On the Benefits of Providing Timely Information in Ticket Queues with Balking and Calling Times

Abstract

We study a phenomenon causing server time loss in ticket queues with balking and calling time. A customer who balks from the queue after printing a ticket leaves a virtual entity in the queue that requires server time to be cleared. The longer the queue, the larger the proportion of customers abandoning their place, and the larger the server time loss due to calling customers that left the queue. The solution is suggested by giving the customer the best possible estimate of her expected waiting time before printing a ticket, thus ensuring that, if she balks, no number in the queue is created that will waste server time. Although partially observable ticket queues have been studied in the literature, the addition of a calling time for absent customers creates a new type of problem that has been observed in real life but has not been formally addressed yet. We analyze this stochastic system, formulate its steady state probabilities, and calculate the system’s performance measures. The analytical solution provided here is robust and can be applied to a wide range of customers’ behavior functions. Finally, numerical analysis is performed that demonstrates the benefits of providing timely information to customers for different levels of traffic congestion.