the influence of network topology on the efficiency of qos multicast heuristic algorithms

The Influence of Network TopologyThe Influence of Network Topologyon the Efficiency of QoS Multicaston the Efficiency of QoS MulticastHeuristic AlgorithmsHeuristic Algorithms

Maciej PiechowiakMaciej Piechowiak

Piotr ZwierzykowskiPiotr Zwierzykowski

Poznan University of Technology, PolandPoznan University of Technology, PolandInstitute of Electronics and TelecommunicationsInstitute of Electronics and Telecommunications

CSNDSP '2006CSNDSP '2006

OutlineOutline

1.1. Network topology modelNetwork topology model

2.2. Constrained multicast algorithmsConstrained multicast algorithms

3.3. Topology generation methodsTopology generation methods

4.4. Topology visualizationTopology visualization

5.5. Network parametersNetwork parameters

6.6. Simulation resultsSimulation results

7.7. ConclusionsConclusions

Communication Systems, Networks and Digital Signal Processing 2006Communication Systems, Networks and Digital Signal Processing 2006

Network modelNetwork model

• network is represented by a directed, connected graphnetwork is represented by a directed, connected graph N = N = ((V,EV,E)),, where where VV is a set of nodes and is a set of nodes and EE is a set of is a set of links,links,

• with each linkwith each link ee((u,vu,v) ) EE two parameters are coupled: two parameters are coupled: costcost CC((u,vu,v)) and delayand delay DD((u,vu,v)),,

• multicast group is a set of nodes that are receivers of multicast group is a set of nodes that are receivers of group trafficgroup traffic G = G = {{gg11,...,g,...,gnn} } VV, node , node ss is a source for is a source for

group group GG,,

• multicast tree multicast tree TT((s,Gs,G)) EE is a tree rooted in source node is a tree rooted in source node ss that includes all members of the group that includes all members of the group GG..


Minimum Steiner Tree (MST)Minimum Steiner Tree (MST)

N=N=((V,EV,E))

Steiner tree is a good Steiner tree is a good representation for solving representation for solving multicast routing problem.multicast routing problem.

Finding Steiner tree isFinding Steiner tree is

NPNP-complete problem.-complete problem.

Heuristic algorithms are Heuristic algorithms are most preferable.most preferable.


OutlineOutline









Constrained algorithmsConstrained algorithms

Constrained algorithms compute least cost path (tree) Constrained algorithms compute least cost path (tree) without violating the constraint implied by the upper without violating the constraint implied by the upper bound on delay (bound on delay ().).

,)(min),('

Te

GsTtec

Te

ed )(subject to:subject to:

• KPP algorithm (KPP algorithm (KompellaKompella, , PasqualePasquale, , PolyzosPolyzos),),• CSPT (CSPT (Constrained Shortest Path TreeConstrained Shortest Path Tree),),• LD (LD (Least DelayLeast Delay).).

Representative algorithms:Representative algorithms:


OutlineOutline









Waxman methodWaxman method

Probability of edge betweenProbability of edge between uu and and vv::

dd – – Euclidean distance between node Euclidean distance between node uu and and vv,,

LL – – maximum distance between any two nodes in graphmaximum distance between any two nodes in graph,,

, , – – topology parameterstopology parameters – – an increase in an increase in effects in the increase effects in the increase

in the number of edges; decrease in the number of edges; decrease increases the ratio of the increases the ratio of the

long edges agaist the short ones.long edges agaist the short ones.

1,0


Barabasi methodBarabasi method

Probability that new node Probability that new node uu connects to a node connects to a node vv::

ddVV – degree of a node belonging to the network,– degree of a node belonging to the network,

VV – set of nodes connected to the network,– set of nodes connected to the network,

– – sum of the outdegrees of the nodes previously connected.sum of the outdegrees of the nodes previously connected.

