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Conservation laws and reflection mappings with an application to multiclass mean value analysis for stochastic fluid queues

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  • Konstantopoulos, Takis
  • Zazanis, Michael
  • De Veciana, Gustavo

Abstract

In this paper we derive an alternative representation for the reflection of a continuous, bounded variation process. Under stationarity assumptions we prove a continuous counterpart of Little's law of classical queueing theory. These results, together with formulas from Palm calculus, are used to explain the method for the derivation of the mean value of a buffer fed by a special type stochastic fluid arrival process.

Suggested Citation

  • Konstantopoulos, Takis & Zazanis, Michael & De Veciana, Gustavo, 1996. "Conservation laws and reflection mappings with an application to multiclass mean value analysis for stochastic fluid queues," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 139-146, December.
  • Handle: RePEc:eee:spapps:v:65:y:1996:i:1:p:139-146
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    Cited by:

    1. Y. Wardi & B. Melamed & C.G. Cassandras & C.G. Panayiòtou, 2002. "Online IPA Gradient Estimators in Stochastic Continuous Fluid Models," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 369-405, November.
    2. Benjamin Melamed & Rudolf Leuschner & Weiwei Chen & Dale S. Rogers & Min Cao, 2022. "Inventory turns and finite-horizon Little’s Laws," Annals of Operations Research, Springer, vol. 317(1), pages 129-146, October.

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