Mathematical Model of Call Center in the Form of Multi-Server Queueing System

The paper considers the model of a call center in the form of a multi-server queueing system with Poisson arrivals and an unlimited waiting area. In the model under consideration, incoming calls do not differ in terms of service conditions, requested service, and interarrival periods. It is assumed...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Anatoly Nazarov, Alexander Moiseev, Svetlana Moiseeva
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	multi-server queue hyperexponential service matrix-geometric method hyperexponential approximation Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/7748baba67ed4da89d8dbd20a1b4a876
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:7748baba67ed4da89d8dbd20a1b4a876
record_format	dspace
spelling	oai:doaj.org-article:7748baba67ed4da89d8dbd20a1b4a8762021-11-25T18:16:48ZMathematical Model of Call Center in the Form of Multi-Server Queueing System10.3390/math92228772227-7390https://doaj.org/article/7748baba67ed4da89d8dbd20a1b4a8762021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2877https://doaj.org/toc/2227-7390The paper considers the model of a call center in the form of a multi-server queueing system with Poisson arrivals and an unlimited waiting area. In the model under consideration, incoming calls do not differ in terms of service conditions, requested service, and interarrival periods. It is assumed that an incoming call can use any free server and they are all identical in terms of capabilities and quality. The goal problem is to find the stationary distribution of the number of calls in the system for an arbitrary recurrent service. This will allow us to evaluate the performance measures of such systems and solve various optimization problems for them. Considering models with non-exponential service times provides solutions for a wide class of mathematical models, making the results more adequate for real call centers. The solution is based on the approximation of the given distribution function of the service time by the hyperexponential distribution function. Therefore, first, the problem of studying a system with hyperexponential service is solved using the matrix-geometric method. Further, on the basis of this result, an approximation of the stationary distribution of the number of calls in a multi-server system with an arbitrary distribution function of the service time is constructed. Various issues in the application of this approximation are considered, and its accuracy is analyzed based on comparison with the known analytical result for a particular case, as well as with the results of the simulation.Anatoly NazarovAlexander MoiseevSvetlana MoiseevaMDPI AGarticlemulti-server queuehyperexponential servicematrix-geometric methodhyperexponential approximationMathematicsQA1-939ENMathematics, Vol 9, Iss 2877, p 2877 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	multi-server queue hyperexponential service matrix-geometric method hyperexponential approximation Mathematics QA1-939
spellingShingle	multi-server queue hyperexponential service matrix-geometric method hyperexponential approximation Mathematics QA1-939 Anatoly Nazarov Alexander Moiseev Svetlana Moiseeva Mathematical Model of Call Center in the Form of Multi-Server Queueing System
description	The paper considers the model of a call center in the form of a multi-server queueing system with Poisson arrivals and an unlimited waiting area. In the model under consideration, incoming calls do not differ in terms of service conditions, requested service, and interarrival periods. It is assumed that an incoming call can use any free server and they are all identical in terms of capabilities and quality. The goal problem is to find the stationary distribution of the number of calls in the system for an arbitrary recurrent service. This will allow us to evaluate the performance measures of such systems and solve various optimization problems for them. Considering models with non-exponential service times provides solutions for a wide class of mathematical models, making the results more adequate for real call centers. The solution is based on the approximation of the given distribution function of the service time by the hyperexponential distribution function. Therefore, first, the problem of studying a system with hyperexponential service is solved using the matrix-geometric method. Further, on the basis of this result, an approximation of the stationary distribution of the number of calls in a multi-server system with an arbitrary distribution function of the service time is constructed. Various issues in the application of this approximation are considered, and its accuracy is analyzed based on comparison with the known analytical result for a particular case, as well as with the results of the simulation.
format	article
author	Anatoly Nazarov Alexander Moiseev Svetlana Moiseeva
author_facet	Anatoly Nazarov Alexander Moiseev Svetlana Moiseeva
author_sort	Anatoly Nazarov
title	Mathematical Model of Call Center in the Form of Multi-Server Queueing System
title_short	Mathematical Model of Call Center in the Form of Multi-Server Queueing System
title_full	Mathematical Model of Call Center in the Form of Multi-Server Queueing System
title_fullStr	Mathematical Model of Call Center in the Form of Multi-Server Queueing System
title_full_unstemmed	Mathematical Model of Call Center in the Form of Multi-Server Queueing System
title_sort	mathematical model of call center in the form of multi-server queueing system
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/7748baba67ed4da89d8dbd20a1b4a876
work_keys_str_mv	AT anatolynazarov mathematicalmodelofcallcenterintheformofmultiserverqueueingsystem AT alexandermoiseev mathematicalmodelofcallcenterintheformofmultiserverqueueingsystem AT svetlanamoiseeva mathematicalmodelofcallcenterintheformofmultiserverqueueingsystem
_version_	1718411389263937536

Mathematical Model of Call Center in the Form of Multi-Server Queueing System

Ejemplares similares