QoS Multicast Routing Algorithm in MANET:

An Entropy-Based GA

Hua Chen1, Baolin Sun1,2, and Yue Zeng3

1 Department of Mathematics and Physics,Wuhan University of Science and Engineering, Wuhan, 430073, P.R. China

qiuchen 1022@163.com2 School of Computer Science and Technology, Wuhan University of Technology,

Wuhan, 430063, P.R. Chinablsun@163.com

3 Department of Computer, Jiangxi Vocational College of Finance and Economics,Jiujiang, Jiangxi 332000, P.R. China

Abstract. A mobile ad hoc network (MANET) is an autonomous sys-tem of mobile nodes connected by wireless links. There is no static in-frastructure such as base station in cell mobile communication. Due tothe dynamic nature of the network topology and restricted resources,quality of service (QoS) and multicast routing in MANET is a challeng-ing task. Finding and maintaining QoS multicast routing in the data isstill more challenging. In this paper, we present an entropy-based ge-netic algorithm (GA) to support QoS multicast routing in mobile ad hocnetworks (EQMGA). The key idea of EQMGA algorithm is to constructthe new metric-entropy and select the long-life path with the help ofentropy metric to reduce the number of route reconstruction so as toprovide QoS guarantee in the ad hoc network. The simulation resultsdemonstrate that the proposed approach and parameters provide an ac-curate and efficient method to estimate and evaluate the route stabilityin dynamic mobile networks.

1 Introduction

A mobile ad hoc network (MANET) is an autonomous system of mobile nodesconnected by wireless links. There is no static infrastructure such as base stationas that was in cell mobile communication [1-7,11]. Due to the dynamic natureof the network topology and restricted resources, quality of service (QoS) andmulticast routing in MANET is a challenging task. Finding and maintaining theQoS multicast routing the data is still more challenging [1-7].

Quality of service (QoS) support for multimedia applications is closely relatedto resource allocation, the objective of which is to decide how to reserve resourcessuch that QoS requirements of all the applications can be satisfied. In [1] presentsa QoS multicast routing model and algorithm based on GA. In [2], we proposea methodology to chose optimized fuzzy controller parameters using the GA.

The use of multicasting with the network has many benefits. Multicasting re-duces the communication cost for applications that sending the same data to many

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNAI 4114, pp. 1279–1289, 2006.c© Springer-Verlag Berlin Heidelberg 2006

1280 H. Chen, B. Sun, and Y. Zeng

recipients [1,3-7]. Instead of sending via multiple unicast, multicast reduces thechannel bandwidth, sender and router processing and delivery delay. In additionmulticast gives robust communication whereby the receiver address is unknown ormodifiable without the knowledge of the source within the wireless environment.In [3], we presents an entropy-based stability QoS multicast routing protocol in adhoc network. Multicast ad hoc on-demand distance-vector (MAODV) [6] routingprotocol provides fast and efficient route establishment between mobile nodes thatneed to communicatewith eachother. SinceMAODVhasbeen specificallydesignedfor ad hoc wireless networks, it has minimal control overhead and route acquisitionlatency. In addition to unicast routing, MAODV supports multicast and broadcastas well. The ODMRP [7] protocol is a mesh based rather than a conventional treebased scheme and uses a forwarding group concept.

Entropy [8,9] presents the uncertanity and a measure of the disorder in a sys-tem. There are some common characteristics among self-organization, entropy,and the location uncertainty in mobile ad hoc wireless networks. These commoncharacteristics have motivated our work in developing an analytical modelingframework using entropy concepts and utilizing mobility information as the cor-responding variable features, in order to support route stability in self-organizingmobile ad hoc wireless networks. The corresponding methodology, results andobservations can be used by the routing protocols to select the most stable routebetween a source and a destination, in an environment where multiple paths areavailable, as well as to create a convenient performance measure to be used forthe evaluation of the stability and connectivity in mobile ad hoc networks.

In this paper, we present an entropy-based model to support QoS multicastrouting genetic algorithm in mobile ad hoc networks (EQMGA). The key ideaof EQMGA algorithm is to construct the new metric-entropy and select thelong-life path with the help of entropy metric to reduce the number of routereconstruction so as to provide QoS guarantee in the ad hoc network whosetopology changes continuously.

The rest of the paper is organized as follows. Section 2 introduces the ad hocnetwork model and routing issues. Section 3 describes EQMGA. Section 4 givesthe complexity analysis of the algorithm. Some simulation results are providedin section 5. Finally, the paper concludes in section 6.

