 11 10 1040 nodes 8 9 8 8 8 8 8 8 8 8 8 - 8 8

Zhu and Corson [2001b] proposed a distributed topology-dependent scheduling calledthe Five-Phase Reservation Protocol (FPRP). The first four phases are used for reserva-tion and elimination of the hidden terminal problem, whereas the fifth phase is used forpacking and elimination in order to perform efficient spatial reuse of the same slot andto eliminate deadlocks that may exist between adjacent nodes. Simulation results haveshown that this procedure can produce a schedule as good as those produced by simple,greedy centralized algorithms like the Ephremides and Truong [1990] algorithm.

Papadimitriou et al. [2002] proposed a distributed deterministic TDMA broadcastscheduling algorithm, the Learning Medium Access Control (LMAC) protocol, wherethe schedule is determined by means of Learning Automata (LA) that implement avariation of the Population-Based Incremental Learning (PBIL) algorithm (i.e., a com-bination of competitive learning and GAs). Based on PBIL, a choice probability is



Fig. 5. Flowchart of the LMAC protocol’s operation (redrawn from Papadimitriou et al. [2002]).

assigned to each node that grants its transmission. Thus, an initial probability vectoris constructed. The transmission schedule is constructed by selecting random numbersfrom the (0, 1) interval according to the uniform probability distribution, as the num-ber of nodes in the topology, and comparing them with the corresponding probabilities.If the random number’s value is less than the corresponding probability, the node isincluded in the current transmission schedule. According to the network feeding infor-mation, the choice probability of each node is updated by means of the LAs. Figure 5overviews LMAC protocol operation. Simulation results showed that the proposed ap-proach based on the offered load (packets/slots) achieves a throughput improvementof from 20% to 500% and a delay decrease of from 80% to 90% in comparison withthe conventional TDMA protocol [Rubin and Zhang 1992]. The only additional cost inrelation to TDMA is the processing cost required for LA implementation.

Zhu and Corson [2001a] also proposed another scheduling algorithm based on theFRPR algorithm called Evolutionary-TDMA (E-TDMA). More specifically, in E-TDMA,in contrast with FRPR, many nodes can acquire the same temporary color simultane-ously if they are sufficiently far each other [Loscri 2007]. However, in both algorithms,in order to accommodate the maximum possible number of two-hop neighbors in thecontrol slot schedules, a sufficient number of control slots needs to be allocated a priori[Park and Sy 2008]. This dependency creates inefficient control slot schedules when theactual network size is smaller than planned and also increases latency in exchangingcontrol information [Park and Sy 2008]. A modification of the E-TDMA was proposed byLoscri [2007], called Randomized-MAC (R-MAC). The difference between E-TDMA andR-MAC is that R-MAC does not have a contention policy. Instead, a random functionis used to select a broadcast slot that represents a kind of permission for the node toreserve data slots and to send updated schedules. Simulation results showed that byapplying this modification, better performance is achieved in terms of throughput anddelay.

Other TDMA node distributed scheduling algorithms that are also modifications ofthe FPRP [Zhu and Corson 2001b] can be found in Jurdak et al. [2004].

Rhee et al. [2006] proposed a distributed TDMA scheduling algorithm called Dis-tributed RAND (DRAND) that ensures the collision avoidance of each two-hop neigh-bor. The algorithm does not require synchronization at any time, and it can effectivelyadapt to local topology changes. The authors also showed that DRAND is ideal for



wireless networks with limited mobility, such as wireless mesh networks and wirelesssensor networks. However, DRAND does not provide any method to change or re-pair schedules or any specification on how messages for the initial construction of theschedule must be exchanged [Lessmann and Held 2008]. Also, running and messagecomplexity depend on the number of a node’s two-hop neighbors.

Wang and Henning [2007] proposed the deterministic distributed TDMA scheduling(DD-TDMA) algorithm for wireless sensor networks. In DD-TDMA, each node decidesits own slot according to the information gathered from neighboring nodes. The sched-uled node broadcasts its slot assignment to its one-hop neighbors. Then, those one-hopneighbors broadcast this information to update two-hop neighbors. These processesare repeated in every frame until finally all nodes are scheduled. Simulation resultsshowed that DD-TDMA achieves better performance than DRAND [Rhee et al. 2006]in terms of schedule length, running time, and message complexity. Especially in low-density environments where the transmission range is 1 unit, the running time of DD-TDMA is only 67% of DRAND [Rhee et al. 2006], and the message complexity is only54% of DRAND [Rhee et al. 2006].

Kuang et al. [2008] proposed a distributed TDMA scheduling algorithm, the EvolvedMinimum Degree First (EMDF) algorithm, which is developed based on the DRANDalgorithm [Rhee et al. 2006] to assign slots for nodes. In this algorithm, the node thathas minimum degree in a three-hop neighborhood is the first to be assigned a slot.The node with the highest degree is the last node to be assigned a slot. Simulationresults showed that the proposed algorithm exhibits better performance in comparisonwith DRAND [Rhee et al. 2006] and Zhang et al.’s [2008] algorithms in terms of slotutilization and throughput.

3.1.2. Distributed Topology-Transparent TDMA Scheduling Algorithms. The basic idea of thetopology-transparent TDMA scheduling algorithms is to allow each node to transmitin a number of time slots in each frame. The times when node i transmits in a framecorrespond to a unique code such that, for any given neighbor k of node i, node i hasat least one transmission slot during which its neighbor node k and none of ks ownneighbors are transmitting [Loscri 2007]. Therefore, within any given time frame, anyneighbor of node i can receive at least one collision-free packet from node i [Bao andGarcia-Luna-Aceves 2000].

The first topology-transparent deterministic broadcast TDMA scheduling algorithmwas introduced by Chlamtac and Farago [1994] and made use of the mathematicalproperties of Galois fields. The proposed algorithm assigns to each node a uniquepolynomial function that guarantees that at least one time slot in a frame would becollision-free. The algorithm’s performance depends only on the number of nodes in thenetwork and the maximum degree (i.e., the number of neighbors that each node canhave). However, since no attempt has been made to optimize the performance of thisalgorithm, in many cases it performs worse than the conventional TDMA algorithm[Ju and Li 2006]. Also, the throughput achieved by this algorithm is relatively smallsince the maximum number of transmission is one in a frame [Liu et al. 2012].

Ju and Li [2006] improved Chlamtac and Farago’s [1994] algorithm in order to max-imize minimum throughput. More specifically, in the proposed algorithm, the scheduleis produced by applying code theory (i.e., using the Hamming weight and Hammingdistance to describe the relationship between the transmission slot assignments oftwo nodes). Simulation results showed that the proposed algorithm exceeds the per-formance of the Chlamtac and Farago’s [1994] algorithm in terms of the minimumguaranteed throughput under any traffic conditions and minimum delay (when thesystem is under very light traffic) and maximum delay (when the system is undervery heavy traffic) times. The optimal minimum throughput is also insensitive to



inaccuracies in the estimated design values of the number of nodes and the maximumdegree in the network.

Youn and Bose [2001] proposed another distributed TDMA scheduling method basedon coding theory. The proposed algorithm is quite similar to Chlamtac and Farago’s[1994] algorithm, as well as to Ju and Li’s [2006] algorithm. The main difference inthe proposed algorithm is that the frame length depends on the length of the codewords, whereas in the previous algorithms the authors considered as frame lengththe value of a prime number. Simulation results showed that the proposed algorithmis better than Chlamtac and Farago’s [1994] and Ju and Li’s [2006] algorithms interms of minimum system throughput. However, since there are only a few constantweight codes known to date, the proposed algorithm cannot always provide solutions tothe topology-transparent scheduling problem, especially when the values of the globalnetwork parameters (i.e., the number of nodes in the network and the nodes degree)are large [Su et al. 2004].

Cai et al. [2003] proposed two topology-transparent TDMA algorithms: one for single-channel networks based on the Galois field theory and the Latin square theory, andanother for multichannel networks based on the Galois field theory. Numerical resultsshowed that the proposed algorithms outperform Chlamtac and Farago’s [1994] algo-rithm in terms of achieving the minimum frame length. In addition, the use of Latinsquares achieves a better potential performance gain compared with the only use of themodified Galois field design (MGD) algorithm. However, to avoid secondary collisions,each node transmits the same packet in all of its assigned slots during a frame, leadingto inefficiency in terms of bandwidth usage and throughput [Su 2008]. To overcome Caiet al.’s [2003] algorithm drawback, Su [2008] proposed the use of Maximum-Distance-Separable (MDS) erasure coding. Numerical results showed that by applying MDSerasure coding techniques, the performance of Cai et al.’s [2003] algorithm is improvedfor most of broadcast traffic loads.

Xu et al. [2011] proposed a topology-transparent scheduling algorithm based on aBalanced Incomplete Block Design (BIBD). The goal of the algorithm is to optimizeblock size in order to maximize guaranteed throughput. Numerical results showedthat the proposed algorithm outperforms both Chlamtac and Farago’s [1994] and Juand Li’s [2012] algorithms in terms of guaranteed throughput, maximal transmissiondelay, and shorter minimal transmission delay.

A topology-transparent algorithm for multicast and broadcast communications forwireless multihop networks is proposed by Sun et al. [2008] based on coding theory. Thegoal of the proposed algorithm is, instead of minimizing the TDMA frame length, maxi-mizing the minimum expected throughput. More specifically, the authors use the TimeSlot Allocation Function (TSAF) to calculate the position of a selected transmission slotin a frame for each node. Then, based on the number of each node’s transmission oppor-tunities in each frame, as well as the highest degree among all TSAFs, the minimumexpected number of successful transmissions per frame is computed for both multicast-ing and broadcasting. Simulation results showed that the performance of the proposedalgorithm is better than conventional TDMA in terms of expected delay and minimumexpected throughput.

Su et al. [2004] proposed two topology-transparent broadcast TDMA scheduling al-gorithms for ad hoc networks based on the theory of block designs. More specifically,the authors consider time slots as “treatments” of the Balanced Incomplete Block (BIB)design and the set of node activation times of the scheduling problem as blocks. Thus,their goal is to maximize the minimum number of common treatments between everypair of blocks. Numerical results showed that the proposed algorithms can outperformJu and Li’s [1998] algorithm in achieving a higher minimum system throughput.



Liu et al. [2012] proposed a distributed topology-transparent algorithm for multicastand broadcast communications in mobile wireless ad hoc networks. The authors alsouse, as did Sun et al. [2008], coding theory to design their algorithm. However, theiralgorithm guarantees that the probability of a multicast or broadcast transmissionsucceeding within a frame time exceeds a given threshold. Therefore, the proposedalgorithm achieves better performance in terms of throughput in comparison withChlamtac and Farago’s [1994] and Sun et al.’s [2008] algorithms.

Oikonomou and Stavrakakis [2004] added a probabilistic policy into topology-transparent algorithms by allowing a specific node u not only to access the set oftime slots that it is allowed to transmit, but also other time slots (outside the set) thatdo not belong to node u, with probability p [Chen and Jiang 2006]. Simulation resultsshowed that the probabilistic policy increases system throughput. However, as statedin Chen and Jiang [2006], the main disadvantage of the algorithm is that the authorsdid not tackle the problem of how to choose the nonassigned slots to transmit withprobability p and that only receivers are considered to corrupt the transmission. Inaddition, the algorithm may lead to heavy collisions when traffic load and the numberof neighbors increase too much [Chen and Jiang 2006].

