Continuous Approximations in the Study of Hierarchies
检验了用连续模型近似离散层级结构的有效性，发现用连续层级近似不好，但忽略整数约束在层级足够大时是有效的，并给出了误差的精确界。
Large organizations are typically modeled as hierarchies. Hierarchies are discrete structures (trees), but researchers frequently use continuous approximations. The purpose of this note is to study the validity of these approximations. We show that modeling hierarchies with a continuum of tiers is not a good approximation. We also show that ignoring rounding operators and integer constraints in formulae derived from discrete models call be a valid approximation, when hierarchies are suitably large. This is made precise by tight bounds on the relative errors of the approximations.