The discrete-time queue with autoregressive inputs revisited |
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Authors: | Faouzi Kamoun |
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Institution: | (1) College of Information Technology, Dubai University College, P.O. Box: 14143, Dubai, UAE |
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Abstract: | In this paper, we present an exact queuing analysis of a discrete-time queue whose arrival process is correlated and consists
of a discrete autoregressive model of order 1 (DAR(1)). The functional equation describing this DAR(1)/D/1 queuing model,
originally derived in Hwang and Sohraby (Queuing Systems 43 (2003)29–41), is manipulated and transformed into a mathematical
tractable form. By using simple analytical transform techniques, we show how our proposed approach allows us to derive an
equivalent (yet simpler) expression for the steady-state probability generating function (pgf) of the queue length, as originally
derived in Hwang and Sohraby (Queuing Systems 43 (2003)29–41). From this pgf, we characterize the distribution of the packet
delay. New numerical results related to packet loss ratio and mean delay of the DAR(1)/D/1 queue are also presented. The proposed
approach outlines an alternate solution technique and a general framework under which more complex time-series based queuing
models can be analyzed.
AMS Subject Classifications 60K25 |
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Keywords: | Discrete autoregressive arrivals Transform analysis Functional equations Discrete-time queues |
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