Mean queue size in a queue with discrete autoregressive arrivals of order p
- 72 Downloads
We consider a discrete time single server queueing system where the arrival process is governed by a discrete autoregressive process of order p (DAR(p)), and the service time of a customer is one slot. For this queueing system, we give an expression for the mean queue size, which yields upper and lower bounds for the mean queue size. Further we propose two approximation methods for the mean queue size. One is based on the matrix analytic method and the other is based on simulation. We show, by illustrations, that the proposed approximations are very accurate and computationally efficient.
KeywordsDiscrete autoregressive process Discrete time queueing system Mean queue size
Unable to display preview. Download preview PDF.
- Addie, R. G., & Zukerman, M. (1994). Performance evaluation of a single server autoregressive queue. Australian Telecommunication Research, 28(1), 25–32. Google Scholar
- Hwang, G. U., & Kim, B. (2008). Mean queue length in a discrete time queue with stationary arrivals. Submitted. Google Scholar
- Jacobs, P. A., & Lewis, P. A. W. (1978). Discrete time series generated by mixtures. III: Autoregressive processes (DAR(p)) (Technical Report NPS55-78-022). Naval Postgraduate School. Google Scholar
- Jacobs, P. A., & Lewis, P. A. W. (1983). Stationary discrete autoregressive-moving average time series generated by mixtures. Journal of Time Series Analysis, 4(1), 19–36. Google Scholar
- McKenzie, E. (2003). Discrete variate time series. In D. N. Shanbhag & C. R. Rao (Eds.), Handbook of statistics 21, stochastic processes: modelling and simulation (pp. 573–606). Amsterdam: North-Holland. Google Scholar
- Neuts, M. F. (1989). Structured stochastic matrices of M/G/1 type and their applications. New York: Marcel Dekker. Google Scholar
- Pearce, C. (1966). A queueing system with general moving average input and negative exponential service time. Journal of the Australian Mathematical Society, 6, 223–236. Google Scholar
- Ryu, B. K., & Elwalid, A. (1996). The importance of long-range dependence of VBR video traffic in ATM traffic engineering: myths and realities. In ACM SIGCOMM (pp. 3–14). Stanford, CA. Google Scholar
- Widjaja, I., & Elwalid, A. (1998). Performance issues in VC-merge capable switches for IP over ATM networks. In Proceedings of IEEE INFOCOM’98 (Vol. 1, pp. 372–380). Google Scholar