2 Network Model and Routing Issues

A network is usually represented as a weighted digraph G = (N, E), where N de-notes the set of nodes and E denotes the set of communication links connectingthe nodes. |N | and |E| denote the number of nodes and links in the network re-spectively. In G(N, E), considering a QoS constrained multicast routing problemfrom a source node to multi-destination nodes, namely given a non-empty setM={s, u1, u2, . . . , um}, M ⊆ N, s is source node, U={u1, u2, . . . , um} be a setof destination nodes. In multicast tree T=(NT , ET ), where NT ⊆ N , ET ⊆ E.if C(T ) is the cost of T , PT (s, u) is the path from source node s to destinationu ∈ U in T , BT (s, u) is usable bandwidth of PT (s, u).

QoS Multicast Routing Algorithm in MANET: An Entropy-Based GA 1281

Definition 1: The cost of multicast tree T is:

C(Te) =∑

e∈ETC(e), e ∈ ET .

Definition 2: The bandwidth of multicast tree T is the minimum value of linkbandwidth in the path from source node s to each destination node u ∈ U . i.e.

BT (s, u)= min(B(e), e ∈ ET ).

Definition 3: Assume the minimum bandwidth constraint of multicast tree isB, given a multicast demand R, then, the problem of bandwidth constrainedmulticast routing is to find a multicast tree T , satisfying:

Bandwidth constraint: BT (s, u) ≥ B, u ∈ U .Suppose S(R) is the set, S(R) satisfies the conditions above, then, the multi-

cast tree T which we find is:

C(T ) = min (C(Ts), Ts ∈ S(R)).

3 EQMGA

Genetic algorithms are based on the mechanics of natural evolution. Throughouttheir artificial evolution, successive generations each consisting of a populationof possible solutions, called individuals (or chromosomes, or vectors of genes),search for beneficial adaptations to solve the given problem.

3.1 Encoding Representation

The chromosomes of genetic algorithms is composed of a series of integral queu-ing and the encoding method based on routing representation, which the mostnatural and simplest representing method. Given a source node s and destinationnodes set U={u1, u2, . . . , um}, a chromosome can be represented by a string ofintegers with length m. The chromosome of genetic algorithms is composed ofa series of integral queuing with length m, the gene of genetic algorithms is thepath in path set {P 1

i , . . . , P ji , . . . , P l

i } [4] between s and ui, where, P ji is the j-th

path of destination node ui, l denotes the path number between s and ui. Eachchromosome in population denotes a multicast tree. Now for each destinationnode ui ∈ U , by the k-th the shortest route algorithm, the encoding space can beimproved by finding out all routes that satisfy bandwidth constraint from sourcenode s to destination node ui ∈ U and composing routes set as candidate routesset of genetic algorithm encoding space. Assume that Ui is the set of destinationnode ui which satisfies bandwidth constrained, then

Ui={P 1i , . . . , P j

i , . . . , P ki }, k ≤ l

where, P ji denotes the j-th route which satisfies bandwidth constraint of desti-

nation node ui. Choose arbitrarily a route from each route set Ui respectively,and compose the initial population of chromosomes.

1282 H. Chen, B. Sun, and Y. Zeng

Fig. 1. Representation of chromosomes

3.2 Fitness Sharing Function (Entropy Metric)

The individual with good performance has high fitness level, and the individualwith bad performance has low fitness level.

We also associate each node m with a set of variable features denoted by am,n

where node n is a neighbor of node m. In this paper, two nodes are consideredneighbors if they can reach each other in one hop (e.g. direct communication).These variable features am,n represent a measure of the relative speed among twonodes and are defined rigorously later in this section. Any change of the systemcan be described as a change of variable values am,n in the course of time t suchas am,n(t) → am,n(t + Δt). Let us also denote by v(m,t) the velocity vectorof node m and by v(n,t) the velocity vector of node n at time t. Please notethat velocity vectors v(m,t) and v(n,t) have two parameters, namely speed anddirection. The relative velocity v(m,n,t) between nodes m and n at time t isdefined as:

v(m,n,t) = v(m,t) − v(n,t)

Let us also denote by p(m,t) the position vector of node m and by p(n,t) theposition vector of node n at time t. Please note that position vectors p(m,t)and p(n,t) have two parameters, namely position. The relative position p(m,n,t)between nodes m and n at time t is defined as:

p(m,n,t) = p(m,t) – p(n,t)

Then, the relative mobility between any pair (m,n) of nodes during sometime interval is defined as their absolute relative speed and position averagedover time. Therefore, we have:

am,n =1N

N∑

i=1

|p(m, n, ti) + v(m, n, ti) × Δti | − |p(m, n, ti+1)|R

where N is the number of discrete times ti that velocity information can becalculated and disseminated to other neighboring nodes within time interval Δt.R is radio range of nodes. Based on this, we can define the entropy Hm(t, Δt)

QoS Multicast Routing Algorithm in MANET: An Entropy-Based GA 1283

at mobile during time interval Δt. The entropy can be defined either withinthe whole neighboring range of node (e.g., within set Sm), or for any subsetof neighboring nodes of interest. In general the entropy Hm(t, Δt) at mobile iscalculated as follows [8,9]:

Hm(t, Δt) =−∑

k∈FmPk(t, Δt) log Pk(t, Δt)log C(Fm)

where Pk(t, Δt) = (am,k /∑

i∈Fmam,i ).

