Queuing Theory 

Waiting lines at any service centre are a common phenomena and queuing theory is devoted to the mathematical study of waiting lines. Various alternative models have been used to describe such situations but they basically share the following common features. (i) Units requiring service are generated from an input source from different kinds of queues for service,(ii) a service discipline by which queue members are selected for receiving service, (iii) a service mechanism which defines the type of service after the completion of which the unit leaves the system or rejoins it for further processing. Many alternative assumptions can be made about these common elements, and these give rise to the different queuing problems.

Queuing Theory - An Operation Research Techniques
Queuing theory is the mathematical concepts of waiting lines, or queues. The queuing theory considers with mathematical analysis of various related processes, including arriving at the queue, waiting in the line or queue (basically a storage process), and being served at front of the line or queue. The queuing theory permits the calculation and derivation of several performance measures including the avg. waiting time in the queue or the given system, the expected number of waiting or receiving service, and probability of encountering the system in certain states, such as full, empty, having an availability server or having to wait queue for a certain time to be served.
Queuing theory is generally known as a branch of operations research because the queuing theory results are generally used during making business decisions about the resources needed to provide service. The queuing theory is applicable in a wide variety of situations and conditions that may be encountered in commerce, business, and industry, public service, healthcare and engineering. Applications are frequently encountered in customer service situations as well as telecommunication and transport. Queuing theory is directly applicable to intelligent transportation systems, PABXs, networks, call centers, telecommunications, server queuing, advanced telecommunications systems, mainframe computer of telecommunications terminals, and traffic flow.
Techniques of queuing theory has been applied in large number of problems some of listed below
a.       Scheduling of aircraft at landing and takeoff from busy airports.
b.      Scheduling of mechanical transport fleets
c.       Scheduling a distribution of scarce war material.
d.      Inventory analysis and inventory control
e.      Minimization of congestion due to traffic delay at tool booths
f.        Scheduling of parts and components to assembly lines
Other benefits of queuing theory
1.       Queuing theory attempts to formulate, interpret and predict for purpose of better understanding the queues and for the scope to introduce remedies such as adequate service with tolerate waiting.
2.       Queuing theory provides models that are capable of influencing arrival pattern of customers or determines the most appropriate amount of service3 or number of service stations.
3.       Queuing models help in striking balance between the two opportunity costs to achieve near optimization or correct ratio of waiting cost and service costs.

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