Ordinary CLT and WLLN Versions of L = lambda W

The familiar queueing principle expressed by the formula L = lambda W (Little's law) can be interpreted as a relation among strong laws of large numbers (SLLNs). Here we prove central-limit-theorem (CLT) and weak-law-of-large-numbers (WLLN) versions of L = lambda W. For example, if the sequence of ordered pairs of interarrival times and waiting times is strictly stationary and satisfies a joint CLT, then the queu-length process also obeys a CLT with a related limiting distribution. In a previous paper we proved a functional-central-limit-theorem version of L = lambda W, without stationarity, by very different arguments.