Queue Theory: Study Of Waiting Line

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“Queue Theory is the study of waiting line” Queue is the common activity of customers or people to avail the desired service, which could be processed or distributed one at a time. A queue is a waiting line (like customers waiting at a supermarket checkout counter); queueing model is the mathematical model of waiting lines. More generally, queueing theory is concerned with the mathematical modelling and analysis of systems that provide service to random demands. A queueing model is an abstract description of such a system. Typically, a queueing model represents the system's physical configuration, by specifying the number and arrangement of the servers, which provide service to the customers, and the stochastic (that is, probabilistic or statistical)…show more content…
In 1927, E. C. Molina published “Application of the Theory of Probability to Telephone Trunking Problems” [27], and one year later Thornton Fry printed “Probability and its Engineering Uses” which expand much of Erlang’s earlier work. In the early 1930’s Felix Pollaczeck did some further pioneering work on Poisson input, arbitrary output, and single and multiple channel problems. Other names working in the same field during that period included Kolmogorov and Khintchine in Russia, Crommelin in France and Palm in Sweden. The work in queueing theory picked up momentum rather slowly in its early days, but in 1950 started to accelerate and there have been a great deal of work in the area since…show more content…
This analysis may tell us something about the expected time that a resource will be in use, or the expected time that a customer must wait. This information will be used to make decisions as to when and how to upgrade the system: for an overloaded system to add more servers. The question may arise whether after more than hundred years of research in queueing theory, is it still possible to make a substantial contribution to the theory and to come up with some new results. To account for our positive answer to this question, to place the present work in its proper context, first we give some historical review of the origin and development of queueing theory and subsequently discuss the current state of

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