Fast Engset computation
For queueing theorists and practitioners, this provides a reliable numerical method for a classic problem, though the improvement is incremental.
The paper addresses the computation of blocking probability in finite-source bufferless queues via the Engset formula. It proves that fixed-point iteration can fail to converge and demonstrates that Newton's method is globally convergent and more efficient.
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 Turán-type inequality involving hypergeometric functions, which is of independent interest.