# Little's law in distributional form

**DOI:**https://doi.org/10.1007/1-4020-0611-X_549

Since Little's Law first appeared in 1961, its simplicity and importance have established it as a basic tool of queueing theory. Little's Law relates the *average* number of customers in a system, *N*, with the *average* time in the system, *T*, under very broad conditions. For example, Keilson and Servi (1988) have demonstrated that for many systems, the relationship between the queue length and the time in the system can be characterized beyond just their average value.

- (i)
an ordinary single-server queue,

- (ii)
a single-server queue with one or more classes of priority which processes each class according to a preemptive-resume, preemptive-repeat, or nonpreemptive discipline,

- (iii)
a vacation model system, where the server takes one or more “vacations” when the queue is depleted,

- (iv)
a

*polling system*, where a...

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- [5]
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