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Reducing Response Time in Fork-Join Systems under Heavy Traffic Via Imbalance Control

Part of: Stochastic systems and control Special processes

Published online by Cambridge University Press:  04 January 2016

Saul C. Leite  and
Marcelo D. Fragoso
Saul C. Leite
Affiliation:
Universidade Federal de Juiz de Fora
Marcelo D. Fragoso*
Affiliation:
Laboratório Nacional de Computação Científica
*
∗ Postal address: Department of Systems and Control, National Laboratory for Scientific Computing (LNCC), Laboratório Nacional de Computação Científica, Av. Getulio Vargas 333, Petrópolis, RJ, CEP:25651-075, Brazil. Email address: frag@lncc.br
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Abstract

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We consider the problem of reducing the response time of fork-join systems by maintaining the workload balanced among the processing stations. The general problem of modeling and finding an optimal policy that reduces imbalance is quite difficult. In order to circumvent this difficulty, the heavy traffic approach is taken, and the system dynamics are approximated by a reflected diffusion process. This way, the problem of finding an optimal balancing policy that reduces workload imbalance is set as a stochastic optimal control problem, for which numerical methods are available. Some numerical experiments are presented, where the control problem is solved numerically and applied to a simulation. The results indicate that the response time of the controlled system is reduced significantly using the devised control.

Keywords

Queueing theoryparallel systemheavy traffic analysis

MSC classification

Primary: 60K25: Queueing theory
Secondary: 93E20: Optimal stochastic control
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 4 , December 2013 , pp. 1137 - 1156
Copyright
© Applied Probability Trust 

Footnotes

A preliminary version of this paper was presented at the IFAC World Conference 2011, Milan, Italy.

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