1. The Influence of Network Topology on the Efficiency of QoS Multicast Heuristic Algorithms Maciej Piechowiak Piotr Zwierzykowski Poznan University of Technology, Poland Institute of Electronics and Telecommunications CSNDSP '2006

2. Outline 1.Network topology model 2.Constrained multicast algorithms 3.Topology generation methods 4.Topology visualization 5.Network parameters 6.Simulation results 7.Conclusions Communication Systems, Networks and Digital Signal Processing 2006

3. Outline 1.Network topology model 2.Constrained multicast algorithms 3.Topology generation methods 4.Topology visualization 5.Network parameters 6.Simulation results 7.Conclusions Communication Systems, Networks and Digital Signal Processing 2006

4. Network model network is represented by a directed, connected graph N = (V,E),where V is a set of nodes and E is a set of links,network is represented by a directed, connected graph N = (V,E), where V is a set of nodes and E is a set of links, with each link e(u,v)  E two parameters are coupled: cost C(u,v) and delay D(u,v),with each link e(u,v)  E two parameters are coupled: cost C(u,v) and delay D(u,v), multicast group is a set of nodes that are receivers of group traffic G = {g 1,...,g n }  V, node s is a source for group G,multicast group is a set of nodes that are receivers of group traffic G = {g 1,...,g n }  V, node s is a source for group G, multicast tree T(s,G)  E is a tree rooted in source node s that includes all members of the group G.multicast tree T(s,G)  E is a tree rooted in source node s that includes all members of the group G. Communication Systems, Networks and Digital Signal Processing 2006

5. Minimum Steiner Tree (MST) N=(V,E) Steiner tree is a good representation for solving multicast routing problem. Finding Steiner tree is NP -complete problem. Heuristic algorithms are most preferable. Communication Systems, Networks and Digital Signal Processing 2006

6. Outline 1.Network topology model 2.Constrained multicast algorithms 3.Topology generation methods 4.Topology visualization 5.Network parameters 6.Simulation results 7.Conclusions Communication Systems, Networks and Digital Signal Processing 2006

7. Constrained algorithms Constrained algorithms compute least cost path (tree) without violating the constraint implied by the upper bound on delay (  ). subject to: KPP algorithm (Kompella, Pasquale, Polyzos),KPP algorithm (Kompella, Pasquale, Polyzos), CSPT (Constrained Shortest Path Tree),CSPT (Constrained Shortest Path Tree), LD (Least Delay).LD (Least Delay). Representative algorithms: Communication Systems, Networks and Digital Signal Processing 2006

8. Outline 1.Network topology model 2.Constrained multicast algorithms 3.Topology generation methods 4.Topology visualization 5.Network parameters 6.Simulation results 7.Conclusions Communication Systems, Networks and Digital Signal Processing 2006

9. Waxman method Probability of edge betweenu and v: Probability of edge between u and v: d –Euclidean distance between node u and v, L –maximum distance between any two nodes in graph, ,  –topology parameters – an increase in  effects in the increase in the number of edges; decrease  increases the ratio of the long edges agaist the short ones. Communication Systems, Networks and Digital Signal Processing 2006

10. Barabasi method Probability that new node u connects to a node v: d V – degree of a node belonging to the network, V – set of nodes connected to the network,  – sum of the outdegrees of the nodes previously connected. incremental growth, incremental growth, preferential connectivity. preferential connectivity.features: Communication Systems, Networks and Digital Signal Processing 2006

11. Outline 1.Network topology model 2.Constrained multicast algorithms 3.Topology generation methods 4.Topology visualization 5.Network parameters 6.Simulation results 7.Conclusions Communication Systems, Networks and Digital Signal Processing 2006

12. Topology visualization WAXMANBARABASI n = 100, k = 200, HS = 400 SVG graph visualization: www.svg.teletraffic.pl Communication Systems, Networks and Digital Signal Processing 2006

13. Outline 1.Network topology model 2.Constrained multicast algorithms 3.Topology generation methods 4.Topology visualization 5.Network parameters 6.Simulation results 7.Conclusions Communication Systems, Networks and Digital Signal Processing 2006

