Stationary Queueing Models with Aspects of Customer Impatience and Retrial Behaviour

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By: Christian Dombacher

Introduction to Queueing Theory

  • History

Queueing theory as part of probability theory has evolved from classic teletraffic engineering in the last decades. In 1909 A.K. Erlang, a Danish teletraffic engineer published a paper called The Theory of Probabilities and Telephone Conversations. In the early 1920s he developed the famous Erlang model to evaluate loss probabilities of multi-channel point-to-point conversations. The Erlang model was extended to allow for calculation in finite source input situations by Engset several years later leading to the Engset model. In 1951 D.G. Kendall published his work about embedded Markov chains, which is the base for the calculation of queueing systems under fairly general input conditions. He also defined a naming convention for queueing systems which is still used. Nearly at the same time D.V. Lindley developed an equation allowing for results of a queueing system under fairly general input and service conditions. In 1957 J.R. Jackson started the investigation of networked queues thus leading to so called queueing network models. With the appearance of computers and computer networks, queueing systems and queueing networks have been identified as a powerful analysis and design tool for various applications.

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