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Queueing Systems

, Volume 6, Issue 1, pp 425–435 | Cite as

Bounds and inequalities for single server loss systems

  • Cheng-Shang Chang
  • Michael Pinedo
Short Communication

Abstract

We consider a single server loss system in which arrivals occur according to a doubly stochastic Poisson process with a stationary ergodic intensity functionλ t . The service times are independent, exponentially distributed r.v.'s with meanμ −1, and are independent of arrivals. We obtain monotonicity results for loss probabilities under time scaling as well as under amplitude scaling ofλ t . Moreover, using these results we obtain both lower and upper bounds for the loss probability.

Keywords

Ross's conjecture loss systems variability ordering doubly stochastic Poisson processes 

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Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1990

Authors and Affiliations

  • Cheng-Shang Chang
    • 1
    • 2
  • Michael Pinedo
    • 1
    • 3
  1. 1.Center for Telecommunications ResearchColumbia UniversityNew YorkUSA
  2. 2.IBM Research Division, T.J. Watson Research Center, H2-K06Yorktown HeightsUSA
  3. 3.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA

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