A Taylor series approach for service-coupled queueing systems with intermediate load
type: Item
instance of: scholarly article
title: A Taylor series approach for service-coupled queueing systems with intermediate load
zbMATH Open document ID: 1426.90068
DOI: 10.1155/2017/3298605
author: Ekaterina Evdokimova
author: Sabine Wittevrongel
author: Dieter Fiems
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40\% to 50\%.
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 6971975
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/3298605
OpenAlex ID: W2599498934
Wikidata QID: Q59147473
cites work: Jackson networks with single-line nodes and limited sojourn or waiting times
cites work: Finite-buffer polling systems with threshold-based switching policy
cites work: Priority queueing systems: from probability generating functions to tail probabilities
cites work: Product form in networks of queues with batch arrivals and batch services
cites work: Numerical Methods for Structured Markov Chains
cites work: Queues with paired customers
cites work: Bounds and heuristics for assembly-like queues
cites work: A Maclaurin-series expansion approach to multiple paired queues
cites work: A formula for singular perturbations of Markov chains
cites work: Perturbation analysis for denumerable Markov chains with application to queueing models
cites work: Analytic perturbation theory and its applications
cites work: Q4325374
cites work: Optimization of polling systems with Bernoulli schedules
cites work: Q4878847
cites work: Rare events in queueing systems -- A survey
description: scientific article; zbMATH DE number 6971975