1. Introduction

In a queueing system items arrive to be processed. The words “item” and “processed” are generic terms. An “item” could refer to customers. They could be customers arriving at a system such as a bank to receive service (be “processed”). Another example is in a manufacturing setting where an item could be a partially completed component that needs to be machined and is thus sent to a station where it is duly processed. Most of us go through city streets driving vehicles or as passengers in a vehicle. A vehicle going through a signalized intersection is an item that needs to be served and the service is provided by the intersection signal light in the form of giving the customer a green light to go through. The types of queueing systems that motivated me to write this book are the types encountered in a communication system. In such a system, an item could be a data packet arriving at a router (or at a switch) and needs its headers read so it can be forwarded to the appropriate next router or final destination. However, in the end, the systems considered in the book are generic and include any systems where items arrive to seek service (i.e. be processed). In this introductory chapter we will use all the similies of queueing system characteristics interchangeably so as to emphasize that we are dealing with a phenomenon that occurs in diverse walks of life. Generally in a queueing system there is a physical or a virtual location (sometimes moving) where items arrive to be processed. An item may be processed immediately after arrival if the processor is available, otherwise it has to wait if the processor is busy. Somehow, the waiting component that may occur if the processor is busy seems to dominate in the descriptor of the system, i.e. “queueing” or “waiting”. In reality, this system can also be called a service system – sometimes a better descriptor. But we will stay with queueing system to maintain tradition.