Metaheuristic Algorithms for Optimization of Survivable

Multicast Overlay in Dual Homing Networks

Wojciech Kmiecik, Krzysztof Walkowiak

Department of Systems and Computer Networks, Wroclaw University of Technology,

Wroclaw, Poland

{wojciech.kmiecik,krzysztof.walkowiak}@pwr.wroc.pl

Abstract. Overlay multicasting providing live streaming services became cru-

cial service in contemporary Internet. In this paper, we focus on applying the

overlay multicasting for delivering of critical data that require to be transmitted

safely, intact and with as little delay as possible, e.g., financial data, software

security patches, antivirus signature database updates etc. To improve surviva-

bility of the overlay multicasting, we propose to use dual homing approach, i.e.,

each peer is connected to the overlay by two separate access links. We consider

the following network failures: overlay link failure, uploading node failure and

ISP interconnection failure. The objective is to minimize the maximum delay in

the network. The optimization problem is formulated in the form of an Integer

Linear Programming (ILP) model. We introduce a Simulated Annealing (SA)

algorithm and a Tabu Search (TS) algorithm for the considered problem and

compare them with optimal results provided by CPLEX solver. Our studies

demonstrate that both SA and TS methods yield results close to optimal and

provide better scalability comparing to CPLEX, since they can solve in reason-

able time much larger problem instances than CPLEX. Furthermore, our studies

show that the additional survivability requirements do not have a substantial

impact on the overlay multicasting system expressed as the maximum delay.

Keywords: multicasting, survivability, dual homing, simulated annealing, over-

lay network, tabu search

1 Introduction

The concept of overlay networks plays a crucial role in the contemporary Internet.

The overlay network is a layer of a virtual network topology on the top of underlying

physical network. Nodes of the overlay network can be considered of as being con-

nected by virtual or logical links, each of which corresponds to a path, possibly

through many physical links, in the underlying physical network [Firdhous 2011].

Thanks to that independence from physical layer, overlay networks are flexible, scal-

able and robust. Moreover, it is comparatively easy to design and implement new

overlay communication protocols and environments.

Due to the growing popularity of various streaming services offered in the Internet,

the idea of multicasting is gaining much attention. Multicasting defined as one to

many transmission is the most effective (in terms of cost and performance) method to

provide streaming in computer networks. Currently, there are two main approaches to

deploy multicasting: IP multicast and overlay multicast. The former solution, that

works in the IP layer, is based on a set of dedicated protocols. However, the main

drawback of the IP multicasting is that to configure this technique an access to spe-

cialized routers is required, while the telecommunication operators and Internet Ser-

vice Providers (ISPs) are not willing to allow outside parties to configure their devic-

es. Therefore, usually the operators provide IP multicasting only for their own busi-

ness needs. Overlay multicasting uses a multicast delivery tree constructed among

peers (end hosts) in the overlay network. In contrast to classical IP multicasting, the

uploading (non-leaf) nodes in the overlay tree are normal end hosts. The main ad-

vantage of overlay multicasting is relatively simple and cost effective deployment of

streaming services. Therefore, the concept of overlay multicasting is widely used in

various Internet systems, e.g., Internet TV, video on demand, software distribution.

Survivability defined as the capability to deliver services in the presence of failures

is one of the most critical attributes of modern computer networks [Vasseur et al.

2004]. This follows naturally from the fact that more and more human activities de-

pend on computer networks and a network failure can lead to severe consequences. In

this paper, we assume that the overlay multicasting is used to send critical content that

requires to be delivered fast and undamaged, e.g., hurricane warnings, financial in-

formation, critical updates in large IT systems etc. Therefore, we propose to apply the

dual homing approach to improve survivability of overlay multicasting. The key idea

of dual homing is to connect each node to the overlay using two disjoint access links

(homes).

The main contributions of the paper are threefold. First, we formulate new ILP (In-

teger Linear Programming) models related to optimization of multicast overlay sys-

tems protected by the dual homing approach with the objective function to minimize

the maximum delay function. Second, we propose two effective metaheuristic algo-

rithms based on the Simulated Annealing and Tabu Search methods. Third, we pre-

sent results and conclusions of extensive numerical experiments. To the best of our

knowledge, this work is the first one that address the problem of maximum delay

function optimization in overlay networks with dual homing protection. Note that the

concept of overlay multicasting protection by dual homing have been introduced in

our recent papers [Kmiecik 2012a], [Kmiecik 2011], [Kmiecik 2012b] in the context

of streaming cost objective function. The main novelty of this work is that we consid-

er another objective defined as the maximum delay considering all receivers. In more

detail, the goal is to minimize the maximum distance from the streaming server (root)

to the receiver calculated as the sum of link delays.

