UNSTABLE ASYMPTOTICS FOR NONSTATIONARY QUEUES

We relate laws of large numbers and central limit theorems for nonstat ionary counting processes to corresponding limits for their inverse pr ocesses. We apply these results to develop approximations for queues t hat are unstable in a nonstationary manner. We obtain unstable nonstat ionary analogs of the queueing relation L = lambdaW and associated cen tral-limit-theorem versions. For modeling and to obtain the first limi ts, we can construct nonstationary point processes as random time-tran sformations of familiar point processes, such as renewal processes and stationary point processes. We deduce the asymptotic behavior of the nonstationary point process from the asymptotic behavior of the famili ar point process and the time transformation.