• incremental growth,incremental growth,

• preferential connectivity.preferential connectivity.

features:features:


OutlineOutline









Topology visualizationTopology visualization

WAXMANWAXMAN BARABASIBARABASI

nn = 100,= 100, kk = 200,= 200, HSHS = 400= 400

SVG graph visualization:SVG graph visualization:

www.svg.teletraffic.plwww.svg.teletraffic.pl


OutlineOutline









Networks parametersNetworks parameters

• number of nodes – number of nodes – nn, number of links – , number of links – kk,,

• average node degree (average node degree (DDavav),),

• diameterdiameter – length of the longest shortest-path between any two – length of the longest shortest-path between any two nodes,nodes,

• hop-diameter hop-diameter – shortest paths are computed using – shortest paths are computed using hop countshop counts metric,metric,

• length-diameterlength-diameter – shortest paths are computed using Euclidean – shortest paths are computed using Euclidean distancedistance metric,metric,


Networks parametersNetworks parameters

((vv)) – neighbourhod of – neighbourhod of vv, , kkvv – outdegrees of node – outdegrees of node vv,,

• average clustering coefficient,average clustering coefficient,

• number of multicast nodes – number of multicast nodes – mm..

• clustering coefficientclustering coefficient – – proportionproportion of links between the verticesof links between the vertices within its neighbourhoodwithin its neighbourhood divided by the number of links that coulddivided by the number of links that could possibly exist between thempossibly exist between them::


OutlineOutline









Simulation resultsSimulation results

((mm = 10, = 10, DDavav = 4, = 4, = 10) = 10)



((nn = 100, = 100, DDavav = 4, = 4, = 10) = 10)



((nn = 40,= 40, mm = 10, = 10, DDavav = 4, = 4, = 10) = 10)


OutlineOutline









ConclusionsConclusions

• Literature shows relationship between topology Literature shows relationship between topology generation methods and efficiency of routing algorithm.generation methods and efficiency of routing algorithm.

• Representative muticast heuristic algorithms were Representative muticast heuristic algorithms were examined.examined.

• Algorithms were compared using the same network Algorithms were compared using the same network topologies.topologies.

• Algorithms comparison using many network parameters Algorithms comparison using many network parameters – network parameters influence.– network parameters influence.


The Influence of Network TopologyThe Influence of Network Topologyon the Efficiency of QoS Multicaston the Efficiency of QoS MulticastHeuristic AlgorithmsHeuristic Algorithms

Maciej PiechowiakMaciej Piechowiak

Piotr ZwierzykowskiPiotr Zwierzykowski

Poznan University of Technology, PolandPoznan University of Technology, PolandInstitute of Electronics and TelecommunicationsInstitute of Electronics and Telecommunications

CSNDSP '2006CSNDSP '2006

KPP algorithm (example)KPP algorithm (example)

N=N=((V,EV,E))

NN11==((VV11,E,E11))

• for an undirected graph for an undirected graph NN construct graph construct graph NN11, which contains source , which contains source node node ss and set of destination nodes and set of destination nodes GG (edges represents cheapest (edges represents cheapest paths between nodes in paths between nodes in NN))

TT11==((VV11,E,E11))

• find minimum spanning tree find minimum spanning tree TT11 of of

GG11 for each for each ((u,vu,v)) set and cost set and cost

CC((u,vu,v),), and delay and delay DD((u,vu,v)) according to cost function according to cost function ffCC::

1010


KPP algorithm (example)KPP algorithm (example)

• replace edges of the found tree by paths from the replace edges of the found tree by paths from the original graph original graph GG,,

• remove loops using Dijkstra algorithm.remove loops using Dijkstra algorithm.

1010

NNSS==((VVSS,E,ESS))


Time complexityTime complexity

algorithmalgorithm solving routing solving routing problemproblem time complexitytime complexity

MOSPFMOSPF least-delay O(N log N)

KMBKMB least-delay O(G|N|2)

KPPKPPdelay-constrained

least-costO(|N|3)

CSPTCSPTdelay-constrained

least-costO(|N|2) / O(N log N)*

DCSPDCSPdelay-constrained

least-costO(K2|N|2)


the influence of network topology on the efficiency of qos multicast heuristic algorithms

Documents

digital signal processing

node v

v set of nodes

multicast group

multicast tree ts

topology parameters

esteiner tree

group g