Analyzing Contention and Backoff in Asynchronous Shared Memory

Abstract

Randomized backoff protocols have long been used to reduce contention on shared resources. They are heavily used in communication channels and radio networks, and have also been shown to greatly improve the performance of shared memory algorithms in real systems.However, while backoff protocols are well understood in many settings, their effect in shared memory has never been theoretically analyzed. This discrepency may be due to the difficulty of modeling asynchrony without eliminating the advantage gained by local delays. In this paper, we introduce a new cost model for contention in shared memory. Our model allows for adversarial asynchrony, but also provides a clear notion of time, thus enabling easy calculation of contention costs and delays. We then consider a simple use case in which n processes try to update a single memory location. Using our model, we first show that a naive protocol, without any backoff, requires \Omega(n^3) work until all processes successfully update that location. We then analyze the commonly used exponential delay protocol, and show that it requires \Theta(n^2 \log n) work with high probability. Finally, we show that the exponential delay protocol is suboptimal, by introducing a new backoff protocol based on adaptive probabilities and showing that, for the same use case, it requires only O(n^2) work with high probability.