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A convexity result for single-server exponential loss systems with non-stationary arrivals

  • Antony Svoronos (a1) and Linda Green (a1)

Abstract

We consider single-server loss systems with exponential service times and non-stationary Poisson input. We prove that if the arrival rate is given by a periodic function, the proportion of lost customers is convex increasing in the amplitude.

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Postal address: Graduate School of Business, Uris Hall, Columbia University, New York, NY 10027, USA.

References

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Heyman, D. P. (1982) On Ross's conjectures about queues with non-stationary Poisson arrivals. J. Appl. Prob. 19, 245249.
Heyman, D. P. and Whitt, W. (1984) The asymptotic behavior of queues with time-varying arrival rates. J. Appl. Prob. 21, 143156.
Rolski, T. (1981) Queues with non-stationary input stream: Ross's conjecture. Adv. Appl. Prob. 13, 603618.
Rolski, T. (1983) Comparison theorems for queues with dependent interarrival times. Proceedings of the International Seminar , Paris, France.
Ross, S. M. (1978) Average delay in queues with non-stationary Poisson arrivals. J. Appl. Prob. 15, 602609.

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