1 / 23

QoS Routing

QoS Routing. Hanoch Levy March 2001. b. source. Destination. f. c. e. What is Routing. Need to find a route from source to destination. Single Objective Routing. b. Assign certain weights (additive, typically, hopefully) to edges of graph.

xannon
Download Presentation

QoS Routing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. QoS Routing Hanoch Levy March 2001 Hanoch Levy, CS, TAU

  2. b source Destination f c e What is Routing Need to find a route from source to destination Hanoch Levy, CS, TAU

  3. Single Objective Routing b • Assign certain weights (additive, typically, hopefully) to edges of graph. • Find “shortest” route from source to destination (the route for which the SUM of weights is minimal). S f D e c Hanoch Levy, CS, TAU

  4. 12 b S 10 D f 4 6 5 7 c e 5 1. Shortest hop-count: S-b-D = 2 2. Shortest edge length: S-c-e-D = 17 Hanoch Levy, CS, TAU

  5. Marks are delay over edge: Delay is additive Yields minimum delay path Marks are edge costs: Cost is additive Yields minimum cost path 12 b S 10 D f 4 6 5 7 c e 5 Use of Single objective Routing to achieve certain QoS Hanoch Levy, CS, TAU

  6. Marks are jitter over edge: Jitter is additive? Depends on definition E.g. – if jitter is max delay difference between neighboring packets: additive. Yields minimum jitter path (if additive) 12 b S 10 D f 4 6 5 7 c e 5 Use of Single objective Routing to achieve certain QoS Hanoch Levy, CS, TAU

  7. Marks are available bandwidth over edge: Is Bandwidth additive? No But: is subject to MIN operation and can fit under this transformation to algorithms . Yields Maximum bandwidth path 12 b S 10 D f 4 6 5 7 c e 5 Use of Single objective Routing to achieve certain QoS Hanoch Levy, CS, TAU

  8. Marks are Probability of loss over edge: Is loss additive? No Multiplicative: 1-L=(1-L1)(1-L2) Log is additive (or, can modify algorithm to deal with products) If loss is small, approximately additive Can use algorithm for Minimal loss path. 12 b S 10 D f 4 6 5 7 c e 5 Use of Single objective Routing to achieve certain QoS Hanoch Levy, CS, TAU

  9. Put all nodes in not-finalized with distance infinity. Distance (S)  0. vS Add v to finalized For all edges e from v to u (u in not) do: Update distance(u) using MIN operation. Select minimal weight node in not-finalized, denote it v, and go to 4. 12 b S 10 D f 4 6 5 7 c e 5 Dijkstra’s Algorithm Hanoch Levy, CS, TAU

  10. Works for non-negative weights. Complexity 1: Updating all edges : O(E) Finding MIN, V times: Complexity 2: Implement binary heap: Complexity 3: Implement Fibonacci Heap All operations but deletemin are in O(1) amortized. Thus: 12 b S 10 D f 4 6 5 7 c e 5 Dijkstra’s Algorithm: properties Hanoch Levy, CS, TAU

  11. Centralized algorithm in nature Hard to distribute. Result is shortest path from S to D With a little more effort (and same worst case) – get shortest path from S to ALL. 12 b S 10 D f 4 6 5 7 c e 5 Dijkstra’s Algorithm: properties (cont) Hanoch Levy, CS, TAU

  12. BellMan Ford Algorithm • Algorithm Bellman Ford: • For i=1 to |V| do • For each edge (v,u) do relax(u,v) • End • Relax:= d(u) := min { d(u), d(v) + w((v,u))} Hanoch Levy, CS, TAU

  13. BellMan Ford Algorithm: Properties • Complexity: O(VE) • Can conduct in a distributed mode on a graph: • Each node u performs: • For each edge e=v  u do: d(u):=min {d(u), d(v)+w(e)} • Distributed algorithms for network routing based on BF. Hanoch Levy, CS, TAU

  14. Multi Constraint Routing • Two weight functions, w1, w2. • Problem: Find a path from S to D such that • Problem is NP complete • Heuristic solution in polynomial time Hanoch Levy, CS, TAU

  15. Heuristic Solution • Due to: S. Chen, K.Nahrstedt, 1998, “On Finding Multi-Constrained Paths”, IEEE ICC ’98, June 1998. • Problem Transformation: Make the second weight discrete: W2 can get only discrete values. • Example: weights are only the integers. Costs in whole dollars. • Note: practically it affects problem very little (depending on GRANULRITY of weights). • Theorem 1: A solution to transformed problem is a solution to original problem. • Reverse: If no solution found to transformed problem, there may exist a solution to the original problem. Hanoch Levy, CS, TAU

