Joint Queue-Length Distribution for the Non-Preemptive Multi-Server
Multi-Level Markovian Priority Queue
Abstract
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.