The rest of the paper is organized in the following way. In Section 2, we present

previous research on overlay multicasting and dual homing. Section 3 introduces the

concept of survivable overlay multicasting based on the dual homing approach. In

Section 4, we formulate ILP models for survivable dual homing overlay multicast.

Section 5 presents our metaheuristic algorithms – Simulated Annealing (SA) and

Tabu Search (TS). In Section 6, we present results of our experiments. Finally, the

last section concludes this work.

2 Related works

In this section, we present previous papers related to dual homing, overlay mul-

ticast and metaheuristic approach for those subjects. Dual homing is a subject of sev-

eral articles. In [Jianping et al. 2005], the authors introduce a concept of partial pro-

tection for the multicast dual homing network and propose the partition and sharing

(PAS) algorithm for finding the best partial multicast protection. The authors claim

that simulation results show that the novel algorithm achieves performance very close

to the computed lower bounds.

The authors of [Wang et al. 2005] studied IP-over-WDM (wavelength division

multiplexing) network survivability with a dual homing infrastructure. The paper

focuses on a problem of adding survivability to IP WDM multicasting networks for

both static and dynamic traffic. The authors created and evaluated a coordinated pro-

tection design. A scalable multicast protection scheme based on the dual homing ar-

chitecture was introduced in [Wang 2006]. The solution proposed by the authors can

be used to choose dynamically two edge routers for a multicast host. The authors of

[Thulasiraman et al. 2006] addressed disjoint multipath routing in the dual homing

network problem. An algorithm for constructing colored trees in dual-homing using

colored trees is proposed.

Overlay multicast (application-layer multicast) [Feng and Yang 2007] is a technol-

ogy, which uses the overlay network topology, that enables multicast functionality for

end hosts instead of routers. The authors propose a proactive tree recovery mechanism

to make the overlay multicast resilient to peer failures. Simulations are used to prove

that the proactive method can recover from node failures much faster than reactive

methods. In [Imran et al. 2011], the authors propose a novel protocol named Efficient

Overlay Multicast Routing (EOMR), in which multilayer multicast methods are inte-

grated and the conversion among these methods is performed dynamically. Moreover,

a Multicast Address and Port Translation (MAPT) protocol is used to achieve low-

level overlay forwarding in intermediate systems, while the application-level mul-

ticast can only be implemented in end systems. Authors claim the overhead of EOMR

is relatively low while maintaining comparative forwarding performance to pure IP

multicast protocols.

The Virtual Direction Multicast (VDM), which aims to minimize network usage

and disconnection time for video multicast applications on peer-to-peer overlay net-

works, is proposed in [Suat and Murat 2011]. Authors compared VDM against a

Closest Node Multicast (CNM) protocol and simulation results show that the pro-

posed technique VDM consistently outperforms CNM under different churn rates.

The authors of [Samir et al. 2011] deal with a problem of joint optimization of 2-tier

dual-homing for NodeBs and Radio Network Controllers (RNCs) in Universal Mobile

Telecommunications System (UMTS) networks. They combined the optimization

problems across the two tiers, mapped the joint dual homing optimization problem

into a classical search problem and used two metaheuristic techniques to solve the

above problem. Results of the experiments reveal that the joint dual homing performs

considerably better than individual dual homing that attacks NodeB level and RNC

level separately and independently. In [Konstantin et al. 2011], a polynomial time

metaheuristic algorithm for constructing an overlay multicast network for streaming

live media events over the Internet is presented. Authors prove that their algorithm

can be used to efficiently construct large-scale overlay networks in practice with near-

optimal cost.

3 Survivability for the overlay multicasting

The overlay multicasting is an effective technique to deliver content from one source

to many receivers. The overlay multicasting is implemented at the application layer,

i.e., end hosts (peers) are connected via the overlay network. Connections between

peers are established as unicast connections over the underlying physical layer. Each

host is connected to the overlay by an access link. We propose to apply the dual hom-

ing approach to protect the system against a failure of the access link. The process of

creating two overlay multicasting trees guaranteeing that each of access links carries

traffic only of one of the trees is the essence of our solution. The fact that, because of

the dual homing, each node has two access links, enables it to receive the streaming

data from both trees on two separate links. Thus, if one of access links is broken, the

node is still connected to the stream and moreover, it can upload the stream to subse-

quent peers located in the tree. This procedure guarantees very low restoration time.

The overlay system we consider is assumed to be protected against the following

types of failures:

Overlay link failure - it comprises breakdown of a link between two nodes (both

directed links between the node pair are down),

Uploading node failure – this failure impacts all successors of the failed peer in the

tree,

ISP link failure - all overlay links between peers of first ISP and the second ISP are

not available.

