1. Fast Engset computation
- Author
-
Parsiad Azimzadeh and Tommy Carpenter
- Subjects
Discrete mathematics ,33C05, 90B22 ,Applied Mathematics ,Computation ,010102 general mathematics ,Numerical Analysis (math.NA) ,02 engineering and technology ,Management Science and Operations Research ,Fixed point ,01 natural sciences ,Industrial and Manufacturing Engineering ,020210 optoelectronics & photonics ,Fixed-point iteration ,Simple (abstract algebra) ,Convergence (routing) ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Mathematics - Numerical Analysis ,Uniqueness ,0101 mathematics ,Hypergeometric function ,Queue ,Software ,Mathematics - Abstract
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., Comment: 13 pages, 2 figures, 4 tables. Error in statement of Lemma 11 in [v2] fixed. Error in proof of Lemma 2 in [v3] fixed
- Published
- 2016