Abstract
The purpose of this paper is to suggest a method and software for evaluating queuing approximations. A numerical queuing model with priorities is used to explore the behaviour of exponential phase‐type approximation of service‐time distribution. The performance of queuing systems described in the event language is used for generating the set of states and transition matrix between them. Two examples of numerical models are presented - a queuing system model with priorities and a queuing system model with quality control.
Highlights
Queuing models are important tools for studying the performance of complex systems, but despite the substantial queuing theory literature, it is often necessary to use approximations in case a system is non-markovian
The purpose of this paper is to suggest a method and software for evaluating queuing approximations
A method for automatic construction of numerical models for systems described by Markov chains with a countable space of states and continuous time is used in the work
Summary
Queuing models are important tools for studying the performance of complex systems, but despite the substantial queuing theory literature, it is often necessary to use approximations in case a system is non-markovian. Use of phase-type (PH) distributions is a common means of obtaining tractable queuing models [1,2,3,4]. The approach of this investigation is to begin with service-time distribution to be approximated. A simple three-moment approximation, along with a more refined approximation taking into account distribution shape, is presented for an original input distribution Both the original and approximating distributions are used in modelling the queue with simple priorities. A method for automatic construction of numerical models for systems described by Markov chains with a countable space of states and continuous time is used in the work
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