Gaussian skewness approximation for dynamic rate multi-server queues with abandonment
type: Item
instance of: scholarly article
title: Gaussian skewness approximation for dynamic rate multi-server queues with abandonment
zbMATH Open document ID: 1285.60091
author: William A. Massey
author: Jamol Pender
published in: Queueing Systems
publication date: 2013-12-09T00:00:00Z
review text: The paper under review studies \(M(t)/M/c(t)+M\) queueing systems, where \(M(t)\) in the first position denotes a non-homogeneous Poisson arrival Process, \(M\) in the second position denotes exponentially distributed service time, \(c(t)\) denotes the number of agents (servers) at time \(t\) and \(+M\) in the last position denotes the exponential distribution for an abandonment time. This model is referred to as Erlang-A model, see [\textit{N. Gans}, \textit{G. Koole} and \textit{A. Mandelbaum}, ``Telephone call centers: tutorial, review and research prospects'', Manuf. Serv. Oper. Manag. 5, No. 2, 79--141 (2003)] and describes large scale service systems such as call centers or hospitals. The paper presents a simple method generating new algorithms that are successively better approximations of the stochastic dynamics for the \(M(t)/M/c(t)+M\) queueing system that are known for this type of system from the available literature, see [\textit{Y. M. Ko} and \textit{N. Gautam}, INFORMS J. Computing; \textit{A.Mandelbaum} et al., Queueing Syst. 30, No. 1--2, 149--201 (1998; Zbl 0911.90167); \textit{A. Mandelbaum} et al., ``Queue lengths and waiting times for multi-server queues with abandonment and retrials'', Telecommun. Syst. 21, 149--172 (2002)]. This is achieved by computing a low dimensional, deterministic dynamic system.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 6236691
zbMATH Keywords: multi-server queues
zbMATH Keywords: abandonment
zbMATH Keywords: dynamical systems
zbMATH Keywords: asymptotics
zbMATH Keywords: time-varying rates
zbMATH Keywords: time inhomogeneous Markov processes
zbMATH Keywords: Hermite polinomials
zbMATH Keywords: fluid and diffusion limits
zbMATH Keywords: skewness
zbMATH Keywords: cumulant moments
reviewed by: Vyacheslav Abramov
MaRDI profile type: Publication
full work available at URL: s11134-012-9340-8
OpenAlex ID: W2023263624
cites work: The Physics of the Mt/G/∞ Queue
cites work: A TIME-VARYING CALL CENTER DESIGN VIA LAGRANGIAN MECHANICS
cites work: Correlation inequalities on some partially ordered sets
cites work: Heavy-Traffic Limits for Queues with Many Exponential Servers
cites work: Q3996398
cites work: Q3268573
cites work: Strong Approximations for Time-Dependent Queues
cites work: Strong approximation for Markovian service networks
cites work: Q4842684
cites work: On Poisson and composed Poisson stochastic set functions
cites work: Q3408861
cites work: A Closure Approximation for the Nonstationary M/M/s Queue
cites work: Q4000424
DOI: 10.1007/S11134-012-9340-8
Recommended article: New perspectives on the Erlang-A queue
Recommended article: Approximate solution for multi-server queueing systems with Erlangian service times
Recommended article: Dynamic rate Erlang-A queues
Recommended article: Sensitivity of Performance in the Erlang-A Queueing Model to Changes in the Model Parameters
Recommended article: Q3530746
Recommended article: Approximation to the transient solution of the \(M/e_{k}/1\) queue
Recommended article: Transient analysis of the Erlang A model
Recommended article: Shortest expected delay routing for Erlang servers
Recommended article: Q5676893
description: scientific article; zbMATH DE number 6236691