An optimal dynamic resources partitioning auction model for virtual private networks

Telecommun SystDOI 10.1007/s11235-013-9710-5

An optimal dynamic resources partitioning auction modelfor virtual private networks

Ahmad Nahar Quttoum · Abdallah Jarray ·Hadi Otrok · Zbigniew Dziong

© Springer Science+Business Media New York 2013

Abstract In this paper, we consider the problem of optimiz-ing the Internet Service Provider (ISP) profit by providinga periodic Dynamic Partitioning (DP) model for utilizingnetwork resources in the context of Virtual Private Net-works (VPN). In literature, Complete Sharing (CS), Com-plete Partitioning (CP), and Bandwidth Borrowing (BR)techniques have been proposed for resource allocationwhere the following limitations can be noticed: VPN opera-tors can exaggerate about their required resources, resourcesmight be underutilized, and optimal bandwidth utilizationis not guaranteed. To overcome the above limitations, wepropose to dynamically partition the resources over differ-ent QoS classes through periodic auctions that can reducethe reasoning of exaggeration and maximize the ISP profit.Thus, we formulate our problem based on the Integer Lin-ear Programming (ILP) that allows us to maximize the ISPprofit and provides the optimal: (1) set of profitable VPNconnections, (2) bandwidth division of each network linkamong QoS classes, and (3) routing scheme for the accepted

A.N. Quttoum (�)Computer Engineering Department, The Hashemite University,P.O. Box 150459, Zarqa, Jordane-mail: [email protected]

A. Jarray · Z. DziongElectrical Engineering Dep., ETS, Université du Québec,Montréal, QC, Canada

A. Jarraye-mail: [email protected]

Z. Dzionge-mail: [email protected]

H. OtrokDepartment of Computer Eng., Khalifa University of Science,Technology & Research, Abu Dhabi, UAEe-mail: [email protected]

demand. Furthermore, the proposed ILP model allows us tostudy the sensitivity of the ISP profit to a targeted revenueobjective.

Keywords Virtual Private Network (VPN) · Resourceallocation · Dynamic partitioning · Periodical auction ·Linear programming

1 Introduction

We are witnessing an unprecedented demand for InternetService Providers (ISPs) to support a wide variety of VirtualPrivate Networks (VPNs). These VPNs use the ISPs’ publicinfrastructure to establish secure and reliable services ac-cording to contracted Service Level Agreements (SLA) [9].Resource management is one of the main challenges facingISPs, where each VPN may have different requirements andrequired Quality of Service (QoS) guarantees. The growingdemands for such VPN services with certain QoS satisfac-tion conditions necessitate the ISPs to efficiently utilize theirbandwidth resources. Models to provide an efficient and ef-fective resource allocation schemes are extremely important.Relying on the current management models that attempt di-rect interactions with the ISPs is not satisfying anymore, asthey have many limitations that can be summarized as fol-lows: (1) These models increase the management operationexpenses. (2) They provide slow response times. Such limi-tations can lead to high rates of users’ dissatisfaction. Conse-quently, the need is emerging to find an alternative resourcemanagement models that overcome the current limitations.Complete Sharing (CS) [14, 17] and Complete Partition-ing (CP) [5, 13, 14] models are proposed in the literatureto cope with the above management problem by creatinga framework for automated management. In CS, network

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A.N. Quttoum et al.

resources are shared over all classes without any division.While, in CP, resources are statically divided among QoSclasses where each class uses its own allocated resources.Such approaches are able to automate the resources alloca-tion, while at the same time they create several problems thatcan be summarized as follows:

– In CS approach, resources are allocated in a First AskFirst Allocate (FAFA) scheme, where one QoS class canoverwhelm all other classes in a way that reduces the ISPprofit.

– In CP approach, resources can be underutilized which re-duces ISPs profits.

– Due to the long-term SLA agreement, VPN operatorsmight exaggerate about their required resources to guar-antee their QoS and to cope with any unpredicted vari-ations in the network state. Such a behavior can affectthe ISP profit, and maximize the VPN demands block-ing rates. Indeed, when demand for the resources exceedsthe capacity, avoiding exaggeration allows to admit moreVPN connections (using the same amount of bandwidthresources), which can reduce the blocking rates while col-lecting the same profits.

To overcome the problem of underutilization in CP, theBandwidth Borrowing (BR) technique has been proposed,[6, 21], to enable the ISPs to provide better resource utiliza-tion that guarantees the QoS for all VPNs. According to thedynamicity of the traffic, the BR technique allows the ISPto borrow the extra resources of the underloaded links andreallocate them to the overloaded ones. While yet, as longas the CP attempts a static partitioning scheme, BR cannotprovide an optimal bandwidth utilization solution, where wemay have many underloaded links with no overloaded ones(or vice-versa), in such a case how the BR would work?

To overcome the above limitations, we propose deploy-ing a periodic-dynamic resource partitioning model (DP) forallocating the network bandwidth resources to VPN oper-ators. In DP, the dynamic class division process will takeplace in a periodic auction manner, where VPN operatorswill be competing to win the resource allocations throughtheir submitted prices and connections’ demands. The net-work planning time is divided into a set of periods in or-der to reduce the reasoning of exaggeration and to eliminatethe needs for any borrowing technique. The length of there-optimization period depends on the provided service du-ration. Demands with different service durations can be di-vided into groups, each with certain period length. At eachnew period, the profitable VPN connections are selectedthrough an auction mechanism in order to maximize the ISPprofit. Therefore, we develop and implement an Integer Lin-ear Program (ILP) solved using the ILOG CPLEX concerttechnology environment. The Proposed ILP maximizes theISP profit and comes-up with:

– The optimal set of the profitable VPN connections.– The optimal bandwidth division of each network link

among different QoS classes.– The optimal routing scheme of the accepted VPN connec-

tions, with respect to their QoS specifications.

Furthermore, the proposed ILP allows us to study thesensitivity of the ISP profit to a targeted revenue objec-tive represented by the Profit Percentage Parameter (PPP).Through PPP, we are able to find the optimal tradeoff set-ting that maximizes the ISP profit while not breaking thedemands blocking constraint. Consequently, our contribu-tion is a model that is able to:

– Efficiently utilize the network bandwidth resources,where through the dynamic partitioning we are able toconsider the changes of traffic demands.

