Bounds and inequalities for single server loss systems |
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| Authors: | Cheng-Shang Chang Michael Pinedo |
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| Affiliation: | (1) Center for Telecommunications Research, Columbia University, 10027 New York, NY, USA;(2) IBM Research Division, T.J. Watson Research Center, H2-K06, P.O. Box 704, 10598 Yorktown Heights, NY, USA;(3) Department of Industrial Engineering and Operations Research, Columbia University, 10027 New York, NY, USA |
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| 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. |
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| Keywords: | Ross's conjecture loss systems variability ordering doubly stochastic Poisson processes |
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