• DocumentCode
    851013
  • Title

    The transient solution of time-dependent M/M/1 queues

  • Author

    Zhang, Ji ; Coyle, Edward J., Jr.

  • Author_Institution
    Rensselaer Polytech. Inst., Troy, NY, USA
  • Volume
    37
  • Issue
    6
  • fYear
    1991
  • fDate
    11/1/1991 12:00:00 AM
  • Firstpage
    1690
  • Lastpage
    1696
  • Abstract
    The transient behavior of time-dependent M/M/1 queues is studied. The boundary probability function π0(t), which is the probability that the queue is empty at time t, is shown with analyticity arguments to satisfy a Volterra-type integral equation. The boundary integral equation is derived, and a numerical algorithm is used to solve the integral equation and to find the expected queue size from π0(t). The approach can be applied to many other types of time-dependent queues. Examples are given
  • Keywords
    integral equations; queueing theory; transient response; Volterra-type integral equation; boundary integral equation; numerical algorithm; oundary probability function; time-dependent M/M/1 queues; transient behavior; Approximation methods; Difference equations; Differential equations; Integral equations; Iterative methods; Linear systems; Manufacturing; Markov processes; Partial differential equations; Queueing analysis;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/18.104335
  • Filename
    104335
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=851013