– Increase the VPN operators’ satisfaction rates, since re-sources are utilized efficiently and the allocation pricesare market competing.

– Minimize the SLAs violations as exaggeration motiva-tions are reduced.

The rest of the paper is organized as follows: Sect. 2presents the problem statement. Section 3 illustrates ourdynamic resource partitioning model and the proposed se-lection algorithm. Section 4 lists the proposed performancemetrics, followed by the computational results in Sect. 5. InSect. 6, we present the related work. Finally, Sect. 7 con-cludes the paper.

2 Problem statement

The Complete Sharing (CS) approach proposes an auto-nomic management framework, where the whole networkresources are shared between all VPN operators, so eachof them can use any bandwidth available at any given mo-ment. With no link bandwidth division, in the CS approach,all QoS classes can share the network resources withoutdiscrimination. Through this, the model is supposed to en-sure the delivery of services according to predefined SLAs.These SLAs are constructed after negotiations between theISP and the VPN operators. From the ISP prospective, giv-ing the VPN operators such a privilege can provide bet-ter utilization of the network resources, assuming that theVPN operators know well their changing requirements, andaccordingly they can acquire the required resources basedon their actual needs. Naturally, as long as the VPN opera-tors behave according to their declarations, deploying suchan approach can increase bandwidth utilization due to thestatistical multiplexing, which results in better satisfactionrates and higher profits at the same time. However, in real-ity, VPNs can exceed their declarations as long as there isno link bandwidth division, and one class may overwhelm

An optimal dynamic resources partitioning auction model for virtual private networks

all other classes which creates several problems like SLAsviolations, high blocking ratios, and low profit rates.

In the Complete Partitioning (CP) approach, the scenariois somehow different. Here the resources are partitionedamong the provided service classes in a static way, based ona one-time bandwidth partition for all network links. Withsuch a static scheme, each class is allowed to exclusivelyuse its portion of the provided resources. This can solve theSLAs violation problem, but it may lead to low bandwidthutilization as resources might be underutilized.

Exaggeration is considered as a common drawback ofboth CS and CP, where VPN operators might exaggeratetheir requirements in order to cope with any sudden or un-predictable changes in the network state and link conditions,so they tend to keep a spare amount of resources that enablesthem to overcome and cope with such situations. This is dueto the long-term SLA that does not allow users to changetheir resource requirements according to their needs. Such aproblem can be solved either through a short term resourcesharing model that reduces the reasoning of exaggeration orthrough a penalization model that penalizes any exaggera-tion behavior [19, 20].

To overcome the problem of resource underutilization,the Bandwidth Borrowing (BR) [6] technique has been pro-posed. The BR attempts the idea of borrowing the resourcesfrom the underloaded links and allocating them to the over-loaded ones. Accordingly, the BR scheme can provide betterutilization of the network bandwidth resources, and betterSLAs guarantees. However, resources are utilized in a non-optimal way that can reduce ISP profit. Also, such behav-ior can entail a high management load to cope up with thechanges of traffic load and utilize the unused resources inrealtime.

3 Dynamic resource partitioning approach

In this section, we present our Dynamic Partitioning (DP)approach that improves the CS and CP techniques, and over-comes their limitations by virtually partitioning the networkbandwidth resources in an efficient way based on periodicauctions, where resources are allocated to the best biddersproviding profit maximization. In this context, we proposea resource management approach based on short-term SLAsthat takes into account the desired ISP objectives over thetime. To achieve this, VPN operators are asked to reveal theirconnection demands in terms of: source-destination nodes,required QoS classes, and their offered prices (bids). Ac-cordingly, the DP algorithm presented in Table 1 is deployedto provide an optimal allocation mechanism.

Table 1 DP selection algorithm

Algorithm2: Selecting the Winning VPN operators in DP

1: Input: At each auction round t , the ISP broker do;

2: Collect the VPN operators connection demands K

(pk , QoSk, sk, dk) received through time (t − 1, t];

3: Formulate the problem as an ILP;

4: Solve the ILP, and find the optimal set of VPN connections;

5: Output: the VPN connections that won the resource allocationsand the profit collected from these connections;

3.1 DP approach

3.1.1 Algorithm

In our DP approach, resources are allocated based on dy-namic auctions that are held in a periodic manner, withthe aim of selecting the best set of VPN operators from acompeting environment. VPN operators’ requests are repre-sented in terms of connection demands. The term connectionhere is defined as a secure network tunnel that is layered ontop of a public network, such tunnel has some QoS param-eters (i.e. bandwidth capacity, maximum number of hops),and it is used to send data from a source node sk to anotherdestination node dk . The process of selecting the winning setof VPN connections for resource allocations deploy an op-timal selection algorithm presented in Table 1. In which, ateach auction period t , the ISP broker firstly collects the newconnection demands received in the period of (t − 1, t] andform a new demand matrix, then from each demand matrix itchooses the most profitable set of connections to accept. Todo so, using the Linear Programming Theory we developedan Integer Linear Program (ILP) to formulate the bandwidthallocation problem. By solving this ILP, we are showinghow it can choose the optimal set of bidding VPN operators,and provide the optimal bandwidth utilization rates. The ILPchecks the offered bids of the competing VPN operators if itis larger than or equal certain selling-price thresholds, wheresuch thresholds depend on the ISP broker profit objectives,the corresponding QoS classes, and demand blocking con-straints. Demand blocking is mainly related to the numberof offered bids, and the bandwidth availability over the as-signed candidate paths.

To overcome the problem of exaggeration, we proposeperforming a dynamic partitions of resources over differentQoS classes through short periods of time comparing withthat of the static scenarios. This can reduce the motivationsof exaggeration actions, where bidding VPN operators willnot be motivated anymore to ask for more resources, as theydo not have to care about their future connections or the sud-den changes in the network state, at least at this stage, sincecurrent allocations are only valid for a short period of time,comparatively.

A.N. Quttoum et al.

