Abstract
We consider multiclass feedforward queueing networks with abandonments
under FCFS (first-come, first-served) service disciplines and prove a diffusion
approximation theorem for the queue lengths and workloads in those networks under
heavy traffic. The diffusion limit is the unique solution to a multidimensional reflected
stochastic differential equation with a nonlinear drift term as the limit of abandonmentcount
process. The desired convergence is shown by taking the following steps: first,
obtaining the stochastic boundedness of (scaled) workload in use of the feedforward
property of class routing; second, proving the C-tightness of abandonment-count process;
third, establishing the condition of state-space collapse; fourth, showing the Ctightness
of workload. In the final step we prove the uniqueness (in law) of the solution
to the limit equation for workload by reducing it to the uniqueness of a semimartingale
reflecting Brownian motion via the Girsanov transformation technique.
