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 journalArticle

16 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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