Fig. 1. Simple P2P multicast scheme

In Fig. 1, we present a simple example to illustrate our concept. There are two disjoint

multicast trees A, B that connect 7 nodes - a, b, c, d, e, f, g. In the case of tree A, nodes

a, d and f are uploading nodes, while remaining ones are leafs. We use the term level

to describe the location of nodes in the multicast tree. For example, node a is on level

1 of tree B, nodes b and e are on level 2 of tree B and rest of the nodes are on level 3.

4 ILP models

Presented below ILP models are based on the formulations shown in [Kmiecik 2011],

[Kmiecik 2012b]. However, the models are enhanced with a new objective function

of maximum delay. To formulate the problem we use the notation as in [Pioro and

Medhi 2004]. Let indices v,w = 1,2,…,V denote peers – nodes of the overlay network.

There are K receivers (clients) indexed k = 1,2,…,K that are leafs in one of the mul-

ticast tree and only receive data. Index t = 1,2,…,T denotes streaming trees. We as-

sume that T = 2. In trees, nodes are located on levels l = 1,2,…,L. For instance, the

root node is located on level 1, the direct children of the root are located on level 2,

and so on. That gives us possibility to set a limit on the maximum depth of the tree.

The motivation behind this additional constraint is to improve the QoS (Quality of

Service) parameters of the overlay multicasting, e.g., network reliability and transmis-

sion delay. If node v is root of the tree t, then rvt = 1, otherwise rvt = 0. Constant cwv

denotes streaming cost on an overlay link (w,v).

To model survivable overlay multicasting, we modify formulations presented in

previous papers [Kmiecik 2011], [Walkowiak and Przewozniczek 2011]. As in

[Kmiecik 2011] we introduce the constant τ(v), which adds a virtual node associated

with the node v. Together they form a primal node. Every primal node has in fact four

capacity parameters – constants dv and uv are respectively download and upload ca-

pacity of the node v and constants dτ(v) and uτ(v) are parameters of the virtual node τ(v).

The objective function is maximum delay in the network, defined as the longest delay

path from the root to the receiver.

Fig. 2 depicts an example of the dual homing modeling. Dual homes are marked

with a pattern of sequential lines and dots.

Fig. 2. Modeling dual homing

4.1 Flow Maximum Delay – No Survivability (FMD-NS)

First, we formulate a basic ILP model that does not include additional survivability

constraints. To model overlay multicasting we use a set of binary variables. First vari-

able xwvtk denotes an individual flow for each streaming path from the root node to

node (receiver) k. This variable is set to 1, when streaming path to node k in tree t

includes an overlay link between nodes w and v; 0 otherwise. Additional binary varia-

ble xwvt is set to 1, if a link from node w to node v (no other peer nodes in between) is

established in the multicast tree t; 0 otherwise. Auxiliary binary variable xvt is set to 1,

if an access link of node v is used to download or upload flow of the multicast tree t;

0, otherwise.

indices

v,w,b = 1,2,…,V overlay nodes (peers)

k = 1,2,…,K receiving nodes (peers)

t = 1,2,…,T streaming tree index

l = 1,2,…,L levels of the tree

constants

dv download capacity of node v (Kbps)

uv upload capacity of node v (Kbps)

rvt = 1, if node v is the root (streaming node) of tree t;0, otherwise

q streaming rate (Kbps)

cwv streaming delay on overlay link from node w to node v (ms)

M large number

L The maximum number of levels of the tree

variables

xwvtk = 1, if in multicast tree t the streaming path from the root to node k includes

an overlay link from node w to node v (no other peer nodes in between); 0,

otherwise (binary)

xwvt = 1, if link from node w to node v (no other peer nodes in between) is in

multicast tree t; 0, otherwise (binary)

xvt = 1, if access link of node v is used to download or upload flow of multicast

tree t; 0, otherwise (binary)

β - maximum delay[ms]

objective

minimize β (1)

constraints

t xvvt =0 v = 1,2,…,V (2)

wtxwvtq dv v = 1,2,…,V (3)

vtxwvtq uw w = 1,2,…,V (4)

w xwvt + w xvwt Mxvt v = 1,2,…,V t = 1,2,…,T (5)

t xvt = 1 v = 1,2,…,V (6)

w xwvkt – w xvwkt = xkt v = k v = 1,2,…,V k = 1,2,…,V t = 1,2,…,T (7)

w xwvkt – w xvwkt = –xkt rvt = 1 v = 1,2,…,V k = 1,2,…,V t = 1,2,…,T (8)

w xwvkt – w xvwkt = 0 v≠k rvt≠1 v = 1,2,…,V k = 1,2,…,V t = 1,2,…,T (9)

xwvkt xwvt v = 1,2,…,V w = 1,2,…,V k = 1,2,…,V t = 1,2,…,T (10)

w v xwvkt L k = 1,2,…,V t = 1,2,…,T (11)

wv xwvktcwv β k = 1,2,...,K t = 1,2,...,T (12)

