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Mathematical Problems in Engineering
Volume 2017, Article ID 5964272, 10 pages
https://doi.org/10.1155/2017/5964272
Research Article

Analysis of the Optimal Resource Allocation for a Tandem Queueing System

School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China

Correspondence should be addressed to Gang Chen; moc.361@uschtamgnehc

Received 1 May 2017; Accepted 2 November 2017; Published 28 November 2017

Academic Editor: Qingling Zhang

Copyright © 2017 Zaiming Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a controllable two-station tandem queueing system, where customers (jobs) must first be processed at upstream station and then the downstream station. A manager dynamically allocates the service resource to each station to adjust the service rate, leading to a tradeoff between the holding cost and resource cost. The goal of the manager is to find the optimal policy to minimize the long-run average costs. The problem is constructed as a Markov decision process (MDP). In this paper, we consider the model in which the resource cost and service rate functions are more general than linear. We derive the monotonicity of the optimal allocation policy by the quasiconvexity properties of the value function. Furthermore, we obtain the relationship between the two stations’ optimal policy and conditions under which the optimal policy is unique and has the bang-bang control property. Finally, we provide some numerical experiments to illustrate these results.