Structural interpretation and derivation of necessary and sufficient conditions for delay moments in FIFO multiserver queues

Alan Scheller-Wolf, Rein Vesilo*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    19 Citations (Scopus)

    Abstract

    Scheller-Wolf [12] established necessary and sufficient conditions for finite stationary delay moments in stable FIFO GI/GI/s queues that incorporate the interaction between service time distribution, traffic intensity (ρ) and the number of servers in the queue. These conditions can be used to show that when the service time has finite first but infinite αth moment, s slow servers can give lower delays than one fast server. In this paper, we derive an alternative derivation of these moment results: Both upper bounds, that serve as sufficient conditions, and lower bounds, that serve as necessary conditions are presented. In addition, we extend the class of service time distributions for which the necessary conditions are valid. Our new derivations provide a structural interpretation of the moment bounds, giving intuition into their origin: We show that FIFO GI/GI/s delay can be represented as the minimum of (s - k) i.i.d. GI/GI/1 delays, when ρ satisfies k < ρ < k+1.

    Original languageEnglish
    Pages (from-to)221-232
    Number of pages12
    JournalQueueing Systems
    Volume54
    Issue number3
    DOIs
    Publication statusPublished - Nov 2006

    Keywords

    • Finite moment conditions
    • Multiserver queues
    • Necessary and sufficient conditions

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