A queue is a waiting line (like customers waiting at a supermarket checkout counter); queueing theory is the mathematical theory of waiting lines.This theory is concerned with the mathematical modeling and analysis of systems that provide service to random demands. Examples of enterprises where these ideas are traditionally applied include grocery stores, airline ticket counters, fast-food restaurants, retail stores, auto license agencies, and banks.In the case of information systems, queuing theory is commonly used to help plan, design, and reconfigure communication networks. The theory permits the derivation and calculation of several performance measures including the average waiting time in the queue or the system, the expected number waiting or receiving service and the probability of encountering the system in certain states, such as empty, full, having an available server or having to wait a certain time to be served.

Queueing theory is generally considered a branch of operations research as the results are often used when making business decisions about the resources . transport and telecommunication, customer service all have applications of this theory. Notation for describing the characteristics of a queueing model was first suggested by David G. Kendall

Concepts
In a simple waiting line, a customer arrives, joins a queue, is serviced (by a server of some kind), and leaves. Queuing theory uses the arrival rate and the service rate to quickly compute such statistics like the time to service and the time the customer spends etc. disk access, printer spooling, interrupt management, process queuing etc are the applications in the computer scenario

for more details , visit these links:

http://www.hit.ac.il/staff/leonidm/infor.../ch79.html
http://en.wikipediawiki/Queuing_theory#See_also
http://www.lanceglasserBusiness/Queuing.html
http://www.cse.fau.edu/~bob/publications...opedia.pdf