Strategic joining rules in unobservable queues with dynamic service rate

Abstract

This paper considers an unobservable queue with adjustable service rate and strategic customers. A queueing-game-theoretic model is built to capture the interaction between the server’s service rate and customers’ joining decisions. Iterative and recursive methods are used to derive the steady-state distribution and the expected sojourn time in the queue. We obtain customers’ equilibrium and socially optimal joining strategies under two information scenarios which are unobservable and partially unobservable queues, separately. It is found that there are four equilibrium joining strategies at most in the fully unobservable queue and two equilibrium joining strategies in the almost unobservable queue. Interestingly, the social optimal arrival rate is between the minimum and maximum stable equilibria. Thus, in most cases, managers need to charge a price to induce the social optimal customers’ behavior. However, if the minimum equilibrium is achieved, managers are required to provide a subsidy to maximize the social welfare. unobservable queue; $(m, N)$ policy; equilibrium strategy; social welfare.