Unstable asymptotics for nonstationary queues

The authors relate laws of large numbers and central limit theorems for nonstationary counting processes to corresponding limits for their inverse processes. They apply these results to develop approximations for queues that are unstable in a nonstationary manner. The authors obtain unstable nonstationary analogs of the queueing relation L=λW and associated central-limit-theorem versions. For modeling and to obtain the first limits, nonstationary point processes can be constructed as random time-transformations of faimilar point processes, such as renewal processes and stationary point processes. The authors deduce the asymptotic behavior of the nonstationary point process from the asymptotic behavior of the familiar point process and the time transformation.