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Queuing Theory: Simeon-Denis Poisson

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Simeon-Denis Poisson, a French mathematician, was the first to introduce the Poisson random variable. He discovered it as a limit of the binomial distribution with the number of trials being n  ∞. Random arrivals of customers correspond to a Poisson stream of arrivals. In a Poisson stream, successive customers arrive after independently exponentially distributed intervals. Furthermore, a Poisson stream is defined by the single parameter of the average arrival rate of customers. Whereas the binomial distribution determines the probability of a specific number of successes in a given number of independent trials being obtained, the Poisson distribution determines the probability of obtaining a specific number of successes within a certain interval. …show more content…

The first queueing theory problem and research paper was published by the Danish engineer Agner Krarup Erlang in 1909. Erlang worked for the Copenhagen Telephone Exchange and spent much of his time considering the required size of a telephone exchange so that a reasonable number of telephone calls being not connected due to the exchange being busy was maintained. Within ten years, he developed a complex formula to solve this problem. Now known as queuing theory, this formula has become an integral part of the global telecommunications industry. Queuing theory has countless possible uses in everyday life. The main reason I decided to explore it further is because I’ve always been a rather impatient person and have not necessarily enjoyed waiting in line. Thus, when I stumbled upon queuing theory in my math textbook it struck my interest. Finally, a way to find the shortest line using math. However, after working through this IA I have come to the conclusion that it is not quite that easy. Yet the topic itself is fascinating. Queuing theory All queuing systems can essentially be broken down into individual sub-systems made up of entities queuing for an activity. Typically, this individual sub-system is thought of as dealing with customers queuing for a service. Possible examples include: • Modelling traffic • Predicting the length of queues at local

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