The asymptotic variance rate of the output process of finite capacity birth-death queues

Y. Nazarathy, G. Weiss

    Research output: Contribution to journalArticleAcademicpeer-review

    16 Citations (Scopus)

    Abstract

    We analyze the output process of finite capacity birth-death Markovian queues. We develop a formula for the asymptotic variance rate of the form ¿ *+¿v i where ¿ * is the rate of outputs and v i are functions of the birth and death rates. We show that if the birth rates are non-increasing and the death rates are non-decreasing (as is common in many queueing systems) then the values of v i are strictly negative and thus the limiting index of dispersion of counts of the output process is less than unity. In the M/M/1/K case, our formula evaluates to a closed form expression that shows the following phenomenon: When the system is balanced, i.e. the arrival and service rates are equal, is minimal. The situation is similar for the M/M/c/K queue, the Erlang loss system and some PH/PH/1/K queues: In all these systems there is a pronounced decrease in the asymptotic variance rate when the system parameters are balanced.
    Original languageEnglish
    Pages (from-to)135-156
    JournalQueueing Systems: Theory and Applications
    Volume59
    Issue number2
    DOIs
    Publication statusPublished - 2008

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