Our objective is to minimize the maximum distance from the root to the receiver cal-

culated as the sum of delays of links on the path between those nodes. Equation (2)

assures that the node internal flow is zero. This constraint guarantees that in each tree

there is at most one transmission per overlay link (w,v). Constraints (3) and (4) are

respectively the download and upload capacity constraints. Condition (5) specifies

definition of the xvt variable. The survivability constraint (6) assures, that multicast

trees are separate – each node v (access link) can only be used in one tree t. Equations

(7)-(9) are called flow conservation laws and define flows in overlay multicasting

trees. Connection between (w,v) exists in tree t, when there is at least one transmission

from root node to to any receiving node k that uses overlay link (w,v), what is assured

in condition(10). Constraint (11) sets the levels upper limit in the path to each receiv-

ing node. Finally, constraint (12) state, that β is upper bound for all xwvkt flows in all

multicast trees and for every receiving node k = 1,2,...,K.

Model (1)-(12) is a basic flow model of overlay multicasting in dual homing net-

works. Below we introduce additional constraints to formulate new survivability

models taking into account the following types of network failures:

Overlay link failure,

Uploading node failure,

ISP link failure.

4.2 Flow Maximum Delay – Link Disjoint (FMD-LD)

In this section, we address the overlay link failure and present additional con-

straints necessary to include this scenario in the ILP modeling.

constants (additional)

τ(v) index of node associated with node v (virtual node)

constraints (additional)

xvt + xτ(v)t= 1 v = 1,2,…,V t = 1,2,…,T (13)

t xvτ(v)t = 0 v = 1,2,…,V (14)

Survivable constraints (13), (14) state, that only one node from the primal node can

belong to tree t and there cannot be connection within primal node, e.g., between

node v and τ(v). Those constraints ensure that every primal node is connected to both

multicast trees and each tree is using different access link of the primal node e.g. rep-

resented by nodes v and τ(v). Note that such a configuration protects the system

against a single overlay link failure.

4.3 Flow Maximum Delay – Node Disjoint (FMD-ND)

Below we introduce an ILP model related to a node disjoint dual homing network.

To be able to denote if a particular node is uploading in a given multicast tree, new

variable yvt is introduced.

variables (additional)

yvt = 1, if node v is uploading in multicast tree t; 0, otherwise (binary)

constraints (additional)

v xwvt Mywt, w = 1,2,…,V t = 1,2,…,T (15)

ywt v xwvt, w = 1,2,…,V t = 1,2,…,T (16)

t (yvt + y τ(v)t) 1, rvt≠1 rτ(v)≠1 v = 1,2,…,V (17)

Constraints (15)-(16) are used to define the new variable yvt. Constraint (17) as-

sures that from nodes forming the primal node at most only one node can upload data

in the multicast tree.

4.4 Flow Maximum Delay – ISP Disjoint (FMD-ID)

Lastly, we introduce an ILP model that addresses the problem of ISP link failure.

indices (additional)

p,m = 1,2,…,P Internet Service Providers (ISPs)

constants (additional)

(v,p) = 1, if node v belongs to ISP p; 0, otherwise

variables (additional)

zpmt = 1, if in multicast tree t there is at least one link from a node located in ISP

p to a node located in ISP m or in opposite direction; 0, otherwise (binary)

constraints (additional)

w:(w,p)=1v:(v,m)=1 (xwvt + xvwt) Mzpmt p = 1,2,…,P

m = 1,2,…,P p m t = 1,2,…,T (18)

zpmt w:(w,p)=1v:(v,m)=1 (xwvt + xvwt) p = 1,2,…,P

m = 1,2,…,P p m t = 1,2,…,T (19)

t zpmt 1 p = 1,2,…,P m = 1,2,…,P (20)

Note that the ISP link failure includes the failure of both directed ISP links, i.e.

(p,m) and (m,p). Constraints (18)-(19) define the new variable zpmt, while the last con-

dition (20) assures that each ISP link is applied in at most one tree.

