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

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

3. 1. Introduction

4. Multi-hop Networks in the Future

5. Optimal Resource Allocation in multi-hop networks

6. Research Roadmap

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. 3. RPC (Random Peak and Compare)

11. 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)

12. Characteristic of RPC • Method of reducing complexity of MW scheduling • Solve this NP problem → Pick the random S’ • Reduce the complexity • 추후 그림 삽입 • → 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 schedule with polynomial time complexity

13. Complexity, Delay Tradeoff • If γ=1, throughput region of RPC is exactly same as throughput region of MW with polynomial complexity • RPC is a method of infrequent computation of optimal schedule • 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

14. 4. GMM(Greedy Maximal Matching)

18. 5. Conclusion

19. MW, RPC, and GMM

20. 3-D Tradeoff • 간략적인 설명 및 그림

21. 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., SchroffN.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.

22. Thank You!