American Institute of Mathematical Sciences

Advanced
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

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
[1]

Zsolt Saffer, Wuyi Yue. A dual tandem queueing system with GI service time at the first queue. Journal of Industrial & Management Optimization, 2014, 10 (1) : 167-192. doi: 10.3934/jimo.2014.10.167
[2]

Eungab Kim. On the admission control and demand management in a two-station tandem production system. Journal of Industrial & Management Optimization, 2011, 7 (1) : 1-18. doi: 10.3934/jimo.2011.7.1
[3]

Gang Chen, Zaiming Liu, Jingchuan Zhang. Analysis of strategic customer behavior in fuzzy queueing systems. Journal of Industrial & Management Optimization, 2020, 16 (1) : 371-386. doi: 10.3934/jimo.2018157
[4]

Sin-Man Choi, Ximin Huang, Wai-Ki Ching. Minimizing equilibrium expected sojourn time via performance-based mixed threshold demand allocation in a multiple-server queueing environment. Journal of Industrial & Management Optimization, 2012, 8 (2) : 299-323. doi: 10.3934/jimo.2012.8.299
[5]

Sofian De Clercq, Koen De Turck, Bart Steyaert, Herwig Bruneel. Frame-bound priority scheduling in discrete-time queueing systems. Journal of Industrial & Management Optimization, 2011, 7 (3) : 767-788. doi: 10.3934/jimo.2011.7.767
[6]

Jian Zhang, Tony T. Lee, Tong Ye, Liang Huang. An approximate mean queue length formula for queueing systems with varying service rate. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2019106
[7]

Jianyu Cao, Weixin Xie. Optimization of a condition-based duration-varying preventive maintenance policy for the stockless production system based on queueing model. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1049-1083. doi: 10.3934/jimo.2018085
[8]

M. M. Ali, L. Masinga. A nonlinear optimization model for optimal order quantities with stochastic demand rate and price change. Journal of Industrial & Management Optimization, 2007, 3 (1) : 139-154. doi: 10.3934/jimo.2007.3.139
[9]

Zhanyou Ma, Pengcheng Wang, Wuyi Yue. Performance analysis and optimization of a pseudo-fault Geo/Geo/1 repairable queueing system with N-policy, setup time and multiple working vacations. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1467-1481. doi: 10.3934/jimo.2017002
[10]

Lizhao Yan, Fei Xu, Yongzeng Lai, Mingyong Lai. Stability strategies of manufacturing-inventory systems with unknown time-varying demand. Journal of Industrial & Management Optimization, 2017, 13 (4) : 2033-2047. doi: 10.3934/jimo.2017030
[11]

David Russell. Structural parameter optimization of linear elastic systems. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1517-1536. doi: 10.3934/cpaa.2011.10.1517
[12]

Vadim Azhmyakov. An approach to controlled mechanical systems based on the multiobjective optimization technique. Journal of Industrial & Management Optimization, 2008, 4 (4) : 697-712. doi: 10.3934/jimo.2008.4.697
[13]

Pierre Fabrie, Elodie Jaumouillé, Iraj Mortazavi, Olivier Piller. Numerical approximation of an optimization problem to reduce leakage in water distribution systems. Mathematical Control & Related Fields, 2012, 2 (2) : 101-120. doi: 10.3934/mcrf.2012.2.101
[14]

Yanqing Liu, Yanyan Yin, Kok Lay Teo, Song Wang, Fei Liu. Probabilistic control of Markov jump systems by scenario optimization approach. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1447-1453. doi: 10.3934/jimo.2018103
[15]

Tuan Phung-Duc, Ken’ichi Kawanishi. Multiserver retrial queues with after-call work. Numerical Algebra, Control & Optimization, 2011, 1 (4) : 639-656. doi: 10.3934/naco.2011.1.639
[16]

Tuan Phung-Duc. Single server retrial queues with setup time. Journal of Industrial & Management Optimization, 2017, (3) : 1329-1345. doi: 10.3934/jimo.2016075
[17]

Jesus R. Artalejo, Tuan Phung-Duc. Markovian retrial queues with two way communication. Journal of Industrial & Management Optimization, 2012, 8 (4) : 781-806. doi: 10.3934/jimo.2012.8.781
[18]

Tetsuji Hirayama. Analysis of multiclass feedback queues and its application to a packet scheduling problem. Journal of Industrial & Management Optimization, 2010, 6 (3) : 541-568. doi: 10.3934/jimo.2010.6.541
[19]

Feng Zhang, Jinting Wang, Bin Liu. Equilibrium joining probabilities in observable queues with general service and setup times. Journal of Industrial & Management Optimization, 2013, 9 (4) : 901-917. doi: 10.3934/jimo.2013.9.901
[20]

Tuan Phung-Duc, Wouter Rogiest, Sabine Wittevrongel. Single server retrial queues with speed scaling: Analysis and performance evaluation. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1927-1943. doi: 10.3934/jimo.2017025

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (19)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences