Rate of convergence of fluid approximation for a multi-class single-server queue

A multi-class single-server queue is considered in this paper. Under uniform topology, if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate, the authors prove that the scaled processes characterizing the queue converge to the corresponding fluid limits with the exponential rate. Here the scaled processes include the queue length process, workload process, sojourn time process, departure process, idle time process.