Dynamic service sharing with heterogeneous preferences
Queueing Systems: Theory and Applications
A model for rational abandonments from invisible queues
Queueing Systems: Theory and Applications
INDIVIDUAL EQUILIBRIUM DYNAMIC ROUTING IN A MULTIPLE SERVER RETRIAL QUEUE
Probability in the Engineering and Informational Sciences
Multi-agent learning for engineers
Artificial Intelligence
User equilibria for a parallel queueing system with state dependent routing
Queueing Systems: Theory and Applications
Discounted Robust Stochastic Games and an Application to Queueing Control
Operations Research
Monotonicity properties of user equilibrium policies for parallel batch systems
Queueing Systems: Theory and Applications
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We consider a processor-sharing service system, where the service rate to individual customers decreases as the load increases. Each arriving customer may observe the current load and should then choose whether to join the shared system. The alternative is a constant-cost option, modeled here for concreteness as a private server (e.g., a personal computer that serves as an alternative to a central mainframe computer). The customers wish to minimize their individual service times (or an increasing function thereof). However, the optimal choice for each customer depends on the decisions of subsequent ones, through their effect on the future load in the shared server. This decision problem is analyzed as a noncooperative dynamic game among the customers. We first 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 consider a reasonable dynamic learning scheme, which converges to the symmetric Nash equilibrium point. In this model customers simply choose the better option based on available performance history. Convergence of this scheme is illustrated here via a simulation example and is established analytically in subsequent work.