In this relation by Fm we denote the set (or any subset) of the neighboringnodes of node m, and by C(Fm) the cardinality (degree) of set Fm. As can beobserved from the previous relation the entropy Hm(t, Δt) is normalized so that0 ≤ Hm(t, Δt) ≤ 1. It should be noted that the entropy, as defined here, is smallwhen the change of the variable values in the given region is severe and largewhen the change of the values is small [8,9]. Let us present the route stabilitybetween two nodes s and u ∈ U during some interval Δt as route stability. Wealso define and evaluate two different measures to estimate and quantify endto end route stability, denoted by F

′(s, u) and F (s, u) and defined as follows

respectively:

F′(s, u) =

Nr∏

i=1

Hi(t, Δt)

where Nr denotes the number of intermediate mobile nodes over a route betweenthe two end nodes (s, u).

F (s, u) = − lnF′(s, u) = −

Nr∑

i=1

ln Hi(t, Δt)

3.3 Selection Operations

Selection operation is used to certain or crossover individuals, and selected in-dividual can produce many sub-individuals. Selection operation has two proce-dures: firstly, computing fitness value; secondly, queuing it from the smallest tothe biggest, namely, F (s,u′

1) ≤ F (s, u′2) ≤ . . .≤ F (s, u′

m) ({u′1, u′

2, . . . , u′m}⊂

{u1, u2, . . . , um}), then, the min fitness value is the best individual, selecting thebest individual as father-individual, the selection probability of each individualis proportional to its fitness value, the selected probability is higher when theindividual fitness value is bigger. If the same chromosomes have been got, onlyone chromosome exists. The rest chromosomes can be canceled.

3.4 Crossover and Mutation Operations

In the proposed scheme, two chromosomes chosen for crossover should have atleast one common gene (node), but there is no requirement that they be locatedat the same locus. That is to say, the crossover does not depend on the position ofnodes in routing paths [1,4]. Fig. 2 shows an example of the crossover procedure.

1284 H. Chen, B. Sun, and Y. Zeng

Fig. 2. Overall procedure of the crossover

Fig. 3. Overall procedure of the mutation

The population undergoes mutation by an actual change or flipping of one ofthe genes of the candidate chromosomes, which keeping away from local optima[1,4]. Fig. 3 shows the overall procedure of the mutation operation.

4 Complexity of the Algorithm

The genetic operators crossover and mutation requires O(n) time, where n isthe total number of network nodes. Since, the genetic operations are performedon every string in the population, the complexity of a single iteration of thealgorithm will be: O(P × n), where P is the population size. Finally, since, thealgorithm is executed for g generations, the total complexity of the algorithmbecomes O(g × P × n). The simulation experiments in Section 5 makes it clearthat in most of the cases, only a few generations will give a near-optimal result.It is true that the number of iterations g varies with the population size P .A poor guess of choosing the initial population might increase the number ofiterations leading to a relatively slower solution. However, such penalty is oftentolerated while solving such a NP-hard problem.

5 Simulation Experiments

5.1 Random Graph Generation

In generating random graphs, we have adopted the method used in [11], wherevertices are placed randomly in a rectangular coordinate grid by generating uni-formly distributed values for their x and y coordinates. The graphs connectivityis ensured by first constructing a random spanning tree. This tree is generated

QoS Multicast Routing Algorithm in MANET: An Entropy-Based GA 1285

by iteratively considering a random edge between nodes and accepting thoseedges that connect distinct components. The remaining edges of the graph arechosen by examining each possible edge (u,v) and generating a random number0 ≤ r < 1. If r is the less than a probability function P (u, v) based on the edgedistance between u and v, then the edge is included in the graph. The distancefor each edge is the Euclidean distance (denoted as d(u, v) between the nodesthat form the end-points of the edge. We used the probability

P (u, v) = β exp(−d(u, v)αL

)

where α and β are tunable parameters and L is the number of nodes in thegraph. Increasing an increase the number of connections between far off nodesand increasing β increases the degree of each node.

5.2 Simulation Model

To conduct the simulation studies, we have used randomly generated networkson which the algorithms were executed. This ensures that the simulation resultsare independent of the characteristics of any particular network topology. Usingrandomly generated network topologies also provides the necessary flexibility totune various network parameters such as average degree, number of nodes, andnumber of edges, and to study the effect of these parameters on the performanceof the algorithms.

