An algorithm to compute the waiting time distribution for the M/G/1 queue

An algorithm to compute the waiting time distribution for the M/G/1 queue

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Article ID: iaor20063680
Country: United States
Volume: 16
Issue: 2
Start Page Number: 152
End Page Number: 161
Publication Date: Mar 2004
Journal: INFORMS Journal On Computing
Authors: , , , ,
Keywords: M/G/1 queues
Abstract:

In many modern applications of queueing theory, the classical assumption of exponentially decaying service distributions does not apply. In particular, Internet and insurance risk problems may involve heavy-tailed distributions. A difficulty with heavy-tailed distributions is that they may not have closed-form, analytic Laplace transforms. This makes numerical methods, which use the Laplace transform, challenging. In this paper, we develop a method for approximating Laplace transforms. Using the approximation, we give algorithms to compute the steady state probability distribution of the waiting time of an M/G/1 queue to a desired accuracy. We give several numerical examples, and we validate the approximation with known results where possible or with simulations otherwise. We also give convergence proofs for the methods.

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