  16. We have two objectives: D1, D2. During the algorithm each node is marked with two distances : (d1, d2). D1 is continuous while D2 is discrete with g values. Each real node v is represented by g virtual nodes, one for each value of the 2nd distance. We mark this node (v, g). Initially we set D(v,g) = infinity. Put all nodes (v,g) in not-finalized. 6. D (S, 0)  0. 7. (v,g) (S,0) Add (v,g) to finalized For all edges e from v to u do: Consider the node (u, g+g’) where g’ is the second weight of the edge e. Update the distance of (u, g+g’) to: Min {D(v,g) +D(e), D(u,g+g’} Select minimal weight node in not-finalized, denote it (v,g), and go to 8. Approach of Solution (Dijkstra version) Hanoch Levy, CS, TAU

  17. 12 12 12 b b b S S S 10 10 10 D D D f f f 4 4 4 6 6 6 5 5 5 7 7 7 e e e c c c 5 5 5 Approach of Solution (Dijkstra version): cont 0 1 2 Hanoch Levy, CS, TAU

  18. Put all nodes in not-finalized with distance infinity. Distance (S)  0. vS Add v to finalized For all edges e from v to u (u in not) do: Generate a new node (u,g) where distance is sum of distances and g is sum of constraints.Update distance(u) using MIN operation Select minimal weight node in not-finalized, denote it v, and go to 4. 12 b S 10 D f 4 6 5 7 e c 5 Approach of Solution (Dijkstra version) Hanoch Levy, CS, TAU

  19. Complexity of Solution • Time Complexity: • Where g= granularity of constraint (the number of different values the constraint can get). • If Fibonacci heap is used: Hanoch Levy, CS, TAU

  20. BellMan Ford Version • Use a similar approach (“virtual nodes at g layers) and run BF on it. • Time Complexity: • Where g= granularity of constraint (the number of different values the constraint can get). Hanoch Levy, CS, TAU

  21. Lagrange Relaxation Based Method for the QoSRouting Problem • Alp´ar J¨uttner, Bal´azs Szviatovszki, Ildik´o M´ecs, Zsolt Rajk’o, INFOCOM 2001 • Consider the one objective to be minimized (cost) and one constraint (delay) to be met. • Each edge has two weights w1(e) and w2(e). • Want to minimize the two objectives (or minimize one while constraining the other). • Approach : consider an objective function of linear sum of the two: w1 + w2. will be variable. • For given , run Dijkstra and find shortest route. • If w2 constraint is met: OK. Done. • Otherwise: decrease x and go back to 4. Hanoch Levy, CS, TAU

  22. Lagrange Relaxation :cont • Procedure LARAC (s=source,t=tar,c=cost,d=delay,Ddel=max delay) • Pc:=Dijkstra (s,t,c) /* path of min cost */ • If d(Pc) < Ddel then return Pc /* if legal – done */ • Pd:=Dijkstra (s,t,d) /* path on min delay */ • If d(Pd) > Ddel then return (“no solution”) /* not ok -> no chance */ • Repeat • Lam:= {c(Pc)-c(Pd)}/{d(Pd)-d(Pc)} /* diff(cost)/diff(delay) */ • r:= Dijkstra (s,t, Clam) /* Clam = c+ lam * d • If Clam(r) = Clam (Pc) then return Pd:=r • Else if d(r) < Ddel then Pd:= r • Else Pc:=r • End repeat • End procedure Hanoch Levy, CS, TAU

  23. References • S. Chen, K.Nahrstedt, 1998, “An Overview of Quality-of-Service Routing for the next generation High-Speed Networks: Problems and Solutions”, IEEE Network, Special Issue on Transmission and Distribution of Digital Video, Nov./Dec. 1998 • S. Chen, K.Nahrstedt, 1998, “On Finding Multi-Constrained Paths”, IEEE ICC ’98, June 1998. • T. H. Cormen, C. E. Leiserson, R. L. Rivest, 1995, “Introduction To Algorithms”, MIT Press. • H. de Neve, P. van Meighem, 2000, “TAMCRA: Tunable Accuracy Multiple Constraints Routing Algorithm”, Computer Communications, 23:667-679. • R Guerin, A. Orda, 1997, “QoS-Based Routing in Networks with Inaccurate Information: theory and Algorithms”, IEEE INFOCOM ’97, Japan, April 1997. • Alp´ar J¨uttner, Bal´azs Szviatovszki, Ildik´o M´ecs, Zsolt Rajk’o, “Lagrange Relaxation Based Method for the QoS Routing Problem”, IEEE INFOCOM’ 2001. Hanoch Levy, CS, TAU

More Related