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Two limit theorems for queueing systems around the convergence of stochastic integrals with respect to renewal processes

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  • Yamada, Keigo

Abstract

Two limit theorems on asymptotic behaviors of some processes related to some queueing systems are investigated. In the first result (Theorem 1), sticky diffusions appear as limit processes for queues with vacations. In the second result (Theorem 2), limiting behavior of occupation times and counting processes related to open queueing networks is discussed. The core of the arguments for obtaining our results is to discuss the convergence of stochastic integrals with respect to renewal processes.

Suggested Citation

  • Yamada, Keigo, 1999. "Two limit theorems for queueing systems around the convergence of stochastic integrals with respect to renewal processes," Stochastic Processes and their Applications, Elsevier, vol. 80(1), pages 103-128, March.
    • Handle: RePEc:eee:spapps:v:80:y:1999:i:1:p:103-128
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    References listed on IDEAS

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    1. Slominski, Leszek, 1989. "Stability of strong solutions of stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 173-202, April.
    2. Martin I. Reiman, 1984. "Open Queueing Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 441-458, August.
    3. Yamada, Keigo, 1994. "Reflecting or sticky Markov processes with Lévy generators as the limit of storage processes," Stochastic Processes and their Applications, Elsevier, vol. 52(1), pages 135-164, August.
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