Complexity in wireless scheduling: impact and tradeoffs

It has been an important research topic since 1992 to maximize stability region in constrained queueing systems, which includes the study of scheduling over wireless ad hoc networks. In this paper, we propose a framework to study a wide range of existing and future scheduling algorithms and characterize the achieved tradeoffs in stability, delay, and complexity. These characterizations reveal interesting properties hidden in the study of any one or two dimensions in isolation. For example, decreasing complexity from exponential to polynomial, while keeping stability region the same, generally comes at the expense of exponential growth of delays. Investigating trade-offs in the 3-dimensional space allows a designer to fix one dimension and vary the other two jointly. For example, incentives for using scheduling algorithms with only partial throughput-guarantee can be quantified with regards to delay and complexity. Trade-off analysis is then extended to systems with congestion control through utility maximization for non-stabilizable arrival inputs, where the complexity-utility-delay trade-off is shown to be different from the complexity-stability-delay tradeoff. Finally, we analyze more practical models with bounded message size, and consider "effective throughput" which reflects resource occupied by control messages. We show that effective throughput may degrade significantly in certain scheduling algorithms, and suggest a mechanism to avoid this problem in light of the 3D tradeoff framework.

[1]  Koushik Kar,et al.  Achieving 2 / 3 Throughput Approximation with Sequential Maximal Scheduling under Primary Interference Constraints , 2006 .

[2]  Devavrat Shah,et al.  Delay bounds for approximate maximum weight matching algorithms for input queued switches , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[3]  Eytan Modiano,et al.  Dynamic power allocation and routing for time varying wireless networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[4]  Edward W. Knightly,et al.  Distributed Low-Complexity Maximum-Throughput Scheduling for Wireless Backhaul Networks , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[5]  Saikat Ray,et al.  Arbitrary Throughput Versus Complexity Tradeoffs in Wireless Networks Using Graph Partitioning , 2008, IEEE Transactions on Automatic Control.

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

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

[8]  Robert Preis,et al.  Linear Time 1/2-Approximation Algorithm for Maximum Weighted Matching in General Graphs , 1999, STACS.

[9]  Eytan Modiano,et al.  Fairness and optimal stochastic control for heterogeneous networks , 2005, INFOCOM.

[10]  Alessandro Panconesi,et al.  On the Distributed Complexity of Computing Maximal Matchings , 1997 .

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

[12]  Leandros Tassiulas,et al.  Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks , 1990, 29th IEEE Conference on Decision and Control.

[13]  Ness B. Shroff,et al.  Performance of Random Access Scheduling Schemes in Multi-Hop Wireless Networks , 2006, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

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

[15]  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.

[16]  Eytan Modiano,et al.  Tradeoffs in Delay Guarantees and Computation Complexity for Packet Switches NN , 2002 .

[17]  Kyomin Jung,et al.  Low Delay Scheduling in Wireless Network , 2007, 2007 IEEE International Symposium on Information Theory.

[18]  Ness B. Shroff,et al.  The impact of imperfect scheduling on cross-layer rate control in wireless networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[19]  Xiaojun Lin,et al.  Constant-Time Distributed Scheduling Policies for Ad Hoc Wireless Networks , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[20]  Eytan Modiano,et al.  Polynomial Complexity Algorithms for Full Utilization of Multi-Hop Wireless Networks , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[21]  Mung Chiang,et al.  Wireless Scheduling Algorithms with O(1) Overhead for M-Hop Interference Model , 2008, 2008 IEEE International Conference on Communications.

[22]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[23]  Leandros Tassiulas,et al.  Achieving proportional fairness using local information in Aloha networks , 2004, IEEE Transactions on Automatic Control.

[24]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[25]  Prasanna Chaporkar,et al.  Throughput Guarantees Through Maximal Scheduling in Wireless Networks , 2008 .

[26]  Marco Ajmone Marsan,et al.  Bounds on delays and queue lengths in input-queued cell switches , 2003, JACM.