Analysis of random walks with an absorbing barrier and chemical rule
type: Item
instance of: scholarly article
title: Analysis of random walks with an absorbing barrier and chemical rule
zbMATH Open document ID: 1170.60033
author: A. M. K. Tarabia
published in: Journal of Computational and Applied Mathematics
publication date: 2009-03-17T00:00:00Z
review text: The paper considers continuous random walks with an absorbing barrier and chemical rule for transition rates. It means that transition rate from \(n\) to \(m\) equals either to \(\lambda \) if \(m = 2k + 1,\,n = 2k\) or \(m = 2k,\,n = 2k + 1\) or to \(\mu \) if \(m = 2k - 1,\,n = 2k\) or \(m = 2k,\,n = 2k - 1\). The paper derives explicit expressions for the first passage time and the transient state distributions. The derived formula for the transient state is free of Bessel functions or any integral forms. It is demonstrated that the busy period distribution of a non-empty \(M/M/1/\infty \) queueing model is a special case of the derived result.
reviewed by: Oleg K. Zakusilo
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 5529481
zbMATH Keywords: chemical queue
zbMATH Keywords: busy period
zbMATH Keywords: continuous random walk
zbMATH Keywords: first passage time
zbMATH Keywords: differential difference-equations
MaRDI profile type: Publication
full work available at URL: j.cam.2008.08.043
OpenAlex ID: W1969763866
cites work: Some remarks on the duality of continuous time markov chains
cites work: Q4371373
cites work: Time-Dependent Statistics of the Ising Model
cites work: Q3806522
cites work: Q5589310
cites work: A Simple Formula for the Transient State Probabilities of an M/M/1/∞Queue
cites work: A simple transient analysis of an M/M/1/N queue
cites work: On the busy period of a multichannel Markovian queue
cites work: A new formula for the busy period of a non-empty multiserver queueing system
cites work: Exact transient solutions of nonempty Markovian queues
DOI: 10.1016/J.CAM.2008.08.043
description: scientific article; zbMATH DE number 5529481