3.1.2 Mathematical modeling

We model the DP approach as an ILP model. Through thismodel, we study the case where we assume having a num-ber of VPN operators N competing for bandwidth alloca-tions over a network that is managed through an ISP broker.Bandwidth allocation requests are modeled through connec-tion demands, where each VPN operator i, i ∈ N , has aset of connection demands k belonging to a set of serviceclasses J . Logically, VPN operators are assumed to be ratio-nal, and thus their aim is to have their connection demandsadmitted with the lowest possible prices, and at the sametime acquire satisfactory QoS levels. On the other side, theISP broker aims to utilize its network bandwidth resourcesbetter, and maximize its profit by accepting the maximumnumber of VPN operators while providing them with sat-isfactory QoS levels by competing prices. Accordingly; theISP broker profit PB function can be expressed as:

PB = max

( |K|∑k=1

pk −∑k∈K

ck

)(1)

where the PB equals the sum of bids pk collected from con-nection demands being admitted for allocation, reduced bythe total cost of the bandwidth resources required to satisfyeach connection demand ck . Accordingly, to maximize thePB(ILP), the ISP broker has to choose the best set of VPNoperators’ connections that maximizes the first term of thefunction, and also, deploy an efficient bandwidth utilizationscheme in order to minimize the second term.

Choosing the best set of VPN operators’ connections istypically done in accordance to their offered bids, wherehigher bids increases the chance for their correspondingdemands to be accepted. To create a form of competitionbetween the bidding VPN operators, we assume that theamount of bandwidth resources required to satisfy the re-ceived connection demands exceeds the available networkcapacity. Connection demands are also classified into set ofdifferent QoS classes summarized in Table 2, where for eachauction period t , the model receives a different set of con-nection demands’ patterns reflecting the diversity of the re-quired services at the different auction periods. Periods canvary between day and night times, weekdays, and weekends.

Model parameters The ISP network is basically defined asa set of nodes V , connected by a set of bidirectional linksL, where each physical link offers certain bandwidth capac-ity bl . The requests of the VPN operators N form the shapeof the demands matrix K , where K represents all the con-nection demands submitted by the bidding VPN operators,each demand consists of a VPN operator ID i, connectionsource node sk , destination node dk , and a class of servicej , j ∈ J . Henceforth, a connection demand k of class j ,

Table 2 QoS classes

QoSclass

Connections Quality of Service Bandwidth perConnection

Max.of Hops

5 Golden Load (<100ms Latency) 5 Mbps 2 Hops

4 Excellent Load (Business Critical) 4 Mbps 3 Hops

3 Controlled Load (Streaming Video) 3 Mbps 4 Hops

2 Standard (IP Packet Delivery) 2 Mbps 5 Hops

1 Best Effort 1 Mbps 6 Hops

consumes a bandwidth amount of bj . Dividing the links’bandwidth capacities among the set of connection demandsK and their corresponding service classes J highly dependson the period’s traffic pattern. αl

j denotes the percentage ofbandwidth capacity allocated to a connection of class j overthe network link l, where αl

j ≤ bl .

Model variables To facilitate the process of measuring theISP broker utility presented in Eq. (1), we refer to the admit-ted/rejected connections using the variable zk , where:

zk ={

1 if connection demand k is admitted

0 otherwise(2)

and we also refer to the selected path that holds the consid-ered connection using the variable xπ

k , where:

xπk =

{1 if connection demand k uses path π

0 otherwise(3)

Objective function According to the parameters and vari-ables defined above, the objective function of Eq. (1) can bereformulated as:

PB =∑k∈K

(pkzk −

∑π∈πk

xπk

∑l∈π

clk

)(4)

Model constraints For this objective function presented inEq. (4), we have the following constraints:

– Link Capacity: For each link l, the available bandwidthfor the admitted connection demands k of class j cannotexceed the total link capacity reserved for this class.∑k∈Kj

∑π∈πk

ηπl xπ

k bj ≤ αlj bl; l ∈ L, j ∈ J (5)

where the variable ηπl refers to:

ηπl =

{1 if path π uses link l

0 otherwise(6)

and Kj refers to the set connections belonging to QoSclass j .


– Link bandwidth Division among QoS classes: The sum-mation of the defined class divisions over the networklinks must not exceed the total link capacity.∑j∈J

αlj = 1; αl

j ∈ [0,1], l ∈ L (7)

– Minimum Selling-Price Threshold: To be considered as acompeting connection demand for the allocation process,the minimum offered bid pk for a connection demand k

of QoS class j must at least be higher than or equal toa certain threshold. The calculation of this threshold isderived in Sect. 3.1.4.

pk ≥∑π∈πk

xπk

∑l∈π

plth,j ; k ∈ Kj , j ∈ J (8)

– Routing Path Assignment: Only one routing path can beassigned to carry each connection.∑π∈πk

xπk ≤ 1; xπ

k ∈ {0,1}, k ∈ K (9)

– Linking decision variables: If there is no way to route theconnection while the connection is rejected.

zk ≤∑π∈πk

xπk ; zk ∈ {0,1}, k ∈ K (10)

• Routing Path Length: The length of the assigned path lπfor a connection demand k of QoS class j cannot exceedHj hops, one hop represents one physical link.

lπ ≤ Hj ; π ∈ πk, j ∈ J (11)

ILP complexity However, it is worth to find the compu-tational complexity of the model. This can be measuredthrough the number of model variables and constraints, asfollows:

– Number of variables:

|K| + |K| × |πK| + |L| × |J |which can be simplified as:

|K| × |πK| + |L| × |J |– Number of constraints:

|L| × |J | + 3|K| + |K| × |πK|which can be simplified as:

|L| × |J | + |K| × |πK|From this, we can conclude that the number of variablesequals the number of constraints, which is in the order

of O(n2). Moreover, to deal with the complexity issues,if exist, in such a problem we can use the technology ofCloud Computing that is considered as an efficient solu-tion to deal with high combinatorial problems.

3.1.3 Link bandwidth division scheme

To assign the VPN operators’ connection demands to themost profitable paths, the ILP do the following:

– In accordance to the offered bid rates and the networklinks capacities, it generates a class division map thatshows the percentages of bandwidth capacities reservedfor each QoS class over the network links.