To overcome Oikonomou and Stavrakakis’s [2004] algorithm drawback, Chen andJiang [2006] proposed the stealing-TDMA algorithm (sTDMA) that uses an ACK mech-anism to reserve time slots for solving collision problems. Simulation results showedthat the proposed method achieves better performance in terms of collision probabil-ity and power consumption in comparison with the one proposed by Oikonomou andStavrakakis [2004].

An overview of the basic characteristics of the distributed TDMA node schedulingalgorithms described in this article, as well as their advantages and disadvantages, ispresented in Table IV.

4. TDMA LINK SCHEDULING ALGORITHMS

In link scheduling, a set of time slots is assigned to each link so that all packets trans-mitted by the scheduled transmitters are received successfully at the corresponding(intended) receivers [Gore and Karandikar 2011]. However, since the successful re-ception of a transmission depends on several parameters, such as the received signalstrength, the interference caused by nodes transmitting simultaneously, and the like,several different interference models may be found in the literature. For TDMA linkscheduling, two basic interference models are used: the protocol interference modeland the physical interference model.

According to the protocol interference model, all nodes are assumed to lie in a planarregion. A transmission by a node vi is successfully received by a node v j if and only if theintended destination v j is sufficiently apart from the source of any other simultaneoustransmissions [Wang et al. 2006].

In the physical interference (or path-loss) model, the signal quality perceived bya receiver is measured by the Signal to Interference and Noise Ratio (SINR). Morespecifically, in this model, the transmission from node vi is successfully received atnode v j if and only if the received SINR is at least the minimum SINR thresholdrequired by node v j [Wang et al. 2008]. This is often referred to as the abstract (ornongeometric or exact) SINR model [Halldorsson and Mitra 2012]. Santi et al. [2009]extended this threshold-based version of the SINR model to a more general gradedprobabilistic SINR model that not only considers SINR less than the threshold but alsopredicts the probability of successful reception.

In addition to the abstract SINR model, there is also the geometric SINR model,where the gain between two nodes is determined by the distance between them. Al-though the geometric model does not capture obstacles, reflection, and other real-world



Table IV. TDMA Node-Distributed Scheduling Algorithms Overview

Scheduling TopologyRef. Det. Prob. Dep. Tran. Advantages DisadvantagesET[Ephremidesand Truong1990]

� � Simple. It does not ensure fairslot assignmentsamong all MSs.

MGD [Cai et al.2003]

� � It is applicable formulti-channelnetworks.

Each node transmitsthe same packet inall of its assignedslots.

FPRP [Zhu andCorson 2001b]

� � Efficient handling of thehidden terminalproblem.

Scalable with thenetwork size.

Suitable for dynamicenvironments.

Increased overhead.Slow slot utilization.

DDETSA[Vergados et al.2006]

� � Emphasizes end-to-enddelay.

Does not optimizeglobally.

[Ju and Li 2006] � � The algorithm’sperformance dependsonly on the number ofnodes in the networkand the maximumdegree.

The optimal minimumthroughput issensitive toinaccuracies in theestimated designvalues of thenumber of nodesand the maximumdegree in thenetwork.

LMAC[Papadimitriouet al. 2002]

� � Capable of being adaptedto the sharp loadchanges of a burstytraffic environment.

Doesn’t supportmobility.

DRAND [Rheeet al. 2006]

� � Does not acquire anysynchronization at anytime.

Can be effectivelyadapted to localtopology changes.

The running time aswell as messagecomplexity aresubject to thenumber of two-hopneighbors of a node.

Schedules cannot bechanged or repaired.

[Chlamtac andFarago 1994]

� � The algorithm’sperformance dependsonly on the number ofnodes in the networkand the maximumdegree.

Low throughput.The optimal minimum

throughput issensitive toinaccuracies in theestimated designvalues of thenumber of nodesand the maximumdegree in thenetwork.

RMAC [Loscri2007]




Does not ensure thatthe schedules areconflict-free.

(Continued)



Table IV. Continued

Scheduling TopologyRef. Det. Prob. Dep. Tran. Advantages Disadvantages[Xu et al. 2011] � � Maximizes the

guaranteedthroughput.

Requires timesynchronization.

[Sun et al.2008]

� � Maximizes the minimumexpected throughput.

Considers multicastingand broadcasting.

Not suitable for highlydynamicenvironments.

Does not eliminatecollisions.

[Youn and Bose2001]

� � Performs efficiently insaturated conditions.

Difficult to providesolution when thevalues of the globalnetwork parametersare large.

Mapping I andMapping II [Suet al. 2004]

� � Considers node mobility;maximizes theminimum systemthroughput.

An exhaustive searchmethod to find theoptimal solution isrequired.

ETDMA [Zhuand Corson2001a]




Inefficient controlschedule in smallnetwork topologies.

Control exchangeoverhead.

[OikonomouandStavrakakis2004]

� � Increased throughput. No mechanism forchoosing thenonassigned slots totransmit withprobability p isdetermined.

Does not eliminatecollisions.

sTDMA [Chenand Jiang 2006]

� � Reduces powerconsumption.

Decreases collisionprobability.

Increased overheaddue to ACKs.

EMDF [Kuanget al. 2008]

� � Relies on local topologyinformation.

Spends low time andcommunicationoverhead to achievehigh throughput andhigh slot reuse.

Time and messageoverheads areanalogous to themaximum size of athree-hopneighborhood.

DD–TDMA[Wang andHenning 2007]

� � Efficiently allocates timeslots to avoid collisionswhile minimizingenergy use.

Can be applied inwireless sensornetworks with largenumber of nodes.

Long running timedue to initializationof frame size.

Requires timesynchronization.

[Liu et al. 2012] � � Considers multicastingand broadcasting.

Guarantees onesuccessful transmissionexceeding a givenprobability andachieves a much betteraverage throughput.

Not suitable for densenetworks.



distortions [Halldorsson and Mitra 2012], it covers the main features of sophisticatedfading models such as the two-ray ground model without losing too much of the sim-plicity needed for algorithmic results [Katz et al. 2008].

Moscibroda et al. [2006b] proposed the generalized physical model. In this model,given a parameter θ , the received signal power (as well as the interference causedby simultaneously transmitting nodes) can deviate from the theoretically receivedpower by a factor of at most θ [Goussevskaia et al. 2010]. Several other variationsof the abstract SINR model may be found in the literature. A comprehensive surveyconcerning interference in wireless ad hoc networks can be found in Cardieri [2010].

Based on the interference model that the link scheduling algorithms use, we distin-guish the algorithms into two broad categories: the graph-based and the interference-based (or SINR-based [Gore et al. 2007]) scheduling algorithms. Graph-based schedul-ing algorithms use the protocol interference model, whereas interference-based linkscheduling algorithms use the so-called physical interference model [Gupta and Kumar2000]. The interference-based link scheduling algorithms can be classified as follows[Moscibroda et al. 2007; Wan et al. 2011]:

(1) Uniform power assignment class: All senders of the links have the same transmis-sion power.

(2) Linear power assignment class: The sender of a link transmits at a power propor-tional to the link’s path loss factor.

(3) Square root assignment class: The sender of a link transmits at a power proportionalto the square-root of the link’s path-loss factor.

In the literature, these power assignment classes are often called oblivious powerassignments; that is, the power level assigned to a pair is defined as a function of theloss (or the distance) between the nodes of a pair [Fanghanel et al. 2009]. The advantageof oblivious power assignments is their simplicity since they do not depend on the globalstructure and allow an immediate implementation in a distributed setting.

The remainder of this section presents and discusses issues concerning graph- andinterference-based link scheduling TDMA algorithms. It should be noted that in thissection we discuss only interference-based link scheduling TDMA algorithms with nopower control since interference-based link scheduling TDMA algorithms with powercontrol are considered cross-layer solutions.

4.1. Link Scheduling TDMA Algorithms Based on the Protocol Interference Model

Link scheduling TDMA algorithms based on the protocol interference model utilize acommunication or two-tier graph model to determine the link schedule. Because nu-merous different types of graphs exist, such as trees, planar graphs, unit disc andquasi disc graphs, random graphs, and the like, with each one having different prop-erties, the proper representation may be selected depending on the network model.Also, graph-based scheduling algorithms utilize various graph coloring methodologiesto color different communication edges [Behzad and Rubin 2003].

Ramanathan and Lloyd [1993] proposed a link graph-based broadcast schedulingalgorithm for packet radio networks. The authors modeled the radio networks using tworestricted classes of graphs: trees and planar graphs. The optimal broadcast schedulewas produced by applying a graph coloring algorithm called the arborical link schedule.Experimental results showed that the proposed algorithm used, on average, roughly8% fewer slots than a pure greedy algorithm. The difference in performance widens aswe tend toward higher ranges and a higher population.

Zhang et al. [2007] proposed a multichannel graph-based TDMA scheduling algo-rithm for ad hoc networks called CC-TDMA that combines edge coloring in orderto avoid primary collisions and algebraic coding theory in order to avoid secondary



collisions. Numerical results showed that the proposed algorithm exhibits better per-formance than Ju and Li’s [1998] algorithm.

Gandham et al. [2005] proposed a two-stage distributed link graph-based TDMAscheduling algorithm for wireless sensor networks. During the first phase, a color isassigned to each edge in the sensor network so that no two edges of the same color areincident on the same sensor node. This is achieved through a distributed edge coloringalgorithm that needs at most (δ+1) colors, where δ is the maximum degree of the graph.In the second phase, they map each color to a unique time slot, attempting to identifya direction of transmission along each edge in order to avoid the exposed terminalproblem. Next, taking into consideration topologies for which a feasible solution doesnot exist, they obtain a direction of transmission for each edge using additional timeslots. Finally, they show that the reversing of the direction of transmission along everyedge leads to another feasible direction of transmission. However, the drawback ofthis algorithm is that, due to its two-stage nature, it needs large numbers of messageexchanges by the nodes [Zhang et al. 2007].

Zhang et al. [2008] proposed a distributed graph-based TDMA link scheduling algo-rithm for wireless ad hoc networks named the CP-TDMA. The proposed algorithmuses a distributed edge coloring algorithm to deal with primary interference andprobabilistic assignment to deal with secondary interference. Numerical results showedthat the proposed algorithm exhibits better performance in terms of throughput in com-parison with Rhee et al.’s [2006] algorithm. However, as stated by Kuang et al. [2008],the proposed algorithm has the following drawbacks:

(1) It cannot avoid implicit conflicts completely.(2) Although the impact of interference is decreased, it also wastes lots of slots.(3) It does not develop much slots reuse.

Ali et al. [2002] proposed a graph-based TDMA link scheduling by applying two dis-tributed algorithms. The first algorithm is used to adjust the slot assignment in case ofnew link detection, whereas the second is used to modify the TDMA slot assignments incase two terminals are no longer within range of each other. Simulation results showedthat this technique outperforms the centralized approach in terms of slot assignmentefficiency and convergence time.

