Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
INFORMS Journal on Computing
An Algorithm to Compute the Waiting Time Distribution for the M/G/1 Queue
INFORMS Journal on Computing
A Unified Framework for Numerically Inverting Laplace Transforms
INFORMS Journal on Computing
A simple solution for the M/D/c waiting time distribution
Operations Research Letters
Wide-area Internet traffic patterns and characteristics
IEEE Network: The Magazine of Global Internetworking
Analysis of an M/{Dn}/1 retrial queue
Journal of Computational and Applied Mathematics
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This paper considers an M/G/1 queue where the service time for each customer is a discrete random variable taking one of N values. We call this an M/DN/1 queue. There are potential numerical problems inverting Laplace transforms associated with this queue because the service distribution is discontinuous. The purpose of this paper is to investigate the performance of numerical transform-inversion methods in analyzing this queue. We first derive continuity properties of the steady-state distribution of wait in the M/DN/1 queue. Then, we show analytically how continuity properties affect the performance of the Fourier method for inverting transforms. In particular, continuity is not required in all derivatives for best performance of the method. We also present a new inversion method specifically for the M/DN/1 queue. Finally, we give numerical experiments comparing these and four other inversion methods. Although no method clearly dominates, the recursion method performs well in most examples.