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A NEW LOOK ON THE SHORTEST QUEUE SYSTEM WITH JOCKEYING

Published online by Cambridge University Press:  23 December 2019

Rachel Ravid Open the ORCID record for Rachel Ravid [Opens in a new window]
Rachel Ravid*
Affiliation:
ORT Braude College, Karmiel 2161002, Israel E-mail: [email protected]
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Abstract

We introduce a Markov queueing system with Poisson arrivals, exponential services, and jockeying between two parallel and equivalent servers. An arriving customer admits to the shortest line. Every transition, of only the last customer in line, from the longer line to the shorter line may accompanied by a certain fixed cost. Thus, a transition from the longer queue to the shorter queue occurs whenever the difference between the lines reaches a certain discrete threshold (d = 2, 3, …). In this study, we focus on the stochastic analysis of the number of transitions of an arbitrary customer.

Keywords

queueing theory
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 557 - 564
Copyright
© Cambridge University Press 2019

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References

1.Adan, I.J.B.F., Wessels, J., & Zijm, W.H.M. (1991). Analysis of the asymmetric shortest queue problem with threshold jockeying. Communications in Statistics. Stochastic Models 7(4): 615–627.CrossRefGoogle Scholar
2.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
3.Adan, I.J.B.F., Van Houtum, J.G., & Van der Wal, J. (1994). Upper and lower bounds for the waiting time in the symmetric shortest queue system. Annals of Operations Research 48: 197–217.CrossRefGoogle Scholar
4.Dehghanian, A. & Kharoufeh, J.P. (2016). Strategic dynamic jockeying between two parallel queues. Probability in the Engineering and Informational Sciences 30(1): 41–60.CrossRefGoogle Scholar
5.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
6.Elsayed, E.A. & Bastani, A. (1985). General solutions of the jockeying problem. European Journal of Operational Research 22(3): 387–396.CrossRefGoogle Scholar
7.Gertsbakh, I. (1984). The shorter queue problem: A numerical study using the matrix-geometric solution. European Journal of Operational Research 15(3): 374–381.CrossRefGoogle Scholar
8.Haight, F.A. (1958). Two queues in parallel. Biometrika 45: 401–410.CrossRefGoogle Scholar
9.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.CrossRefGoogle Scholar
10.Haviv, M. & Ritov, Y. (1987). The variance of the waiting time in a queueing system with jockeying. Communications in Statistics. Stochastic Models 4(1): 161–182.Google Scholar
11.Jeganathan, K., Sumathi, J., & Mahalakshmi, G. (2016). Markovian inventory model with two parallel queues, jockeying and impatient customers. Yugoslav Journal of Operations Research 26(4): 467–506.CrossRefGoogle Scholar
12.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
13.Reuveni, S. (2014). Catalan's trapezoids. Probability in the Engineering and Informational Sciences 28: 353–361.CrossRefGoogle Scholar
14.Stagje, W. (2009). A queueing system with two parallel lines, cost-conscious customers, and jockeying. Communications in Statistics. Theory and Methods 38(16–17): 3158–3169.CrossRefGoogle Scholar
15.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
16.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
17.Zhao, Y. & Grassmann, W.K. (1995). Queueing analysis of a jockeying model. Operations Research 43(3): 520–529.CrossRefGoogle Scholar
18.Wilf, H.S. (2006). Generating functionology. 3rd ed. Wellesley, Mass: A K Peters, Ltd.Google Scholar