Quasi-product forms for Levy-driven fluid networks

• 成果类型: Article
• 署名作者: Debicki, K.; Dieker, A. B.; Rolski, T.
• 署名单位: University of Wroclaw; Centrum Wiskunde & Informatica (CWI); University of Twente
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1070.0259
• 发表日期: 2007
• 页码: 629-647
• 关键词: path decomposition

摘要

We study stochastic tree fluid networks driven by a multidimensional Levy process. We are interested in (the joint distribution of) the steady-state content in each of the buffers, the busy periods, and the idle periods. To investigate these fluid networks, we relate the above three quantities to fluctuations of the input Levy process by solving a multidimensional Skorokhod reflection problem. This leads to the analysis of the distribution of the componentwise maximums, the corresponding epochs at which they are attained, and the beginning of the first last-passage excursion. Using the notion of splitting times, we are able to find their Laplace transforms. It turns out that, if the components of the Levy process are ordered, the Laplace transform has a so-called quasi-product form. The theory is illustrated by working out special cases, such as tandem networks and priority queues.