On finite capacity queues with time dependent arrival rates

Xiaoqian Tan, Charles Knessl and Yang, Yongzhi (Peter)

Stochastic Processes and their Applications, 2013, vol. 123, issue 6, 2175-2227

Abstract: We consider the finite capacity M/M/1−K queue with a time dependent arrival rate λ(t). Assuming that the capacity K is large and that the arrival rate varies slowly with time (as t/K), we construct asymptotic approximations to the probability of finding n customers in the system at time t, as well as the mean number. We consider various time ranges, where the system is nearly empty, nearly full, or is filled to a fraction of its capacity. Extensive numerical studies are used to back up the asymptotic analysis.

Keywords: Time-dependent queues; Asymptotics; Finite capacity (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2013.02.002

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