The attractiveness of the fixed points of a ./GI/1 queue

• 成果类型: Article
• 署名作者: Prabhakar, B
• 署名单位: Stanford University; Stanford University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1068646384
• 发表日期: 2003
• 页码: 2237-2269
• 关键词: NETWORKS; output

摘要

We consider an infinite tandem of first-come-first-served queues. The service times have unit mean, and are independent and identically distributed across queues and customers. Let I be a stationary and ergodic interarrival sequence with marginals of mean tau > 1, and suppose it is independent of all service times. The process I is said to be a fixed point for the first, and hence for each, queue if the corresponding interdeparture sequence is distributed as I. Assuming that such a fixed point exists, we show that it is the distributional limit of passing an arbitrary stationary and ergodic interarrival process of mean tau through the infinite queueing tandem.