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Contributions to the theory of first‐exit times of some compound processes in queueing theory

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Abstract

We consider compound processes that are linear with constant slope between i.i.d. jumps at time points forming a renewal process. These processes are basic in queueing, dam and risk theory. For positive and for negative slope we derive the distribution of the first crossing time of a prespecified level. The related problem of busy periods of single‐server queueing systems is also studied.

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Authors and Affiliations

  1. Department of Statistics, University of Haifa, 31905, Haifa, Israel

    D. Perry

  2. Department of Mathematics and Computer Science, University of, Osnabrück, 49069, Osnabrück, Germany

    W. Stadje

  3. Department of Mathematical Sciences, Binghamton University, P.O. Box 6000, Binghamton, NY, 13902‐6000, USA

    S. Zacks

Authors
  1. D. Perry
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  2. W. Stadje
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  3. S. Zacks
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Perry, D., Stadje, W. & Zacks, S. Contributions to the theory of first‐exit times of some compound processes in queueing theory. Queueing Systems 33, 369–379 (1999). https://doi.org/10.1023/A:1019140616021

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  • DOI: https://doi.org/10.1023/A:1019140616021

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