Our simulation modeled a network of mobile nodes placed randomly within1km × 1km area. Radio propagation range for each node was 250 meters andchannel capacity of 2 Mbps is chosen. There were no network partitions through-out the simulation. Each simulation is executed for 600 seconds of simulationtime. Multiple runs with different seed values were conducted for each scenarioand collected data was averaged over those runs. Table 1 lists the simulationparameters which are used as default values unless otherwise specified. A freespace propagation model was used in our experiments. A traffic generator wasdeveloped to simulate CBR sources. The size of the data payload is 512 bytes.Data sessions with randomly selected sources and destinations were simulated.Each source transmits data packets at a minimum rate of 4 packets/sec. andmaximum rate of 10 packets/sec.

During the experiment, we research EQMGA mainly from cost to control in-formation, the success rate to find the path and the feature of data transmission,the average cost to control information, the success rate to find the path [1,3-7]and the feature of data transmission are decided by following formula:

The cost to control information =

Total number of routed information controlsTotal number of connection request

The success rate =

Total number of routed connection requestsTotal number of connection request

1286 H. Chen, B. Sun, and Y. Zeng

Table 1. Simulation parameters

Number of nodes 100 Number of multicast receivers 5-30

Terrain range 1km × 1km Channel bandwidth 2 Mbps

Speed 0-20 m/s Transmission range 250 m

Mobility model Random way point Simulation time 600 seconds

Traffic type CBR Node pause time 0-20 seconds

Data payload 512 bytes/packet Examined routing protocol MAODV

The data transmission rate =

Total number of data transferred to destinationTotal number of data sent by the source node

5.3 Simulation Results

In order to evaluate the performances of our EQMGA, we simulate the proposedmechanisms using NS-2 [12] extended by a complete implementation of IEEE802.11.

Fig. 4 depicts a comparison of cost to control information MAODV andEQMGA. We can see that comes out with a smaller cost and an increased scaleof network in comparison with MAODV [6], with the extend QoS constraintsinto MAODV, the cost to control information also increased; but for EQMGA,with its feasible path and QoS restrictive diffuse scheme, the growth of costto control information is lower, so EQMGA will not incur the flooding storm.Due to the scarcity of wireless ad hoc network resource, EQMGA has apparentadvantages, in solving ad hoc network multicast routing problems.

Fig. 5 depicts a comparison of number of route reconstructions against mo-bility between MAODV and EQMGA. Whenever path error occurs, it needs toreconstruct, and route number of reconstructions characterize the route’s stabil-ity to some extent. From Fig. 5 we can see that the times of route reconstructionsfor EQMGA is superior and more stable.

Fig. 4. Cost-comparison with control information

QoS Multicast Routing Algorithm in MANET: An Entropy-Based GA 1287

Fig. 5. Number of route reconstructions against mobility

Fig. 6. Comparison of success rate to find the path

Fig. 7. Comparison of success rate to find the path

Fig. 6 depicts a comparison among success rate to find the path throughMAODV and EQMGA. With the relaxation of Bandwidth constraints, the suc-cess rate becomes larger for MAODV and EQMGA. EQMGA’s success rate isstill higher than that of MAODV, which mean EQMGA is more suitable forthe routing choosing under timely data transmission application and dynamicnetwork structure.

Fig. 7 and Fig. 8 depicts the comparison of success rate to find the path anddata transmission rate under nodes’ changing movement speed for MAODV andEQMGA. From Fig. 7 and Fig. 8 we can see that when the movement speed ofthe node increase, EQMGA success rate and data transmission rate is still higher

1288 H. Chen, B. Sun, and Y. Zeng

Fig. 8. Comparison of data transmission rate

than that of MAODV, due to the fact that when the movement speed increasefor the nodes, the network’s topology structure changes faster. The reason isthat QoS multicast tree can select the most stable multicast routing betweensource node and destination node.

6 Conclusion

In this paper, we present an entropy-based GA to support QoS multicast rout-ing algorithm in mobile ad hoc networks (EQMGA). The basic motivations ofthe proposed modeling approach stem from the commonality observed in thelocation uncertainty in mobile ad hoc wireless networks and the concept of en-tropy. The performance evaluation of our proposed method is accomplished viamodeling and simulation. The simulation results demonstrate that the proposedapproach and parameters provide an accurate and efficient method of estimatingand evaluating the route stability in dynamic mobile networks.

Acknowledgement

This work is supported by National Natural Science Foundation of China (No.90304018), NSF of Hubei Province of China (No. 2005ABA231), and Key Sci-entific Research Project of Hubei Education Department (No. D200617001).

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