A multiclass Station with Markovian Feedback in Heavy Traffic

This paper proves a heavy traffic limit theorem for a multiclass service station with Markovian feedback. This result generalizes the one proved by Reiman (Reiman, M. I. 1988. A multiclass feedback queue in heavy traffic. Adv. Appl. Probab.20 179–207.). Our approach also significantly simplifies Reiman's original proof. Numerical examples are presented to illustrate the effectiveness of the QNET method which is rooted in the theorem.