Abstract
We consider an M/PH/1 queue with workload-dependent balking. An arriving customer joins the queue and stays until served if and only if the system workload is no more than a fixed level at the time of his arrival. We begin by considering a fluid model where the buffer content changes at a rate determined by an external stochastic process with finite state space. We derive systems of first-order linear differential equations for the mean and LST (Laplace-Stieltjes Transform) of the busy period in this model and solve them explicitly. We obtain the mean and LST of the busy period in the M/PH/1 queue with workload-dependent balking as a special limiting case of this fluid model. We illustrate the results with numerical examples.
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Liu, L., Kulkarni, V.G. Busy period analysis for M/PH/1 queues with workload dependent balking. Queueing Syst 59, 37–51 (2008). https://doi.org/10.1007/s11134-008-9074-9
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DOI: https://doi.org/10.1007/s11134-008-9074-9