A queueing system with discrete autoregressive arrivals

Authors:
Bara Kim;Yong Chang;Yeong Cheol Kim;Bong Dae Choi
Affiliations:
Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Republic of Korea;Telecommunication Systems Division, Information and Communication Business, Samsung Electronics Co., Ltd, Suwon-si, Gyeonggi-do, 442-742, Republic of Korea;Department of Mathematics, Mokpo National University, Muan-gun, Chonnam, 534-729, Republic of Korea;Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Republic of Korea
Venue:
Performance Evaluation
Year:
2007

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Abstract

We consider a discrete time single server queue with discrete autoregressive process of order 1 (DAR(1)) input. By extracting a Markov process from the queue size process and applying the BASTA property, we derive simple recursive formulae for the stationary distributions of the queue size and the waiting time. These formulae are simple, numerically stable and transform-free. A stochastic decomposition property is given for the stationary waiting time, and relations between the distributions of the stationary queue size and the stationary waiting time are discussed. Numerical examples are given for stationary distributions of the queue size and the waiting time for various DAR(1) inputs.