The considered optimization problem is complex and NP-hard, since it can be re-

duced to the hop-constrained minimum spanning tree problem, which is known to be

NP-hard [Dahl et al. 2006]. Due to that fact, branch-and-bound or branch-and-cut

methods have to be applied to obtain optimal solution.

5 Metaheuristic algorithms

Solving ILP models including a large number of variables and constraints can take

a huge amount of processing time and computing power. Moreover, relatively small

instances of the considered problem can be solved by ILP solvers to optimality in

reasonable time. Therefore, in order to solve such models in a relatively short period

of time and also for larger problem instances, in this Section we introduce two me-

taheuristic algorithms based in the Simulated Annealing and Tabu Search approaches.

5.1 Simulated Annealing (SA) Algorithm

The starting solution of the algorithm is arranged by taking the following steps

[Kmiecik 2011]:

1. Pick a node that is root for tree t.

2. Randomly pick any remaining node and connect it to the tree t by making it a child

of the node connected before; if node v is connected to tree t then node τ(v) has to

be connected to the other tree.

3. If all nodes are connected – terminate.

The main goal of this procedure it to guarantee that there are no loops in the net-

work. The starting solution does not have to meet all the constraints at this point.

We decided to use an insert method to create a random solution from the neighbor-

hood of the current solution. We randomly pick node v with rvt = 0 for t = 1,2…T and

choose its new parent w. All the children of node v become children of its former

parent. If new parent w is in the same tree as node τ(v), then that node is reconnected

to a different tree.

Originally, Simulated Annealing algorithm was created to solve unconstrained

problems. We propose a penalty method (22) similar to the Tabu Search algorithm

described in [4] in order to use SA algrithm for our optimization problem that in-

cludes numerous constraints:

f(cp,lp,up,ndp,idp)=x1cp+x2lp+x3up+x4ndp+x5idp (22)

cp cost penalty, which is a difference between the cost of generated

solution and the cost of current solution,

lp level penalty, number of nodes placed on higher levels in the mul-

ticast trees than L value; 0 otherwise,

up upload penalty, which is a number of nodes that are uploading more

than their upload capacity,

ndp node disjoint penalty, number of nodes in the multicast trees that are

uploading along with their virtual nodes,

idp ISP disjoint penalty, number of violations on ISP disjoint con-

straints.

x1,x2,x3,x4,x5 weights for each module of penalty method.

SA algorithm has the following input parameters:

Ts starting temperature

Te ending temperature

Iter_sa number of iterations

start_n number of starting solutions

We assume that SA uses geometric progression of temperature. The common ratio

λ for geometric progression is calculated according to the following formula:

λ = (𝑇𝑒

𝑇𝑠)

(1

𝐼𝑡𝑒𝑟_𝑠𝑎)

(23)

Moreover, we developed an additional optimization method, which is invoked after

all iteration of the algorithm [5]. More precisely, the method tries to find cheaper

alternatives for the most expensive connections in the multicast trees. For the maxi-

mum delay objective function, it searches for alternatives for expensive links within

most expensive path in terms of delay. If reconnection is successful, the maximum

delay value in the network is recalculated. The obtained maximum delay must be

lower than the current one for a new solution to be accepted.

5.2 Tabu Search (TS) Algorithm

Our TS algorithm is improved version of the algorithm from [4]. We use the addi-

tional optimization method as in the SA and new penalty function (22). Input parame-

ters for this metaheuristic algorithm are:

Iter_tabu number of iterations

t_length tabu list length

start_n number of starting solutions

In Fig. 3, we present the overall scheme of our TS algorithm:

Fig. 3. Tabu Search scheme [4]

We also use a new, adaptive way of choosing the number of iterations and starting

solutions. For highly constrained problems, e.g., with low L and high q, after fixed

number of failed attempts of finding feasible solutions, the algorithm increases num-

ber of starting solutions (and decreases number of iterations to maintain chosen exe-

cution time) for a bigger chance of finding feasible solutions.

6 Numerical Results

We randomly generated networks with 10 (small network), 15 (medium network) and

20 (big network) primal nodes and two disjoint multicast trees. Our main goal was

first to tune metaheuristic algorithms and next to compare the algorithms against

CPLEX for networks with different number of nodes, L values and streaming rates.

