SOME EFFECTS OF NONSTATIONARITY ON MULTISERVER MARKOVIAN QUEUING-SYSTEMS

• 成果类型: Article
• 署名作者: GREEN, L; KOLESAR, P; SVORONOS, A
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.39.3.502
• 发表日期: 1991
• 页码: 502-511
• 关键词: Queues; MULTICHANNEL MARKOVIAN; EFFECTS OF NONSTATIONARITY; queues; NONSTATIONARY; BEHAVIOR AS A FUNCTION OF NONSTATIONARITY

摘要

We examine the effects of nonstationarity on the performance of multiserver queueing systems with exponential service times and sinusoidal Poisson input streams. Our primary objective is to determine when and how a stationary model may be used as an approximation for a nonstationary system. We focus on a particular question: How nonstationary can an arrival process be before a simple stationary approximation fails? Our analysis reveals that stationary models can seriously underestimate delays when the actual system is only modestly nonstationary. Other findings include confirmation and elaboration of S. M. Ross's conjecture that expected delays increase with nonstationarity, and the identification of easily computed and tight lower and upper bounds for expected delay and the probability of delay. These empirical results are based on a series of computer experiments in which the differential equations governing system behavior are solved numerically.