A new method for finding the characteristic roots of \(E_{n }/E_{m }/1\) queues
type: Item
instance of: scholarly article
title: A new method for finding the characteristic roots of \(E_{n }/E_{m }/1\) queues
zbMATH Open document ID: 1253.60095
author: Winfried K. Grassmann
published in: Methodology and Computing in Applied Probability
publication date: 2012-06-20T00:00:00Z
review text: The author derives a set of equations, one for each complex root, which can be solved by Newton's method using real arithmetic. This method simplifies the programming logic because it avoids deflation and the subsequent polishing of the roots. Using the waiting time distribution, Syski (cf. [\textit{R. Syski} and \textit{N. H. G. Morris}. Introduction to congestion theory in telephone systems. Edinburgh-London: Oliver \& Boyd (1960; Zbl 0095.32801)]) derived the distribution of the number in the system after a departure. \(E_{n }/E_{m }/1\) queues can also formulated as quasi birth-death (QBD) processes, and, in this case, the characteristic roots discussed by Syski are closely related to the eigenvalues of the QBD process. The QBD process provides information about the number in system at random times, but they are much more difficult to formulate and solve.
reviewed by: János Sztrik
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 65H04
zbMATH DE Number: 6048540
zbMATH Keywords: Erlang queues
zbMATH Keywords: characteristic equations
zbMATH Keywords: waiting time
zbMATH Keywords: matrix analytic methods
zbMATH Keywords: solutions of polynomials
MaRDI profile type: Publication
full work available at URL: s11009-010-9199-2
OpenAlex ID: W2031646574
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DOI: 10.1007/S11009-010-9199-2
description: scientific article; zbMATH DE number 6048540