Moreover, we wanted to test how the level limit L and the streaming rate q would

affect the maximum delay criterion achieved by CPLEX and the metaheuristic algo-

rithms. An additional objective for this experiment was to check how the additional

survivability constraints will influence the chosen performance metric. To solve the

ILP models in an optimal way, we used newest CPLEX solver v12.4 [ILOG CPLEX

12.4 User’s Manual 2009]. We created networks with link costs in range 1-50 and

with either symmetric (100Mbps/100Mbps - 10% of all nodes) or asymmetric nodes

(1Mbps/256Kbps, 2Mbps/512Kbps, 6Mbps/512Kbps, 10/1Mbps, 20/1Mbps,

50/2Mbps, 100/4Mbps). Number of ISPs P was set to 5. Nodes are assigned to ISPs

by random, but with an additional condition, which states that any pair of nodes v and

τ(v) cannot be part of the same ISP. We assume that the first node is the streaming

node for tree t = 1 and node τ(1) is the streaming node for tree t = 2. We set timemax

value to 3600 seconds, limiting the execution time of CPLEX. That gave us the possi-

bility to compare the ILP models and the metaheuristic algorithms in terms of quality

of obtained solution and the time of processing. Overall, we conducted four experi-

ments:

Checking how the number of iterations and execution time would affect results

obtained by the Simulated Annealing algorithm for either size of the network,

Comparing CPLEX, SA and TS algorithms for different size of the network, dif-

ferent L values and streaming rate q in terms of the maximum delay,

Checking how the streaming rate q and different L values would affect the maxi-

mum delay,

Checking the influence of introducing survivability to the overlay multicasting.

6.1 Algorithms’ tuning

We tested how the SA algorithm would perform for different values of starting and

ending temperature (from 1 to 1000 in both cases) and we found that the best parame-

ters were:

Starting temperature Ts: 500,

Ending temperature Te: 1.

Similarly, we performed tests to find best value of the tabu list length t_length and

results indicate that the best value is 10. We set those values for the experiments de-

scribed below.

In another preliminary experiment, we discovered that the best values for the

weights of penalty method were 1, 0.25, 0.15, 0.15 and 0.15 respectively for both

metaheuristic algorithms. The number of iterations (Iter_sa/Iter_tabu) and starting

points (start_n) were set to achieve given processing time in a particular experiment,

e.g., 3600s. We performed a first experiment to check how the number of iterations

would affect the results of the metaheuristic algorithms – for this experiment we

chose the SA algorithm. In Figs 4 – 6, we show the results of SA for all three network

sizes – we present both average and best maximum delay for 100 repetitions of the

algorithm execution. We can easily notice that, with an increase in the number of

iterations, the SA algorithm performs better. The main drawback of increasing the

number of iterations is growth of the execution time. Our conclusion is that for every

experiment we have to find a tradeoff between the number of iterations and quality of

the results.

Fig. 4. Performance of SA - maximum delay as a function of the number of iterations for the

network with 10 primal nodes

Fig. 5. Performance of SA - maximum delay as a function of the number of iterations for the

network with 15 primal nodes

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0

10

20

30

40

50

60

70

1,0E+03 1,0E+04 1,0E+05 1,0E+06 1,0E+07

Time[s]Delay[ms]

Number of iterations

Best

Average

Time

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0

10

20

30

40

50

60

70

80

90

1,0E+03 1,0E+04 1,0E+05 1,0E+06 1,0E+07

Time[s]Delay[ms]

Number of iterations

Best

Average

Time

Fig. 6. Performance of SA - maximum delay as a function of the number of iterations for the

network with 20 primal nodes

To summarize the tuning process, in Table 1 we report the values of tuning param-

eters of SA and TS selected for further experiments.

Table 1. Values of SA and TS parameters after tuning process

Algorithm Parameter Value

SA Ts 500

Te 1

TS t_lenght 10

Both Iter( range) 104 – 107

start_n(range) 10 – 104

6.2 Comparison of Algorithms

In Tables 2 – 5, aggregated results of CPLEX, SA and TS comparison are present-

ed. For networks with 10 primal nodes, CPLEX was able to find the optimum and

both metaheuristic algorithms achieved solutions closed to that optimum (in much

shorter time) – the gap to optimum was 2.8% and 3.3% for SA and TS, respectively.

For network with 15 primal nodes, in one hour time, both metaheuristic algorithms

performed better than CPLEX. Tabu Search outperformed Simulated Annealing for

all networks but Node Disjoint, where both algorithms achieved similar results. Final-

ly, for the network with 20 primal nodes, TS achieved results better than SA by al-

most 100%. We were unable to compare the metaheuristic algorithms against

CPLEX, because it was not able to find any solution in time of 3600 seconds. Gap

between TS and SA is probably caused by the fact, that the TS algorithm more often

accepts solutions worse than the best found and in result it searches through much

larger and diversified solution space.

