Optimal Pricing and Admission Control of Markovian Queueing System with Negative Customers

Optimal Pricing and Admission Control of Markovian Queueing System with Negative Customers

Zaiming Liu Wei Deng Gang Chen 

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

Corresponding Author Email: 
math_lzm@csu.edu.cn, 211082@csu.edu.cn, chengmathcsu@163.com
Page: 
202-218
|
DOI: 
https://doi.org/10.18280/ama_a.540206
Received: 
17 April 2017
| |
Accepted: 
2 May 2017
| | Citation

OPEN ACCESS

Abstract: 

This paper analyses the optimal dynamic pricing and admission control policies to maximize the average benefit in a Markovian queue with negative customers. The negative customers, as a type of job cancellation signals, are frequently employed to solve the congestion problem in the production system. In our model, the manager proposes a price for positive customers, and decide whether or not to accept the arriving negative customers in any decision epoch. Treating the problem as a Markov decision process, the author derived the monotonicity of the optimal pricing policy, proved the optimal admission policy as a threshold policy, and verified the monotonicity of the threshold policy in system parameters. Finally, some numerical experiments were presented to depict the effect of system parameters on the optimal policy and average benefit.

Keywords: 

Queueing system, Dynamic pricing, Admission control, Markov decision process, Negative customers.

1. Introduction
2. Model Description
3. Structure of the Optimal Control Policy
4. Numerical Examples
5. Conclusion
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