– Based on this map, the model assigns different candidatepaths [11] to carry each source-destination connection de-mand.

– In one-shot scheme, the model chooses the most prof-itable combinations of the VPN operators’ demands to becarried over the network links, and consequently assignthem to their routing paths.

To create a form of competition, the assigned candidatepaths might be shared between various connection demandshaving the same source-destination nodes, where the sum ofbandwidth amounts over these candidate paths is less than orequal to that required to satisfy the whole connections withthe same source-destination couples.

The link bandwidth division among QoS classes schemeis mainly depend on the demands’ diversity, where suchdiversity reflects the different VPN operators requirementsfrom time to time. Differences may appear between theday times (i.e. mornings, afternoons, evenings, and nights),weekdays (i.e. workings days, and weekends), or even itmight be affected by the different time-zones.

Consequently, for each period of time we assume havingthe following demand matrix partition:

– γ1 % connection demands of QoS 1.– γ2 % connection demands of QoS 2.– γ3 % connection demands of QoS 3.– γ4 % connection demands of QoS 4.– γ5 % connection demands of QoS 5.

3.1.4 Profit percentage parameter

For each VPN connection k belonging to QoS class j , wecalculate the set of candidate paths πk . Then, if at least onepath π , π ∈ πk , uses the link l, then we add the VPN con-nection k to the set of candidate VPN connections that usethe class of service j over link l. We denote by Kl the set ofcandidate VPN connections to use the link l:

Kl =∑j∈J

Kjl (12)

A.N. Quttoum et al.

where Kjl is the set of VPN connections belonging to QoS

class j , candidates to use the link l. Accordingly, for eachlink l, we can define ratio βl

j of bandwidth allocated to theuse of class j VPN connections by:

βlj = bj |Kj

l |bl

(13)

Having the allocation percentage βlj and the original cost-

unit cl of link l, we can define threshold plth,j as:

plth,j = bj cl + bj cl

(aβl

j

)(14)

where cl is the bandwidth original cost-unit over the link l,and the parameter a refers to the profit percentage parameter(PPP). This PPP reflects a tradeoff relationship between theISP broker profit objective and the demand blocking ratios.Consequently, as long as the demand blocking ratio BK isless than the blocking constraint Bc

K , BK < BcK , optimal ISP

broker profit can be achieved by assigning higher a values.Additionally we assumed in Eq. (14) that the profit is pro-portional to percentage βl

j . That means that the value of thethreshold is larger for the QoS classes that use more band-width. The motivation behind this scheme is as follows:

– It reduces the likelihood of exaggeration. Indeed, withsuch a scheme, the VPN users will be motivated to use thelowest amount of bandwidth resources that satisfy theirneeds, especially is the QoS class that use a lot of re-sources.

– It limits situations where one QoS class overwhelmsthe others. This provides a kind of fairness between theclasses.

Obviously, in general, one can substitute βlj in (14) by an-

other function of system parameters (being one in the sim-plest case) to realize particular objectives of given ISP.

Results in Sect. 5.2 show the tradeoff relationship be-tween both blocking ratios and ISP broker profits for dif-ferent values of the PPP a. Accordingly, Eq. (4) can be re-formulated as:

PB =∑j∈J

∑k∈Kj

(pkzk −

∑π∈πk

xπk

∑l∈π

plth,j

)(15)

where bids accepted for the competition must be larger thanor equal the candidate path minimum price threshold.

3.2 Benchmark models

In DP, the dynamic class division process will take place in aperiodic auction manner, where VPN operators will be com-peting to win the resource allocations through their submit-ted prices and connections’ demands. The network planningtime is divided into a set of periods in order to reduce the

Table 3 CS selection algorithm

Algorithm1: Selecting the Winning VPN connections in CS

1: Input: VPN operator submit its connection demand k → ISPbroker where, for each k we have (pk , QoSk, sk, dk),QoSk = (bk,Hk);

2: Sort the connection demands k according to their arrivalsequence;

3: for each demand k, do;3.1: Find the set of candidate paths πk to hold its connection where

each π ∈ πk , uses less than Hk hops (i.e., links);3.2: For each π , π ∈ πk check if:

∀l ∈ π , bk ≤ bl(residual);pk ≥ ∑

l∈π plth,QoSk

;3.3: If πk �= ∅, then:3.4: Choose one random path π to hold the connection k;3.5: else, reject;

4: Output: the set of VPN connections that won the resourceallocations and the ISP profit collected from these connections;

reasoning of exaggeration and to eliminate the needs for anyborrowing technique. Thus, there is no need for such a BRtechnique since there is no underloaded links as result of ex-aggeration. To evaluate our model, we selected to adapt theCS [6] and CP [14] models to run periodically.

3.2.1 CS model

In this technique, in addition to the poor QoS guarantees, theVPN connections selection is non-efficient since the processof allocating the network bandwidth resources is done ac-cording to a First Ask First Allocate (FAFA) scenario. Ac-cordingly, new VPN operators can guarantee the resourcesfor their connection demands as long as: (1) Their offeredbids p are larger than or equal certain selling cost thresh-olds. (2) At their arrival time, there exist enough bandwidthresources to hold their connection demands over the consid-ered paths. The algorithm presented in Table 3 illustrates theallocation mechanism in the CS model.

In the first step, for each connection demand k, the corre-sponding VPN operator is asked to submit its offered bid pk ,required QoSk commitments, i.e., bandwidth bk and max-imum number of hops Hk , and source-destination nodes(sk, dk) to an ISP broker in order to consider its requests.In step two, the ISP broker sorts the connection demandsaccording to their arrival sequence. In step three, for eachconnection demand k, the ISP broker finds the set of candi-date paths πk to hold the connection (shortest paths), checkstheir bandwidth availability and the corresponding offeredbid price. Next, the ISP broker verifies that there exists atleast one candidate path to hold the connection. Once thebandwidth availability and the bid price conditions are sat-isfied, the broker choose randomly [6] one path from the setπk and assign it to hold the connection of the correspondingVPN operator. Last, in step four, the ISP broker calculates


the profit collected from the admitted VPN connections ac-cording to their offered bid prices.

