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Traffic Input and Service Distributions
The Simplest Traffic System
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A. K. Erlang arbitrary arrival epoch arrival rate Bell polynomial binomial moments busy period Chapter connection delay constant service corresponding D. G. Kendall delay distribution function delay function derived determined differential equation distribution of service e-bt Erlang Erlangian exponential distribution function exponential generating function exponential service fcth Felix Pollaczek first-served service follows fully accessible given group of servers Hence idle infinite-server input and exponential interarrival intervals Kosten Laplace transform Laplace-Stieltjes transform last-come loss system mathematical induction notation Note number of arrivals number of demands number of servers order of arrival order of service overflow Pn(t Poisson distribution Poisson input Poisson-Charlier polynomials Pollaczek priority queueing theory R. I. Wilkinson recurrence relation recurrent input retrials roots servers are busy service distribution service rate set of equations solution stationary state probabilities strict queueing Takacs telephone theory tion traffic input transition probabilities Vaulot Write zero