Mathematical Methods of Operations Research

, Volume 47, Issue 1, pp 83–97

The advantage of small machines in a stochastic fluid production process

  • Nicole Bäuerle

DOI: 10.1007/BF01193838

Cite this article as:
Bäuerle, N. Mathematical Methods of Operations Research (1998) 47: 83. doi:10.1007/BF01193838


We consider a stochastic fluid production model, where m machines which are subject to breakdown and repair, produce a fluid at ratep > 0 per machine if it is working. This fluid is fed into an infinite buffer with stochastic output rate. Under the assumption that the machine processes are independent and identically distributed, we prove that the buffer content at timet is less or equal in the increasing convex ordering to the buffer content at time t of a model withm′m machines and production ratep′ =m/m′ p. This formulation includes a conjecture posed by Mitra [6]. More-over, it is shown how to extend this result to Brownian flow systems, systems obtained by diffusion approximation and simple stochastic flow networks like tandem buffer and assembly systems.

Key words

Stochastic fluid models Increasing convex ordering Brownian flow systems Tandem buffer systems Assembly systems 

Copyright information

© Physica-Verlag 1998

Authors and Affiliations

  • Nicole Bäuerle
    • 1
  1. 1.Department of Mathematics VIIUniversity of UlmUlmGermany

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