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Workload distribution of discrete‐time parallel queues with two servers

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  • P. Patrick Wang

Abstract

We study discrete‐time, parallel queues with two identical servers. Customers arrive randomly at the system and join the queue with the shortest workload that is defined as the total service time required for the server to complete all the customers in the queue. The arrivals are assumed to follow a geometric distribution and the service times are assumed to have a general distribution. It is a no‐jockeying queue. The two‐dimensional state space is truncated into a banded array. The resulting modified queue is studied using the method of probability generating function (pgf) The workload distribution in steady state is obtained in form of pgf. A special case where the service time is a deterministic constant is further investigated. Numerical examples are illustrated. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 440–454, 2000

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  • P. Patrick Wang, 2000. "Workload distribution of discrete‐time parallel queues with two servers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(5), pages 440-454, August.
    • Handle: RePEc:wly:navres:v:47:y:2000:i:5:p:440-454
    DOI: 10.1002/1520-6750(200008)47:53.0.CO;2-W
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    1. Kao, Edward P. C. & Lin, Chiunsin, 1990. "A matrix-geometric solution of the jockeying problem," European Journal of Operational Research, Elsevier, vol. 44(1), pages 67-74, January.
    2. B. M. Rao & M. J. M. Posner, 1987. "Algorithmic and approximation analyses of the shorter queue model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 381-398, June.
    3. Gertsbakh, Ilya, 1984. "The shorter queue problem: A numerical study using the matrix-geometric solution," European Journal of Operational Research, Elsevier, vol. 15(3), pages 374-381, March.
    4. J. P. C. Blanc, 1992. "The Power-Series Algorithm Applied to the Shortest-Queue Model," Operations Research, INFORMS, vol. 40(1), pages 157-167, February.
    5. Yiqiang Zhao & Winfried K. Grassmann, 1995. "Queueing Analysis of a Jockeying Model," Operations Research, INFORMS, vol. 43(3), pages 520-529, June.
    6. Yiqiang Zhao & W. K. Grassmann, 1990. "The shortest queue model with jockeying," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 773-787, October.
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