The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector

The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector

We model a common teller–customer interaction occurring in the Ghanaian banking sector via a Double-X queuing network consisting of three single servers with infinite-capacity buffers. The servers are assumed to face independent general renewal of customers and independent identically distributed ge...

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Main Authors: Hong Zhang, Saviour Worlanyo Akuamoah, Wilson Osafo Apeanti, Prince Harvim, David Yaro, Paul Georgescu
Format: Article
Language:English
Published: MDPI AG 2021-08-01
Series:Mathematics
Subjects:
Double-X cascade network
Lyapunov function
fluid limit approach
interacting server
Online Access:https://www.mdpi.com/2227-7390/9/16/1957
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spelling doaj-48446cf36e24432d9be1895badbc197f2021-08-26T14:02:25ZengMDPI AGMathematics2227-73902021-08-0191957195710.3390/math9161957The Stability Analysis of a Double-X Queuing Network Occurring in the Banking SectorHong Zhang0Saviour Worlanyo Akuamoah1Wilson Osafo Apeanti2Prince Harvim3David Yaro4Paul Georgescu5School of Economics and Management, Changzhou Institute of Technology, Changzhou 213032, ChinaDepartment of Mathematics and Statistics, Ho Technical University, Ho Volta Region P.O. Box HP 217, GhanaFaculty of Science, University of Education, Winneba P.O. Box 25, GhanaDepartment of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, CanadaDepartment of Mathematics and Statistics, School of Applied Sciences and Technology, Cape Coast Technical University, Cape Coast P.O. Box DL 50, GhanaDepartment of Mathematics, Technical University of Iaşi, Bd. Copou 11A, 700506 Iaşi, RomaniaWe model a common teller–customer interaction occurring in the Ghanaian banking sector via a Double-X queuing network consisting of three single servers with infinite-capacity buffers. The servers are assumed to face independent general renewal of customers and independent identically distributed general service times, the inter-arrival and service time distributions being different for each server. Servers, when free, help serve customers waiting in the queues of other servers. By using the fluid limit approach, we find a sufficient stability condition for the system, which involves the arrival and service rates in the form of a set of inequalities. Finally, the model is validated using an illustrative example from a Ghanaian bank.https://www.mdpi.com/2227-7390/9/16/1957Double-X cascade networkLyapunov functionfluid limit approachinteracting server
collection DOAJ
language English
format Article
sources DOAJ
author Hong Zhang
Saviour Worlanyo Akuamoah
Wilson Osafo Apeanti
Prince Harvim
David Yaro
Paul Georgescu
spellingShingle Hong Zhang
Saviour Worlanyo Akuamoah
Wilson Osafo Apeanti
Prince Harvim
David Yaro
Paul Georgescu
The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector
Mathematics
Double-X cascade network
Lyapunov function
fluid limit approach
interacting server
author_facet Hong Zhang
Saviour Worlanyo Akuamoah
Wilson Osafo Apeanti
Prince Harvim
David Yaro
Paul Georgescu
author_sort Hong Zhang
title The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector
title_short The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector
title_full The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector
title_fullStr The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector
title_full_unstemmed The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector
title_sort stability analysis of a double-x queuing network occurring in the banking sector
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-08-01
description We model a common teller–customer interaction occurring in the Ghanaian banking sector via a Double-X queuing network consisting of three single servers with infinite-capacity buffers. The servers are assumed to face independent general renewal of customers and independent identically distributed general service times, the inter-arrival and service time distributions being different for each server. Servers, when free, help serve customers waiting in the queues of other servers. By using the fluid limit approach, we find a sufficient stability condition for the system, which involves the arrival and service rates in the form of a set of inequalities. Finally, the model is validated using an illustrative example from a Ghanaian bank.
topic Double-X cascade network
Lyapunov function
fluid limit approach
interacting server
url https://www.mdpi.com/2227-7390/9/16/1957
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