• Preliminary

Waiting for service is part of our daily life. Queues (waiting lines) are usually seen at bus stops, ticket boots, Bank counters, traffic lights, hospitals e.t.c. A queue is a line of customers waiting to be served at a given service point. The unit providing the service is called “server” while the unit requiring the service is called customer or “patient” in this case. When the demand for service exceeds the service facilities, queue is formed; when patients arrive at the hospital, queue is formed when all the patients cannot be served at the same time considering the capacity of the service facility. In a nut shell, queues are formed when demand for any service exceeds its service capacity.

Health is one of the major concerns in today’s stressful life and waiting in a queue in a health service centre is the biggest problem faced by patients. In government hospitals, this problem is more catastrophic because of the low treatment cost as compared to the private hospitals. Long waiting times always cause patients’ dissatisfaction and also affects patients’ compliance with treatment regimens and clinical outcomes. Patients’ satisfaction is one of the major determinant of hospital functioning and also help in improving the quality of health services. It also acts as feedback for the health providers to improve the quality of the care they provide to their patients. Also, on the part of the management as well as the economic benefit, improved quality care will attract new patients to the hospitals and help the economy to grow. This is why queuing theory is being studied.

Queuing theory therefore is a mathematical study or approach to the analysis of waiting lines (queues) in any setting where the arrival rates of customers is faster than the system can handle. It is a branch of operations research as it is related to the customers’ satisfaction and the functionality of the service providers. It is applicable to the health care setting where the hospital has less capacity to accommodate patients. The fundamental goal of queuing theory is to derive an analytical or mathematical model of patients needing service and use that model to predict the arrival rates and waiting times of patients and how the hospital system will perform in a given demand situation.

  • Statement of Problem

The problem of long waiting lines has become a major concern for patients in Ikot Ekpene General Hospital. Queues cause inconveniences to patients and economic cost to hospitals. Patients wait for minutes, hours, days or months to receive medical service. Therefore, this research work tries to look at the traffic intensity of the service facilities in the hospital and also to see how the service time distribution and arrival time distribution conform to the general assumptions of the queuing models.

  • Objectives of the study

The objectives of this study include:

  • To estimate the steady state performance measure of Ikot Ekpene General Hospital.
  • To determine mean the arrival rates of patients.
  • To determine the mean service rates of patients.
  • To test the goodness of fit for the data.
  • To make recommendations on how to improve the system for optimal performance.
    • Theoretical background

Queuing theory is defined as the development of mathematical model to describe various types of queuing systems so that it may be possible to predict how the system will perform in a given demand situation.  It is applied to all areas of human endeavor where there is a little delay in service delivery. Queuing theory is basically a mathematical approach applied to the analysis of waiting lines within the field of operations management. The theory enables the mathematical study of several related processes including arrivals at the queue and being served at the hospital or service facility. The theory permits the deviation and calculation of several performance measures including the mean waiting time on the queue, estimation of the mean service time, fitting the arrival and service time distributions, determining the inter-arrival time of customers (patients) and also calculate the traffic intensity or utilization of service facilities.

A.K. Erlang first introduced the concept of queuing theory in 1909 when he created the model to describe telephone exchange. He gave the basic processes of queuing system as follows:

  1. The arrival pattern
  2. The service pattern
  • Queue discipline (FIFO: First In First Out, LIFO: Last In First Out, SIRO: Selection in Random Order, PIR: Priority of service)
  1. Service mechanism.

According to (Singh, 2006), the objective of queuing analysis and its application in health organizations is to minimize costs to the organization both tangible and intangible. The rising cost of health care can be attributed not only to the ageing population, expensive and advanced treatment modalities, but also to inefficiencies in health delivery. Queuing theory application is an attempt to minimize inefficiencies and delays in the system.

  • Statement of Hypothesis

The following hypothesis will be tested.

Hypothesis 1

HO: The arrival pattern of Patients follows a Poisson distribution.

H1: The arrival pattern of Patients does not follow a Poisson distribution.

Hypothesis 2

HO: The distribution of service time fits an exponential distribution.

H1: The distribution of service time does not fit an exponential distribution.

  • Assumption of the study