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The waiting time analysis of a discrete-time queue with arrivals as a discrete autoregressive process of order 1

Part of: Computer system organization Special processes

Published online by Cambridge University Press:  14 July 2016

Gang Uk Hwang ,
Bong Dae Choi  and
Jae-Kyoon Kim
Gang Uk Hwang*
Affiliation:
Korea Advanced Institute of Science and Technology
Bong Dae Choi*
Affiliation:
Korea University
Jae-Kyoon Kim*
Affiliation:
Korea Advanced Institute of Science and Technology
*
∗ Postal address: Division of Applied Mathematics, Korea Advanced Institute of Science and Technology, 373-1 Kusong-Dong, Yusong-Gu, Taejon 305-701, South Korea.
∗∗ Postal address: Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, Anam-dong, Sungbuk-ku, Seoul 136-701, South Korea. Email address: bdchoi@semi.korea.ac.kr
∗∗∗ Postal address: Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, 373-1 Kusong-Dong, Yusong-Gu, Taejon 305-701, South Korea.
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Abstract

We consider a discrete-time queueing system with the discrete autoregressive process of order 1 (DAR(1)) as an input process and obtain the actual waiting time distribution and the virtual waiting time distribution. As shown in the analysis, our approach provides a 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 distributions. 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.

Keywords

Discrete autoregressive process of order 1waiting timeheavy traffic analysisdecay ratequeue

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 619 - 629
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

This work was supported by grant number 98-0101-02-01-3 from the Basic Research Program of the Korea Science and Engineering Foundation.

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