Cheng and Li [2007] proposed a graph-based broadcast TDMA link scheduling al-gorithm for sensor networks called Edge Coloring on Directed Graphs (ECDiG). Theproposed algorithm operates in two stages. During the first stage, the directed graph isbuilt; colors are assigned during the second stage to the directed edges directly basedon the following rules:

(1) Conflicting edges must use different colors.(2) Nonconflicting edges can use the same or different colors.

Simulation results showed that the proposed algorithm guarantees that there is no hid-den terminal problem and exposed terminal problem at any time in any communicationmodes, and it achieves low access delay and high channel utilization.

Djukic and Valaee [2007] proposed a two-stage graph-based TDMA scheduling algo-rithm for wireless mesh networks. During the first stage, the scheduling problem findsa relative transmission order by assigning ranks to each round trip path originatedand the point-of-presence (i.e., base station) and then schedules the links to minimizethe maximum delay along the longest path in the tree. At the second stage, a modifiedBellman-Ford algorithm is applied to find a feasible schedule in polynomial time. Sim-ulation results shown that the proposed algorithm can find effective min-max delayschedules.



Fig. 6. The fPrIM interference model.

Wang et al. [2006, 2008] proposed a modified interference model called the fixedPower Protocol Interference Model (fPrIM) in which it is assumed that there is nopower adaptation at the packet level and also that power is not adjustable for a certainperiod of time. In the protocol interference model, the transmission from a node vk (withinterference range rk) to a node v j is successful if ‖vk−v j‖ for every node vk transmittingin the same time slot using the same channel (Figure 6). Based on the fPrIM, bothefficient centralized and distributed TDMA link scheduling algorithms are proposed.They also introduced the notion of weighted coloring, in which different weights areassigned to different communication links based on the link’s traffic load. Simulationresults showed that simple link coloring does not imply good throughput and that ageneral weighted link coloring problem may give better performance. In addition, theproposed distributed algorithm is proved to achieve performance comparable to theoptimum, but with much fewer communication messages.

4.2. Link Scheduling TDMA Algorithms Based on the Interference Model

Although graph-based models consider interference as a binary and local measure, ininterference-based models the successful transmission depends on the ratio betweenthe received signal strength on one side and the interference from concurrent transmis-sions plus the background noise on the other side [Moscibroda et al. 2006a]. Therefore,in interference-based models, we cannot build an interference graph a priori since theSINR of a receiver depends on the set of nodes that are simultaneously transmittingin each time slot [Xu and Tang 2009]. Also, the nonlocality and additive nature of in-terference in the physical interference model render traditional graph-based coloringtechniques inapplicable [Wan et al. 2010].

Link scheduling has proved to be NP-hard under the interference model withoutconsidering power control [Goussevskaia et al. 2009], even if the background noiseis neglected [Andrews and Dinitz 2009]. Several variations link scheduling problemshave been formulated, including:

—Maximum Independent Set of Links (MISL) problem [Wan et al. 2010, 2011]: Givena set of links L, MILS’s objective is to find the largest independent subset of L (underthe SINR constraint).

—Shortest Link Schedule (SLS): The objective is to find a link schedule of shortestlength for a given subset of links.

—Maximum Weighted Independent Set of Links (MWISL): Given a set of links L as-signed with a weight value, the problem’s goal is to find a maximum weighted inde-pendent set of links S, where S is a subset of L.

Since all these problems are proved to be NP-hard, the majority of research works useheuristics or approximation algorithms to find a solution [Goussevskaia et al. 2010].

Gronkvist [2006] proposed an interference-based TDMA link scheduling algorithmthat tries to combine the advantages of link and node scheduling. More specifically,



when a link is assigned a time slot, the node first checks whether there is a messageto transmit on that link. If there is no such message, any other link with the sametransmitting node may be used if the node has a message to transmit. Preferably, linksthat are conflict-free should have priority in order to avoid unnecessary packet loss.

Bjorklund et al. [2004] proposed a link interference-based TDMA scheduling algo-rithm with the objective of finding minimum-length schedules. The authors formulatedthe TDMA link assignment problem as a mathematical optimization problem and pro-posed a column generation solution method to this problem. Numerical results showedthat the proposed method generated a very tight bound to the optimal schedule lengthand thereby enabled optimal or near-optimal solutions.

Brar et al. [2006] proposed a heuristic algorithm, GreedyPhysical, for link schedulingunder the physical interference model in wireless mesh networks. The authors repre-sent the wireless network as a communication graph and verify the SINR conditionsat the receivers [Gore and Karandikar 2011]. They assume uniform power assign-ment and also that interference from remote transmitters is neglected. The algorithmconsists of two stages. During the first stage, the links to be scheduled are ordered ac-cording to the interference number; that is, the number of edges in the communicationgraph that are in pair with a specific edge infeasible. Then, the edges of the communi-cation graph are scheduled in a greedy way, starting with the edge that has the biggestinterference number. Simulation results showed that throughput with STDMA andphysical-interference based scheduling can be up to three times higher than 802.11 forthe parameter values simulated.

Gore et al. [2007] proposed a link TDMA scheduling algorithm that tries to maxi-mize network throughput. The authors use spatial reuse as a performance metric andassume uniform transmission power at all nodes. More specifically, the authors parti-tion the communication graph into a minimum number of subgraphs using matroids(i.e., finding a maximum cardinality set of edges of a graph that can be partitionedinto k forests and finding as many disjoint spanning trees as possible [Gabow andWestermann 1992]) and then apply edge coloring in each subgraph while checking forSINR threshold conditions. Simulation results showed that the proposed algorithmresults in 40% higher spatial reuse than Behzad and Rubin’s [2003] and Ramanathanand Lloyd’s [1993] algorithms, without compromising on computational complexity.

Papadaki and Friderikos [2008] proposed an optimization approach for the problemof minimum frame length schedule in STDMA networks under log-normal fading basedon a Mixed Integer Linear Programming (MILP) formulation. They also derived prop-erties on the expected frame length and provided bounds on the probability of SINRconstraint violation and on the number of time slots needed for retransmission. Nu-merical investigations showed that the proposed approach leads to shorter schedulesthan the traditional approach that uses average values for the link gains results whenretransmissions are also taken into account. An overview of the basic characteristics,advantages, and disadvantages of the TDMA link scheduling algorithms referred to inthis article is presented in Table V.

5. CROSS-LAYER TDMA SCHEDULING ALGORITHMS

TDMA scheduling can be used for optimizing different network operations, such asdata aggregation, topology control, power efficiency, and more. For this reason, severalcross-Layer TDMA scheduling algorithms have been proposed to combine the TDMAscheduling problem with issues concerning these operations, such as route selection,load balancing, and power consumption.

Sgora et al. [2008b] proposed a joint routing and TDMA broadcast scheduling algo-rithm; the proposed scheduling algorithm schedules transmissions in a fair manner,taking into consideration the communication requirements of the active flows of the



Table V. TDMA Link Scheduling Algorithms Overview

SchedulingRef. Graph Inter. Advantages DisadvantagesArborical LinkSchedule[Ramanathan andLloyd 1993]

� Simple. Suitable only for a fewreal-life networkenvironments.

[Gronkvist 2006] � Achieves the higherthroughput of linkassignment without thecost of higher delay for lowtraffic loads.

Increased power consumption.Increased computational

overhead.

Greedy Physical[Brar et al. 2006]

� Increased spatial reuse. Increased computationalcomplexity.

Uniform random distributionis assumed.

The power-based interferencegraph does not consider theaccumulation effect ofinterference.

[Gore et al. 2007] � Achieves high spatial reuse,even under realisticchannel conditions likefading and shadowing.

Has polynomial timecomplexity.

Increased computationalcomplexity.

CC-TDMA [Zhanget al. 2007]

� Eliminates explicit conflictscompletely and minimizesimplicit conflicts.

Considers multichannelscheduling.

Secondary collisions may behappen.

[Gandham et al.2005]

� A distributed algorithm.Conserves energy at sensor

nodes.

Due to its two-stage nature,needs a large number ofmessage exchanges by thenodes.

Only allows for one slot to beallocated to each link, whichmakes it impractical formesh networks.

CP-TDMA [Zhanget al. 2008]

� Requires only localinformation to assigndifferent subframes to linkswith explicit conflicts.

Minimizes implicit conflicts

Cannot avoid implicit conflictscompletely.

Wastes lots of slots.Does not develop much slots

reuse.[Ali et al. 2002] � Adapts TDMA assignment to

dynamic topologies.Increased convergence time.

ECDiG [Chengand Yin 2007]

� Guarantees conflict-free timeslot assignment if eachedge carries the same load.


[Djukic and Valaee2007]

� Finds schedules withminimum round tripscheduling delay.

Computational overhead forfinding the ranking withminimum delay.

High worst-case complexity.[Wang et al. 2006] � Proposed weighted coloring

takes into account thetraffic load of each link.

Increased time complexity forthe distributed algorithm.

[Bjorklund et al.2003]

� Generates a very tight boundto the optimal schedulelength.


(Continued)



Table V. Continued

SchedulingRef. Graph Inter. Advantages Disadvantages[Papadaki andFriderikos 2008]

� A general framework that canbe used on any collision-freescheduling scheme.

Achieves shorter schedules.

Does not consider the trafficdemand of each link.

Does not take into account theimpact of transmissionfailure on the increase intraffic demand.

network. Simulation results showed that the proposed policy can further improve theperformance of the network in terms of throughput and frame length.

Wolf et al. [2006] proposed a distributed Load-Balanced Node TDMA scheduling (Lo-BaTS) algorithm for wireless ad hoc networks. In the proposed algorithm, the nodesfirst coordinate to acquire one initial transmission slot and then gain or lose slotsbased on load [Yackoski and Shen 2010]. In this way, nodes that are required to for-ward more traffic can reserve additional transmission slots, thereby alleviating trafficbottlenecks. This is achieved by assigning additional colors to congested nodes. Simula-tions results showed that the proposed algorithm greatly improves end-to-end packetdelay, throughput, and completion rate in comparison with a transmission schedulethat does not account for traffic load.

Wang et al. [2012] proposed the Fairness Adaptive TDMA scheduling algorithm(FATS) scheduling algorithm for wireless sensor networks with unreliable links. Inthis algorithm, time slots are assigned to the nodes according to link quality and dataamount. Therefore, it is possible that the ownership of a time slot can be transferredfrom one node to any other node in the network following changes in link quality.Simulation results showed that the proposed algorithm is quite efficient in termsof fairness for the sensor network. It can significantly reduce the difference of theend-to-end packet delivery ratio, track the variation of link quality quickly, and achievefairness in resource allocation.

Vergados et al. [2012] proposed a joint TDMA scheduling/load balancing algorithm,Load-Balanced-Fair Flow Vector Scheduling Algorithm (LB-FFVSA), for wireless mul-tihop networks to determine the optimal slot assignment in terms of overall perfor-mance and fairness per flow. This is achieved through the combination of a schedulingalgorithm that assigns the appropriate transmission slots to each node and a load bal-ancing technique that improves the scheduling performance by limiting the requiredframe length. Simulation results showed that the proposed algorithm exhibits im-proved performance compared to other TDMA scheduling algorithms (MFA [Wang andAnsari 1997], HNN-GA [Salcedo-Sanz et al. 2003], SVC [Yeo et al. 2002], the Fuzzy[Shen and Wang 2008], Factor [Chen et al. 2006], Ephremides and Truong’s [1990]algorithm, and Lyui’s [1991] scheme) not only in terms of fairness, but also in terms ofthroughput.

