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 , and that subsequently they move independently around a system of nodes. Write for some particular part of the system and the probability that a customer who arrives at time is in at time . Then the number of customers in at time has a Poisson distribution with mean
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