International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1999 / Article

Open Access

Volume 12 |Article ID 780913 |

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.

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

Received01 Sep 1997
Revised01 Aug 1998


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.

More related articles

 PDF Download Citation Citation
 Order printed copiesOrder

Related articles

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.