Wang et al. [2007] proposed the joint-oblivious routing and scheduling (TORS)scheduling for wireless mesh networks. The objective of TORS is to handle uncer-tainty in traffic information and achieve worst-case optimal performance under thegiven range of traffic information. To achieve this goal, the authors use a Linear Pro-gramming (LP) formulation with no specific assumption on the interference model.TORS’s performance adapts to the granularity of traffic information available. Themore accurate the information, the better the performance. Simulation results showedthat the proposed scheme achieves very good average performance under a large errormargin on traffic estimation and is robust when the estimation largely deviates fromthe actual traffic patterns.



Fig. 7. Flowchart of the ElBatt and Ephremides [2004] algorithm.

ElBatt and Ephremides [2004] proposed a two-stage joint link scheduling and powercontrol algorithm for wireless ad hoc networks to minimize power consumption. Duringthe first phase, the scheduling algorithm determines the set of users (nodes) that canattempt transmission simultaneously in a given slot; during the second stage, powercontrol is executed in a distributed fashion to determine the “admissible” set of powerlevels that could be used by the scheduled nodes, if one exists. In case no set of positivepower levels can be found, control is transferred again to the first phase in order toreduce interference via deferring the transmissions of one or more users participatingin this scenario. Figure 7 represents the flowchart of the proposed algorithm.

Tang et al. [2006] proposed a joint link scheduling and power control TDMA algorithmfor multihop wireless network with the objective of maximizing network throughput. Toachieve this goal, the authors use a MILP formulation to describe the problem and theneither find optimal solutions or apply a polynomial-time heuristic algorithm, the SerialLinear Programming Rounding (SLPR) heuristic, to solve the problem. Numericalresults showed that the bandwidth can be fairly allocated among all links by solving theMILP formulation or by using the heuristic algorithm at the cost of a minor reductionof network throughput. However, it is difficult to evaluate the performance of theseheuristic algorithms when optimal solutions are not known [Fu et al. 2010].

Mao et al. [2007] proposed a joint link scheduling and power control algorithm formany-to-one communications in wireless sensor networks with the objectives of min-imizing energy consumption and TDMA frame length. To obtain this goal, a hybridgenetic and particle swarm optimization algorithm is applied to enhance searchingability. Simulation results showed that the proposed algorithm outperforms the classi-cal node Max Degree First coloring algorithm [Vergados et al. 2009].

Wang et al. [2005] proposed a joint distributed interference-based TDMA linkscheduling and power control algorithm for ad hoc networks supporting multicasttraffic. The proposed algorithm eliminates links, which cause most interference, in or-der to allow the remaining links to reach an acceptable SINR level [Moscibroda et al.2007].



Li and Ephremides [2007] proposed a two-stage centralized joint power controlTDMA link scheduling and routing algorithm for ad hoc networks. In the first stage, thescheduling algorithm is responsible for coordinating independent users’ transmissionsto eliminate primary interference. In the second stage, power control is executed to de-termine the admissible set of power levels that could be used by the scheduled nodes,if one exists. If no such set of positive power levels can be found, control is transferredback to the scheduling phase to reduce interference via deferring the transmissions ofone or more users participating in this scenario.

Burri et al. [2007] proposed Dozer, a protocol for data gathering applications inwireless sensor networks. The proposed protocol combines TDMA scheduling, topologycontrol, and routing in order to prolong the network’s lifetime and achieve increaseddelivery rate. To achieve this goal, it uses a tree routing structure, where the treestructure is constructed and maintained by beacon messages originating at one ormore sink nodes, serving synchronization and data flow control purposes. Upon receiptof the beacons, the nodes send connection-requests to one of the beacon sink nodesand store the others locally for quick recovery when current connections fail. Data aretransported from the children to the parent during the dedicated upload slots that aredetermined by a link-based schedule. The main drawbacks of the algorithm are theincreased latency and a completely asynchronous application that is hard to maintain[Di Marco et al. 2010].

Behzad and Rubin [2007] developed a mathematical programming formulation forminimizing the frame size in wireless multihop networks based on optimal joint TDMAscheduling and power control under the physical interference model. It is based on apower-based interference graph that describes the interference relationship of everytwo links according to the SINR of the receiver. Then, based on this graph, the authorstry to find a maximal link-independent set using a heuristic algorithm, the MinimumDegree Greedy Algorithm (MDGA).

An overview of the basic characteristics of the cross-layer TDMA scheduling algo-rithms referred to in this article is presented in Table VI.

6. HYBRID MAC PROTOCOLS

In wireless multihop networks, the density of nodes plays an important role in theperformance of the network. In special-purpose networks, such as wireless sensornetworks, where energy consumption is also a crucial parameter, TDMA schedulinghas several disadvantages [Rhee et al. 2008; Ahn et al. 2006; Kim et al. 2008]:

—The development of an efficient schedule with a high degree of concurrency or channelreuse is very complex. The tight synchronization that is needed for scheduling causesincreased overhead since it requires frequent message exchanges.

—Sensor networks may undergo frequent topology changes due to time-varying chan-nel conditions, physical environmental changes, battery outage, and node failures.

—In such networks, it is difficult to deal with the radio irregularity phenomenon (i.e.,the phenomenon in which radio interference ranges are different from communi-cation ranges, and some interfering nodes may not be in a direct communicationrange).

—In low-traffic networks, TDMA gives much lower channel utilization and higherdelays than CSMA because in TDMA, a node can transmit only during its scheduledtime slots.

—Bursty traffic is difficult to handle.—It may be impractical to apply TDMA scheduling algorithms in dense wireless sen-

sor networks since the sink requires complete topology information to compute theTDMA schedule, and every node requires precise time synchronization.



Table VI. Cross-Layer Scheduling Algorithms Overview

Ref. Layer Advantages Disadvantages[Sgora et al.2008b]

SchedulingRouting

Takes into account thecommunication requirementsof the active flows.

Provides fairness.

Frame length increaseslinearly with the numberof connections.

Doesn’t take into accountlink quality duringscheduling.

LoBaTS [Wolfet al. 2006]

SchedulingRouting

Alleviates traffic bottlenecks. Overhead caused by messageexchange.


[ElBatt andEphremides2004]

SchedulingPower Control

Minimizes thepower consumption.

Increased processing time.

[Li andEphremides2007]

SchedulingRoutingPower Control

Achieves increased throughputand decreased delay.

Considers energy consumption.

Due to its two-stage nature,it needs a large number ofmessage exchanges by thenodes.

[Tang et al.2006]


Bandwidth can be fairlyallocated among all links.

Difficult to evaluate theperformance of theseheuristic algorithms whenoptimal solutions are notknown.

[Mao et al.2007]


Ensures a powerful searchingability to find the optimal slotallocation scheme.

Guarantees that there is noempty slot during scheduling.

Does not provide anyguarantees toperformance.


[Behzad andRubin 2007]


Minimizes the frame length. Does not consider theaccumulation effect ofinterference

[Wang et al.2005]


Eliminates strong interferersand enables the entitledtransmitters to solve thepower control problem.

Does not provide aworst-case analysis onperformance.

Dozer [Burriet al. 2007]

SchedulingRoutingPower Control

Suitable for data gatheringapplications in wirelesssensor networks.

Prolongs network lifetime.Achieves increased delivery

rate.

Increased latency.A completely asynchronous

application that is hard tomaintain.

FATS [Wanget al. 2012]

SchedulingRouting

Assigns time slots to the nodesadaptively andenergy-efficiently according tothe variation of link quality.

Can obtain overall fairness ofsensor networks undervariations of link quality.

Increased overhead due toACK messages.

LB-FFVSA[Vergados et al.2012]

SchedulingRouting

Considers per-flow fairness.Takes into consideration the

communication requirementsof the active flows.

Frame length is increaseddynamically with thenumber of connections.

TORS [Wanget al. 2007]

SchedulingRouting

Works under the wholespectrum of trafficinformation uncertainty fromperfect traffic information tono traffic information.


Optimization on theworst-case performance isover-conservative.



Fig. 8. Funneling effect in wireless sensor networks.

To overcome these issues, several hybrid MAC protocols that combine the advan-tages of CSMA, FDMA, and TDMA have been proposed. Rhee et al. [2008] proposedthe Zebra-MAC (Z-MAC), a hybrid MAC protocol for wireless sensor networks thatcombines the benefits of TDMA and CSMA. More specifically, in Z-MAC, each nodein the network executes a distributed slot selection algorithm to get a collision-freeTDMA slot based on its two-hop neighborhood schedule information [Sivrikaya andYener 2009]. Like CSMA, Z-MAC achieves high channel utilization and low latencyunder low contention, and, like TDMA, it achieves high channel utilization under highcontention and reduces collision among two-hop neighbors at a low cost. In addition,Z-MAC requires limited processing and memory resources, but these benefits come atthe cost of protocol overhead, primarily caused by the TDMA structure [Kredo andMohapatra 2007].

Ahn et al. [2006] proposed the Funneling-MAC, a hybrid protocol to deal with thefunneling effect (Figure 8), the phenomenon in which sensors closer to the sink areusually responsible for relaying more than transmitting network traffic [Yang et al.2008]. More specifically, the Funneling-MAC algorithm is based on CSMA/CA with alocalized TDMA algorithm overlaid in the funneling region (i.e., within a small numberof hops from the sink). Experimental results showed that the Funneling-MAC mitigatesthe funneling effect; improves throughput, loss, and energy efficiency; and outperformsthe Z-MAC. However, the fact that the authors assume that the sink node has relativelylonger transmission range and can reach all nodes in the intensity region may not bealways true, e.g. in environmental applications some stations of the intensity regionmay be behind obstacles or too far too reach [Song et al. 2009].

Salajegheh et al. [2007] proposed a hybrid TDMA/FDMA protocol for wireless sen-sor networks, the HyMAC. The proposed protocol assigns time slots and frequenciesbased on a Breadth First Search (BFS) algorithm that constructs a tree that has theBase Station (BS) as its root. Simulation results showed that HyMAC achieves highthroughput and bounded end-to-end delay. However, there are still issues to be solved,such as the maintaining of time-synchronized communication, collision resolution, anddetails concerning how new nodes are joining the network [Incel et al. 2011]. Also, theHyMAC may incur higher energy consumption due to control message transmissions[Suriyachai et al. 2012].

Hohlt et al. [2004] proposed the Flexible Power Scheduling (FPS) protocol for sen-sor networks. FPS is based on the distributed node scheduling approach for tree-based topologies, allowing each node to schedule its own children. More specifically, inFPS, a parent chooses randomly reserved slots from its idle slots and broadcast them.Whenever a child has to send or forward data to the sink, it must reserve a slot in



the parent’s schedule. Once a slot is reserved, data transmission suffers no collisionsbetween children of the same father. In FPS, only coarse-grain synchronization is re-quired due to the relatively large time slots. Both implementation and simulationresults showed that FPS reduces energy consumption at all levels of the network andthat the network can adapt schedules locally to changing demand. However, FPS hasthe following drawbacks:

(1) It is limited when dealing with the funneling effect because it does not preventnodes with different parents from using the same slot [Ahn et al. 2006].