Consequently, in CS, the ISPs broker profit function PB

can be represented by:

PB =kmax∑k=1

pk −∑π

∑l∈π

clπ (16)

where it equals the sum of bids collected from the acceptedVPN operators’ connection demands k, (k = 1,2, . . . , kmax),given that kmax is the index of the last admitted demand(sorted in a FAFA order) that can fit within the available net-work bandwidth resources, reduced by the cost of resourcesclπ used on the assigned routing paths. Also each of the ac-

cepted bids has to fulfill the following requirements: (1) Thechosen path to hold the VPN operator connection k must atleast meet the QoSk commitments, in terms of the allocatedbandwidth bk and the maximum number of hops Hk . (2) To-tal bandwidth amounts allocated to the accepted connectionscannot exceed the sum of physical bandwidth capacities ofthe network links. (3) Accepted bids must at least be largerthan or equal certain selling-price threshold, associated withthe required QoSk class at the chosen path π to hold theconnection.

3.2.2 CP model

The process of selecting the winning set of VPN connec-tions for resource allocations uses the selection algorithmpresented in Table 1 except we add the following variations.As aforementioned previously, the link bandwidth divisionamong QoS classes is done at the beginning of the networkplanning (period 0) based on the shortest path algorithm, andthe traffic pattern statistics. In other words, we fix the vari-ables αl

j to the resulting value calculated at period 0. Theresulting link partitioning among QoS classes is used for therest of planning periods.

4 Performance metrics

As mentioned in the previous section we propose to use CSand CP as benchmark models to evaluate the performanceof the DP approach. For each model we are measuring thefollowing metrics:

4.1 ISP broker’s profit

The ISP broker’s profit, Eq. (4), is measured based on thebids collected from the admitted connection demands, re-duced by the cost-unit of the carrier network links. The bidsand the cost-units are expressed in terms of $X, which repre-sents the price of 1 Mb of bandwidth. This metric representsthe profits collected from the whole bandwidth resources al-located over the network links.

4.2 ISP broker’s profit-unit

The profit-unit value represents the gains collected per 1 Mbof bandwidth, which is measured as the ratio between theISP broker profit, calculated in Eq. (4), and the amount ofbandwidth over the whole network links, as:

P uB = PB∑

l∈L bl

(17)

4.3 Demands’ blocking ratio

Demands’ blocking ratio represents the VPN operators’ sat-isfaction rates, where it is measured as the ratio between thenumber of admitted connection demands to the number ofthe whole demands participated in the allocation auction, as

BK =∑

k∈K zk

|K| (18)

4.4 Bandwidth utilization

Bandwidth Utilization is measured as the ratio between theused and the total bandwidth amounts, as:

Ub =∑

j∈J

∑k∈Kj

bj zk∑l∈L bl

(19)

4.5 Routing scheme efficiency

To evaluate the routing scheme efficiency of the above men-tioned scenarios, we proposed measuring the following pa-rameters:

4.5.1 End-to-end delay

The average end-to-end delay per admitted connection de-mand is measured through the average number of hops usedto form a routing path, which is given by the ratio betweenthe number of hops counted in composing the whole routingscheme to the number of admitted demands. Only routingpaths of the admitted connection demands are counted. Thiscan be formulated as:

H =∑

k∈K

∑π∈πk

xπk lπ∑

k∈K zk

(20)

4.5.2 Number of used network links

In this we measured the number of links used to form thewhole routing scheme in the assigned period of time.

A.N. Quttoum et al.

5 Computational results

To assess the efficiency of this work, in this section, we il-lustrate an example of a network that consists of 10 nodes,connected by 40 bidirectional links, for which we assumethat each link holds a 25 Mb of bandwidth resources. Forthis network we assume receiving 100 VPN operators’ con-nection demands per period of time, and the network plan-ning time is divided into 12 periods per week in a way thatshows the main periods of a 24-hour day, representing a newallocation auction every 6 hours.

However, the length of the re-optimization period de-pends on the provided service duration. Demands of dif-ferent service durations can be divided into groups, eachwith certain period length. In this work, we assume that theISP broker is selling certain service packages that standsfor 6 hours of time, where there is no dependency betweenany two consecutive periods and each period starts by anew auction. Such service packages can vary between aVoIP call, chat session, an on-line game, video streamingor even a movie show. Table 4 shows the periods’ divisionmap. Through this network, we will study the behavior of

Table 4 Periods’ division map

Period index Corresponding time period

1 Monday to Friday: Morning

2 Monday to Friday: Afternoon

3 Monday to Friday: Evening

4 Monday to Friday: Night

5 Saturday: Morning

6 Saturday: Afternoon

7 Saturday: Evening

8 Saturday: Night

9 Sunday: Morning

10 Sunday: Afternoon

11 Sunday: Evening

12 Sunday: Night

the above mentioned three scenarios (DP, CP, and the CSFAFA).

5.1 Numerical results

In the studied scenarios, different bandwidth divisionschemes are followed. As mentioned before, the CS modelfollows a FAFA allocation scheme, where there is no linkbandwidth division among QoS classes at all. In CP, themodel uses a static bandwidth division scheme. At period 0,the ISP broker attempts a heuristic link partitioning based onthe shortest path algorithm and the traffic pattern statistics.The resulting division of link bandwidth among QoS classesis used for the rest of planning periods. On the contrary, inDP approach a dynamic link bandwidth division process isperformed at each period, and it is handled by the ILP in theOptimal manner. The provided QoS classes, their reservedbandwidth amounts, and their corresponding profits at threedifferent periods are presented in Tables 5, 6, and 7. To im-prove the readability of the results, the resulting profit-unitsof both CS and CP are also given.

