Low Complexity MAC Scheduling Algorithms with Performance Guarantee

1. Low Complexity MAC Scheduling Algorithms with Performance Guarantee Soohwan Lee EE, KAIST shlee@lanada.kaist.ac.kr Hyeon-je Cho Math, KAIST geniijhj@gmail.com TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

2. Contents • 1. Introduction • 2. System model • 3. MW (Max-Weight) • 4. GMM (Greedy Maximal Matching) • 5. RPC (Random Peak and Compare) • 6. Conclusion

3. 1. Introduction

4. Scheduling in Multi-hop Networks

5. Optimal Resource Allocation in multi-hop networks

6. Research Roadmap • Max-Weight(L. Tassiulas 1992) • RPC(L. Tassiulas 1998) • Maximal(Dai J.G. 2000, P.Chaporkar 2005) • Greedy(X.Lin 2005) • 3D Trade-off(Y. Yi 2008) Max-Weight RPC Maximal Greedy Gossip Trade-Off 1992 1998 2000 2005 2006 2008

7. 2. System Model

8. Network and Traffic Model • Network model • Single-hop wireless network (for focusing on scheduling) • K - hop interference model • Each link has own queue : Ql (t) • Queuing dynamics • Traffic model • Assume that unsaturated system, • E[Al (t)] = ¸l • Arrival vector : ¸ = (¸1,…,¸L) 2¤ ,where ¤ is throughput region

9. Performance Metric • Objective • Throughput maximization (unsaturated system) • Utility maximization (saturated system) • Optimal algorithm : • Throughput maximization • Max-differential backlog routing + MW scheduling • Utility maximization • Congestion control + Max-differential backlog routing + MW scheduling where R: routing vector, x : source rate vector, c: link capacity vector

10. Performance Metric • Stability • Delay : sum of the stationary queue length • Complexity : the number of basic operation (step, round)

11. 3. MW (Maximum Weigth)

12. MW(Maximum Weight) • TassilulasEphremides 1992 • The max-weight algorithm is choosing the S*(t) at each slot t: • S : Set of feasible schedules • Throughput-optimal, Maximum stability region • General yet complex. How to make it simple and distributed?

13. 4. GMM(Greedy Maximal Matching)

14. Maximal & Greedy • One natural way of complexity reduction is to take approximation of original algorithm to have polynomial time complexity algorithm approximate MW in terms of weight at each slot. • Algorithm • Step 1. Start with an empty schedule and a set • Step 2. Choose a link in the following manner, and remove from the links interfering with link • Maximal : a random link , • Greedy : the link that has a largest queue length • Step3. repeat Step 2. until is empty

15. Maximal & Greedy • Example of these algorithms using conflict graph • Maximal : a random link • Greedy : the link that has the largest queue length (*) Figure from WiOPT2009 keynote presentation by Prof. Mung Chiang

16. Characteristic of Maximal, Greedy • The best complexity of maximal, greedy algorithms for the one-hop interference model • Maximal : • Greedy : • Throughput region (Stability) • Maximal : achieve 1/2 of the throughput region in the worst case. • Greedy : guarantee 1/2 of the weight from MW at each slot. • The two algorithms are equivalent in terms of worst-case throughput performance.

17. 5. RPC (Random Peak and Compare)

18. RPC (Random Pick and Compare) • Key idea • For the complexity reduction of MW scheduling,compute optimal schedules infrequently • Algorithm • At each time slot, • Step 1: Generate the random schedule S’(t) satisfying C1 • Step 2: Schedule S(t) defined in C2 • C1: (Pick) There is a 0 < δ· 1 s.t. P[S’(t) = S|Q(t)] ¸δ, for some schedule S, where W(S) ¸γW*(t), γ> 0 • C2: (Compare) S(t) = argmaxS={S(t-1),S’(t)}W(S)

19. Characteristic of RPC • Method of reducing complexity of MW scheduling • Solve this NP problem → Pick the random S’ • Reduce the complexity • → Compare to previous S(t-1) and selectS(t) which has larger weight • Tracking the optimal scheduling with long term time scale: infrequently solve • RPC can achieve γ-optimal stability with polynomial time complexity

20. Complexity, Delay Tradeoff • If γ=1, throughput region of RPC is exactly same as throughput region of MW with polynomial complexity • Because throughput region ¤is defined by long term time scale • But, infrequent computation of optimal schedule involves delay • RPC tracks the optimal scheduling with long term time scale so, it is obvious • In conclusion, RPC pays the delay for reducing complexity • Tradeoff between complexity and delay

21. 5. Conclusion

22. MW, RPC, and GMM • MW • Optimal resource allocation algorithm • RPC • Infrequently solve algorithm • Complexity-delay trade off • GMM • Weight approximation algorithm • Stability-complexity trade off

23. 3-D Tradeoff • Future algorithm • Mixture GMM and RPC algorithm • Trade-off between performance and implementation complexity complexity O(2L) O(2L) MW MW Many other future algorithms Greedy Greedy delay O(2L) RPC RPC 1 1 Stability Stability

24. Reference • [1] Tassiulas L., Ephremides A., Stability properties of constrained queuing systems and scheduling policies for maximum throughput in multihop radio networks, Vol. 37, No. 12., December 1992, IEEE Transaction on Automatic Control. • [2] Tassiulas L., Linear complexity algorithms for maximum throughput in radio networks and input queued switched, In Proceedings of IEEE Infocom. • [3] Lin X., Ness B., The impact of imperfect scheduling on cross-layer rate control in wireless networks, • [4] Georgiadis L. et al,. Resource allocation and cross layer control in wire- less networks, Vol. 1, No. 1, Foundations and Trends in Networking. • [5] Shedon M. Ross, Stochastic process, second edition, John Wiley&Sons, Inc. • [6] Lin X., Schroff N.B., The impact of imperfect scheduling on corss-layer rate control in wireless networks. • [7] Yi Y., Proutiere A., Chiang M.(2008), Complexity in wireless scheduling: Impact and tradeoffs, In proceedings of ACM Mobihoc.

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