IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v34y1987i4p555-567.html
   My bibliography  Save this article

Stochastic comparisons for single‐server queues

Author

Listed:
  • Carl M. Harrissp
  • N. U. Prabhu

Abstract

We consider single‐server queueing systems with the queue discipline “first come, first served,” interarrival times {uk, k ≥ l}, and service times {uk, k ≥ l}, where the {uk} and {uk} are independent sequences of non‐negative random variables that are independently but not necessarily identically distributed. Let Xk = uk − uk (k ≥ 1), S0 0, Sn = X1 + X2 … + Xn(n≥1). It is known that the (possibly nonhomogeneous) random walk {Sn} determines the behavior of the system. In this paper we make stochastic comparisons of two such systems σ1,σ2 whose basic random variables X (1)k and X (1)k are stochastically ordered. The corresponding random walks are also similarly ordered, and this leads to stochastic comparisons of idle times, duration of busy period and busy cycles, number of customers served during a busy period, and output from the system. In the classical case of identical distributions of {uk} and {uk} we obtain further comparisons. Our results are for the transient behavior of the systems, not merely for steady state.

Suggested Citation

  • Carl M. Harrissp & N. U. Prabhu, 1987. "Stochastic comparisons for single‐server queues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(4), pages 555-567, August.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:4:p:555-567
    DOI: 10.1002/1520-6750(198708)34:43.0.CO;2-7
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(198708)34:43.0.CO;2-7
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(198708)34:43.0.CO;2-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Douglas R. Miller, 1979. "Almost Sure Comparisons of Renewal Processes and Poisson Processes, with Application to Reliability Theory," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 406-413, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Smeitink, E. & Dijk, N.M. van & Haverkort, B.R., 1990. "Product forms for availability," Serie Research Memoranda 0040, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    2. Ira Gerhardt & Barry L. Nelson, 2009. "Transforming Renewal Processes for Simulation of Nonstationary Arrival Processes," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 630-640, November.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:34:y:1987:i:4:p:555-567. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.