A central-limit-theorem version of \(L=\lambda W\) (Q1122879)

The authors have shown that in the well-known queueing formula \(L=\lambda W\) the customer-average wait (W) obeys a CLT (central limit theorem) iff the time average queue length (L) obeys a CLT. The authors have further related the two limits. Just as the classical CLTs can be regarded as refinements of the classical LLNs (laws of large numbers), so the authors have shown that their result is a refinement of the standard relation between the limits of the averages w.p. 1 (with probability one). To relate the CLT behaviour of the time averages and customer averages, the authors have worked with FCLTs (functional central limit theorems) instead of ordinary CLTs, using the theory of weak convergence of probability measures on the function space \(D\equiv D[0,\infty)\). The FCLTs have also been used for estimation of queueing system parameters by computer simulation.