An emergency facility with minimal admission

We study an M/M/[∞] queuing system in which each arrival has a random urgency and is admitted if and only if it is more urgent than all individuals currently receiving service. The system represents, for example, a less-than-magnanimous emergency facility. For this system, and also for a closely related “Parody”, we study the busy period distribution and, to a lesser extent, occupancy. Both exact and heavy traffic results are given.