(2) It relies on CSMA to provide collision avoidance in this case [Ahn et al. 2006].(3) It requires global time synchronization [Burri et al. 2007].

Sitanayah et al. [2010] proposed the ER-MAC, a hybrid MAC protocol for emer-gency response wireless sensor networks. The ER-MAC initially communicates usingCSMA/CA with a random-access mechanism. During the startup phase, the data gath-ering tree and TDMA schedules are created. The nodes wake up for their scheduledslots, but otherwise sleep to conserve energy. In case of an emergency, nodes that par-ticipate in the emergency monitoring process change their MAC behavior by allowingcontention in TDMA slots. Simulation results showed that ER-MAC, compared withZ-MAC, outperforms in terms of delivery ratio and low latency, along with lower energyconsumption. However, it is not scalable for high-density networks.

Lee et al. [2008] proposed the Flexi-TP, a CSMA/TDMA hybrid protocol that providesend-to-end guarantees on data delivery within energy and memory constraints in wire-less sensor networks. FlexiTP also adapts to traffic fluctuations and topology changes.It consists of two phases: the network setup phase and the periodic data gatheringphase. During the initial network setup, FlexiTP uses CSMA/CA for packet transmis-sion, and, after this phase finishes, nodes perform regular data gathering tasks usingtheir TDMA schedule. They can also modify their schedules when the network topologychanges. FlexiTP becomes fault tolerant and energy efficient because nodes can build,modify, or extend their scheduled number of slots during execution based on local infor-mation [Gajjar et al. 2012]. However, the cost for network setup is extremely high, andthe schedules are fragile [Lo et al. 2010]. Also, the fact that child selection is based ona simple broadcast reply mechanism may lead to improper parent-child pairs [Gajjaret al. 2012].

An overview of the basic characteristics of the hybrid TDMA scheduling algorithmsreferred to in this article is presented in Table VII. An analysis of hybrid mechanismsin wireless sensor nodes can be found in Pawar et al. [2011].

7. EVALUATION OF THE TDMA SCHEDULING ALGORITHMS

7.1. Comparative Assessment

The main advantage of the centralized algorithms is that they can generate scheduleswith good bandwidth efficiency [Zhu and Corson 2001b]. In addition, centralized linkscheduling achieves higher throughput than node scheduling [Gronkvist 2006]. How-ever, the main disadvantage of centralized scheduling is that it takes a lot of overheadfor the controller to gather information about the entire network, and, in the presenceof node mobility, this information may be obsolete [Zhu and Corson 2001b]. It is alsocomputation-intensive for the controller to generate the schedules, and the centralcontroller is a single point of failure [Zhu and Corson 2001b]. In addition, althoughin centralized link scheduling the gain in throughput increases with the size of thenetwork, this increase in throughput comes at a cost of higher delay for low trafficloads [Gronkvist 2006].



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Moreover, centralized TDMA algorithms that are based on coloring algorithms havethe following drawbacks [Ali et al. 2002]:

—The maximum color number for the network must be known by all terminals, makingit difficult to change their frame sizes and slot assignments.

—Allowing only those terminals with the same color number to transmit in a givenslot can be inefficient if the network topology could allow two or more terminals withdifferent color numbers to transmit simultaneously without interference.

Distributed TDMA node scheduling algorithms that operate under the probabilis-tic policy consume on a per-frame basis more power in comparison with the dis-tributed TDMA node scheduling algorithms that operate under a deterministic policy[Oikonomou and Stavrakakis 2006].

On the other hand, topology-dependent algorithms perform worse in terms of band-width than topology independent algorithms due to the inherent redundancy in orderto work topology-independently [Zhu and Corson 2001b]. However, these algorithmsmay suffer instability if changes in traffic or topology occur too rapidly [Chu et al. 2006].The topology-dependent method will generate significant overhead, especially in highlydynamic environments [Cai et al. 2003]. Also since these algorithms are based on afixed network topology, their performance and robustness deteriorate substantially ina highly dynamic environment [Sun et al. 2008; Amouris 2005].

The benefit of topology-independent scheduling is that the schedule is independent ofnetwork topology and thus they are suitable for dynamic scenarios where the topologychanges frequently [Cheng et al. 2013]. On the other hand, the drawbacks of thesealgorithms are that the length of the scheduling cycle is generally very long, and theobtained frame length always depends on the network size [Cheng et al. 2013].

Amouris [2005] state the following limitations for topology-independent scheduling:

—The sender is unable to know which neighbor(s) can correctly receive the packet itsends in a particular slot.

—The efficiency of the scheduling method drops quadratically as the density of thenetwork increases.

—It is not suitable for networks that can exhibit significant variance in their densityand/or size.

Analytical and simulation results showed that, due to the aggregate nature of inter-ference in wireless communication networks, the graph-based scheduling algorithmsare not necessarily realistic since they may result in serious interferences in terms ofSINR and, hence, dramatic deterioration in network performance [Behzad and Rubin2003].

Also, the fact that most graph-based scheduling algorithms use coloring techniquesto obtain feasible schedules can lead to contradictory results. As stated by Moscibrodaet al. [2006b], modeling interference as coloring can be, on the one hand, too pessimisticsince it does not reflect the fact that even nearby communication is tolerable if it takesplace at sufficiently low power, and, on the other, too optimistic since the simultaneoustransmission even of weak signals can build up considerable interference.

Graph-based scheduling also assumes a limited knowledge of interference and resultsin low throughput, whereas SINR-based scheduling algorithms require a completeknowledge of the interference and lead to higher throughput [Gore et al. 2007]. Also, inmany scenarios, a significant portion of transmissions scheduled based on the protocolinterference model result in unacceptable SINR at intended receivers [Behzad andRubin 2003].

In addition, since graph-based scheduling algorithms employ uniform or linearpower, assignment schemes have poor efficiency. In particular, any such protocol mayrequire a linear number of time slots even if every node merely wants to transmit to its



closest neighbor in the network [Moscibroda et al. 2007]. Also, graph-based schedulingalgorithms have the following drawbacks [Gao et al. 2008]:

(1) Since the node degree does not capture interference adequately, interference in theresulting topology may be high, resulting in low network capacity.

(2) A wireless link that exists in the communication graph may not in practice existunder the physical model due to high interference. Thus, network connectivity maynot even be sustained.

As already mentioned, link scheduling has proved to be NP-hard under the interfer-ence model without considering power control [Goussevskaia et al. 2009] and even if thebackground noise is neglected [Andrews and Dinitz 2009]. Moscibroda and Wattenhofer[2006a] proved that every protocol employing a uniform or linear power assignmentscheme has a poor worst-case efficiency.

Goussevskaia and Wattenhofer [2008] also showed that the problem of schedul-ing wireless links under the interference model remains NP-hard when analog net-work coding (i.e., network coding in the physical layer) is considered. In addition,the fact that, in reality, antennas are not perfectly isotropic—and, even more impor-tantly, the environment is obstructed by walls or plants—the SINR model is unrealistic[Moscibroda et al. 2006a].

Hybrid TDMA solutions can be very beneficial, especially for wireless sensor net-works, since they can deal efficiently with several problems such as congestion, funnel-ing congestion, and the like. However this comes with the following drawbacks [Pawaret al. 2011]:

—The hybrid mechanisms introduce a significant amount of processing delay, mostlydue to neighbor discovery and slot assignment.

—Clock synchronization incurs extra energy overhead by transmitting clock synchro-nization messages periodically.

—The overhead is increased because, during the transmission phase, nodes are chang-ing mode according to traffic conditions.

Finally, cross-layer TDMA solutions can improve spatial channel utilization by al-lowing more concurrent interference-limited transmissions in the same vicinity of areceiver at the cost of a reasonable increase in power consumption [Tang et al. 2006].However, to achieve this goal, the complexity of the algorithms is increased.

7.2. Qualitative Assessment

In Figure 9, we present a qualitative assessment of different types of node schedulingalgorithms. It should be noted that the values are for illustrative purposes and donot necessarily reflect the actual difference in performance. For the purpose of thecomparison, we set a score equal to 1 for the type of algorithms that have the bestperformance in the metric, a score equal to 2/3 for the one that comes second in themetric, and a score equal to 1/3 for the third one. The performance metrics that weselected were overhead, system reliability, how well mobility is supported, the level ofQoS provisioning available, system performance, and the complexity of the algorithm.We evaluated centralized algorithms, distributed topology-dependent algorithms, andtopology-transparent algorithms.

In terms of overhead, the topology-transparent algorithms are superior. Since the slotassignment of each node does not depend on the node’s neighborhood, no informationexchange is required for maintaining topology information, so the overhead of topology-transparent algorithms is minimal. Distributed topology-dependent algorithms needinformation to be exchanged locally, usually inside a two-hop neighborhood. Thus, theirperformance in terms of overhead has the second position. Centralized algorithmsneed the scheduler to maintain updated topology information for the entire network.



Fig. 9. Qualitative assessment of node scheduling algorithms.

Thus, every time the topology changes, information has to be forwarded to the sched-uler. Therefore, the centralized algorithms have the worst performance in terms ofoverhead.

In terms of reliability, the topology-transparent algorithms are again superior. Sincea schedule for each node is implemented, node failures will not affect the rest of thenetwork. Distributed topology-dependent node scheduling algorithms come second inreliability because local failures may occur with topology changes. Centralized algo-rithms are third in reliability since not only suffer from the single point of failure,but also impose additional delay in responding to changes due to the fact that manyretransmissions may be needed to reach the scheduler and back.

In terms of mobility, the ranking is similar mostly for the same reasons. Topology-transparent algorithms have excellent mobility support, with distributed ones comingin second, and centralized coming in third.

The situation is different in terms of QoS provisioning. The centralized algorithmscan maintain a global view of the entire network, which means that end-to-end guaran-tees are easier to be established as long as the network is relatively static. Distributedalgorithms can also have end-to-end QoS capabilities, but now information exchange isless local. Topology-transparent algorithms assign slots to nodes without consideringtraffic demands, and thus their QoS provisioning is low.

In terms of performance, the centralized algorithms have the best performance.These algorithms can use different optimization techniques to create a slot assignmentthat is near optimal. This allows for greater throughput as well as lower delays. Thedistributed algorithms also have good performance since slot assignments may dependon the actual traffic requirements, but, in general, they are easier to converge to localminima. The topology-transparent algorithms by nature waste a lot of bandwidth sincethe opportunity for spatial reuse is minimal. This leads to lower throughput and largerdelays than in the other algorithms.

In Figure 10, we present a qualitative assessment of the different types of linkscheduling algorithms. Graph-based algorithms are better in terms of complexity sinceonly binary information regarding interference is maintained. This greatly simplifiesthe scheduling algorithm. On the other hand, interference-based algorithms use a far



Fig. 10. Qualitative assessment of link scheduling algorithms.

more accurate interference model, and this allows for greater spatial reuse. Thus, the ef-ficiency of these algorithms is superior, leading to higher throughput and lower delays.

