When does forced idle time improve performance in polling models?

• 成果类型: Article
• 署名作者: Cooper, RB; Niu, SC; Srinivasan, MM
• 署名单位: State University System of Florida; Florida Atlantic University; University of Texas System; University of Texas Dallas; University of Tennessee System; University of Tennessee Knoxville
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.44.8.1079
• 发表日期: 1998
• 页码: 1079-1086
• 关键词: polling models; cyclic production systems; setup times; switchover times; Waiting times; variance paradox; vacation models; DECOMPOSITION

摘要

Sarkar and Zangwill (1991) showed by numerical examples that reduction in setup times can, surprisingly, actually increase work in process in some cyclic production systems (that is, reduction in switchover times can increase waiting times in some polling models). We present, for polling models with exhaustive and gated service disciplines, some explicit formulas that provide additional insight and characterization of this anomaly. More specifically, we show that, for both of these models, there exist simple formulas that define for each queue a critical value z* of the mean total setup time z per cycle such that, if z < z*, then the expected waiting time at that queue will be minimized if the server is forced to idle for a constant length of time z* - z every cycle; also, for the symmetric polling model, we give a simple explicit formula for the expected waiting time and the critical value z* that minimizes it.