Abstract
When A. Erlang suggested a mathematical model of a telephone exchange at the beginning of this century, he did not even suspect that he had started a new discipline — the theory of queues. Paradoxically, in Erlang’s model the queue itself was absent, as calls, having entered the exchange and having received no demanded connection, could not wait and were lost. The model proposed by Erlang, though simple mathematically, incorporated such factors as the irregularity of arrivals of calls to the station and indefiniteness of the duration of every successful connection. In the 1930s A. Khinchine applied similar models for studying the maintenance of machines in a textile factory serviced by a group of repairmen. After the 1950s the flow of works on queueing theory became an avalanche. Models of emergency medical aid, passenger service in air terminals, computer systems, operating systems, road traffic and many other processes represented as some operations on material, informational or other flows have been developed.
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© 1994 Springer Science+Business Media Dordrecht
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Kalashnikov, V.V. (1994). Queueing Theory. In: Mathematical Methods in Queuing Theory. Mathematics and Its Applications, vol 271. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2197-4_1
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DOI: https://doi.org/10.1007/978-94-017-2197-4_1
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