14. Networks parameters number of nodes – n, number of links – k,number of nodes – n, number of links – k, average node degree (D av ),average node degree (D av ), diameter – length of the longest shortest-path between any two nodes,diameter – length of the longest shortest-path between any two nodes, hop-diameter – shortest paths are computed using hop counts metric,hop-diameter – shortest paths are computed using hop counts metric, length-diameter – shortest paths are computed using Euclidean distance metric,length-diameter – shortest paths are computed using Euclidean distance metric, Communication Systems, Networks and Digital Signal Processing 2006

15. Networks parameters  (v) – neighbourhod of v, k v – outdegrees of node v, average clustering coefficient,average clustering coefficient, number of multicast nodes – m.number of multicast nodes – m. clustering coefficient – proportion of links between the vertices within its neighbourhood divided by the number of links that could possibly exist between them: clustering coefficient – proportion of links between the vertices within its neighbourhood divided by the number of links that could possibly exist between them: Communication Systems, Networks and Digital Signal Processing 2006

16. Outline 1.Network topology model 2.Constrained multicast algorithms 3.Topology generation methods 4.Topology visualization 5.Network parameters 6.Simulation results 7.Conclusions Communication Systems, Networks and Digital Signal Processing 2006

17. Simulation results (m = 10, D av = 4,  = 10) Communication Systems, Networks and Digital Signal Processing 2006

18. Simulation results (n = 100, D av = 4,  = 10) Communication Systems, Networks and Digital Signal Processing 2006

19. Simulation results ( n = 40, m = 10, D av = 4,  = 10) Communication Systems, Networks and Digital Signal Processing 2006

20. Simulation results ( n = 40, m = 10, D av = 4,  = 10) Communication Systems, Networks and Digital Signal Processing 2006

21. Simulation results ( n = 40, m = 10, D av = 4,  = 10) Communication Systems, Networks and Digital Signal Processing 2006

22. Simulation results ( n = 40, m = 10, D av = 4,  = 10) Communication Systems, Networks and Digital Signal Processing 2006

23. Outline 1.Network topology model 2.Constrained multicast algorithms 3.Topology generation methods 4.Topology visualization 5.Network parameters 6.Simulation results 7.Conclusions Communication Systems, Networks and Digital Signal Processing 2006

24. Conclusions Literature shows relationship between topology generation methods and efficiency of routing algorithm.Literature shows relationship between topology generation methods and efficiency of routing algorithm. Representative muticast heuristic algorithms were examined.Representative muticast heuristic algorithms were examined. Algorithms were compared using the same network topologies.Algorithms were compared using the same network topologies. Algorithms comparison using many network parameters – network parameters influence.Algorithms comparison using many network parameters – network parameters influence. Communication Systems, Networks and Digital Signal Processing 2006

25. The Influence of Network Topology on the Efficiency of QoS Multicast Heuristic Algorithms Maciej Piechowiak Piotr Zwierzykowski Poznan University of Technology, Poland Institute of Electronics and Telecommunications CSNDSP '2006

26. KPP algorithm (example) N=(V,E) N 1 =(V 1,E 1 ) for an undirected graph N construct graph N 1, which contains source node s and set of destination nodes G (edges represents cheapest paths between nodes in N)for an undirected graph N construct graph N 1, which contains source node s and set of destination nodes G (edges represents cheapest paths between nodes in N) T 1 =(V 1,E 1 ) find minimum spanning tree T 1 of G 1 for each (u,v) set and cost C(u,v), and delay D(u,v) according to cost function f C :find minimum spanning tree T 1 of G 1 for each (u,v) set and cost C(u,v), and delay D(u,v) according to cost function f C :   10 Communication Systems, Networks and Digital Signal Processing 2006

27. KPP algorithm (example) replace edges of the found tree by paths from the original graph G,replace edges of the found tree by paths from the original graph G, remove loops using Dijkstra algorithm.remove loops using Dijkstra algorithm.   10 N S =(V S,E S ) Communication Systems, Networks and Digital Signal Processing 2006

28. Time complexity algorithm solving routing problem time complexity MOSPFleast-delayO(N log N) KMBleast-delayO(G|N|2)O(G|N|2) KPP delay-constrained least-cost O(|N|3)O(|N|3) CSPT delay-constrained least-cost O(|N| 2 ) / O(N log N)* DCSP delay-constrained least-cost O(K2|N|2)O(K2|N|2) Communication Systems, Networks and Digital Signal Processing 2006