A tandem queueing system with applications to pricing strategy

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January 2009, 5(1): 103-114. doi: 10.3934/jimo.2009.5.103

A tandem queueing system with applications to pricing strategy

Wai-Ki Ching ^1, , Tang Li ^1, , Sin-Man Choi ^1, and Issic K. C. Leung ^2,

1.	Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China, China, China
2.	Department of MSST, The Hong Kong Institute of Education, Hong Kong, China

Received January 2008 Revised September 2008 Published December 2008

Abstract
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In this paper, we analyze a Markovian queueing system with multiple types of customers and two queues in tandem. All customers have to go through two stages of services. In Stage 1, the queueing system has multiple identical servers while in Stage 2, there is one single-server queue for each type of customers. The queueing discipline in the whole system is Blocked Customer Delayed (BCD). We first obtain the steady-state probability distribution of the queueing system and the expected waiting time for customers. We then apply the queueing model to solve an optimal pricing policy problem in assuming that the demand rate is dependent on the price. The objective is to minimize the number of servers in the first stage and also maximize the expected earnings by taking into account the demand and the prices. We also obtained some analytic results for the optimal pricing strategy.

Keywords: demand., queues in tandem, optimization, Queueing systems.

Mathematics Subject Classification: Primary: 65C20; Secondary: 65F1.

Citation: Wai-Ki Ching, Tang Li, Sin-Man Choi, Issic K. C. Leung. A tandem queueing system with applications to pricing strategy. Journal of Industrial & Management Optimization, 2009, 5 (1) : 103-114. doi: 10.3934/jimo.2009.5.103

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