www.ajms.com 75 ISSN 2581-3463 RESEARCH ARTICLE Application of Multi-server Queue Model (m/m/c) for Waiting Lines Management in Banking System S. A. Akande, U. N. Mohammed, A. M. Ibrahim, O. A. Adedayo Department of Mathematics, Federal University Technology, Minna, Nigeria Received: 20-01-2021; Revised: 10-02-2022; Accepted: 05-03-2022 ABSTRACT Queues or waiting lines arise when the demand for service exceeds the capacity of a service facility. One of the major challenges bank customers encounter in banks is the waiting lines in automated teller machines (ATMs). This study formulated a Multi-Server Queue Model (M/M/C) for Queue Management in Banking ATM. The performance level of a typical bank ATM has been effectively investigated using the M/M/S queuing model. It was observed that the busy time of the machine is 2.6 h while the idle time is 7.4 h in the 10 h of banking time which is attributed to the availability of many servers in the system. The utilization factor is 0.26 or 26.0% shows that the service delivery of the machine is very efficient and there is no urgent need for an additional server. The researcher thereby recommended that banks should consider the use of the queue model to test the performance of waiting lines in the ATMs. Key words: Multi-server, Queue model, Waiting line, Banking system Address for correspondence: S. A. Akande, siqlam@yahoo.com INTRODUCTION The act of joining a line or waiting is referred to as a queue. Customers (arrivals) wanting service must wait because the number of servers available exceeds the number of servers available, or the facility does not perform smoothly or takes longer than the time allotted to serve a client. [1] It is a common occurrence in gas stations, supermarkets, and banks, among other places. Electronic banking is one of the many technological achievements in the banking industry. In the banking business, an automated teller machine (ATM) is one of various electronic banking channels. In the banking business, ATMs are one of the most crucial service facilities. [2] ATMs first introduced in Nigeria in 1989 and have since gained widespread acceptance and usage. Nigeria exchange group is a company based in Nigeria. [3] More than half of respondents in a study stated that preference for the situation becomes compounded during festive periods and month finishes, when demand for cash is at its peak. According [4] to they described, queuing theory is a research that aims to assist business owners in analyzing the percentage of time customers wait for services to be delivered to them and improving the percentage of services delivered in this way. Erlang, a Danish mathematician, conducted the first investigation on queuing theory, which led to the development of the world-renowned Erlang telephone model. He looked at the phone network system and sought to figure out what influence variable service demands had on call volume and the use of automatic dialing equipment. [5] Queuing theory, often known as congestion theory, is an area of operational research that investigates the relationship between demand for a service system and the delays experienced by its users. [6] Other researchers [7,8] worked on improving performance inside the banking hall. The application of queuing theory in banking operations is still in its early stages of research, with notable studies being conducted in various areas. [1] Salami et al. [9] investigated strategies for Chinese commercial banks to increase their efficiency in terms of customer queuing in bank halls. The focus was on using queuing theory to investigate the queue problem, which was based on supposed data with an arrival rate of 32 and a service rate of 20.