Heavy tails and long range dependence in on/off processes and associated fluid models

• 成果类型: Article
• 署名作者: Heath, D; Resnick, S; Samorodnitsky, G
• 署名单位: Cornell University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.23.1.145
• 发表日期: 1998
• 页码: 145-165
• 关键词: self-similarity; distributions

摘要

On/off models are common inputs for a variety of communication network models as well as storage and inventory models. A stationary renewal process alternating periods of activity (active transmission, fluid buildup, etc) with periods of inactivity (silence, no transmission, inputs off, etc) induces a stationary indicator process which indicates if the system is active or not. Heavy tails for the on periods induces a covariance function for the indicator process which decreases slowly at a rate characteristic of long range dependence. This has dramatic consequences for fluid models where fluid flows in at constant rate and there is a constant rate of release.