华中师范大学 HuaZhong Normal University

1. 华中师范大学HuaZhong Normal University 基于蚂蚁算法的多播服务器选择研究Research of Multicast Server Select Based on Ant Algorithm 基于蚂蚁算法的多播服务器选择研究Research of Multicast Server Select Based on Ant Algorithm Author：JiWei Cao Supervisor:Prof.Yuhua Liu 2005.11

2. Research of Multicast Server Select Based on Ant Algorithm • Abstract • Introduction • Modeling • Research of Server Selection Algorithm • Simulation Result and Analysis • Conclusion

3. Abstract • In this paper, we proposed a novel model of considering a pair of guests as the minimal gene. These minimal genes were assigned secretion separately based on proper modification of ant algorithm. We transformed the problem of client selecting server to the problem of server selecting client. We applied GT-ITM as Internet topology generator to generate transit-stub model topology for simulation. In the case of large-scale network topology, the simulation results show that the modified ant algorithm behaves better than other heuristics algorithm such as the widest path and the optimized widest path. • Keywords: Ant algorithm, Multi-Cast, Server selection, Guest pair

4. 1、Introduction With the rapid growth of Internet application, traditional unicast network are bearing heavier and heavier load, The appearance of multicast solved some problems with video conference, movie etc. but multicast introduce some new problems, so the strategy of duplicating of multicast server appears. (1) Collect the requests from users and decide whether use multicast to response these requests; (2) As to some demand of reliable multicast, it is needed to return confirm information to the data source. In the case of that there is large number of customers, the data source may be flooded by the affirmation information enormous in quantity, and the duplicate servers can deal with the feedback and lighten the burden of information.

5. (3) Customers belong to the same server must use the same speed to receive data. The customers with lower speed will influence the speed of higher speed users. As to some flow media applications, server duplication strategy can divide service quality into different grades to different bandwidth and offer corresponding quality to the users with different bandwidth. The problem of multicast server select was proved a NP hard one [1]. Some heuristic algorithms based on experience were proposed in some present research, but there is a very great disparity between the result received and overall ideal speed. Ant algorithm has advantage of solving NP hard problem. here we employ its main idea to solve multicast server select problem. We did simulation with the model of stable client. We obtained a better simulation result than other heuristic algorithm.

6. 2、 Modeling 2.1 Review of Ant Algorithm • Research finds that in the early phase of the formation of shortest path, the ant has very great randomness in the choice of the branch at forks. The ant going in the wrong direction should wind a very big circle to reach the destination, but the ant that selected a right branch reaches the destination soon. • The ant will leave some secretion that can be recognized by their companion during the walking. After some time, the density of secretion on the shortest path will be higher and higher. • Finally, all ants will choose this optimum route with extremely high probability. • Each ant only needs choosing according to the density of secretion on the route, then leave proper secretion, the group of ant can find the best route between foods and nest finally.

7. In the process of solving TSP with ant algorithm, the selected probability function of a branch is: • Formula 1 described the basis of choosing route: at time, ant computes a probability of selecting path according to the secretion density of path between and the distance between city.

8. 2.2 Modeling • We use undirected connected graph denote a network model. Let denote the union of server set and client set. , denote server set, , denote client set. denote the edge set of a network. , denote the start and end of edge. denotes ’s average weight. • we assume that each client can only select one server and all the clients select the same server receive data at the same speed which is the smallest one of all client’s access speed. • From the point of view of server, the solution can be denoted as a set of dimension vectors: , where denotes the choice of server , if server selected client , then , otherwise . • From the point of view of server, the solution can be denoted as a set of dimension vector: , and , if client selected server , then =1, otherwise =0. We can get each client’s receiving speed according the solution. Our algorithm’s purpose is to compute. First, we consider a model in which the clients who have similar access rate are grouped.

9. Remove the clients, regard each LAN as a client, so the problem is simplified further as computing a division about these LANs. Fig. 1 Group partition model

10. Fig.2 demonstrates a random network model in which double circle denotes server; single circle denotes client, and number besides the edge denote bandwidth and time delay. • These trees may share some links in the network according to choosing different algorithm. So, the distribution of sharing link’s bandwidth should be considered. Fig. 2 Random distribution model

11. 3、 Research of Server SelectioAlgorithm 3.1 Selection Algorithm Based on Group partition Model • The problem of group partition model can be transformed to searching a shortest path between two nodes in a graph, and it can be solved by Dijkstra algorithm in polynomial time. • We got the length of the path highlight with bold line: . The purpose of sever selecting is to group clients reasonably and try to lower the wasted bandwidth, so the server selecting problem in group partition model has converted to compute shortest path between and in Fig. 3. Fig. 3 Map group partition model to shortest path problem

