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

Hong Zhang, Saviour Worlanyo Akuamoah, Wilson Osafo Apeanti, Prince Harvim, David Yaro and Paul Georgescu
Additional contact information
Hong Zhang: School of Economics and Management, Changzhou Institute of Technology, Changzhou 213032, China
Saviour Worlanyo Akuamoah: Department of Mathematics and Statistics, Ho Technical University, Ho Volta Region P.O. Box HP 217, Ghana
Wilson Osafo Apeanti: Faculty of Science, University of Education, Winneba P.O. Box 25, Ghana
Prince Harvim: Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada
David Yaro: Department of Mathematics and Statistics, School of Applied Sciences and Technology, Cape Coast Technical University, Cape Coast P.O. Box DL 50, Ghana
Paul Georgescu: Department of Mathematics, Technical University of Iaşi, Bd. Copou 11A, 700506 Iaşi, Romania

Mathematics, 2021, vol. 9, issue 16, 1-21

Abstract: 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.

Keywords: Double-X cascade network; Lyapunov function; fluid limit approach; interacting server (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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