The Impact of Access Probabilities on the Delay Performance of Q-CSMA Algorithms in Wireless Networks

It has been recently shown that queue-based carrier sense multiple access (CSMA) algorithms are throughput-optimal. In these algorithms, each link of the wireless network has two parameters: a transmission probability and an access probability. The transmission probability of each link is chosen as an appropriate function of its queue length, however the access probabilities are simply regarded as some random numbers since they do not play any role in establishing the network stability. In this paper, we show that the access probabilities control the mixing time of the CSMA Markov chain and, as a result, affect the delay performance of the CSMA. In particular, we derive formulas that relate the mixing time to access probabilities and use these to develop the following guideline for choosing access probabilities: Each link i should choose its access probability equal to 1/(di+1), where di is the number of links that interfere with link i. Simulation results show that this choice of access probabilities results in good delay performance.

[1]  John Odentrantz,et al.  Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues , 2000, Technometrics.

[2]  Jean C. Walrand,et al.  A Distributed CSMA Algorithm for Throughput and Utility Maximization in Wireless Networks , 2010, IEEE/ACM Transactions on Networking.

[3]  R. Srikant,et al.  Stable scheduling policies for fading wireless channels , 2005, IEEE/ACM Transactions on Networking.

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

[5]  Jian Ni,et al.  On the achievable throughput of CSMA under imperfect carrier sensing , 2011, 2011 Proceedings IEEE INFOCOM.

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

[7]  Murat Alanyali,et al.  Delay performance of CSMA in networks with bounded degree conflict graphs , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[8]  Jian Ni,et al.  Q-CSMA: Queue-Length Based CSMA/CA Algorithms for Achieving Maximum Throughput and Low Delay in Wireless Networks , 2010, INFOCOM 2010.

[9]  W. Marsden.  I and J , 2012 .

[10]  Koushik Kar,et al.  Throughput modelling and fairness issues in CSMA/CA based ad-hoc networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[11]  Patrick Thiran,et al.  A Packing Approach to Compare Slotted and Non-Slotted Medium Access Control , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[12]  Jian Ni,et al.  Improved bounds on the throughput efficiency of greedy maximal scheduling in wireless networks , 2011, TNET.

[13]  Mark Jerrum,et al.  Approximating the Permanent , 1989, SIAM J. Comput..

[14]  Ness B. Shroff,et al.  The impact of imperfect scheduling on cross-Layer congestion control in wireless networks , 2006, IEEE/ACM Transactions on Networking.

[15]  Soung Chang Liew,et al.  Back-of-the-Envelope Computation of Throughput Distributions in CSMA Wireless Networks , 2007, 2009 IEEE International Conference on Communications.

[16]  Devavrat Shah,et al.  Network adiabatic theorem: an efficient randomized protocol for contention resolution , 2009, SIGMETRICS '09.

[17]  A. Girotra,et al.  Performance Analysis of the IEEE 802 . 11 Distributed Coordination Function , 2005 .

[18]  Dana Randall,et al.  Rapidly mixing Markov chains with applications in computer science and physics , 2006, Computing in Science & Engineering.

[19]  R. Srikant,et al.  On the design of efficient CSMA algorithms for wireless networks , 2010, 49th IEEE Conference on Decision and Control (CDC).

[20]  Peter Marbach,et al.  Throughput-optimal random access with order-optimal delay , 2010, 2011 Proceedings IEEE INFOCOM.

[21]  Basil S. Maglaris,et al.  Throughput Analysis in Multihop CSMA Packet Radio Networks , 1987, IEEE Trans. Commun..

[22]  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.

[23]  Michele Garetto,et al.  Modeling per-flow throughput and capturing starvation in CSMA multi-hop wireless networks , 2008, TNET.

[24]  D. Vere-Jones.  Markov Chains , 1972, Nature.

[25]  Patrick Thiran,et al.  Modeling the 802.11 Protocol Under Different Capture and Sensing Capabilities , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[26]  John N. Tsitsiklis,et al.  Hardness of Low Delay Network Scheduling , 2011, IEEE Transactions on Information Theory.