Fluid approximation for generalized Jackson network with vacations

doi:10.1007/s11464-012-0206-5

Front Math Chin

0, Vol.

Issue () : 459-485 https://doi.org/10.1007/s11464-012-0206-5

RESEARCH ARTICLE

Fluid approximation for generalized Jackson network with vacations

Yongjiang GUO(

)

School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

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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.

Keywords Generalized Jackson network (GJN) with vacations fluid approximation exponential convergence rate

Corresponding Author(s): GUO Yongjiang,Email:yongjiangguo@163.com

Issue Date: 01 June 2012

Cite this article:

Yongjiang GUO. Fluid approximation for generalized Jackson network with vacations[J]. Front Math Chin, 0, (): 459-485.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-012-0206-5
https://academic.hep.com.cn/fmc/EN/Y0/V/I/459

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