Introduction to Probability and Stochastic Processes with Applications

CHAPTER 10

INTRODUCTION TO QUEUEING MODELS

10.1   INTRODUCTION

The queueing theory is considered to be a branch of applied probability theory and is often used to describe the more specialized mathematical models for waiting lines or queues. The concept of queueing theory has been developed largely in the context of telephone traffic engineering originated by A. K. Erlang in 1909. Queueing models find applications in a wide variety of situations that may be encountered in health care, engineering, and operations research (Gross and Harris, 1998). In this chapter, the reader is introduced to the fundamental concepts of queueing theory and some of the basic queueing models which are useful in day-to-day real life. Important performance measures such as queue length, waiting time and loss probability are studied for some queueing models.

Queueing systems are comprised of customer(s) waiting for service and server(s) who serve the customer. They are frequently observed in some areas of day-to-day life, for example:

1. People waiting at the check-in counter of an airport
2. Aeroplanes arriving in an airport for landing
3. Online train ticket reservation system
4. People waiting to be served at a buffet
5. Customers waiting at a barber shop for a hair cut
6. Sequence of emails awaiting processing in a mail server     

Certain factors which affect the performance of queueing systems are as follows: