The Waiting Time Analysis of A Discrete Time Queue with Arrivals as A Discrete Autoregressive Process of Order 1

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We consider a discrete time queueing system with the discrete autoregressive process of order 1 (shortly, the DAR(1)) as an input process and obtain the actual waiting time distribution and the virtual waiting time distibution. As shown in the analysis, our approach provides natural numerical algorithm to compute the waiting time distributions, based on the theory of the GI/G/1 queue, and consequently we can easily investigate the effect of the parameters of the DAR(1) on the waiting time distribution. We also derive a simple approximation of the asymptotic decay rate of the tail probabilities for the virtual waiting time in the heavy traffic case.
Publisher
Applied Probability Trust
Issue Date
2002
Keywords

Discrete Autoregressive Process of Order 1; Waiting Time; Heavy Traffic Analysis; Decay Rate; Queue

Citation

Journal of Applied Probability

URI
http://hdl.handle.net/10203/24859
Appears in Collection
MA-Journal Papers(저널논문)
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