Essay On Queueing Theory

1. Introduction

A queue is a waiting line (like customers waiting at a supermarket checkout counter); it is formed whenever the current demand for a service exceeds the current capacity to provide that service. The unit demanding service is called ‘customer’ and the device at which it receives service is known as ‘server’. The queuing theory is the mathematical theory of waiting lines. More generally, queuing theory is concerned with the mathematical modeling and analysis of the system that provide service to random demands. It is the area of applied mathematics dealing with the analysis of processes in production systems, maintenance, management, in which homogeneous events are repeated many times. The purpose of queuing theory is to develop

The tasks of queueing theory are optimization and eventually definition of the system, which will provide minimum total cost of waiting for service, loss of time, resources for the service and downtime of

Typically, simple queuing models are specified in terms of the arrival process, the service mechanism and the queue discipline. The arrival process specifies the probabilistic structure of the way the demands for service occur in time; the service mechanism specifies the number of servers and the probabilistic structure of the duration of time required to serve a customer, and the queue discipline specifies the order in which waiting customers are selected from the queue for service. Selecting or constructing a queuing model that is rich enough to reflect the complexity of the real system, yet simple enough to permit mathematical analysis is an art. The ultimate objective of the analysis of queuing systems is to understand the behavior of their underlying processes so that informed and smart decisions can be made in their