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: | Massey W.A., Mandelbaum Avishai |
Keywords: | M/M/1 queues |
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.