On the Exact Analysis of a Discrete-Time Queueing System with Autoregressive Inputs

Authors:
Gang Uk Hwang;Khosrow Sohraby
Affiliations:
Division of Applied Mathematics, Korea Advanced Institute of Science and Technology, 373-1 Kuseong-dong, Yuseong-gu, Daejeon 305-701, South Korea guhwang@amath.kaist.ac.kr;School of Interdisciplinary Computing and Engineering, University of Missouri–Kansas City, 5100 Rockhill Road, Kansas City, MO 64110, USA
Venue:
Queueing Systems: Theory and Applications
Year:
2003

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Abstract

In this paper, we provide an exact analysis of a discrete-time queueing system driven by a discrete autoregressive model of order 1 (DAR(1)) characterized by an arbitrary marginal batch size distribution and a correlation coefficient. Closed-form expressions for the probability generating function and mean queue length are derived. It is shown that the system performance is quite sensitive to the correlation of the arrival process. In addition, a comparison with traditional Markovian processes shows that arrival processes of DAR(1) type exhibit larger queue length as compared with the traditional Markovian processes when the marginal densities and correlation coefficients are matched.