Minimizing equilibrium expected sojourn time      via performance-based mixed threshold demand allocation      in a multiple-server queueing environment

Sin-Man Choi; Ximin Huang; Wai-Ki Ching

doi:10.3934/jimo.2012.8.299

Article Contents

2012, Volume 8, Issue 2: 299-323. Doi: 10.3934/jimo.2012.8.299

This issue Previous Article A decision making process application for the slurry production in ceramics via fuzzy cluster and data mining Next Article Fabric defect detection using multi-level tuned-matched Gabor filters

Minimizing equilibrium expected sojourn time via performance-based mixed threshold demand allocation in a multiple-server queueing environment

1.
Department of Industrial Engineering and Operations Research, University of California, Berkeley
2.
College of Management, Georgia Institute of Technology, 800 West Peachtree Street NW Atlanta, Georgia 30308-0520
3.
Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong

Received: September 30, 2010

Revised: July 31, 2011

Published: March 2012

Abstract Related Papers Cited by

Abstract

We study the optimal demand allocation policies to induce high service capacity and achieve minimum expected sojourn times in equilibrium in a queueing system with multiple strategic servers. We propose the mixed threshold allocation policy as an optimal state-dependent policy that induces optimal service capacity from strategic servers. Compensation to the server can be paid at customer allocation or upon job completion. Our study focuses on the use of a multiple-server mixed threshold allocation policy to replicate the demand of a given state-independent policy to achieve a symmetric equilibrium with lower expected sojourn time. The results indicate that, under both payment schemes, for any given multiple-server state-independent policy, there exists a multiple-server threshold policy that produces identical demand allocation and Nash equilibrium (if any). Moreover, the policy can be designed to minimize the expected sojourn time at a symmetric equilibrium. Furthermore, under the payment-at-allocation scheme, our results, combining with existing results on the optimality of the multiple-server linear allocation policy, show that the mixed threshold policy can achieve the maximum feasible service capacity and thus the minimum feasible equilibrium expected sojourn time. Hence, our results agree with previous two-server results and affirm that a trade-off between incentives and efficiency need not exist in the case of multiple servers.

Keywords:

Mathematics Subject Classification: Primary: 60K25, 68M20; Secondary: 91A80.

Citation:

Related Papers

Cited by

References

[1]	G. Cachon and F. Zhang, Obtaining fast service in a queueing system via performance-based allocation of demand, Management Science, 53 (2007), 408-420.doi: 10.1287/mnsc.1060.0636.
[2]	W. Ching, S. Choi and M. Huang, Optimal service capacity in a multiple-server queueing system: A game theory approach, Journal of Industrial and Management Optimization, 6 (2010), 73-102.doi: 10.3934/jimo.2010.6.73.
[3]	S. Choi, X. Huang, W. Ching and M. Huang, Incentive effects of multiple-server queueing networks: the principal-agent perspective, East Asian Journal on Applied Mathematics, 1 (2011), 379-402.
[4]	S. Choi, X. Huang and W. Ching, Inducing optimal service capacities via performance-based allocation of demand in a queueing system with multiple servers, in "The 40^th International Conference on Computers and Engineering," Hyogo, Japan, 2010.
[5]	T. Crabill, D. Gross and M. Magazine, A classified bibliography of research on optimal design and control of queues, Operations Research, 25 (1977), 219-232.doi: 10.1287/opre.25.2.219.
[6]	S. Gilbert and Z. Weng, Incentive effects favor nonconsolidating queues in a service system: The principal-agent perspective, Management Science, 44 (1998), 1662-1669.doi: 10.1287/mnsc.44.12.1662.
[7]	E. Kalai, M. Kamien and M. Rubinovitch, Optimal service speeds in a competitive environment, Management Science, 38 (1992), 1554-1163.doi: 10.1287/mnsc.38.8.1154.
[8]	J. Laffont and D. Martimort, "The Theory of Incentives: The Principal-Agent Model," Princeton University Press, Princeton, NJ, 2002.
[9]	W. Lin and P. Kumar, Optimal control of a queueing system with two heterogeneous servers, IEEE Trans. Automatic Control, 29 (1984), 696-703.doi: 10.1109/TAC.1984.1103637.
[10]	H. Luh and I. Viniotis, Threshold control policies for heterogeneous server systems, Mathematical Methods of Operations Research, 55 (2002), 121-142.doi: 10.1007/s001860100168.
[11]	M. Osborne, "An Introduction to Game Theory," Oxford University Press, New York, 2004.
[12]	M. Rubinovitch, The slow server problem, Journal of Applied Probability, 22 (1985), 205-213.doi: 10.2307/3213760.
[13]	F. Véricourt and Y. Zhou, On the incomplete results for the heterogeneous server problem, Queueing Systems, 52 (2006), 189-191.doi: 10.1007/s11134-006-5067-8.
[14]	F. Zhang, "Coordination of Lead Times in Supply Chains," Dissertation, University of Pennsylvania, Philadelphia, PA, 2004.