Structural interpretation and derivation of necessary and sufficient conditions for delay moments in FIFO multiserver queues |
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Authors: | Alan Scheller-Wolf Rein Vesilo |
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Institution: | (1) Tepper School of Business, Carnegie Mellon University, Pittsburgh, USA;(2) Department of Electronics, Macquarie University, Sydney, Australia |
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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.
AMS Subject Classification 60K25 |
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Keywords: | Multiserver queues Finite moment conditions Necessary and sufficient conditions |
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