This paper provides an algorithmic analysis for a dynamic, non-preemptive priority queueing system with a single server and two independent Poisson streams of customers with general service time distributions. Type 2 customers have a finite waiting room of size K-1, and type 1 customers have infinite waiting space. The server affords higher priority to type 2 customers when they are at least N in number, and to type 1 customers otherwise. The methodology used is the one developed by M.F. Neuts for models ‘of M/G/1 type’ which, for the model at hand, becomes simpler because of certain structural properties of the model. The model is motivated by practical computer applications where a small subset of users (batch jobs, for example) could clog the system if left uncontrolled. The system permits the control of such customers by appropriately choosing the waiting room size afforded to them and also by fine tuning the threshold parameter N governing the switching rules.
