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Sojourn times in a two‐stage queueing network with blocking

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  • A. Gómez‐Corral

Abstract

The model considered in this paper involves a tandem queue consisting of a sequence of two waiting lines. The main feature of our model is blocking, i.e., as soon as the second waiting line reaches a certain upper limit, the first line is blocked. The input of units to the tandem queue is the MAP (Markovian arrival process), and service requirements are of phase type. Our objective is to study the sojourn time distribution under the first‐come‐first‐serve discipline by analyzing the sojourn time through times until absorption in appropriately defined quasi‐birth‐and‐death processes and continuous‐time Markov chains. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

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  • A. Gómez‐Corral, 2004. "Sojourn times in a two‐stage queueing network with blocking," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(8), pages 1068-1089, December.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:8:p:1068-1089
    DOI: 10.1002/nav.20044
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    References listed on IDEAS

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    1. N. U. Prabhu, 1967. "Transient Behaviour of a Tandem Queue," Management Science, INFORMS, vol. 13(9), pages 631-639, May.
    2. B. Avi-Itzhak & M. Yadin, 1965. "A Sequence of Two Servers with No Intermediate Queue," Management Science, INFORMS, vol. 11(5), pages 553-564, March.
    3. Gordon C. Hunt, 1956. "Sequential Arrays of Waiting Lines," Operations Research, INFORMS, vol. 4(6), pages 674-683, December.
    4. Nicholas G. Hall & Chelliah Sriskandarajah, 1996. "A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process," Operations Research, INFORMS, vol. 44(3), pages 510-525, June.
    5. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
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