Randomized coordination in an autonomous decentralized system

We investigate the performance of a randomized coordination mechanism for resource access in an autonomous decentralized system. Given n users and r resources, each user decides to access a resource with probability a, and each resource is selected with equal likelihood. The goal i s to select a so that mutually conjicting decisions, where multiple users try to access the same resource, are minimized. We present results on the optimal access probabiliry, the maximum expected gain, the optimal number of users given some number of resources, and the limiting performance as the number of users approaches infinity. We also show that given n = kr users and r resources, it is better to partition users and resources so that each resource is accessed by a separate group of k users rather than to allow all n users to compete for all r resources.