Robustness of Rootfinding in Queueing Analyses

摘要

There has been frequent controversy over the years regarding the use of numerical rootfinding for the solution of queueing problems. It has been said that such problems quite often present fairly typical computational difficulties. However, it turns out that rootfinding in queueing is so well structured that problems do not occur. There are fundamental properties possessed by the well-known queueing models that eliminate classical rootfinding problems. Most importantly, we show that uniqueness of roots is standard within simply determined regions in the complex plane and prove that the G/EK/1 model has unique roots easily found inside the complex unit circle. Extensive computational results are given to support our contentions. Keywords: Applied probability, Computations, Stochastic models, Numerical methods and procedures. (kr)