RESEARCH ARTICLE

Fluid approximation for generalized Jackson network with vacations

  • Yongjiang GUO
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  • School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received date: 20 Sep 2010

Accepted date: 20 Mar 2012

Published date: 01 Jun 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

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.

Cite this article

Yongjiang GUO . Fluid approximation for generalized Jackson network with vacations[J]. Frontiers of Mathematics in China, 0 , 7(3) : 459 -485 . DOI: 10.1007/s11464-012-0206-5

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