Title: Optimisation of a generalised M(k)/M/k queueing system

Authors: Tao Yang, Wuyi Yue, Jianfen Zhan, Qiying Hu

Addresses: R&D Management Consulting Co., Ltd, Beijing 100013, China. ' Department of Intelligence and Informatics, Konan University, Kobe 6588501, Japan. ' Hangzhou Institute of Administration, Hangzhou 310002, China. ' School of Management, Fudan University, Shanghai 200433, China

Abstract: We study a generalised M(k)/M/k queueing system where the arrival rate depends on the number of servers. There are holding costs reflecting the waiting cost of customers and service costs relating to operation of the servers. The objective is to minimise the total system cost in a steady state. We analyse the cost structure and show that the system holding cost rapidly decreases with the number of servers under some weak conditions. Based on this, we present an upper bound of the optimal number of servers. Finally, numerical examples are given to illustrate the model and the results.

Keywords: queueing systems; optimisation; cost structure; server number; revenue management; holding costs; service costs.

DOI: 10.1504/IJRM.2009.027608

International Journal of Revenue Management, 2009 Vol.3 No.4, pp.428 - 440

Published online: 03 Aug 2009 *

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