Through the presented tables, we are showing the effectof the different link bandwidth partitioning schemes used bythe three studied scenarios. At each case, we compare theresulting total profits and the corresponding profit-units. Forbetter comparison and to show how our model can deal withdifferent traffic patterns, in each table, we present the resultsof the afternoon period at the Working weekdays, Saturdays,and Sundays. Table 5 shows the results of period 2 (Mon-day to Friday Afternoons). By aggregating the resulting to-tal profits of the different scenarios, and assuming $X = $1we collect: $1173 from the CS FAFA, $1592 from the CP,and $2312 from the DP. Results reflect the impact of thedeployed link bandwidth partitioning scheme on the finalprofits, where the CS FAFA provides the worst rates, fol-lowed by the CP providing an increase of 35 %. DP providesthe best results, showing an increase of 97 % and 45 % tothat provided by the CS FAFA and the CP, respectively. Thesame conclusions can be drawn from Tables 6 and 7 where atthe period 6 (Saturday Afternoon) results in Table 6 show a

Table 5 Bandwidth class division, bandwidth amounts allocated and corresponding total and per-unit profits in three scenarios. (Scenario A: Com-plete Sharing, B: Complete Partitioning, C: Dynamic Partitioning.) (Profit Percentage Parameter a = 1.3, Period = 2)

QoSclass

CS: complete sharing CP: complete partitioning DP: dynamic partitioning Profit unitin CP

Profit unitin DPBandwidth amount

allocatedTotal profitin ($X)

Bandwidth amountallocated

Total profitin ($X)


Total profitin ($X)

1 No Division 157 252 248 251 248 0.98 0.98

2 No Division 260 231 351 228 481 1.51 2.10

3 No Division 391 321 661 262 850 2.05 3.24

4 No Division 98 48 119 25 163 2.47 6.52

5 No Division 267 117 213 226 570 1.82 2.52


Table 6 Bandwidth class division, bandwidth amounts allocated and corresponding total and per-unit profits in three scenarios. (Scenario A:Complete Sharing, B: Complete Partitioning, C: Dynamic Partitioning.) (Profit Percentage Parameter a = 1.3, Period = 6)

QoSclass





Total profitin ($X)


Total profitin ($X)

1 No Division 86 105 125 110 134 1.19 1.21

2 No Division 80 127 138 130 211 1.08 1.62

3 No Division 388 456 935 320 1088 2.05 3.40

4 No Division 224 63 112 98 204 1.77 2.08

5 No Division 752 221 558 336 1244 2.52 3.70

Table 7 Bandwidth class division, bandwidth amounts allocated and corresponding total and per-unit profits in three scenarios. (Scenario A:Complete Sharing, B: Complete Partitioning, C: Dynamic Partitioning.) (Profit Percentage Parameter a = 1.3, Period = 10)

QoSclass





Total profitin ($X)


Total profitin ($X)

1 No Division 86 105 125 117 134 1.19 1.14

2 No Division 89 110 133 115 184 1.20 1.60

3 No Division 383 491 1002 420 1209 2.04 2.87

4 No Division 692 219 680 280 975 3.10 3.48

5 No Division 122 52 121 50 180 2.32 3.60

$1530 collected from the CS FAFA, $1868 from the CP, and$2881 from the DP by an increase of 88 % and 54 % to bothCS FAFA and the CP, respectively. However, in some caseswe see that the CS FAFA may provide higher instant prof-its like that for QoS classes 4 and 5 in Table 6. This resultsfrom the random allocation of the resources which might beprofitable in some cases. Though, what concerns the ISP isthe final profit rates, and experiments show that the result-ing total profits of the CS FAFA are always much lower thanthat provided by the DP schemes. Records of Table 7 arealso showing that the DP scheme delivers the highest profitrates, providing an increase of 95 % and 30 % to both CSFAFA and the CP schemes, respectively.

Comparing the three different scenarios shows that theDP scheme always provide the best results in terms of effi-cient bandwidth division and final profit rates, followed bythe CP and lastly the CS FAFA scheme. It is worth to men-tion that the DP scheme also provides the lowest demandblocking ratio, while it is much bigger for the CS FAFAscheme.

5.2 Performance results

Through this subsection, we studied the behaviour of ourproposed DP model compared to both CS and CP in termsof: (1) Bandwidth efficiency. (2) ISP broker total profits.(3) Demand blocking ratios. (4) ISP broker profit-unit, and(5) Routing efficiency in terms of average end-to-end delay,

and number of used links. Moreover, we are also present-ing some results that show the tradeoff relation between thePPP a, and some other parameters like ISP broker profitsand demand blocking ratios.

In DP, we are expecting to deliver an efficient resourceutilization model that provides higher ISP broker profitsand lower blocking ratios for the VPN operators demands.In addition, we are expecting that our dynamic bandwidthpartitioning model can provide an efficient routing scheme.Moreover, comparing with the CS FAFA, our model is ex-pected to deliver a wider room for the tradeoff relation be-tween the demand blocking ratios, and the resulting ISPbroker profits. Based on the above assumptions, we derivethe following analysis. Figure 1a shows the percentage ofbandwidth utilization (usage patterns) to the allocation timeperiods. In this figure, the DP scheme provides an averageutilization of 75 % of the networks’ bandwidth resourcesthrough the periods 1 to 12. The CS FAFA used an averageof 45 %, while it is around the average of 40 % for the CPcase.

Figure 1b shows the resulting ISP broker total profits tothe allocation time periods. In this figure, it is shown thatthe DP provides the highest profits, followed by the CP andlastly the CS FAFA providing the lowest rates. Figure 1cshows the demand blocking ratios to the allocation time pe-riods. Similarly, the DP provided the lowest blocking ratios,followed by the CP providing an average scheme comparingwith the CS FAFA that shows the highest blocking ratios. In

A.N. Quttoum et al.

Fig. 1 Performance metrics

this figure, we are showing the demand blocking ratio con-straint Bc

K , which we assumed to be 15 % on average.Analyzing the previous three figures, we can clearly no-

tice the following: (1) The DP scheme used the largestamount of bandwidth resources, and at the same time, pro-vided the highest profits and the best satisfaction rates rep-resented by the lowest blocking ratios. (2) The CP schemeused the lowest amount of resources, but on the contrary,

Fig. 2 Profit-unit and routing efficiency

it provided higher profits and better satisfaction rates com-pared to that provided by the CS FAFA. (3) The CS FAFAscheme used more resources compared to that used by theCP, but still, it provided the lowest profits along with thehighest blocking ratios. Consequently, we can conclude thatthe conducted experiments showed that the DP provides thebest utilization rates of bandwidth resources.

