  We consider a Markovian many server queueing system in which customers are
preemptively scheduled according to exogenously assigned priority levels. The
priority levels are randomly assigned from a continuous probability measure
rather than a discrete one and hence, the queue is modeled by an infinite
dimensional stochastic process. We analyze the equilibrium behavior of the
system and provide several results. We derive the Radon-Nikodym derivative
(with respect to Lebesgue measure) of the measure that describes the average
distribution of customer priority levels in the system; we provide a formula
for the expected sojourn time of a customer as a function of his priority
level; and we provide a formula for the expected waiting time of a customer as
a function of his priority level. We verify our theoretical analysis with
discrete-event simulations. We discuss how each of our results generalizes
previous work on infinite dimensional models for single server priority queues.