0

2000

4000

6000

8000

10000

12000

14000

16000

0

20

40

60

80

100

120

140

160

1,0E+03 1,0E+04 1,0E+05 1,0E+06 1,0E+07

Time[s]Delay[ms]

Number of iterations

Best

Average

Time

Table 2. Comparison of CPLEX, SA and TS for networks with 10, 15 and 20 primal nodes in

terms of the maximum delay – No Survivability (NS)

V

NS

CPLEX SA TS

Delay[ms] Time[s] Delay[ms] Diff[%] Time[s] Delay[ms] Diff[%] Time[s]

10 25.5 290 26.2 2.7% 60 27.1 5.9% 60

15 45.2 3600 30.4 -48.7% 3600 22.3 -102% 3600

20 X 3600 36.8 X 3600 15.3 X 3600

Table 3. Comparison of CPLEX, SA and TS for networks with 10, 15 and 20 primal nodes in

terms of the maximum delay – Link Disjoint (LD)

V

LD

CPLEX SA TS

Delay[ms] Time[s] Delay[ms] Diff[%] Time[s] Delay[ms] Diff[%] Time[s]

10 29.1 431.1 29.9 2.7% 60 30.3 4.0% 60

15 46.3 3600 32.3 -43.3% 3600 27.8 -66.5% 3600

20 X 3600 48.4 X 3600 23.0 X 3600

Table 4. Comparison of CPLEX, SA and TS for networks with 10, 15 and 20 primal nodes in

terms of the maximum delay – Node Disjoint (ND)

V

ND

CPLEX SA TS

Delay[ms] Time[s] Delay[ms] Diff[%] Time[s] Delay[ms] Diff[%] Time[s]

10 31.9 1321.3 33.3 4.2% 60 33.7 5.3% 60

15 47.0 3600 34.5 -36.2% 3600 34.2 -37.4% 3600

20 X 3600 40.1 X 3600 24.2 X 3600

Table 5. Comparison of CPLEX, SA and TS for networks with 10, 15 and 20 primal nodes in

terms of the maximum delay – ISP Disjoint (ID)

V

ID

CPLEX SA TS

Delay[ms] Time[s] Delay[ms] Diff[%] Time[s] Cost Diff[%] Time[s]

10 33.0 464.3 33.9 2.7% 60 33.1 0.3% 60 15 53.4 3600 33.7 -58.6% 3600 29.3 -82.4% 3600

20 X 3600 55.2 X 3600 28.0 X 3600

6.3 Impact of the Streaming Rate

The next goal of the experiment was to test how the streaming rate q would affect the

maximum delay. In Fig. 7, we present results of the this experiment. We chose net-

work with 10 primal nodes because in that case CPLEX obtained optimum for all of

48 generated networks. We can observe that the maximum delay grows with increase

of the streaming rate for networks with and without survivability constraints. Those

results are in line with our previous research [5]. Very small difference in maximum

delay for q=384 and q=512 can be explained by the fact, that for both q values all

nodes with upload capacity equals 256 Kbps can only be leafs in the multicast trees,

what shrinks the solution space significantly and strongly influence the results.

Fig. 7. Maximum delay as a function of the steaming rate q for the network with 10 primal

nodes

6.4 Impact of the Level Limit

This experiment is analogous to the previous one. In Fig. 8, we report the impact of

the level limit on the objective function for 10 node network. Opposite dependence

comparing to Fig. 7 can be noticed when increasing the L level. For every network

there is a point, from which increasing the number of levels does not decrease the

maximum delay.

Fig. 8. Maximum delay as a function of the level limit L for the network with 10 primal nodes

6.5 Comparison of Survivability Scenarios

Figure 9 depicts the average difference (over 48 experiments) of the particular sur-

vivability scenarios in comparison to the basic model without survivability constraints

in terms of the maximum delay. The additional cost of providing link disjoint surviv-

151719212325272931333537

128 256 384 512

Delay[ms]

q[Kbps]

NS

LD

ND

ID

20

25

30

35

40

45

2 3 4 5

Delay[ms]

L

NS

LD

ND

ID

ability was 12.4% of the maximum delay, for node disjoint constraints that value was

20% and for ISP disjoint constraints it was 22.3%.

Fig. 9. Additional cost of providing survivability for network with 10 primal nodes

7 Conclusion

In this paper, we addressed the problem of developing robust and flexible metaheuris-

tic algorithms for optimization of survivable multicast overlay multicasting in dual

homing networks. Experiments testing the impact of the streaming rate and the num-

ber of levels on the maximum delay in the network were conducted along with the

experiments focusing on comparison of the introduced metaheuristic algorithms and

the ILP models. The results indicate that proper selection of parameters has big influ-

ence on the maximum delay. Both the streaming rate and the level limit impact the

maximum delay. Moreover, The Simulated Annealing and Tabu Search algorithms

proved to be useful for finding the delay efficient solutions for all sizes of networks

and achieved quality solutions close to the optimum.

