Explicit Results for the Distributions of Queue Lengths for a
Non-Preemptive Two-Level Priority Queue
Abstract
Explicit results are derived using simple and exact methods for the
joint and marginal queue-length distributions for the M/M/c queue with
two non-preemptive priority levels. Equal service rates are assumed. Two
approaches are considered. One is based on numerically robust quadratic
recurrence relations. The other is based on a complex contour-integral
representation that yields exact closed-form analytical expressions, not
hitherto available in the literature, that can also be evaluated
numerically with very high accuracy.