Abstract: We consider a processor-sharing service station which serves all its customers simultaneously, with the service rate to individual customers decreasing as the load increases. Each arriving customer observes the current load, and may then choose to join the shared system or use an alternative service option { modeled here as a private server (e.g., a personal computer, as an alternative to a central mainframe computer). Customers make individual decisions, and each wishes to minimize her own service time. However, the optimal decision for each customer depends on the choices of subsequent ones, since these a ect the future load on the shared server. This decision problem is analyzed as a non-cooperative dynamic game between all customers. We rst show that any Nash equilibrium point consists of threshold decision rules, and establish the existence and uniqueness of a symmetric equilibrium point. Computation of the equilibrium threshold is demonstrated for the case of Poisson arrivals, and some of its properties are delineated. We next turn attention to a plausible dynamic learning scheme, where arriving customers employ a simple decision rule solely based on observed performance history in the shared system. Convergence to the symmetric equilibrium point is established, thereby underscoring the relevance of the Nash equilibrium solution for this system. Subject classi cation: Queues, optimization: processor sharing. Games/group decisions, stochastic: games in queues. 1 This paper is a revised and extended version of the report \Individually optimal dynamic routing in a processor sharing system: stochastic game analysis".
REF analyze a processor sharing model.
Individual Equilibrium and Learning in a Processor Sharing System
Operations Research
Computer Science