Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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MARKOVIAN EARLY ARRIVAL DISCRETE TIME JACKSON NETWORKS

  • Aboul-Hassan A. (Department of Engineering Mathematics and Physics, Alexandria University) ;
  • Rabia S.I. (Department of Engineering Mathematics and Physics, Alexandria University)
  • Published : 2006.09.01
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Abstract

In an earlier work, we investigated the problem of using linear programming to bound performance measures in a discrete time Jackson network. There it was assumed that the system evolution is controlled by the early arrival scheme. This assumption implies that the system can't be modelled by a Markov chain. This problem was resolved and performance bounds were calculated. In the present work, we use a modification of the early arrival scheme (without corrupting it) in order to make the system evolves as a Markov chain. This modification enables us to obtain explicit expressions for certain moments that could not be calculated explicitly in the pure early arrival scheme setting. Moreover, this feature implies a reduction in the linear program size as well as the computation time. In addition, we obtained tighter bounds than those appeared before due to the new setting.

Keywords

References

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