The effect of catastrophes on the strategic customer behavior in queueing systems

We consider the single server Markovian queue subject to Poisson generated catastrophes. Whenever a catastrophe occurs, all customers are forced to abandon the system, the server is rendered inoperative and an exponential repair time is set on. During the repair time new arrivals are allowed to join the system. We assume that the arriving customers decide whether to join the system or balk, based on a natural linear reward‐cost structure with two types of rewards: A (usual) service reward for those customers that receive service and a (compensation) failure reward for those customers that are forced to abandon the system due to a catastrophe. We study the strategic behavior of the customers regarding balking and derive the corresponding (Nash) equilibrium strategies for the observable and unobservable cases. We show that both types of strategic behavior may be optimal: to avoid the crowd or to follow it. The crucial factor that determines the type of customer behavior is the relative value of the service reward to the failure compensation. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Equilibrium customer strategies and social–profit maximization in the single‐server constant retrial queue

We consider the single‐server constant retrial queue with a Poisson arrival process and exponential service and retrial times. This system has not waiting space, so the customers that find the server busy are forced to abandon the system, but they can leave their contact details. Hence, after a service completion, the server seeks for a customer among those that have unsuccessfully applied for service but left their contact details, at a constant retrial rate. We assume that the arriving customers that find the server busy decide whether to leave their contact details or to balk based on a natural reward‐cost structure, which incorporates their desire for service as well as their unwillingness to wait. We examine the customers' behavior, and we identify the Nash equilibrium joining strategies. We also study the corresponding social and profit maximization problems. We consider separately the observable case where the customers get informed about the number of customers waiting for service and the unobservable case where they do not receive this information. Several extensions of the model are also discussed. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011