Analyzing Contention and Backoff in Asynchronous Shared Memory

Randomized backo‚ protocols have long been used to reduce contention on shared resources. Œey 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 backo‚ protocols are well understood in many seŠings, their e‚ect in shared memory has never been theoretically analyzed. Œis discrepency may be due to the diculty 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 €rst show that a naı̈ve protocol, without any backo‚, requires Ω(n3) work until all processes successfully update that location. We then analyze the commonly used exponential delay protocol, and show that it requires Θ(n2 logn) work with high probability. Finally, we show that the exponential delay protocol is suboptimal, by introducing a new backo‚ protocol based on adaptive probabilities and showing that, for the same use case, it requires only O (n2) work with high probability. ACM Reference format: Naama Ben-David and Guy E. Blelloch. 2017. Analyzing Contention and Backo‚ in Asynchronous Shared Memory. In Proceedings of PODC’17, July 25-27, 2017, Washington, DC, USA, , 10 pages. DOI: 10.1145/3087801.3087828