Figure 2a shows the resulting ISP broker profit-units withrespect to the allocation time periods. Clearly, we can re-mark that the highest profit-units are always provided by


the DP scheme, giving an average of $4.5 profit-unit com-pared with $2.5 and $1.5 provided by the CP and the CSFAFA, respectively. Accordingly, the DP provides an aver-age of 3 times to what the CS FAFA provides. Figures 2b,and 2c show results of the routing efficiency of the differ-ent partitioning schemes. In Fig. 2b, results represent theaverage number of hops per path used to route the admit-ted connection demands at the different time periods from 1to 12, in which we can notice that the DP used the lowestaverage number of hops, which reflects the routing schemeefficiency. Figure 2c gives the number of links used to con-struct the routing paths for the admitted connection demandsat each period. The conducted results show that the DPused the minimum number of network links, despite thefact that it served around 55 % more connections comparedwith that served by the CS FAFA, and 30 % more to whatthe CP served. Additionally, we can also state that experi-ments showed that the DP provides the most efficient rout-ing scheme.

Figures 3a, 3b, and 3c present the relationship be-tween the Profit Percentage Parameter (PPP) a, Eq. (14),and the corresponding ISP broker total profit, ISP brokerprofit-unit, and the demand blocking ratios, respectively.Hence, we studied the effect of different values of a (a =0.1,0.3,0.5,0.7,1.0,1.3,1.5), and presented the results interms of the three partitioning scenarios. As expected, re-sults show that the DP provided the best outcomes in termsof profits and blocking ratios. On the contrary, the CS FAFAprovided the worst outcomes which reflects the weaknessof the deployed resource allocation scheme. However, inthe three figures, we can clearly notice a direct relationshipbetween the PPP a and the studied performance metrics,where as the value of parameter a increases, both profitsand blocking ratio increase. Accordingly, based on the de-mand blocking ratio constraint Bc

K or the ISP broker profitobjective we can find the optimal PPP a. To do so, for thegiven different values of a, in Fig. 4, we present the tradeoffrelationship between the ISP broker profit and the demandblocking ratios. Consequently, for a PPP of (a = 1.3) wehave the following: (1) With the DP, results in Fig. 4a showa $2500 of total profit, and a 15 % of demand blocking ra-tio. (2) With the CP, results in Fig. 4b show a $1750 of totalprofit, and a 35 % of demand blocking ratio. (3) With the CSFAFA, results in Fig. 4c show a $1250 of total profit, and a43 % of demand blocking ratio.

6 Related work

In literature, different works studied the resource manage-ment and bandwidth allocation problems in both wired andwireless networks like that in [15], [1], and [8]. However,non of the these targeted the option of autonomic resource

Fig. 3 Sensitivity to the PPP a

management, while the whole management responsibilitiesare centralized at the ISP side.

On the other hand, the CS model has been proposed inprior research to resolve the issue of autonomic resourcemanagement, by enabling the network users to self-manage,self-control, self-heal, and self-protect their network re-sources [14, 17]. In their work, authors claimed that CS canprovide a solution to the challenging management loads atthe ISPs side, and deliver a satisfying resource utilization

A.N. Quttoum et al.

Fig. 4 Tradeoff with the PPP a

rates. Although it provides good utilization rates, but on thecontrary it proved that it can lead to SLA violations. In [14],the authors presented a comparison between both CS and CPmodels, where they show that the CP model can provide bet-ter QoS satisfaction rates, but on the other hand it providesless utilization. Same in [5, 13], authors proved that the CP

model can provide higher QoS compliance rates comparedto that of the CS model. To overcome the resource utiliza-tion problem of the CP, authors in [2–4] proposed a hybridapproach that takes the advantages and overcomes the prob-lems of both CS and CP models. Such hybrid approach isknown by the Virtual Partitioning (VP) approach. Depend-ing on the actual network traffic load, VP behaves eitheras CS or CP. Accordingly, it behaves as a CS at the lighttraffic case, while it is a CP at the extreme one [7]. TheVP allows a heuristic resource sharing between the under-loaded and the overloaded links in order to provide better re-source utilization rates. Moreover, in the wireless networksdomain, other authors proposed using the same hybrid VPapproach. Where in [22], an approximate analytical formu-lation of the VP is proposed to handle multiclass serviceswith grand channel in a cellular system. In this work, theauthors investigated a resource allocation model with pre-emptions for the provided service classes, to do so, theyproposed using a balancing scheme that combines the opensharing and the static allocation properties of the CS and CPmodels, respectively. Accordingly, in heavy-load situations,resources are allocated the same way in CP, but underuti-lized resources are borrowed from the underloaded classesto the overloaded ones. While in the light-loaded situations,overloaded classes can use the nominal resources of all otherclasses. Similarly, in [10, 16] the authors proposed a fairresource allocation protocol for multimedia wireless net-works, which uses a combination of bandwidth reservationand bandwidth sharing models to provide higher utilizationrates and QoS guarantees. Such a hybrid approach soundsgood, but the problem here is that the lender links (origi-nally under-loaded) have no guarantees that they can returntheir resources back when they are needed. This encouragesmalicious over-loading. What is more, the resource shar-ing scheme in VP attempts a static design, in which, a pre-defined static configurations for the resource sharing pro-cess is applied at all possible traffic load conditions. To solvethis, the Bandwidth Borrowing (BR) technique is proposedto automate the resource sharing process [21], and provide asolution for the static load-configurations attempted by theVP approach [6, 12]. Accordingly, the BR technique maypartially solve the bandwidth utilization problem of the CP.While yet, as long as the CP attempts a static partitioningscheme, BR cannot provide an optimal bandwidth utilizationsolution, where we may have many underloaded links withno overloaded ones, in such a case how the BR would work?However, none of the above mentioned work addresses theproblem of exaggeration. In fact, especially in such auto-nomic allocation environments, addressing the problem ofexaggeration is a necessity. In our work, we are allocat-ing the bandwidth resources based on a dynamic auctionmechanism. To win the auction, auctioneers (VPN opera-tors) should avoid any extra payments in order to submit


a competing bid. This can be considered as the first mo-tivation to prevent exaggeration. Secondly, deploying suchperiodic dynamic allocations will motivate the VPN oper-ators not to exaggerate, since current allocations are validfor short times only, and so, there is no need to care aboutthe future network changes. It is worth to mention that in ourprevious works [19, 20], we proposed an efficient model thatreduces the tendency of exaggeration, where we developeda threat model based on the Vickrey-Clarke-Groves (VCG)mechanism [18]. Accordingly, exaggeration actions are re-duced by charging the exaggerating users according to theinconvenience they cause to the whole system. However, thework targeted the case of autonomic resource allocation overa single network link for specific connection periods. In thiswork, we are dealing with the exaggeration problem in a dif-ferent way, while we are targeting a full network case withmulti-links and paths.

