Little’s Law when the Average Waiting Time is Infinite

Abstract

We briefly discuss three versions of Little's Law where one is a purely deterministic relation between averages along a sample path, and the other two are in a stochastic setting. The other two readily extend to the case where the average waiting time is infinite. Extending the deterministic relation is usually done by making an assumption that does not hold in some elementary situations. Through a truncation argument, we obtain a different sufficient condition for the extension to hold. It also is not necessary, but holds with probability one in the stochastic setting of the other versions.