ABSTRACT

The queuing theory is a mathematical study of queues or waiting lines. It is of course common phenomenon, whenever the current demand for a service exceeds the available capacity to provide it, that queues are formed. In industry and other sectors, it is necessary to make frequent decisions on the level of capacity that can be provided. However, these decisions are often difficult due to the fact that it is not always possible to predict accurately when units will arrive and how long they would need to wait for a service. Excessive costs are involved in the supply of too many services. By contrast, it is at times that the waiting line gets excessively long due to lack of sufficient service capacity. In this project, we will examine some different queuing systems and take account of features such as the average time it takes for a customer to pass through an operation from initiation to completed service, the number of customers waiting in queues at any given moment or the percentage of servers that are busy. One specific and essential application of queue theory is the type of queues we all know from supermarkets, banks, restaurants. In order to make decisions on matters such as whether more staff are needed to process customers at specific times of the day, or whether more queuing space is needed, help can be obtained by analysing these situations and finding average waiting times, average queue length, etc.  However, the results of queuing theory should also be applied even if not to more serious situations in industry like broken machines that require repair and joining a system for queues or lorries coming into production where unloading is required.