  Explicit results are obtained using simple and exact methods for the joint
queue-length distribution of the M/M/c queue with an arbitrary number of
non-preemptive priority levels. This work is the first to provide explicit
results for the joint probability generating function and joint probability
mass function for a general number of priority levels. A fixed-point iteration
is developed for the stationary balance equations, which enables direct
computation of the joint queue-length distribution. A multi-variate probability
generating function is also derived, from which the joint probability mass
function can be computed by means of a multi-dimensional fast Fourier transform
method.
