Large‐time asymptotics for the G

t
/M

t
/s

t
+GI

t
 many‐server fluid queue with abandonment

Large‐time asymptotics for the G t /M t /s t +GI t many‐server fluid queue with abandonment

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Article ID: iaor20111984
Volume: 67
Issue: 2
Start Page Number: 145
End Page Number: 182
Publication Date: Feb 2011
Journal: Queueing Systems
Authors: ,
Keywords: fluid queue, GI/M/c queues, periodic
Abstract:

We previously introduced and analyzed the G t /M t /s t +GI t many‐server fluid queue with time‐varying parameters, intended as an approximation for the corresponding stochastic queueing model when there are many servers and the system experiences periods of overload. In this paper, we establish an asymptotic loss of memory (ALOM) property for that fluid model, i.e., we show that there is asymptotic independence from the initial conditions as time t evolves, under regularity conditions. We show that the difference in the performance functions dissipates over time exponentially fast, again under the regularity conditions. We apply ALOM to show that the stationary G/M/s+GI fluid queue converges to steady state and the periodic G t /M t /s t +GI t fluid queue converges to a periodic steady state as time evolves, for all finite initial conditions.

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