Torpid Mixing of Some Monte Carlo Markov Chain Algorithms in Statistical Physics
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Slow mixing of glauber dynamics via topological obstructions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Sampling independent sets in the discrete torus
Random Structures & Algorithms
Network adiabatic theorem: an efficient randomized protocol for contention resolution
Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems
Back-of-the-Envelope Computation of Throughput Distributions in CSMA Wireless Networks
IEEE Transactions on Mobile Computing
Distributed random access algorithm: scheduling and congestion control
IEEE Transactions on Information Theory
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Performance analysis of the IEEE 802.11 distributed coordination function
IEEE Journal on Selected Areas in Communications
Hardness of Low Delay Network Scheduling
IEEE Transactions on Information Theory
Delays and mixing times in random-access networks
Proceedings of the ACM SIGMETRICS/international conference on Measurement and modeling of computer systems
| Hi-index | 0.00 |
We examine the impact of torpid mixing and meta-stability issues on the delay performance in wireless random-access networks. Focusing on regular meshes as prototypical scenarios, we show that the mean delays in an LxL toric grid with normalized load @r are of the order (11-@r)^L. This superlinear delay scaling is to be contrasted with the usual linear growth of the order 11-@r in conventional queueing networks. The intuitive explanation for the poor delay characteristics is that (i) high load requires a high activity factor, (ii) a high activity factor implies extremely slow transitions between dominant activity states, and (iii) slow transitions cause starvation and hence excessively long queues and delays. Our proof method combines both renewal and conductance arguments. A critical ingredient in quantifying the long transition times is the derivation of the communication height of the uniformized Markov chain associated with the activity process. We also discuss connections with Glauber dynamics, conductance, and mixing times. Our proof framework can be applied to other topologies as well, and is also relevant for the hard-core model in statistical physics and sampling from independent sets using single-site update Markov chains.