Bartlett's theorem
{{Short description|Seminar Theories}}
{{About|the theorem in probability|the theorem in electricity|Bartlett's bisection theorem}}
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In queueing theory, Bartlett's theorem gives the distribution of the number of customers in a given part of a system at a fixed time.
Theorem
Suppose that customers arrive according to a non-stationary Poisson process with rate A(t), and that subsequently they move independently around a system of nodes. Write E for some particular part of the system and p(s,t) the probability that a customer who arrives at time s is in E at time t. Then the number of customers in E at time t has a Poisson distribution with mean{{cite book | title = Poisson Processes | url = https://archive.org/details/poissonprocesses00king | url-access = limited | page = [https://archive.org/details/poissonprocesses00king/page/n56 49] | first = John | last = Kingman | authorlink = John Kingman | year = 1993 | isbn = 0198536933 | publisher = Oxford University Press }}
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