Approximations of the mean waiting time in an M/G/s queueing system

O.J. Boxma, J.W. Cohen, N. Huffels

    Research output: Contribution to journalArticleAcademicpeer-review

    63 Citations (Scopus)

    Abstract

    This paper considers the problem of obtaining approximate expressions for the first moment WGs of the stationary waiting time distribution in an M/G/s queueing system. Special attention is paid to the case G D, i.e., constant service times. Most known approximations are in fact heavy traffic approximations which have rather large relative errors in the light traffic case. In the present study both the light traffic and heavy traffic behavior of WGs (WDs) are taken into account. In order to obtain mean waiting time approximations it appears to be useful to introduce a quantity (the "normed cooperation coefficient") which is inversely proportional to WGs and which is in some sense a measure for the "cooperation" between the servers of the service facility. A part of the paper is devoted to the analysis of this normed cooperation coefficient.
    Original languageEnglish
    Pages (from-to)1115-1127
    Number of pages13
    JournalOperations Research
    Volume27
    Issue number6
    DOIs
    Publication statusPublished - 1979

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