On the discrete-time \(\mathrm{Geo}/\mathrm{G}/1\) queue with vacations in random environment
type: Item
instance of: scholarly article
title: On the discrete-time \(\mathrm{Geo}/\mathrm{G}/1\) queue with vacations in random environment
zbMATH Open document ID: 1417.60076
DOI: 10.1155/2016/4029415
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: A discrete-time \(\mathrm{Geo}/\mathrm{G}/1\) queue with vacations in random environment is analyzed. Using the method of supplementary variable, we give the probability generating function (PGF) of the stationary queue length distribution at arbitrary epoch. The PGF of the stationary sojourn time distribution is also derived. And we present the various performance measures such as mean number of customers in the system, mean length of the type-\(i\) cycle, and mean time that the system resides in phase \(0\). In addition, we show that the \(\mathrm{M}/\mathrm{G}/1\) queue with vacations in random environment can be approximated by its discrete-time counterpart. Finally, we present some special cases of the model and numerical examples.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 7026882
zbMATH Keywords: queue with vacations
Wikidata QID: Q59123481
author: Jianjun Li
author: Li-Wei Liu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/4029415
OpenAlex ID: W2433191412
cites work: Queueing systems with vacations - a survey
cites work: Q3999697
cites work: Vacation queueing models. Theory and applications
cites work: Q3326556
cites work: Discrete-Time Queuing Theory
cites work: Discrete time geo\(/G/1\) queue with multiple adaptive vacations
cites work: Vacation models in discrete time
cites work: A discrete-time \(\operatorname{Geo}/G/1\) retrial queue with the server subject to starting failures
cites work: The discrete-time GI/Geo/1 queue with working vacations and vacation interruption
cites work: The \(GI/Geo/1\) queue with Bernoulli-schedule-controlled vacation and vacation interruption
cites work: Analysis of a discrete-time working vacation queue with balking
cites work: Queuing Problems with Heterogeneous Arrivals and Service
cites work: A queue subject to extraneous phase changes
cites work: The M/G/1 queue with two service speeds
cites work: The UnreliableM/M/1 Retrial Queue in a Random Environment
cites work: An \(M/M/1\) queue in random environment with disasters
cites work: Analysis of the M/G/1 queue in multi-phase random environment with disasters
cites work: On the steady-state queue size distribution of the discrete-time \(\text{Geo}/G/1\) queue with repeated customers
description: scientific article; zbMATH DE number 7026882