Optimal reservation policy for two queues in tandem

Authors:
Cheng-Yuan Ku;Din-Yuen Chan;Lain-Chyr Hwang
Affiliations:
Department of Information Management, National Chung Cheng University, 160 San-Hsing, Chia-Yi County, Taiwan, R.O.C.;Department of Information Engineering, I-Shou University, Taiwan, R.O.C.;Department of Electrical Engineering, I-Shou University, Taiwan, R.O.C.
Venue:
Information Processing Letters
Year:
2003

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Abstract

In this paper, we consider the optimal reservation problem for two multi-server loss queues in tandem, which is usually used to model network and communication systems. In previous work [European J. Oper. Res. 21 (1985) 399-409; Ph.D. diss., 1995; IEEE Trans. Automatic Control 42 (1997) 1017-1023], under appropriate conditions, the optimal reservation policy that maximizes the expected total discounted reward over an infinite horizon is shown to be a switching curve in two-dimensional state space. However, some counterintuitive examples for variation do exist in the numerical experiments. We therefore discuss and analyze the variation in these switching curves with the number of customers in the system. We propose two sufficient conditions under which the counterintuitive situation will not occur.