Some results for the mean waiting-time and workload in GI/GI/k queues

Some results for the mean waiting-time and workload in GI/GI/k queues

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Article ID: iaor19971674
Country: United States
Volume: 1
Issue: 1
Start Page Number: 35
End Page Number: 60
Publication Date: Jan 1997
Journal: Frontiers in Queueing
Authors:
Keywords: GI/GI/ queues
Abstract:

This paper studies stationary equ1 queueing systems with first-come first-served discipline and generic interarrival and service times T and S, respectively, both with first two moments finite and (relative) traffic intensity equ2. The components of the stationary Kiefer-Wolfowitz vector, equ3equ4, equ5, of workloads form an associated family of random variables. The first moments are bounded below as in equ6, the bound being tight in equ7 systems for which equ8 for some equ9. If equ10, then there is a system for which the mean waiting-time equ11. By considering the limit as equ12 of a sequence of systems with two-point service time distributions specified by equ13, where equ14, an asymptotic decomposition result is established for the sum equ15 amongst systems with given first two moments for S and T; it is new even for the single-server case. From this and further detailed asymptotic results it follows that when equ16, amongst systems with given first two moments finite for S and T, there is always a sequence of systems for which equ17. Heuristic calculations indicate the nature of all the equ18 when equ19. Evidence concerning conjectured upper bounds on equ20 is reviewed.

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