Stationary and transient solution of Markovian queues -- an alternate approach
type: Item
instance of: scholarly article
title: Stationary and transient solution of Markovian queues -- an alternate approach
zbMATH Open document ID: 1390.90258
DOI: 10.1504/IJMOR.2013.053627
author: R. Sudhesh
author: L. Francis Raj
published in: International Journal of Mathematics in Operational Research
publication date: 2018-06-06T00:00:00Z
review text: Summary: This paper aims at presenting an alternate approach to derive the exact transient solution of Markovian queues. The continued fraction (Jacobi fraction) is expressed as power series and the power series coefficients are connected by a two-dimensional recurrence relation associated with infinite Stieltjes matrix equation. The recurrence relation is solved by using generating functions. A novel state-dependent birth-death queueing model is taken and expressed as continued fractions by employing integral transforms. The stationary probabilities of general state-dependent Markovian queues are obtained from the continued fractions and its associated tridiagonal determinants. As a special case the time-dependent system size probabilities and busy period distribution of a classical single server queue are deduced using continued fraction and its power series. Numerical illustrations are also presented.
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 6881321
zbMATH Keywords: continued fractions
zbMATH Keywords: Jacobi fractions
zbMATH Keywords: CFs
zbMATH Keywords: two-dimensional recurrence relation
zbMATH Keywords: generating functions
zbMATH Keywords: power series
zbMATH Keywords: time-dependent probabilities
zbMATH Keywords: stationary probabilities
zbMATH Keywords: numerical solutions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6881321