International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1999 / Article

Open Access

Volume 12 |Article ID 780913 | https://doi.org/10.1155/S1048953399000052

Doo Il Choi, Charles Knessl, Charles Tier, "A queueing system with queue length dependent service times, with applications to cell discarding in ATM networks", International Journal of Stochastic Analysis, vol. 12, Article ID 780913, 28 pages, 1999. https://doi.org/10.1155/S1048953399000052

A queueing system with queue length dependent service times, with applications to cell discarding in ATM networks

Received01 Sep 1997
Revised01 Aug 1998

Abstract

A queueing system (M/G1,G2/1/K) is considered in which the service time of a customer entering service depends on whether the queue length, N(t), is above or below a threshold L. The arrival process is Poisson, and the general service times S1 and S2 depend on whether the queue length at the time service is initiated is <L or L, respectively. Balance equations are given for the stationary probabilities of the Markov process (N(t),X(t)), where X(t) is the remaining service time of the customer currently in service. Exact solutions for the stationary probabilities are constructed for both infinite and finite capacity systems. Asymptotic approximations of the solutions are given, which yield simple formulas for performance measures such as loss rates and tail probabilities. The numerical accuracy of the asymptotic results is tested.

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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