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The advantage of small machines in a stochastic fluid production process

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  • Nicole Bäuerle

Abstract

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. Copyright Physica-Verlag 1998

Suggested Citation

  • Nicole Bäuerle, 1998. "The advantage of small machines in a stochastic fluid production process," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(1), pages 83-97, February.
    • Handle: RePEc:spr:mathme:v:47:y:1998:i:1:p:83-97
    DOI: 10.1007/BF01193838
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    References listed on IDEAS

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    1. Rajeeva L. Karandikar & Vidyadhar G. Kulkarni, 1995. "Second-Order Fluid Flow Models: Reflected Brownian Motion in a Random Environment," Operations Research, INFORMS, vol. 43(1), pages 77-88, February.
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