Analysis of multiclass M/G/1 queues with a mixture of 1-limited disciplines and gated disciplines

In this paper, we consider single server queues with several groups and several classes of customers. We consider priority scheduling algorithms for the multiclass queues in which the server admits customers in each group into the service facility by 1-limited disciplines or by gated disciplines. Our objective is to show a method for deriving mean waiting times for these multiclass M/G/1 queues. From the analysis of the busy periods, we investigate some linear structure inherent in the mean waiting times conditioned on the system state at each customer's arrival epoch. The steady state mean waiting times can be derived from the linear structure by using the Little's formula and the PASTA property.