Guo, Yong Jiang, On the fluid approximation for a multiclass queue under non-preemptive SBP service discipline, Acta mathematica Sinica. English series (Print) , 28(2), 2012, pp. 379-404
A multi-class single server queue under non-preemptive static buffer priority (SBP) service discipline is considered in this paper. Using a bounding technique, we obtain the fluid approximation for the queue length and busy time processes. Furthermore, we prove that the convergence rate of the fluid approximation for the queue length and busy time processes is exponential for large N. Additionally, a sufficient condition for stability is obtained.