Understanding the capacity region of the Greedy maximal scheduling algorithm in multihop wireless networks

In this paper, we characterize the performance of an important class of scheduling schemes, called greedy maximal scheduling (GMS), for multihop wireless networks. While a lower bound on the throughput performance of GMS has been well known, empirical observations suggest that it is quite loose and that the performance of GMS is often close to optimal. In this paper, we provide a number of new analytic results characterizing the performance limits of GMS. We first provide an equivalent characterization of the efficiency ratio of GMS through a topological property called the local-pooling factor of the network graph. We then develop an iterative procedure to estimate the local-pooling factor under a large class of network topologies and interference models. We use these results to study the worst-case efficiency ratio of GMS on two classes of network topologies. We show how these results can be applied to tree networks to prove that GMS achieves the full capacity region in tree networks under the K-hop interference model. Then, we show that the worst-case efficiency ratio of GMS in geometric unit-disk graphs is between 1/6 and 1/3.

[1]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[2]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[3]  Alon Itai,et al.  A Fast and Simple Randomized Parallel Algorithm for Maximal Matching , 1986, Inf. Process. Lett..

[4]  Bruce E. Hajek,et al.  Link scheduling in polynomial time , 1988, IEEE Trans. Inf. Theory.

[5]  Dimitri P. Bertsekas,et al.  Data networks (2nd ed.) , 1992 .

[6]  Leandros Tassiulas,et al.  Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks , 1992 .

[7]  J. Dai.  On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models , 1995 .

[8]  Nick McKeown,et al.  Scheduling algorithms for input-queued cell switches , 1996 .

[9]  Leandros Tassiulas,et al.  Linear complexity algorithms for maximum throughput in radio networks and input queued switches , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[10]  Marco Ajmone Marsan,et al.  On the stability of input-queued switches with speed-up , 2001, TNET.

[11]  Eytan Modiano,et al.  Power allocation and routing in multibeam satellites with time-varying channels , 2003, TNET.

[12]  Rene L. Cruz,et al.  Optimal routing, link scheduling and power control in multihop wireless networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[13]  Leandros Tassiulas,et al.  End-to-end bandwidth guarantees through fair local spectrum share in wireless ad-hoc networks , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[14]  Jaap-Henk Hoepman,et al.  Simple Distributed Weighted Matchings , 2004, ArXiv.

[15]  Aravind Srinivasan,et al.  End-to-end packet-scheduling in wireless ad-hoc networks , 2004, SODA '04.

[16]  Madhav V. Marathe,et al.  The distance-2 matching problem and its relationship to the MAC-Layer capacity of ad hoc wireless networks , 2004, IEEE Journal on Selected Areas in Communications.

[17]  Aravind Srinivasan,et al.  Algorithmic aspects of capacity in wireless networks , 2005, SIGMETRICS '05.

[18]  R. Srikant,et al.  Scheduling Efficiency of Distributed Greedy Scheduling Algorithms in Wireless Networks , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[19]  Eytan Modiano,et al.  Enabling distributed throughput maximization in wireless mesh networks: a partitioning approach , 2006, MobiCom '06.

[20]  Eytan Modiano,et al.  Maximizing throughput in wireless networks via gossiping , 2006, SIGMETRICS '06/Performance '06.

[21]  Ness B. Shroff,et al.  Performance of Random Access Scheduling Schemes in Multi-hop Wireless Networks , 2006 .

[22]  Xiaojun Lin,et al.  The impact of imperfect scheduling on cross-Layer congestion control in wireless networks , 2006, IEEE/ACM Transactions on Networking.

[23]  Ness B. Shroff,et al.  On the Complexity of Scheduling in Wireless Networks , 2006, MobiCom '06.

[24]  Xiaojun Lin,et al.  Constant-Time Distributed Scheduling Policies for Ad Hoc Wireless Networks , 2006, CDC.

[25]  J. Walrand,et al.  Sufficient conditions for stability of longest-queue-first scheduling: second-order properties using fluid limits , 2006, Advances in Applied Probability.

[26]  R. Srikant,et al.  Low-Complexity Distributed Scheduling Algorithms for Wireless Networks , 2007, INFOCOM.

[27]  Ness B. Shroff,et al.  Performance limits of greedy maximal matching in multi-hop wireless networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[28]  Csaba D. Tóth,et al.  Improved Throughput Bounds for Interference-Aware Routing in Wireless Networks , 2007, COCOON.

[29]  E. Modiano,et al.  Distributed Throughput Maximization in Wireless Mesh Networks via Pre-Partitioning , 2008, IEEE/ACM Transactions on Networking.

[30]  Koushik Kar,et al.  Throughput and Fairness Guarantees Through Maximal Scheduling in Wireless Networks , 2008, IEEE Transactions on Information Theory.

[31]  Eytan Modiano,et al.  Multihop Local Pooling for Distributed Throughput Maximization in Wireless Networks , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[32]  Ness B. Shroff,et al.  Understanding the Capacity Region of the Greedy Maximal Scheduling Algorithm in Multihop Wireless Networks , 2008, IEEE/ACM Transactions on Networking.

[33]  R. Srikant,et al.  Distributed Link Scheduling With Constant Overhead , 2006, IEEE/ACM Transactions on Networking.

[34]  Ness B. Shroff,et al.  On the Complexity of Scheduling in Wireless Networks , 2010, EURASIP J. Wirel. Commun. Netw..