APPLICATION OF QUEUING THEORY IN BANKING OPERATIONS.

INTRODUCTION

1.0 Background of Study

Queues can be defined as a waiting line or when used a verb, the act of joining a line. Queues are natural activities that humans indulge in and experience whether at filling stations or in the supermarket, etc. Queuing theory is a branch of operations research that focuses on the study of waiting lines, or queues, and the processes or procedures by which customers or items enter, wait for, and exit from a service system. Queues can form in situations where demand for a service temporarily exceeds the available resources, causing delay of customers desired services. Queuing theory supplies a set of mathematical models and methods to deal with these situations in order to optimize system performance, minimize delays, or maximize the profit over various classes of services e.g., health care service, operations management, telecommunication network, traffic analysis, quality control etc.as mentioned by Gross & Harris (1998)

Queuing theory can be effectively utilized for banking sector to manage customer flow during peak hours and also in find out how the resources are allocated so as to reduce waiting times.

The concept of queuing theory originated with the work of Danish mathematician Agner Krarup Erlang in the early 1900s. At first, Erlang's work concentrated on optimizing telephone networks, particularly tackling the congestion problems that emerged when the number of incoming calls surpassed operators' capacity.

After publishing his groundbreaking work on the topic, The Theory of Probabilities and Telephone Conversations, in 1909, Erlang developed models to forecast call arrival patterns and aid in effective load management (Erlang, 1909).

This study laid the foundation for queuing theory by creating models such as the Erlang equations, and it still influences researches on queuing and telecommunication services today. Erlang's contributions have become crucial to the field since they provide the basic mathematical underpinnings for queuing analysis in a range of service situations (Medhi, 2003).

Queuing theory in banking enterprise can be applied to regulate customer flow and minimize their waiting time, especially during peak hours. Banks, for example — as service-oriented businesses — see their activity level surging at certain hours of the day, week or month. Customers usually go into banks and enter queuing systems randomly to seek assistance from tellers, ATMs or Customer care. Through the application of queuing theory, banks can analyze customer arrival and service patterns enabling them to optimize workforce, set up service channels and reduce the wait time of the customers. This is very essential as prolonged waiting can lead to customer dissatisfaction and in most cases, loss of valuable clients.

Queuing theory has been successfully applied in banking operation in various ways. Using queuing models, banks can predict demand trends and allocate resources accordingly. For example, they can adjust the number of open service counters during periods of high demand. Queuing theory also helps banks evaluate how client wait times affect service quality, which is crucial for customer satisfaction. According to research, shorter wait times are positively correlated with improved customer satisfaction levels, which in turn improves customer retention and loyalty (Gupta & Sharma, 2013).

Common queuing models in banks include the single-server and multi-server queuing model which vary depending on the number of service points accessible to the customers. The single-server paradigm is simpler and is often used in ATMs or specific service windows, where the server or machine attends to one customer at a time. The multi-server model is more complex and consists of multiple service points. They are better suited to large banks with multiple entry points (Taha, 2007). Using these models, banks can effectively analyze customer flow and allocate resources according to demand to ensure that customers encounter minimal delays.

Queue management systems, which use time-stamping, customer monitoring, and service metrics to monitor and supervise queue lengths, provide a real-world illustration of how queuing theory is applied in banking. These systems integrate with queuing models to provide real-time data, allowing bank managers to make data-driven decisions about allocation of resources (Gross & Harris, 1998). In order to reduce wait times during busy hours, banks can also ascertain the ideal number of tellers or service locations by examining queue data.

Queueing theory plays a crucial role in banking by enhancing operational efficiency, customer satisfaction, manage service delays and optimize resource allocation.(Odunukwe, 2013) and (Bakari et al., 2014) studies show that effective queuing models can minimize wait times and improve customer loyalty, as demonstrated in Nigerian banks where increased transaction counters significantly reduced queues. Furthermore, research by Katz et al. (1991) and Taylor (1994) emphasizes the significance of not only shortening actual wait times in queues but also managing customer perceptions, as customer satisfaction is determined by both. Overall, effective queue management in banks improves service delivery, increases system utilization, and maximizes profit.

1.1 STATEMENT OF THE PROBLEM

the issue of waiting lines or queues have been a persistent challenge, negatively impacting customer satisfaction, loyalty and the overall service quality. Despite the technological advancement in the banking system, many banks still struggle with managing fluctuating customer demands. This not only leads to unsatisfied customers but also higher operational cost due to inconsistent service.

This study is directed towards investigating the average amount of customers that enter the queuing system of United Bank for Africa and applying queuing theory to improve customer flow, reduce the waiting times and increase the quality-of-service delivery.

1.2 AIMS AND OBJECTIVES OF THE STUDY

The aim of this study is to determine the effectiveness, efficiency and productivity of using different numbers of servers (i.e., two, three, four. five servers.) in a banking system and the objective is to

i. Estimate the waiting time

ii. Estimate the service time

iii. To estimate the queue length

iv. Learn andmake recommendations on how bank managers can improve customer's satisfaction through queue management byemploying more servers that are capable.

1.3 SIGNIFICANCE OF THE STUDY

The study will shed light on the many advantages that the bank's queuing theory procedure can offer. The management of United Bank for Africa plc's Abakaliki office will also find it quite significant, as it will provide them with the chance to enhance the procedure and boost output. Additionally, service firms (such as shops, airports, and gas stations), students conducting research, the general public, and mankind at large will find value in the study.

1.4 SCOPE AND LIMITATION OF THE STUDY

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