Invariance principles in queueing theory

Several stochastic processes in queueing theory are based upon compound renewal processes Z(t)=Σ−rN(t)â1âXk. For queues in light traffic, however, the summands {Xk} and the renewal counting process {N(t)} are typically dependent on each other. Making use of recent invariance principles for such situations, the authors present some weak and strong approximations for the GI/G/1 queues in light and heavy traffic. Some applications are discussed including convergence rate statements or Darling-Erdös-type extreme value theorems for the processes under consideration.