A heavy traffic limit theorem for a queueing network with multiple customer types and multiple server stations

Queueing networks with multiple customer types and multiple server stations are widely used for computer and communication and transportation networks, but an accurate solution of the quantity index is difficult to evaluate for complex systems, so approximation solutions are used. We used theory of weak convergence of probability measures, under heavy traffic assumptions we obtain limit theorems for the output process, the idle time process and workload process.