Stochastic modelling and analysis: a computational approach
Stochastic modelling and analysis: a computational approach
Computational analysis of steady-state probabilities of M/Ga,b/1 and related nonbulk queues
Queueing Systems: Theory and Applications
Elementary Numerical Analysis: An Algorithmic Approach
Elementary Numerical Analysis: An Algorithmic Approach
Mean waiting time of a Gamma/Gamma/1 queue
Operations Research Letters
Approximations for the conditional waiting times in the GI/G/c queue
Operations Research Letters
An explicit solution to a tandem queueing model
Queueing Systems: Theory and Applications
An Alternating Service Problem
Probability in the Engineering and Informational Sciences
Delay Analysis for the Fixed-Cycle Traffic-Light Queue
Transportation Science
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In this paper we study a single-server system with Erlang-r distributed service times and arbitrarily distributed interarrival times. It is shown that the waiting-time distribution can be expressed as a finite sum of exponentials, the exponents of which are the roots of an equation. Under certain conditions for the interarrival-time distribution, this equation can be transformed to r contraction equations, the roots of which can easily be found by successive substitutions. The conditions are satisfied for several practically relevant arrival processes. The resulting numerical procedures are easy to implement and efficient and appear to be remarkably stable, even for extremely high values of r andfor values of the traffic load close to 1. Numerical results are presented.