Research Paper on Queueing Theory

Queueing theory is a mathematical theory related to the probability theory, which seek optimal solutions for managing queues or waiting lines. A queue is necessary and will be created if it is not expected in all cases where the supply is less than demand, even temporarily. It can be applied to different situations: planes taking off or landing management, customers waiting at the counters, or even computer programs storing prior to their processing. This field of research, originated in 1917, is based on the work of the Danish engineer Erlang on the telephone network management in Copenhagen between 1909 and 1920, including consideration of systems of arrival in a queue, the different priorities of each newcomer, and the statistical modeling of execution time. The theory was really developed thanks to contributions from mathematicians Khinchin, Palm, Kendall, Pollaczek, and Kolmogorov.

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The theory of homogeneous flow of events that formed the basis of queuing theory was invented by the Greeks after defeating Troy, but was developed by Soviet mathematician Khinchin.

An employee of Copenhagen Telephone Company was the first who tried to develop a management system based on queuing theory in the period between 1908 and 1922. Agner Erlang, had to streamline the telephone exchange and to calculate in advance the quality of customer service, depending on the number of devices used.

Queueing theory is the area of applied mathematics dealing with the analysis of processes in production systems, maintenance, management, in which homogeneous events are repeated many times.

The subject of the study of queuing theory are queuing system (QS). Under the queuing system is meant an object (a company, organization, etc.), whose activity is related to the implementation of multiple execution of homogeneous tasks and operations.

The purpose of queueing theory is to develop recommendations for the rational construction of queuing systems, the organization of their work and the regulation of the flow of requests for the high efficiency operation.

The tasks of queuing theory are optimization and eventually definition of the system, which will provide minimum total cost of waiting for service, loss of time, resources for the service and downtime of the service channels.

The theory of queueing becomes increasingly important today and college students, who are about to write their research proposals on the subject, have to realize its significance and carefully analyze the origin and evolution of the theory.

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