Acknowledgment

The work was supported in part by the Polish National Science Centre (NCN), under

the grant N N519 650440.

References 1. Firdhous, M., F., M. 2011. “Multicasting over Overlay Networks – A Critical Review”

(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 2,

No. 3: 54-61.

2. Vasseur, J., P., Pickavet, M., and Demeester, P. 2004. “Network Recovery Protection and

Restoration of Optical, SONET-SDH, IP and MPLS” Morgan Kaufman, 2004.

3. Kmiecik, W. and Walkowiak, K. 2012. „Heuristic approach for survivable P2P multi-

casting flow assignment in dual homing networks” International Joint Conference

CISIS'12-ICEUTE'12-SOCO'12 Special Sessions, Ostrava: 215-224.

0

5

10

15

20

25

30

35

10

Delay[ms]

Network

NS

LD

ND

ID

4. Kmiecik, W. and Walkowiak, K. 2011. „Survivable P2P multicasting flow assignment in

dual homing networks” 3rd International Congress on Ultra Modern Telecommunications

and Control Systems and Workshops (ICUMT), Budapest: 1-7.

5. Kmiecik, W. and Walkowiak, K. 2012. “Survivability aspects of overlay multicasting in

dual homing networks” 4th International Workshop on Reliable Networks Design and

Modeling co-located with 4th International Congress on Ultra Modern

Telecommunications and Control Systems and Workshops (ICUMT 2012), St. Petersburg,

October 3-5: 786-792.

6. Jianping, W., Mei, Y., Xiangtong, Q., and Jiang, Y. 2005. “On finding the best partial

multicast protection tree under dual-homing architecture” HPSR High Performance

Switching and Routing, Hong Kong: 128-132.

7. Wang, J., Vokkarane, V., Jothi, R., Qi, X., Raghavachari, B., and Jue, J. 2005. “Dual-

Homing Protection in IP-Over-WDM Networks” Journal of lightwave technology, vol. 23,

no. 10, UK: 3111-3124.

8. Wang, J., Yang, M., Yang, B., and Zheng, S.Q. 2006. “Dual-Homing Based Scalable

Partial Multicast Protection” IEEE Transactions on Computers, vol. 55, no. 9: 1130-1141.

9. Thulasiraman, P., Ramasubramanian, S., and Krunz, M. 2006 “Disjoint multipath routing

in dual homing networks using colored trees” Proceedings of GLOBECOM - Wireless Ad

Hoc and Sensor Network Symposium, San Francisco: 1-5.

10. Fei, Z. and Yang, M. 2007. “A Proactive Tree Recovery Mechanism for Resilient Overlay

Multicast” IEEE/ACM Transactions on networking, vol.15: 173-185.

11. Imran, A., K., Sajjad, A., M., Mubbashar, S., and Sana, M. 2011. “Efficient Overlay

Multicast Routing for Hybrid Networks” Malaysian Journal of Computer Science, Vol.

24(2): 84-97.

12. Suat, M. and Murat, Y. 2011. “Virtual Direction Multicast for Overlay Networks” IEEE

International Parallel & Distributed Processing Symposium: 1595-1601.

13. Samir, K., S., Swarup, M., Srishti S., and Debashis, S. 2011. “Joint Optimization of 2-tier

Dual-homing for NodeBs and RNCs in UMTS Networks Using Meta-heuristic

Techniques” 3rd International Conference on Communication Systems and Networks

(COMSNETS): 1-8.

14. Konstantin, A., Bruce, M.. M., Adam, M., Jevan, S., and Ramesh, K., S. 2011.

“Algorithms for Constructing Overlay Networks For Live Streaming”, eprint

arXiv:1109.4114.

15. Pioro, M. and Medhi, D. 2004. “Routing, Flow, and Capacity Design in Communication

and Computer Networks” Morgan Kaufman Publishers, ISBN:978-0-12-557189-0.

16. Walkowiak, K. and Przewoźniczek, M. 2011. „Modeling and optimization of survivable

P2P multicasting” Computer Communications, vol. 34, issue 12: 1410-1424.

17. Dahl, G., Gouveia, L., and Requejo, C. 2006. “On formulations and methods for the hop-

constrained minimum spanning tree problem” Handbook of Optimization in Telecommuni-

cations: 493-515.

18. IBM. 2009. “ILOG CPLEX 12.4 User’s Manual”

ftp://public.dhe.ibm.com/software/websphere/ilog/docs/optimization/cplex/ps_usrmancple

x.pdf