Title: Dynamic control policy for the discrete-time queue

Authors: Tsung-Yin Wang; Fu-Min Chang

Addresses: Department of Accounting Information, National Taichung University of Science and Technology, 129, Sec. 3, Sanmin Road, Taichung 404, Taiwan ' Department of Finance, Chaoyang University of Technology, 168, Jifeng E. Road, Wufeng District, Taichung 413, Taiwan

Abstract: In queueing system, when the server is idle, one of control policy for determining the timing of server activated is when a fixed number N of customers accumulates for service in the system. However, on some practical situations such as watching video file online, the threshold value N may vary depending on different situations. For such situation, this paper studies a random N-policy Geo/G/1 queue, where N is determined as each new cycle begins. We derive some system characteristics, such as system size, idle period, busy period and sojourn time, by using the probability generating function and supplementary variable technique. We also prove that the system size of a continuous-time random N-policy M/G/1 queue can be approximated by the presented discrete-time model.

Keywords: random N-policy; system length; busy period; sojourn time; dynamic control policy; discrete-time queues; queueing systems.

DOI: 10.1504/IJSOI.2016.080074

International Journal of Services Operations and Informatics, 2016 Vol.8 No.2, pp.79 - 93

Accepted: 13 Oct 2014
Published online: 01 Nov 2016 *

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