The Impact of Dependence on Unobservable Queues
نویسنده
چکیده
In unobservable queueing systems, customers have several chances to leave the system and forgo their service from an agent. Typically customers may choose to leave by balking, which is based on the queue length or they may leave by reneging from the queue, which is based on the virtual waiting time and the patience of the customer. However, the current literature on unobservable queues assumes that the sequences of balking and reneging random variables are independent and this implies that a customer’s decision to join the line is independent of the their willingness to wait for service. In this paper, we relax the independence assumption and assess the impact of dependence of the balking and reneging distributions on the stochastic behavior of the queue length and workload processes. We find that the dependence of the balking and reneging distributions significantly affects the distribution of the queue length through decreasing the strength of the state dependent drift towards the origin. Lastly, we show that the joint density near the origin and not the correlation of the balking and reneging random variables describes the impact of the queue length and workload processes.
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