Infinite-server queues with time-varying rates
type: Item
instance of: scholarly article
title: Infinite-server queues with time-varying rates
zbMATH Open document ID: 1390.90269
DOI: 10.1504/IJMOR.2013.050514
author: Guichang Zhang
author: Raj Srinivasan
published in: International Journal of Mathematics in Operational Research
publication date: 2018-05-29T00:00:00Z
review text: Summary: In this paper, we study infinite server queues with time-varying rates. Under the assumption of non-homogenous Poisson process for the arrivals and service processes, in addition to deriving the standard Kolmogorov forward equation, we introduce and develop a generalised backward equation for the \(M(t)/M(t)/\infty\) queue using martingales. Explicit solution for these two equations are provided. We also introduce two more Kolmogorov type equations namely, the quasi Kolmogorov Backward Equation and the quasi Generalised Forward Equation for the \(M(t)/M(t)/\infty\) queue. Based on the solutions developed for the \(M(t)/M(t)/\infty\) queue, we provide an alternative and easy to interpret justification for the transition probabilities of the \(M(t)/G(t)/\infty\) queue. Finally we develop expressions to calculate the time dependent version of the mean and variance of the queue length processes.
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 6876009
zbMATH Keywords: Kolmogorov-type equation
zbMATH Keywords: multi-server queues
zbMATH Keywords: martingales
zbMATH Keywords: time-varying rates
MaRDI profile type: Publication
full work available at URL: ijmor.2013.050514
OpenAlex ID: W2065473850
description: scientific article; zbMATH DE number 6876009