8. CONCLUSION

In wireless multihop networks, each node, apart from sending/receiving packets to/fromadjacent nodes, also acts as a router and forwards packets on behalf of other nodes,thus leading to increased interference caused by simultaneous transmissions. Thus, theneed for efficient medium access control is compulsory. TDMA is a promising solution;however, it requires scheduling to avoid primary and secondary collisions.

Several TDMA scheduling algorithms have been proposed in the literature. Thesealgorithms are classified into categories based on several factors, like the entity that isscheduled, the network topology information needed to produce or maintain the sched-ule, and the entity or entities that perform computations for producing and maintainingthe schedules. More specifically, we classify them into TDMA node scheduling, TDMAlink scheduling, TDMA cross-layer scheduling, and hybrid TDMA algorithms.

Each algorithm in each category has its advantages and disadvantages as Tables IIand IV–VII depict. Therefore, further study and several parameters (including networktopology, node degree, and type of node) should be given in order to achieve efficientTDMA scheduling in wireless multihop networks.

REFERENCES

Imtiaz Ahmad, Buthaina Al-Kazemi, and A Shoba Das. 2008. An efficient algorithm to find broadcastschedule in ad hoc TDMA networks. Journal of Computer Systems, Networks, and Communications2008 (2008), 12.

Gahng-Seop Ahn, Se Gi Hong, Emiliano Miluzzo, Andrew T. Campbell, and Francesca Cuomo. 2006.Funneling-MAC: A localized, sink-oriented MAC for boosting fidelity in sensor networks. In Proceedingsof the 4th International Conference on Embedded Networked Sensor Systems. ACM, 293–306.



Farha N. Ali, Praveen K. Appani, Joseph L. Hammond, Vivek V. Mehta, D. L. Noneaker, and H. B. Russell.2002. Distributed and adaptive TDMA algorithms for multiple-hop mobile networks. In Proceedings ofthe 2002 Military Communications Conference (MILCOM’02). Vol. 1. IEEE, 546–551.

K. Amouris. 2001. Space-time division multiple access (STDMA) and coordinated, power-aware MACA formobile ad hoc networks. In Proceedings of the Global Telecommunications Conference (GLOBECOM’01).Vol. 5. IEEE, 2890–2895.

K. Amouris. 2005. Position-based broadcast TDMA scheduling for mobile ad-hoc networks (MANETs) withadvantaged nodes. In Proceedings of the Military Communications Conference (MILCOM’05). IEEE,252–257.

Matthew Andrews and Michael Dinitz. 2009. Maximizing capacity in arbitrary wireless networks in the SINRmodel: Complexity and game theory. In Proceedings of the 28th Conference on Computer Communications(INFOCOM’09). IEEE, 1332–1340.

Deivasigamani Arivudainambi and Durai Rekha. 2012. An evolutionary algorithm for broadcast schedulingin wireless multihop networks. Wireless Networks 18, 7 (2012), 787–798.

Lichun Bao and J. J. Garcia-Luna-Aceves. 2000. Collision-free topology-dependent channel access scheduling.In Proceedings of the Military Communications Conference (MILCOM’00). Vol. 1. IEEE, 507–511.

Arash Behzad and Izhak Rubin. 2003. On the performance of graph-based scheduling algorithms for packetradio networks. In Proceedings of the Global Telecommunications Conference, 2003. GLOBECOM’03.Vol. 6. IEEE, 3432–3436.

Arash Behzad and Izhak Rubin. 2007. Optimum integrated link scheduling and power control for multihopwireless networks. IEEE Transactions on Vehicular Technology 56, 1 (2007), 194–205.

Weixing Bi, Zheng Tang, Jiahai Wang, and Qiping Cao. 2005. An improved neural network algorithm forbroadcast scheduling problem in packet radio. Neural Information Processing-Letters and Reviews 9, 1(2005), 23–29.

Patrik Bjorklund, Peter Varbrand, and Di Yuan. 2003. Resource optimization of spatial TDMA in ad hocradio networks: A column generation approach. In Proceedings of the 22nd Annual Joint Conference ofthe IEEE Computer and Communications (INFOCOM’03). Vol. 2. IEEE, 818–824.

Patrik Bjorklund, Peter Varbrand, and Di Yuan. 2004. A column generation method for spatial TDMAscheduling in ad hoc networks. Ad Hoc Networks 2, 4 (2004), 405–418.

Gurashish Brar, Douglas M. Blough, and Paolo Santi. 2006. Computationally efficient scheduling with thephysical interference model for throughput improvement in wireless mesh networks. In Proceedings ofthe 12th Annual International Conference on Mobile Computing and Networking. ACM, 2–13.

Nicolas Burri, Pascal Von Rickenbach, and Roger Wattenhofer. 2007. Dozer: Ultra-low power data gatheringin sensor networks. In Proceedings of the 6th International Symposium on Information Processing inSensor Networks (IPSN’07). IEEE, 450–459.

Zhijun Cai, Mi Lu, and Costas N. Georghiades. 2003. Topology-transparent time division multiple accessbroadcast scheduling in multihop packet radio networks. IEEE Transactions on Vehicular Technology52, 4 (2003), 970–984.

Paulo Cardieri. 2010. Modeling interference in wireless ad hoc networks. IEEE Communications Surveys &Tutorials 12, 4 (2010), 551–572.

Goutam Chakraborty. 2004. Genetic algorithm to solve optimum TDMA transmission schedule in broadcastpacket radio networks. IEEE Transactions on Communications 52, 5 (2004), 765–777.

Jenhui Chen and Shuhua Jiang. 2006. Improvement of slots utilization with a stealing-TDMA protocol forad hoc network. In Proceedings of the 2006 IEEE 64th Vehicular Technology Conference (VTC’06). IEEE,1–5.

Jung-Chieh Chen, Yeong-Cheng Wang, and Jiunn-Tsair Chen. 2006. A novel broadcast scheduling strategyusing factor graphs and the sum-product algorithm. IEEE Transactions on Wireless Communications 5,6 (2006), 1241–1249.

Hongju Cheng, Naixue Xiong, Larence T. Yang, and Young-Sik Jeong. 2013. Distributed scheduling algo-rithms for channel access in TDMA wireless mesh networks. The Journal of Supercomputing 63, 2(2013), 407–430.

Maggie Cheng and Li Yin. 2007. Transmission scheduling in sensor networks via directed edge coloring. InProceedings of the IEEE International Conference on Communications (ICC’07). IEEE, 3710–3715.

Imrich Chlamtac and Andras Farago. 1994. Making transmission schedules immune to topology changes inmulti-hop packet radio networks. IEEE/ACM Transactions on Networking (TON) 2, 1 (1994), 23–29.

Wensong Chu, Charles J. Colbourn, and Violet R. Syrotiuk. 2006. The effects of synchronization on topology-transparent scheduling. Wireless Networks 12, 6 (2006), 681–690.

Clayton W. Commander, Sergiy I. Butenko, and Panos M. Pardalos. 2004. On the performance of heuristicsfor broadcast scheduling. Theory and Algorithms for Cooperative Systems (2004), 63–80.



Piergiuseppe Di Marco, Pangun Park, Carlo Fischione, and Karl Henrik Johansson. 2010. TREnD: A timely,reliable, energy-efficient and dynamic WSN protocol for control applications. In Proceedings of the 2010IEEE International Conference on Communications (ICC’10). IEEE, 1–6.

Antonis Dimakis and Jean Walrand. 2006. Sufficient conditions for stability of longest-queue-first scheduling:Second-order properties using fluid limits. Advances in Applied Probability (2006), 505–521.

Petar Djukic and Shahrokh Valaee. 2007. Link scheduling for minimum delay in spatial re-use TDMA. InProceedings of the 26th IEEE International Conference on Computer Communications (INFOCOM’07).IEEE, 28–36.

Tamer ElBatt and Anthony Ephremides. 2004. Joint scheduling and power control for wireless ad hocnetworks. IEEE Transactions on Wireless Communications 3, 1 (2004), 74–85.

Anthony Ephremides and Thuan V. Truong. 1990. Scheduling broadcasts in multihop radio networks. IEEETransactions on Communications 38, 4 (1990), 456–460.

Zuyuan Fang and Brahim Bensaou. 2004. Fair bandwidth sharing algorithms based on game theory frame-works for wireless ad-hoc networks. In Proceedings of the 23rd Annual Joint Conference of the IEEEComputer and Communications Societies (INFOCOM’04), Vol. 2. IEEE, 1284–1295.

Alexander Fanghanel, Thomas Kesselheim, Harald Racke, and Berthold Vocking. 2009. Oblivious interfer-ence scheduling. In Proceedings of the 28th ACM Symposium on Principles of Distributed Computing.ACM, 220–229.

Hossam Fattah and Cyril Leung. 2002. An overview of scheduling algorithms in wireless multimedia net-works. IEEE Wireless Communications 9, 5 (2002), 76–83.

Liqun Fu, Soung Chang Liew, and Jianwei Huang. 2010. Fast algorithms for joint power control and schedul-ing in wireless networks. IEEE Transactions on Wireless Communications 9, 3 (2010), 1186–1197.

Nobuo Funabiki and Junji Kitamichi. 1999. A gradual neural network algorithm for broadcast schedulingproblems in packet radio networks. IEICE TRANSACTIONS on Fundamentals of Electronics, Commu-nications and Computer Sciences 82, 5 (1999), 815–824.

Vijay Gabale, Bhaskaran Raman, Partha Dutta, S. Gabale, and S. Kalyanraman. 2013. A classificationframework for scheduling algorithms in wireless mesh networks. IEEE Communications Surveys &Tutorials 15, 1 (2013), 199–222.

Harold N. Gabow and Herbert H. Westermann. 1992. Forests, frames, and games: Algorithms for matroidsums and applications. Algorithmica 7, 1–6 (1992), 465–497.

Sachin Gajjar, Shrikant N. Pradhan, and Kankar Dasgupta. 2012. Performance analysis of cross layerprotocols for wireless sensor networks. In Proceedings of the International Conference on Advances inComputing, Communications and Informatics. ACM, 348–354.

S. Gandham, M. Dawande, and R. Prakash. 2005. Link scheduling in sensor networks: Distributed edgecoloring revisited. In Proceedings of the IEEE 24th Annual Joint Conference of the IEEE Computer andCommunications Societies (INFOCOM’05). Vol. 4. IEEE, 2492–2501.

Yan Gao, Jennifer C. Hou, and Hoang Nguyen. 2008. Topology control for maintaining network connectivityand maximizing network capacity under the physical model. In Proceedings of the 27th Conference onComputer Communications (INFOCOM’08). IEEE, 1013–1021.

Ashutosh Deepak Gore and Abhay Karandikar. 2011. Link scheduling algorithms for wireless mesh networks.IEEE Communications Surveys & Tutorials 13, 2 (2011), 258–273.

Ashutosh Deepak Gore, Abhay Karandikar, and Srikanth Jagabathula. 2007. On high spatial reuse linkscheduling in STDMA wireless ad hoc networks. In Proceedings of the Global TelecommunicationsConference (GLOBECOM’07). IEEE, 736–741.

Olga Goussevskaia, Yvonne-Anne Pignolet, and Roger Wattenhofer. 2010. Efficiency of wireless networks:Approximation algorithms for the physical interference model. Foundations and Trends in Networking4, 3 (2010), 313–420.

