Queues with Simultaneous Arrival of Customers and the Dependence Structure of the Waiting Times

We consider a queueing system where some customers decide to simultaneously wait in two queues, rather than in a single queue, to receive their service. In practice, when there exists a number of queues rendering the same service, the customers may tend to simultaneously wait in more than one queue in order to receive the service sooner and thus scale down their waiting time. In this framework, the customers may abandon one of the queues when they are called to receive the service from the other. We treat this situation as customer reneging or abandonment. We study the customer’s waiting time under this model for the cases of independence and dependence of the waiting time random variables of the queues. In conducting this study, a Copula approach is applied to take into account the dependence structure of the waiting time random variables. We compare the numerical results of the dependence with that of the independence.