Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-23T14:33:41.593Z Has data issue: false hasContentIssue false
  • English
  • Français

STRATEGIC DYNAMIC JOCKEYING BETWEEN TWO PARALLEL QUEUES

Published online by Cambridge University Press:  21 October 2015

Amin Dehghanian ,
Jeffrey P. Kharoufeh  and
Mohammad Modarres
Amin Dehghanian
Affiliation:
Department of Industrial Engineering, University of Pittsburgh, 1048 Benedum Hall, 3700 O'Hara Street, Pittsburgh PA 15261, USA Email: amd120@pitt.edu; jkharouf@pitt.edu
Jeffrey P. Kharoufeh
Affiliation:
Department of Industrial Engineering, University of Pittsburgh, 1048 Benedum Hall, 3700 O'Hara Street, Pittsburgh PA 15261, USA Email: amd120@pitt.edu; jkharouf@pitt.edu
Mohammad Modarres
Affiliation:
Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran Email: modarres@sharif.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider a two-station, heterogeneous parallel queueing system in which each station operates as an independent M/M/1 queue with its own infinite-capacity buffer. The input to the system is a Poisson process that splits among the two stations according to a Bernoulli splitting mechanism. However, upon arrival, a strategic customer initially joins one of the queues selectively and decides at subsequent arrival and departure epochs whether to jockey (or switch queues) with the aim of reducing her own sojourn time. There is a holding cost per unit time, and jockeying incurs a fixed non-negative cost while placing the customer at the end of the other queue. We examine individually optimal joining and jockeying policies that minimize the strategic customer's total expected discounted (or undiscounted) costs over finite and infinite time horizons. The main results reveal that, if the strategic customer is in station 1 with ℓ customers in front of her, and q1 and q2 customers in stations 1 and 2, respectively (excluding herself), then the incentive to jockey increases as either ℓ increases or q2 decreases. Numerical examples reveal that it may not be optimal to join, and/or jockey to, the station with the shortest queue or the fastest server.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 1 , January 2016 , pp. 41 - 60
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Adan, I.J.B.F., Wessels, J. & Zijm, W.H.M. (1993). Matrix-geometric analysis of the shortest queue problem with threshold jockeying. Operations Research Letters 13: 107–112.CrossRefGoogle Scholar
2.Disney, R.L. & Mitchell, W.E. (1970). A solution for queues with instantaneous jockeying and other customer selection rules. Naval Research Logistics Quarterly 17(3): 315–325.CrossRefGoogle Scholar
3.Down, D.G. & Lewis, M.E. (2006). Dynamic load balancing in parallel queueing systems: Stability and optimal control. European Journal of Operational Research 168(2): 509–519.CrossRefGoogle Scholar
4.Elsayed, E.A. & Bastani, A. (1985). General solutions of the jockeying problem. European Journal of Operational Research 22(3): 387–396.CrossRefGoogle Scholar
5.Gertsbakh, I. (1984). The shorter queue problem: A numerical study using matrix-geometric solution. European Journal of Operational Research 15: 374–381.CrossRefGoogle Scholar
6.Glazer, A. & Hassin, R. (1983). Search among queues. Technical Report 406. Institute for Mathematical Studies in the Social Sciences, Stanford University, Palo Alto, CA.Google Scholar
7.Haight, F.A. (1958). Two queues in parallel. Biometrika 45(3/4): 401–410.CrossRefGoogle Scholar
8.Hassin, R. & Haviv, M. (1994). Equilibrium strategies and the value of information in a two line queueing system with threshold jockeying. Communications in Statistics: Stochastic Models 10(2): 415–435.Google Scholar
9.Hassin, R. & Haviv, M. (2003). To queue or not to queue: Equilibrium behavior in queueing systems. Boston, MA: Kluwer Academic.CrossRefGoogle Scholar
10.Hlynka, M., Stanford, D.A., Poon, W.H. & Wang, T. (1994). Observing queues before joining. Operations Research 42(2): 365–371.CrossRefGoogle Scholar
11.Kao, E.P.C. & Lin, C. (1990). A matrix-geometric solution of the jockeying problem. European Journal of Operational Research 44(1): 67–74.CrossRefGoogle Scholar
12.Kingman, J.F.C. (1961). Two similar queues in parallel. Annals of Mathematical Statistics 32: 1314–1323.CrossRefGoogle Scholar
13.Koenigsberg, E. (1966). On jockeying in queues. Management Science 12(5): 412–436.CrossRefGoogle Scholar
14.Lippman, S.A. & Stidham, S. (1977). Individual versus social optimization in exponential congestion systems. Operations Research 25(2): 233–247.CrossRefGoogle Scholar
15.Mandelbaum, A. & Yechiali, U. (1983). Optimal entering rules for a customer with wait option at an M/G/1 queue. Management Science 29(2): 174–187.CrossRefGoogle Scholar
16.Ross, S.M. (1983). Introduction to stochastic dynamic programming. New York, NY: Academic Press, Inc.Google Scholar
17.Tarabia, A.M.K. (2008). Analysis of two queues in parallel with jockeying and restricted capacities. Applied Mathematical Modelling 32(5): 802–810.CrossRefGoogle Scholar
18.Weber, R.R. (1978). On the optimal assignment of customers to parallel servers. Journal of Applied Probability 15(2): 406–413.CrossRefGoogle Scholar
19.Whitt, W.O. (1986). Deciding which queue to join: Some counterexamples. Operations Research 34(1): 55–62.CrossRefGoogle Scholar
20.Xu, S.H. & Zhao, Y.Q. (1996). Dynamic routing and jockeying controls in a two-station queueing system. Advances in Applied Probability 28(4): 1201–1226.CrossRefGoogle Scholar
21.Zhao, Y. & Grassmann, W.K. (1990). The shortest queue model with jockeying. Naval Research Logistics 37(5): 773–787.3.0.CO;2-2>CrossRefGoogle Scholar
22.Zhao, Y. & Grassmann, W.K. (1995). Queueing analysis of a jockeying model. Operations Research 43(3): 520–529.CrossRefGoogle Scholar