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Differentiability of functionals of Poisson processes via coupling with applications to queueing theory

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  • Baccelli, François
  • Hasenfuss, Sven
  • Schmidt, Volker

Abstract

We give some probabilistic conditions based on coupling for a functional of a Poisson point process to be differentiable in the intensity [lambda] of this process in a neighborhood of the origin. These conditions are exemplified on various queueing theory problems, and compared with other conditions of the literature.

Suggested Citation

  • Baccelli, François & Hasenfuss, Sven & Schmidt, Volker, 1999. "Differentiability of functionals of Poisson processes via coupling with applications to queueing theory," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 299-321, June.
    • Handle: RePEc:eee:spapps:v:81:y:1999:i:2:p:299-321
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    References listed on IDEAS

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    1. Martin I. Reiman & Burton Simon, 1989. "Open Queueing Systems in Light Traffic," Mathematics of Operations Research, INFORMS, vol. 14(1), pages 26-59, February.
    2. Blaszczyszyn, B., 1995. "Factorial moment expansion for stochastic systems," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 321-335, April.
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    Cited by:

    1. Ilya Molchanov & Sergei Zuyev, 2000. "Variational Analysis of Functionals of Poisson Processes," Mathematics of Operations Research, INFORMS, vol. 25(3), pages 485-508, August.

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