International Journal of Research and Scientific Innovation (IJRSI) | Volume VI, Issue IV, April 2019 | ISSN 2321–2705

Application of Queueing Theory in Engineering

M. Ragapriya

Department of Mathematics, Annapoorana Engineering College, Tamil Nadu, India 

Abstract:- Queueing theory is a major topic of applied mathematics with phenomenon of waiting and arises from the use of powerful mathematical analysis. In this paper is study the application of queueing theory in engineering also we analyse the basic features of queueing theory.
Keywords:- Arrival process, service process, waiting time, queue length.

I. INTRODUCTION

A queueing system which consists of the customers and the servers. Waiting line or queues are in the schools, hospitals, bookstores, libraries, banks, post office, petrol pumps, theatres etc., all have Queueing problems. Queues are very familiar in our daily life. Queueing theory is a branch of operations research because the results are used for making decisions about the resources needed to provide service. Many valuable applications of the queueing theory are traffic flow (vehicles, aircraft, people, communications), scheduling (patients in hospitals, jobs on machines, programs on computer), and facility design (banks, post offices, super markets). A.K.Erlang (1878-1929) Danish Engineer who is called the father of queueing theory. He published his articles relating to the study of congestion in telephone traffic. A queueing theory is the mathematics of waiting lines. A queueing system can be described by the flow of units for service, forming or joining the queue, if service is not available soon, and leaving the system after being served.

Queue Length

Probability distribution of queue length can be obtained with the help of the given Probability distribution of the arrival and service process. A large queue indicates poor service facility or a need for more space. A small queue indicates excess of service facilities.

Waiting time in Queue

It refers to the time spent by the customer in the queue before the commencement of his service.

Waiting time in system

A basic concept in the analysis of a queuing theory is that of a state of the system. It involves study of a system’s behaviour overtime.