Equilibrium joining strategies in batch service queueing systems

Abstract

We consider strategic customers in a Markovian queue with batch services. We derive customer equilibrium strategies, regarding the joining/balking dilemma, in two cases with respect to the information provided upon arrival, unobservable and observable. In contrast to models with single services, a customer’s decision to join induces both positive and negative externalities to other customers. This fact leads to an intricate mixture of Follow-The-Crowd and Avoid-The-Crowd behavior and possibly multiple equilibrium strategies. Moreover, we discuss the effects of the two levels of information and the batch size on the strategic behavior of the customers and on the overall social welfare. Finally, we present several numerical experiments that reveal important differences in the strategic behavior of customers in batch service systems, in juxtaposition to single service systems.