Analysis of Timing-Based Mutual Exclusion with Random Times

Various timing-based mutual exclusion algorithms have been proposed that guarantee mutual exclusion if certain timing assumptions hold. In this paper, we examine how these algorithms behave when the time for the basic operations is governed by probability distributions. In particular, we are concerned with how often such algorithms succeed in allowing a processor to obtain a critical region and how this success rate depends on the random variables involved. We explore this question in the case where operation times are governed by exponential and gamma distributions, using both theoretical analysis and simulations.