Queueing with priorities and standard service: Stoppable and unstoppable servers

We derive the mean waiting times in an M/G/1 priority queue when the decision who receives the current completed service (production) is determined at the end of the service period. We consider two variations of this scheme. The first is when the server works only when customers are present, while the second is when the server works on a nonstop basis but scraps its work if production is completed when there are no customers in line. We show that for the former variant (whose overall mean is as in the standard head-of-the-line (HOL) priority model), the gain from this scheme in comparison with the HOL case is monotone increasing with the priority level (being positive for the higher classes and negative for the lower classes).