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Diffusion approximation for signaling stochastic networks

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  • Leite, Saul C.
  • Fragoso, Marcelo D.

Abstract

This paper introduces an unified approach to diffusion approximations of signaling networks. This is accomplished by the characterization of a broad class of networks that can be described by a set of quantities which suffer exchanges stochastically in time. We call this class stochastic Petri nets with probabilistic transitions, since it is described as a stochastic Petri net but allows a finite set of random outcomes for each transition. This extension permits effects on the network which are commonly interpreted as “routing” in queueing systems. The class is general enough to include, for instance, G-networks with negative customers and triggers as a particular case. With this class at hand, we derive a heavy traffic approximation, where the processes that drive the transitions are given by state-dependent Poisson-type processes and where the probabilities of the random outcomes are also state-dependent. The objective of this approach is to have a diffusion approximation which can be readily applied in several practical problems. We illustrate the use of the results with some numerical experiments.

Suggested Citation

  • Leite, Saul C. & Fragoso, Marcelo D., 2013. "Diffusion approximation for signaling stochastic networks," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 2957-2982.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:8:p:2957-2982
    DOI: 10.1016/j.spa.2013.03.002
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    References listed on IDEAS

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    1. Arnon Arazi & Eshel Ben-Jacob & Uri Yechiali, 2005. "Controlling an oscillating Jackson-type network having state-dependent service rates," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 453-466, December.
    2. Artalejo, J. R., 2000. "G-networks: A versatile approach for work removal in queueing networks," European Journal of Operational Research, Elsevier, vol. 126(2), pages 233-249, October.
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