Performance analysis of a constrained resource sharing system

We consider a queueing system where the servers are arranged in a circle, a nd each arriving customer requires a pair of resources that is shared by it s server with the respective neighbors on either side. If either resource i s being used, the customer is denied service. Customers arrive at each serv er according to independent Poisson processes, and lengths of service times at each server have an exponential distribution. We derive a closed-form f ormula for the expected fraction of busy servers at any time in terms of th e number of servers and the utilization factor (defined as the arrival rate times the mean service-time duration). This allows us to evaluate system p erformance when these parameters are varied, and to determine whether denyi ng service to arrivals at alternate servers improves performance. We relate the system to Dijkstra's dining philosophers problem, which is an abstract ion for resource sharing in an operating system.