12. 3.2 Selecting Algorithm in Random Distribution Model • In random distribute model, we should consider the following problems: 1) Multicast server selecting. 2) Compute route from server to client. 3) Allocate bandwidth of share links. The problem of server selecting was proved a NP hard one, thus it is very hard to find an optimal solution. we consider each client as a dependent gene, but the result was unsatisfactory. The reason is that finding some way to gather proper clients into a group is the key point of server select problem, so the clients have similar access rate must be distributed in a same group. Therefore, we can conclude that clients in a server’s client set must have similar access rate in optimum solution. We proposed that use the similarity of client’s access rate as a factor that guides the server to select proper clients. In our simulation, a pair of client was considered as the minimal segment of the problem’s solution.

13. We can compute the probability of being selected of each gene according above factors:

14. The following is the pseudo-code of selecting algorithm based on ant algorithm:

15. 3.3 Widest Path Routing Algorithm • We need to compute the route from server to all its clients after clients selecting have finished. In random distribute model, each node joined the network via one or more than one link, therefore, we use the maximum access rate as a node’s optimum access rate. In order to obtain optimal result, the widest path between a server and each of its clients should be worked out. The following is the pseudo-code of widest path algorithm:

16. 4 、Simulation Result and Analysis GT-ITM is a kind of topology generator. It can generate two kinds of topology: random model and transit-stub model. We applied a 400 nodes transit-stub model with randomly select 25% nodes as client. For the conditions of 1,2 4,8,16 servers exist in the network, we did simulation separately. Fig. 4 denotes the ratio of real total receiving rate to optimum rate vary with server number. Fig. 5 denotes the fairness vary with server number. Fig. 4 Ratio of real rate to optimum rate Fig. 5 Fairness

17. As shown in Fig. 4, the line marked with rectangle is result of ant algorithm. Optimized Widest and Shortest are some heuristics present in recent years. Isolated Rate is worded out according client’s optimum rate. We can conclude from Fig. 4, when there are only few servers, the optimization result of ant algorithm is not very obvious, but the performance improved rapidly with the increase of server number. The reason is that the solution space presents index increase with server number’s increase; therefore, the advantage of ant algorithm appeared that it could search optimum solution in whole solution space quickly. Furthermore, client with small different of access rate can be allocated to different group, thus higher access rate client endure less bandwidth loss because of lower access rate clients exist in the same group. The fairness enjoyed by a client has positive relationship with its real receiving rate. So, the fairness line in Fig. 5 is similar with the performance line in Fig. 4. We can conclude from the simulation result that ant algorithm is better than other heuristics in solving multicast server selection problem.

18. 5 、Conclusion • We thought the nuclear thought of ant algorithm is positive energize. Ant algorithm has advantage of searching optimal solution quickly in the whole solution space, but the problem model should be transformed before apply ant algorithm. We proposed that use a pair of client as the minimum gene to be assigned secretion, then convert the server selection problem to the one in which server select clients. We have got better result in several simulations via this method. Another problem is about the parameters in the main formula. We can adjust it to get higher optimal result in each cycle. END

19. Reference • [1] Zongming Fei,Mostafa Ammar etc. Multicast Server Selection: Problems, Complexity and Solutions. IEEE Journal of Selected Areas On Communication 2002. • [2] Marco Dorig. The Ant System:Optimization by a colony of cooperating agents. IEEE Transactions on Systems,Man, and Cybernetics–Part B, 1996. • [3] Akihito Hiromori, Hirozumi Yamaguchi. Improving Scalability in Monitoring-based Multicast Server Selection. IPSJ SIGNotes Distributed Processing System Abstract 2002. • [4] Zongming Fei, Mostafa Ammar etc. Selecting Among Replicated Rate-Adaptive Multicast Servers.

20. [5] Zongming Fei, Mostafa H. Ammar, and Ellen W. Zegura. Selection of replicated adaptive multicast servers. Technical Report GIT-CC-00-16, Georgia Tech, 2000. • [6] Krzysztof Socha The Influence of Run-Time Limits on Choosing Ant System Parameters. • [7] Jose Aguilar. A General Ant Colony Model to Solve Combinatorial Optimization Problem revista colombiana de computacion volumen 2.

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