Invariance principles in queueing theory

Several stochastic processes in queueing theory are based upon compound renewal processes . For queues in light traffic, however, the summands and the renewal counting process 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.