Olga Goussevskaia and Roger Wattenhofer. 2008. Complexity of scheduling with analog network coding.In Proceedings of the 1st ACM International Workshop on Foundations of Wireless Ad Hoc and SensorNetworking and Computing. ACM, 77–84.

Olga Goussevskaia, Roger Wattenhofer, Magnus M. Halldorsson, and Emo Welzl. 2009. Capacity of arbitrarywireless networks. In Proceedings of the 28th Conference on Computer Communications (INFOCOM’09).IEEE, 1872–1880.

Jimmi Gronkvist. 2006. Novel assignment strategies for spatial reuse TDMA in wireless ad hoc networks.Wireless Networks 12, 2 (2006), 255–265.

R. Gunasekaran, S. Siddharth, P. Krishnaraj, M. Kalaiarasan, and V. Rhymend Uthariaraj. 2010. Efficientalgorithms to solve broadcast scheduling problem in WiMAX mesh networks. Computer Communications33, 11 (2010), 1325–1333.



Piyush Gupta and Panganmala R. Kumar. 2000. The capacity of wireless networks. IEEE Transactions onInformation Theory 46, 2 (2000), 388–404.

Magnus M. Halldorsson and Pradipta Mitra. 2012. Wireless capacity with arbitrary gain matrix. In Algo-rithms for Sensor Systems. Springer, 215–224.

Bo Han, Fung Po Tso, Lidong Ling, and Weijia Jia. 2006. Performance evaluation of scheduling in IEEE802.16 based wireless mesh networks. In Proceedings of the 2006 IEEE International Conference onMobile Adhoc and Sensor Systems (MASS’06). IEEE, 789–794.

Barbara Hohlt, Lance Doherty, and Eric Brewer. 2004. Flexible power scheduling for sensor networks. InProceedings of the 3rd International Symposium on Information Processing in Sensor Networks. ACM,205–214.

IEEE. 1999. Wireless LAN medium access control (MAC) and physical layer (PHY) specifications. IEEEStandard 802, 1 (1999), 999.

Ozlem Durmaz Incel, Lodewijk van Hoesel, Pierre Jansen, and Paul Havinga. 2011. MC-LMAC: A multi-channel MAC protocol for wireless sensor networks. Ad Hoc Networks 9, 1 (2011), 73–94.

Changhee Joo, Xiaojun Lin, and Ness B. Shroff. 2009. Understanding the capacity region of the greedymaximal scheduling algorithm in multihop wireless networks. IEEE/ACM Transactions on Networking(TON) 17, 4 (2009), 1132–1145.

Ji-Her Ju and V. O. K. Li. 2006. TDMA scheduling design of multihop packet radio networks based on latinsquares. IEEE Journal on Selected Areas in Communications 17, 8 (2006), 1345–1352.

Ji-Her Ju and Victor OK Li. 1998. An optimal topology-transparent scheduling method in multihop packetradio networks. IEEE/ACM Transactions on Networking (TON) 6, 3 (1998), 298–306.

Raja Jurdak, Cristina Videira Lopes, and Pierre Baldi. 2004. A survey, classification and comparative analysisof medium access control protocols for ad hoc networks. IEEE Communications Surveys & Tutorials 6,1 (2004), 2–16.

Bastian Katz, Markus Volker, and Dorothea Wagner. 2008. Link scheduling in local interference models. InAlgorithmic Aspects of Wireless Sensor Networks. Springer, 57–71.

Youngmin Kim, Hyojeong Shin, and Hojung Cha. 2008. Y-mac: An energy-efficient multi-channel mac protocolfor dense wireless sensor networks. In Proceedings of the 7th International Conference on InformationProcessing in Sensor Networks. IEEE Computer Society, 53–63.

Kurtis Kredo and Prasant Mohapatra. 2007. Medium access control in wireless sensor networks. ComputerNetworks 51, 4 (2007), 961–994.

Luobei Kuang, Ming Xu, and Wei Yu. 2008. EMDF-A broadcast scheduling policy for wireless multi-hopnetworks with interference constraint. In Proceedings of the 9th International Conference for YoungComputer Scientists (ICYCS’08). IEEE, 599–604.

Winnie Louis Lee, Amitava Datta, and Rachel Cardell-Oliver. 2008. FlexiTP: A flexible-schedule-based TDMAprotocol for fault-tolerant and energy-efficient wireless sensor networks. IEEE Transactions on Paralleland Distributed Systems 19, 6 (2008), 851–864.

Johannes Lessmann and Dirk Held. 2008. A mobility-adaptive TDMA MAC for real-time data in wirelessnetworks. In NETWORKING 2008 Ad Hoc and Sensor Networks, Wireless Networks, Next GenerationInternet. Springer, 804–811.

Yun Li and Anthony Ephremides. 2007. A joint scheduling, power control, and routing algorithm for ad hocwireless networks. Ad Hoc Networks 5, 7 (2007), 959–973.

Yiming Liu, Victor O. K. Li, Ka-Cheong Leung, and Lin Zhang. 2012. Topology-transparent distributedmulticast and broadcast scheduling in mobile ad hoc networks. In Proceedings of the 2012 IEEE 75thVehicular Technology Conference (VTC Spring). IEEE, 1–5.

Chun-Chi Lo, Yu-Chen Hu, and Chia-Ying Li. 2010. A distributed communication protocol for wireless sensornetworks with asynchronous superframe. In Proceedings of the 2010 IET International Conference onFrontier Computing. Theory, Technologies and Applications (IETFC’10). 235–240.

Valeria Loscri. 2007. MAC schemes for ad-hoc wireless networks. In Proceedings of the 2007 IEEE 66thVehicular Technology Conference (VTC’07 Fall). IEEE, 36–40.

Wyin-Pyin Lyui. 1991. Design of a New Operational Structure for Mobile Radio Networks. PhD Dissertation.Clemson University.

Jianlin Mao, Zhiming Wu, and Xing Wu. 2007. A TDMA scheduling scheme for many-to-one communicationsin wireless sensor networks. Computer Communications 30, 4 (2007), 863–872.

Thomas Moscibroda, Yvonne Anne Oswald, and Roger Wattenhofer. 2007. How optimal are wireless schedul-ing protocols? In Proceedings of the 26th IEEE International Conference on Computer Communications(INFOCOM’07). IEEE, 1433–1441.



Thomas Moscibroda, Roger Wattenhofer, and Yves Weber. 2006a. Protocol design beyond graph-based models.In Proceedings of the ACM Workshop on Hot Topics in Networks (HotNets-V). 25–30.

Thomas Moscibroda, Roger Wattenhofer, and Aaron Zollinger. 2006b. Topology control meets SINR: Thescheduling complexity of arbitrary topologies. In Proceedings of the 7th ACM International Symposiumon Mobile Ad Hoc Networking and Computing. ACM, 310–321.

Randolph Nelson and Leonard Kleinrock. 1985. Spatial TDMA: A collision-free multihop channel accessprotocol. IEEE Transactions on Communications 33, 9 (1985), 934–944.

Chiu Yeung Ngo and Victor OK Li. 2003. Centralized broadcast scheduling in packet radio networks viagenetic-fix algorithms. IEEE Transactions on Communications 51, 9 (2003), 1439–1441.

Konstantinos Oikonomou and Ioannis Stavrakakis. 2004. Analysis of a probabilistic topology-unaware TDMAMAC policy for ad hoc networks. IEEE Journal on Selected Areas in Communications 22, 7 (2004), 1286–1300.

Konstantinos Oikonomou and Ioannis Stavrakakis. 2006. Energy considerations for topology-unaware TDMAMAC protocols. Ad Hoc Networks 4, 3 (2006), 359–379.

Katerina Papadaki and Vasilis Friderikos. 2008. Robust scheduling in spatial reuse TDMA wireless networks.IEEE Transactions on Wireless Communications 7, 12 (2008), 4767–4771.

Georgios I. Papadimitriou, Mohammad S. Obaidat, and Andreas S. Pomportsis. 2002. On the use of learningautomata in the control of broadcast networks: A methodology. IEEE Transactions on Systems, Man,and Cybernetics, Part B: Cybernetics 32, 6 (2002), 781–790.

Sung Park and Denh Sy. 2008. Dynamic control slot scheduling algorithms for TDMA based mobile ad hocnetworks. In Proceedings of the Military Communications Conference (MILCOM’08). IEEE, 1–7.

Pranav Pawar, Rasmus Nielsen, Neeli Prasad, Shingo Ohmori, and Ramjee Prasad. 2011. Hybrid mecha-nisms: Towards an efficient wireless sensor network medium access control. In Proceedings of the 201114th International Symposium on Wireless Personal Multimedia Communications (WPMC’11). IEEE,1–5.

Y. Peng, B. H. Soong, and L. Wang. 2004. Broadcast scheduling in packet radio networks using mixedtabu-greedy algorithm. Electronics Letters 40, 6 (2004), 375–376.

Subramanian Ramanathan. 1999. A unified framework and algorithm for channel assignment in wirelessnetworks. Wireless Networks 5, 2 (1999), 81–94.

Subramanian Ramanathan and Errol L. Lloyd. 1993. Scheduling algorithms for multihop radio networks.IEEE/ACM Transactions on Networking (TON) 1, 2 (1993), 166–177.

Injong Rhee, Ajit Warrier, Mahesh Aia, Jeongki Min, and Mihail L . Sichitiu. 2008. Z-MAC: A hybrid MACfor wireless sensor networks. IEEE/ACM Transactions on Networking (TON) 16, 3 (2008), 511–524.

Injong Rhee, Ajit Warrier, Jeongki Min, and Lisong Xu. 2006. DRAND: Distributed randomized TDMAscheduling for wireless ad-hoc networks. In Proceedings of the 7th ACM International Symposium onMobile Ad Hoc Networking and Computing. ACM, 190–201.

Izhak Rubin and Zhensheng Zhang. 1992. Message delay analysis for TDMA schemes using contiguous-slotassignments. IEEE Transactions on Communications 40, 4 (1992), 730–737.

Mastooreh Salajegheh, Hamed Soroush, and Antonis Kalis. 2007. Hymac: Hybrid TDMA/FDMA mediumaccess control protocol for wireless sensor networks. In Proceedings of the IEEE 18th InternationalSymposium on Personal, Indoor and Mobile Radio Communications (PIMRC’07). IEEE, 1–5.

Sancho Salcedo-Sanz, Carlos Bousono-Calzon, and Anıbal R. Figueiras-Vidal. 2003. A mixed neural-geneticalgorithm for the broadcast scheduling problem. IEEE Transactions on Wireless Communications 2, 2(2003), 277–283.

Paolo Santi, Ritesh Maheshwari, Giovanni Resta, Samir Das, and Douglas M. Blough. 2009. Wireless linkscheduling under a graded SINR interference model. In Proceedings of the 2nd ACM InternationalWorkshop on Foundations of Wireless Ad Hoc and Sensor Networking and Computing. ACM, 3–12.

Arunabha Sen and Mark L. Huson. 1997. A new model for scheduling packet radio networks. WirelessNetworks 3, 1 (1997), 71–82.

A. Sgora, D. J. Vergados, and D. D. Vergados. 2008a. On per-flow fairness and scheduling in wireless multihopnetworks. In Proceedings of the IEEE International Conference on Communications Workshops. IEEE,217–221.

