Performance bounds for CSMA-based medium access control

In recent work, it was shown that the class of distributed random access MAC schemes leveraging Carrier-Sense Multiple Access (CSMA) is throughput-optimal. To fully assess the potential of such schemes, it is challenging to study their performance in terms of mean delays and compare it against that of centralized scheduling. In this paper, we present upper and lower bounds on the performance of CSMA-based random access MAC. We modify the ideal CSMA model to obtain one that further incorporates queue length information and admits a product-form stationary distribution. We analytically calculate its mean delay at the steady-state, and show that it yields an upper bound on the delay of ideal CSMA. We also derive a lower bound which is independent of the scheduling algorithm. The derived bounds coincide with the best known bounds for the popular max-weight scheduling, whence the performance of such distributed low-complexity schemes lies in the same regime as that of the centralized, generally NP-hard max-weight scheduling. Our results extend to slotted systems, as well as to a wide range of arrival-service processes. Finally, we develop a method for deriving upper and lower bounds on the performance of MAC algorithms by use of Linear Programming (LP) and present comparative simulation results.