  The blocking probability of a finite-source bufferless queue is a fixed point
of the Engset formula, for which we prove existence and uniqueness.
Numerically, the literature suggests a fixed point iteration. We show that such
an iteration can fail to converge and is dominated by a simple Newton's method,
for which we prove a global convergence result. The analysis yields a new
Tur\'an-type inequality involving hypergeometric functions, which is of
independent interest.