7 Conclusion

Based on the Linear Programming theory, we optimizedthe ISP profit by providing a periodic Dynamic Partition-ing (DP) model for utilizing network resources. The re-sources are dynamically partitioned over different QoSclasses through a periodic auction which can reduce thereasoning of exaggeration and maximize the ISP profit byfinding the optimal set of profitable VPN connections. Sucha model will eliminate the need for any borrowing tech-nique. The advantage of our model lies in its ability of find-ing the optimal bandwidth division of each network linkamong QoS classes, and the optimal routing scheme thatcan guarantee the QoS commitments for the accepted VPNconnections. Numerical results were conducted based onCPLEX environment where it showed that the DP modelperformed better than the other models. On average, the ISPprofit is increased by 57 %, the VPN connections blockingratio is reduced by 64 %, and network resources utilizationis increased by 72 %. Finally, we showed that through theproposed ILP model and the profit percentage parameter, wewere able to quantify and study the tradeoff between maxi-mizing the ISP profit and minimizing the VPN connectionsblocking ratio.

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Ahmad Nahar Quttoum holds anAssistant Professor position at theComputer Engineering Departmentin the Hashemite University, Jor-dan. Prior to that, he worked as aPostdoctoral researcher at the LTIRlab in the Université du Québecà Montréal (UQAM), Montreal,Canada. In that, he worked onthe NetVirt project; a project forEricsson-Canada, where mainly, hewas concerned with Cloud-ServiceData Center Networks. In Oct 2011,he obtained a Ph.D. degree from theDepartment of Electrical and Com-

puter Engineering at the University of Quebec, Montreal, Canada. HisPh.D. research topic was about Resource Management for Virtual-ized Networks; a project for Bell Canada. In late 2007, he obtaineda M.Sc. degree in Network Systems from the Department of Engi-neering, Computing & Technology at the University of Sunderland,United Kingdom. During his M.Sc. studies, he worked on various re-search topics on network security ended with a thesis in security at-tacks, detection and prevention. In early 2006, he obtained a B.Eng.degree in Electrical and Computer Engineering from Jordan Univer-sity of Science and Technology, Irbid, Jordan. His research interestsinclude cloud computing, data center networks, virtualized networks,autonomic resource management, and network security. He is also atechnical reviewer for different journals and specialized magazines.

Abdallah Jarray received in 1997the National Engineer Degree fromEcole Nationale des Sciences del’Informatique, Tunis, Tunisia, theMaster and the Ph.D. degrees inComputer Science and OperationsResearch in 2005 and 2009 respec-tively from University of Montreal,Quebec, Canada. During his Ph.D.,he worked on the dimensioning andthe planning of optical backbonenetworks. Prior to starting his mas-ter studies in 2003, he gained indus-trial experience in design and plan-ning of Ethernet network at Coda-

gen, SIMAC and MRS from 1997 to 2002. Currently, he is working as apostdoctoral fellow at the Ecole de Technologie Superieure, Universityof Quebec. His research interests are mainly on the resources manage-ment in Virtual Private Networks and Femtocell/Macrocell WirelessNetworks. Also, he has interest on development of operations researchtools for network design problems: Integer Linear Programming, Col-umn Generation, Meta-heuristics, Game theory and Mechanism De-sign.

Hadi Otrok holds an assistant pro-fessor position in the departmentof computer engineering at KhalifaUniversity. He received his Ph.D. inElectrical and Computer Engineer-ing (ECE) from Concordia Univer-sity, Montreal, Canada. His researchinterests are mainly on network andcomputer security. Also, he has in-terest on resources management invirtual private networks and wire-less networks. His Ph.D. thesis is on“Intrusion Detection System (IDS)”using Game Theory and MechanismDesign. Throughout his Masters de-

gree, he worked on “Security Testing and Evaluation of CryptographicAlgorithms”. Before joining Khalifa University, Dr. Otrok was holdinga postdoctoral position at the École de technologie supérieure (Uni-versity of Quebec). He is serving as a technical program committeemember for different international conferences and regular reviewerfor different specialized journals.

Zbigniew Dziong received hisM.Sc. and Ph.D. degrees from theWarsaw University of Technology,Poland, both in Electrical Engineer-ing where he also worked as anAssistant Professor. From 1987 to1997 he was with INRS-Telecom-munications, Montreal, Canada, asa Professor. From 1997 to 2003 heworked for Performance AnalysisDepartment at Bell Labs, LucentTechnologies, Holmdel, New Jer-sey, USA. Since 2003 he is withÉcole de technologie supérieure(University of Quebec), Montreal,

Canada, where he teaches on both undergraduate and graduate levelas a Full Professor. Zbigniew Dziong is an internationally recognizedexpert in the domain of performance, control, protocol, architectureand resource management for data, wireless and optical networks. Heparticipated in research projects realized for many leading companiesincluding Bell Labs, Nortel, Ericsson, and France Telecom. His re-search achievements are documented in over 100 scientific publica-tions and 15 patents and patent applications. He won the prestigiousSTENTOR Research Award (1993, Canada) for collaborative researchin the domain of resource management for broadband networks. Hismonograph “ATM Network Resource Management” (McGraw Hill,1997) has been used in several universities for graduate courses. Cur-rently he is engaged in several research projects supported by industryand government agencies.

An optimal dynamic resources partitioning auction model for virtual private networks

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