STRONG APPROXIMATIONS FOR TIME-DEPENDENT QUEUES

• 成果类型: Article
• 署名作者: MANDELBAUM, A; MASSEY, WA
• 署名单位: AT&T; Nokia Corporation; Nokia Bell Labs
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.20.1.33
• 发表日期: 1995
• 页码: 33-64
• 关键词: periodic queues; LIMIT-THEOREMS; arrival rates; networks; input

摘要

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.