IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v42y1994i4p750-764.html
   My bibliography  Save this article

Transient Behavior of the M/G/1 Workload Process

Author

Listed:
  • Joseph Abate

    (Bell Communications Research, Piscataway, New Jersey)

  • Ward Whitt

    (AT&T Bell Laboratories, Murray Hill, New Jersey)

Abstract

In this paper we describe the time-dependent moments of the workload process in the M / G /1 queue. The k th moment as a function of time can be characterized in terms of a differential equation involving lower moment functions and the time-dependent server-occupation probability. For general initial conditions, we show that the first two moment functions can be represented as the difference of two nondecreasing functions, one of which is the moment function starting at zero. The two nondecreasing components can be regarded as probability cumulative distribution function (cdf's) after appropriate normalization. The normalized moment functions starting empty are called moment cdf's; the other normalized components are called moment-difference cdf's. We establish relations among these cdf's using stationary-excess relations. We apply these relations to calculate moments and derivatives at the origin of these cdf's. We also obtain results for the covariance function of the stationary workload process. It is interesting that these various time-dependent characteristics can be described directly in terms of the steady-state workload distribution.

Suggested Citation

  • Joseph Abate & Ward Whitt, 1994. "Transient Behavior of the M/G/1 Workload Process," Operations Research, INFORMS, vol. 42(4), pages 750-764, August.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:4:p:750-764
    DOI: 10.1287/opre.42.4.750
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.42.4.750
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.42.4.750?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Britt Mathijsen & Bert Zwart, 2017. "Transient error approximation in a Lévy queue," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 269-304, April.
    2. Peter W. Glynn & Rob J. Wang, 2018. "On the rate of convergence to equilibrium for reflected Brownian motion," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 165-197, June.
    3. Xiaoyuan Liu & Brian Fralix, 2019. "On Lattice Path Counting and the Random Product Representation, with Applications to the Er/M/1 Queue and the M/Er/1 Queue," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1119-1149, December.

    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:inm:oropre:v:42:y:1994:i:4:p:750-764. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.