Randomized coordination in an autonomous decentralized system

The performance of a randomized coordination mechanism for resource access in an autonomous decentralized system is investigated. Given n users and r resources, each user decides to access a resource with probability α, and each resource is selected with equal likelihood. The goal is to select α so that mutually conflicting decisions, where multiple users try to access the same resource, are minimized. Results are presented on the optimal number of users given some number of resources, and the limiting performance as the number of users approaches infinity. It is shown 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