# American Institute of Mathematical Sciences

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Analysis on a queue system with heterogeneous servers and uncertain patterns
January  2010, 6(1): 73-102. doi: 10.3934/jimo.2010.6.73

## Optimal service capacity in a multiple-server queueing system: A game theory approach

 1 Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong 2 College of Information Science and Engineering, Northeastern University, Shenyang, 110004, China

Received  March 2009 Revised  August 2009 Published  November 2009

The economic behavior of service providers in a competitive environment is a very important and interesting research topic. A two-server service network has been proposed by Kalai et al. [14] for this purpose. Their model actually aims at studying both the role and impact of service capacity in capturing larger market share. The market share is important in maximizing individual's long-run expected profit. A Markovian queueing system of two servers was employed in their model for the captured problem. The obvious advantage of such a model is that it is mathematically tractable. They then further formulated the problem as a two-person strategic game and analyzed the equilibrium solutions. The main aim of this paper is to extend the results of their two-server queueing model to the case of a general multiple-server queueing model. Here we will focus on the case when the queueing system is stable. It is found that when the marginal cost of service capacity is low relatively to the revenue per customer, a unique Nash equilibrium exists, in which all servers choose the same service capacity and the expected waiting times are finite.
Citation: Wai-Ki Ching, Sin-Man Choi, Min Huang. Optimal service capacity in a multiple-server queueing system: A game theory approach. Journal of Industrial & Management Optimization, 2010, 6 (1) : 73-102. doi: 10.3934/jimo.2010.6.73
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