Fluid approximation for generalized Jackson network with vacations

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• 作者：Yongjiang Guo (1) yongjiangguo@163.com
• 关键词：Generalized Jackson network (GJN) with vacations – ; fluid approximation – ; exponential convergence rate
• 刊名：Frontiers of Mathematics in China
• 出版年：2012
• 出版时间：June 2012
• 年：2012
• 卷：7
• 期：3
• 页码：459-485
• 全文大小：241.4 KB
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• 作者单位：1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876 China
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-3576

文摘

Using a bounding technique, we prove that the fluid model of generalized Jackson network (GJN) with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic performance of GJN under fluid approximation. Furthermore, in order to present the impact of vacation on the performance of GJN, we show that exponential rate of convergence for fluid approximation only holds for large N, which is different from a GJN without vacations. The results on fluid approximation and convergence rate are embodied by the queue length, workload, and busy time processes.