Strong approximations for time-dependent queues

Strong approximations for time-dependent queues

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Article ID: iaor20033017
Country: United States
Volume: 20
Issue: 1
Start Page Number: 33
End Page Number: 64
Publication Date: Feb 1995
Journal: Mathematics of Operations Research
Authors: ,
Keywords: M/M/1 queues
Abstract:

A time-dependent M(t)/M(t)/1 queue alternates through periods of under-, over-, and critical loading. We derive period-dependent, pathwise asymptotic expansions for its queue length, within the framework of strong approximations. Our main results include time-dependent fluid approximations, supported by a functional strong law of large numbers, and diffusion approximations, supported by a functional central limit theorem. This complements and extends previous work on asymptotic expansions of the queue-length transition probabilities.

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