Abstract
This paper presents a new approach to the functional approximation of the M/G/1/N built on a Taylor series approach. Specifically, we establish an approximative expression for the remainder term of the Taylor series that can be computed in an efficient manner. As we will illustrate with numerical examples, the resulting Taylor series approximation turns out to be of practical value.
Highlights
Queueing models are a well-established tool for the analysis of stochastic systems from areas as divers as manufacturing, telecommunication, transport and the service industry
We investigate the use of Taylor polynomials for the numerical evaluation of the M/G/1/N queue
We have presented a new approach to the functional approximation of finite queues
Summary
Queueing models are a well-established tool for the analysis of stochastic systems from areas as divers as manufacturing, telecommunication, transport and the service industry. Often there is not sufficient statistical data to determine the service and interarrival time distribution, or, in case the type of distribution is known, there is statical uncertainty on the exact values of the parameters of the distribution For these reasons, perturbation analysis of queueing systems (PAQS) has been developed. We will approximate π ∗(θ + ) by a polynomial in To achieve this we will use the Taylor series expansion approach established in Heidergott and Hordijk (2003). Let πθ denote the stationary distribution of the queue-length process embedded at departure epoches in the M/G/1/N queue, where θ ∈ R denotes a control parameter.
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