Queue-length distributions for multi-priority queueing systems

The bottleneck in many telecommunication systems has often been modeled by an M/G/1 queueing system with priorities. While the probability generating function (PGF) for the occupancy distribution of each traffic class can be readily obtained, the occupancy distributions have been obtainable only rarely. However, the occupancy distribution is of great importance, particularly in those cases where the moments are not all finite. We present a method of obtaining the occupancy distribution from the PGF and demonstrate its validity by obtaining the occupancy distributions for a number of cases, including those with regularly varying service time distributions.