CSMA Using the Bethe Approximation: Scheduling and Utility Maximization

Carrier sense multiple access (CSMA), which resolves contentions over wireless networks in a fully distributed fashion, has recently gained a lot of attentions since it has been proved that appropriate control of CSMA parameters guarantees optimality in terms of stability (i.e., scheduling) and system-wide utility (i.e., scheduling and congestion control). Most CSMA-based algorithms rely on the popular Markov chain Monte Carlo technique, which enables one to find optimal CSMA parameters through iterative loops of simulation-and-update. However, such a simulation-based approach often becomes a major cause of exponentially slow convergence, being poorly adaptive to flow/topology changes. In this paper, we develop distributed iterative algorithms which produce approximate solutions with convergence in polynomial time for both stability and utility maximization problems. In particular, for the stability problem, the proposed distributed algorithm requires, somewhat surprisingly, only one iteration among links. Our approach is motivated by the Bethe approximation (introduced by Yedidia, Freeman, and Weiss) allowing us to express approximate solutions via a certain nonlinear system with polynomial size. Our polynomial convergence guarantee comes from directly solving the nonlinear system in a distributed manner, rather than multiple simulation-and-update loops in existing algorithms. We provide numerical results to show that the algorithm produces highly accurate solutions and converges much faster than the prior ones.

[1]  Yung Yi,et al.  Learning contention patterns and adapting to load/topology changes in a MAC scheduling algorithm , 2006, 2006 2nd IEEE Workshop on Wireless Mesh Networks.

[2]  Devavrat Shah,et al.  Counting Independent Sets Using the Bethe Approximation , 2011, SIAM J. Discret. Math..

[3]  Jinsung Lee,et al.  Implementing utility-optimal CSMA , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[4]  Jinwoo Shin,et al.  Provable per-link delay-optimal CSMA for general wireless network topology , 2014, IEEE INFOCOM 2014 - IEEE Conference on Computer Communications.

[5]  Jean C. Walrand,et al.  Distributed Random Access Algorithm: Scheduling and Congestion Control , 2009, IEEE Transactions on Information Theory.

[6]  Petar Djukic,et al.  Scheduling algorithms for tdma wireless multihop networks , 2008 .

[7]  Devavrat Shah,et al.  Randomized Scheduling Algorithm for Queueing Networks , 2009, ArXiv.

[8]  Jinsung Lee,et al.  Making 802.11 DCF Near-Optimal: Design, Implementation, and Evaluation , 2016, IEEE/ACM Transactions on Networking.

[9]  Jinwoo Shin,et al.  CSMA over time-varying channels: optimality, uniqueness and limited backoff rate , 2013, MobiHoc '13.

[10]  Mung Chiang,et al.  Stochastic network utility maximisation - a tribute to Kelly's paper published in this journal a decade ago , 2008, Eur. Trans. Telecommun..

[11]  Sangwoo Moon,et al.  A-DCF: Design and implementation of delay and queue length based wireless MAC , 2015, 2015 IEEE Conference on Computer Communications (INFOCOM).

[12]  Sem C. Borst,et al.  Delay performance in random-access networks , 2014, Queueing Syst. Theory Appl..

[13]  Devavrat Shah,et al.  Medium Access Using Queues , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

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

[15]  Jean C. Walrand,et al.  Fast Mixing of Parallel Glauber Dynamics and Low-Delay CSMA Scheduling , 2010, IEEE Transactions on Information Theory.

[16]  Jinwoo Shin,et al.  Optimal CSMA: A survey , 2012, 2012 IEEE International Conference on Communication Systems (ICCS).

[17]  R. Srikant,et al.  The Impact of Access Probabilities on the Delay Performance of Q-CSMA Algorithms in Wireless Networks , 2013, IEEE/ACM Transactions on Networking.

[18]  William T. Freeman,et al.  Constructing free-energy approximations and generalized belief propagation algorithms , 2005, IEEE Transactions on Information Theory.

[19]  Jiaping Liu,et al.  Towards utility-optimal random access without message passing , 2010, CMC 2010.

[20]  Simone Merlin Cross-layer design in wireless networks , 2008 .

[21]  Michael I. Jordan,et al.  Loopy Belief Propagation for Approximate Inference: An Empirical Study , 1999, UAI.

[22]  George N. Rouskas,et al.  Next-Generation Internet Architectures and Protocols: Network architectures , 2011 .

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

[24]  Jean C. Walrand,et al.  Fair end-to-end window-based congestion control , 2000, TNET.

[25]  Jinsung Lee,et al.  Experimental evaluation of optimal CSMA , 2011, 2011 Proceedings IEEE INFOCOM.

[26]  Alexandre Proutière,et al.  Simulation-based optimization algorithms with applications to dynamic spectrum access , 2012, 2012 46th Annual Conference on Information Sciences and Systems (CISS).

[27]  R. Srikant,et al.  A tutorial on cross-layer optimization in wireless networks , 2006, IEEE Journal on Selected Areas in Communications.

[28]  Soung Chang Liew,et al.  Applications of Belief Propagation in CSMA Wireless Networks , 2012, IEEE/ACM Transactions on Networking.

[29]  Jean C. Walrand,et al.  Approaching Throughput-Optimality in Distributed CSMA Scheduling Algorithms With Collisions , 2010, IEEE/ACM Transactions on Networking.

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

[31]  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.

[32]  Venkat Chandrasekaran,et al.  Complexity of Inference in Graphical Models , 2008, UAI.

[33]  Yung Yi,et al.  From Glauber dynamics to Metropolis algorithm: Smaller delay in optimal CSMA , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.