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The Influence of Network Topology on the Efficiency of QoS Multicast Heuristic Algorithms

CSNDSP '2006. 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. Outline. Network topology model

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The Influence of Network Topology on the Efficiency of QoS Multicast Heuristic Algorithms

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

  2. Outline • Network topology model • Constrained multicast algorithms • Topology generation methods • Topology visualization • Network parameters • Simulation results • Conclusions Communication Systems, Networks and Digital Signal Processing 2006

  3. Outline • Network topology model • Constrained multicast algorithms • Topology generation methods • Topology visualization • Network parameters • Simulation results • Conclusions Communication Systems, Networks and Digital Signal Processing 2006

  4. Network model • network is represented by a directed, connected graphN = (V,E),where V is a set of nodes and E is a set of links, • with each linke(u,v)  Etwo parameters are coupled: costC(u,v)and delayD(u,v), • multicast group is a set of nodes that are receivers of group trafficG = {g1,...,gn}  V, node s is a source for group G, • multicast tree T(s,G) Eis 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 • Network topology model • Constrained multicast algorithms • Topology generation methods • Topology visualization • Network parameters • Simulation results • 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: Representative algorithms: • KPP algorithm (Kompella, Pasquale, Polyzos), • CSPT (Constrained Shortest Path Tree), • LD (Least Delay). Communication Systems, Networks and Digital Signal Processing 2006

  8. Outline • Network topology model • Constrained multicast algorithms • Topology generation methods • Topology visualization • Network parameters • Simulation results • Conclusions Communication Systems, Networks and Digital Signal Processing 2006

  9. Waxman method • Probability of edge betweenuand 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: dV– 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. features: • incremental growth, • preferential connectivity. Communication Systems, Networks and Digital Signal Processing 2006

  11. Outline • Network topology model • Constrained multicast algorithms • Topology generation methods • Topology visualization • Network parameters • Simulation results • Conclusions Communication Systems, Networks and Digital Signal Processing 2006

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

  13. Outline • Network topology model • Constrained multicast algorithms • Topology generation methods • Topology visualization • Network parameters • Simulation results • Conclusions Communication Systems, Networks and Digital Signal Processing 2006

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

  15. Networks parameters • clustering coefficient – proportionof links between the verticeswithin its neighbourhooddivided by the number of links that couldpossibly exist between them: (v) – neighbourhod of v, kv – outdegrees of node v, • average clustering coefficient, • number of multicast nodes – m. Communication Systems, Networks and Digital Signal Processing 2006

  16. Outline • Network topology model • Constrained multicast algorithms • Topology generation methods • Topology visualization • Network parameters • Simulation results • Conclusions Communication Systems, Networks and Digital Signal Processing 2006

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

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

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

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

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

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

  23. Outline • Network topology model • Constrained multicast algorithms • Topology generation methods • Topology visualization • Network parameters • Simulation results • Conclusions Communication Systems, Networks and Digital Signal Processing 2006

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

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

  26. N1=(V1,E1) • for an undirected graph N construct graph N1, which contains source node s and set of destination nodes G (edges represents cheapest paths between nodes in N) KPP algorithm (example) N=(V,E) T1=(V1,E1)   10 • find minimum spanning tree T1 of G1 for each (u,v) set and cost C(u,v), and delay D(u,v) according to cost function fC: Communication Systems, Networks and Digital Signal Processing 2006

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

  28. Time complexity Communication Systems, Networks and Digital Signal Processing 2006

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