A. Sgora, D. J. Vergados, D. D. Vergados, I. Tinnirello, I. Anagnostopoulos, and D. Vouyioukas. 2008b. Jointrouting and per-flow fairness in wireless multihop networks. In Proceedings of the 3rd InternationalSymposium on Wireless Pervasive Computing (ISWPC’08). IEEE, 707–711.

Yu-Ju Shen and Ming-Shi Wang. 2008. Broadcast scheduling in wireless sensor networks using fuzzy hopfieldneural network. Expert Systems with Applications 34, 2 (2008), 900–907.



Haixiang Shi and Lipo Wang. 2005a. Broadcast scheduling in wireless multihop networks using a neural-network-based hybrid algorithm. Neural Networks 18, 5 (2005), 765–771.

Haixiang Shi and Lipo Wang. 2005b. A hybrid neural network for optimal TDMA transmission schedulingin packet radio networks. In Proceedings of the 2005 IEEE International Joint Conference on NeuralNetworks (IJCNN’05), Vol. 5. IEEE, 3210–3213.

Haixiang Shi and Lipo Wang. 2005c. Optimal TDMA frame scheduling in broadcasting packet radio networksusing a gradual noisy chaotic neural network. In Advances in Natural Computation. Springer, 1080–1089.

Lanny Sitanayah, Cormac J. Sreenan, and Kenneth N. Brown. 2010. ER-MAC: A hybrid MAC protocol foremergency response wireless sensor networks. In Proceedings of the 4th International Conference onSensor Technologies and Applications (SENSORCOMM’10). IEEE, 244–249.

Fikret Sivrikaya and Bulent Yener. 2009. Minimum delay routing for wireless networks with STDMA.Wireless Networks 15, 6 (2009), 755–772.

Wen-Zhan Song, Renjie Huang, Behrooz Shirazi, and Richard LaHusen. 2009. TreeMAC: Localized TDMAMAC protocol for real-time high-data-rate sensor networks. Pervasive and Mobile Computing 5, 6 (2009),750–765.

Yi-Sheng Su. 2008. Joint topology-transparent broadcast scheduling and MDS erasure coding in multihopTDMA ad hoc networks. In Proceedings of the IEEE International Symposium on Consumer Electronics(ISCE’08). IEEE, 1–4.

Yi-Sheng Su, Szu-Lin Su, and Jung-Shian Li. 2004. Topology-transparent node activation scheduling schemesfor multihop TDMA ad hoc networks. In Proceedings of the Global Telecommunications ConferenceWorkshops (GlobeCom’04). IEEE. IEEE, 68–73.

Ming Sun, Lin Zhao, Wei Cao, Yaoqun Xu, Xuefeng Dai, and Xiaoxu Wang. 2010. Novel hysteretic noisychaotic neural network for broadcast scheduling problems in packet radio networks. IEEE Transactionson Neural Networks 21, 9 (2010), 1422–1433.

Qiong Sun, Victor O. K. Li, and Ka-Cheong Leung. 2008. Topology-transparent distributed scheduling inmulti-hop wireless networks. In Proceedings of the Global Telecommunications Conference (GLOBE-COM’08). IEEE, 1–5.

Petcharat Suriyachai, Utz Roedig, and Andrew Scott. 2012. A survey of MAC protocols for mission-criticalapplications in wireless sensor networks. IEEE Communications Surveys & Tutorials 14, 2 (2012),240–264.

Yoshiyasu Takefuji, Kuo-Chun Lee, and Hideo Also. 1992. An artificial maximum neural network: A winner-take-all neuron model forcing the state of the system in a solution domain. Biological Cybernetics 67, 3(1992), 243–251.

Jian Tang, Guoliang Xue, Christopher Chandler, and Weiyi Zhang. 2006. Link scheduling with power controlfor throughput enhancement in multihop wireless networks. IEEE Transactions on Vehicular Technology55, 3 (2006), 733–742.

Leandros Tassiulas and Anthony Ephremides. 1992. Stability properties of constrained queueing systemsand scheduling policies for maximum throughput in multihop radio networks. IEEE Transactions onAutomatic Control 37, 12 (1992), 1936–1948.

Dimitrios D. Vergados, Dimitrios J. Vergados, and Christos Douligeris. 2005. A new approach for TDMAscheduling in ad-hoc networks. In Proceedings of the 10th IFIP International Conference on PersonalWireless Communications (PWC’05). World Scientific, 279–286.

Dimitrios D. Vergados, Dimitrios J. Vergados, Christos Douligeris, and Spyridon L. Tombros. 2006. QoS-aware TDMA for end-to-end traffic scheduling in ad hoc networks. Wireless Communications, IEEE 13,5 (2006), 68–74.

Dimitrios J. Vergados, M.-Y. Manolaraki, and Dimitrios D. Vergados. 2009. Evaluation of broadcast schedul-ing algorithms for ad-hoc TDMA networks. In Proceedings of the 1st International Conference on WirelessCommunication, Vehicular Technology, Information Theory and Aerospace & Electronic Systems Tech-nology (Wireless VITAE’09). IEEE, 394–398.

Dimitrios J. Vergados, Aggeliki Sgora, Dimitrios D. Vergados, Demosthenes Vouyioukas, and IoannisAnagnostopoulos. 2012. Fair TDMA scheduling in wireless multihop networks. Telecommunication Sys-tems 50, 3 (2012), 181–198.

Peng-Jun Wan, Ophir Frieder, Xiaohua Jia, Frances Yao, Xiaohua Xu, and Shaojie Tang. 2011. Wirelesslink scheduling under physical interference model. In Proceedings of the 2011 IEEE INFOCOM. IEEE,838–845.

Peng-Jun Wan, Xiaohua Xu, and Ophir Frieder. 2010. Shortest link scheduling with power control underphysical interference model. In Proceedings of the 6th International Conference on Mobile Ad-hoc andSensor Networks (MSN’10). IEEE, 74–78.



Gangsheng Wang and Nirwan Ansari. 1997. Optimal broadcast scheduling in packet radio networks usingmean field annealing. IEEE Journal on Selected Areas in Communications 15, 2 (1997), 250–260.

Kang Wang, Carla-Fabiana Chiasserini, Ramesh R. Rao, and John G. Proakis. 2005. A joint solution toscheduling and power control for multicasting in wireless ad hoc networks. EURASIP Journal on AppliedSignal Processing 2005 (2005), 144–152.

Wei Wang, Xin Liu, and Dilip Krishnaswamy. 2007. Robust routing and scheduling in wireless mesh net-works. In Sensor, Mesh and Ad Hoc Communications and Networks, 2007. SECON’07. 4th Annual IEEECommunications Society Conference on. IEEE, 471–480.

Weizhao Wang, Yu Wang, Xiang-Yang Li, Wen-Zhan Song, and Ophir Frieder. 2006. Efficient interference-aware TDMA link scheduling for static wireless networks. In Proceedings of the 12th Annual Interna-tional Conference on Mobile Computing and Networking. ACM, 262–273.

Yu Wang and Ian Henning. 2007. A deterministic distributed TDMA scheduling algorithm for wireless sensornetworks. In Proceedings of the International Conference on Wireless Communications, Networking andMobile Computing (WiCom’07). IEEE, 2759–2762.

Yu Wang, Weizhao Wang, Xiang-Yang Li, and Wen-Zhan Song. 2008. Interference-aware joint routing andTDMA link scheduling for static wireless networks. IEEE Transactions on Parallel and DistributedSystems 19, 12 (2008), 1709–1726.

Zhiqi Wang, Fengqi Yu, Jian Tian, and Zusheng Zhang. 2012. A fairness adaptive TDMA scheduling algorithmfor wireless sensor networks with unreliable links. International Journal of Communication Systems(2012).

Brian J. Wolf, Joseph L. Hammond, and Harlan B. Russell. 2006. A distributed load-based transmissionscheduling protocol for wireless ad hoc networks. In Proceedings of the 2006 International Conferenceon Wireless Communications and Mobile Computing. ACM, 437–442.

Zhang Xizheng and Wang Yaonan. 2008. Efficient broadcast scheduling based on hybrid fuzzy hopfieldnetwork for ad hoc networks. In Proceedings of the 27th Chinese Control Conference (CCC’08). IEEE,725–728.

Chaonong Xu, Yongjun Xu, Zhiguang Wang, and Haiyong Luo. 2011. A topology-transparent MAC schedul-ing algorithm with guaranteed QoS for multihop wireless network. Journal of Control Theory andApplications 9, 1 (2011), 106–114.

Shugong Xu and Tarek Saadawi. 2001. Does the IEEE 802.11 MAC protocol work well in multihop wirelessad hoc networks? IEEE Communications Magazine 39, 6 (2001), 130–137.

XiaoHua Xu and ShaoJie Tang. 2009. A constant approximation algorithm for link scheduling in arbitrarynetworks under physical interference model. In Proceedings of the 2nd ACM International Workshop onFoundations of Wireless Ad Hoc and Sensor Networking and Computing. ACM, 13–20.

Justin Yackoski and Chien-Chung Shen. 2010. Managing end-to-end delay for VoIP calls in multi-hop wire-less mesh networks. In Proceedings of the INFOCOM IEEE Conference on Computer CommunicationsWorkshops. IEEE, 1–6.

Guanqun Yang, Bin Tong, Daji Qiao, and Wensheng Zhang. 2008. Sensor-aided overlay deployment andrelocation for vast-scale sensor networks. In Proceedings of the 27th Conference on Computer Commu-nications (INFOCOM’08). IEEE, 2216–2224.

Jaehyun Yeo, Heesoo Lee, and Sehun Kim. 2002. An efficient broadcast scheduling algorithm for TDMAad-hoc networks. Computers & Operations Research 29, 13 (2002), 1793–1806.

Jong-Hoon Youn and Bella Bose. 2001. A topology-independent transmission scheduling in multihop packetradio networks. In Proceedings of the Global Telecommunications Conference. (GLOBECOM’01). Vol. 3.IEEE, 1918–1922.

Xuedan Zhang, Jun Hong, Lin Zhang, Xiuming Shan, and Victor O. K. Li. 2007. CC-TDMA: Coloring-and coding-based multi-channel TDMA scheduling for wireless ad hoc networks. In Proceedings of theWireless Communications and Networking Conference (WCNC’07). IEEE, 133–137.

Xuedan Zhang, Jun Hong, Lin Zhang, Xiuming Shan, and Victor O. K. Li. 2008. CP-TDMA: Coloring-and5probability-based TDMA scheduling for wireless ad hoc networks. IEICE Transactions on Communica-tions 91, 1 (2008), 322–326.

Chenxi Zhu and M. Scott Corson. 2001a. An Evolutionary-TDMA scheduling protocol (E-TDMA) for mobilead hoc networks. Technical Research Report, CSHCN TR 2001-17.

Chenxi Zhu and M. Scott Corson. 2001b. A five-phase reservation protocol (FPRP) for mobile ad hoc networks.Wireless Networks 7, 4 (2001), 371–384.

Received September 2013; revised September 2014; accepted October 2014


A Survey of TDMA Scheduling Schemes in Wireless Multihop Networks

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