Calculating steady-state probabilities of single-channel closed queueing systems using hyperexponential approximation

Abstract

In this paper we propose a method for calculating steady-state probability distributions of the single-channel closed queueing systems with arbitrary distributions of customer generation times and service times. The approach based on the use of fictitious phases and hyperexponential approximations with parameters of the paradoxical and complex type by the method of moments. We defined conditions for the variation coefficients of the gamma distributions and Weibull distributions, for which the best accuracy of calculating the steady-state probabilities is achieved in comparison with the results of simulation modeling.

Markov reliability models of series systems with redundancy and repair facilities

“…If we consider the described system as a queueing system, then in the absence of redundant units ( 0), m  it is a classical closed queueing system [3]. The closed system is also known as a system with a finite number of sources or the Engset system.…”

Reliability assessment of a series system with redundancy and repair facilities

“…If we consider the described system as a queueing system, then in the absence of redundant units ( 0 m  ), it is a classical closed queueing system [2]. The closed system is also known as a system with a finite number of sources or the Engset system.…”

“…Works [2,[4][5][6][7][8] show that the use of hyperexponential approximation (denoted by l H ) makes it possible to determine with high accuracy the steady-state probabilities of non-Markovian queuing systems. These probabilities are determined using solutions of a system of linear algebraic equations obtained by the method of fictitious phases.…”