  Mean field modeling is a popular approach to assess the performance of large
scale computer systems. The evolution of many mean field models is
characterized by a set of ordinary differential equations that have a unique
fixed point. In order to prove that this unique fixed point corresponds to the
limit of the stationary measures of the finite systems, the unique fixed point
must be a global attractor. While global attraction was established for various
systems in case of exponential job sizes, it is often unclear whether these
proof techniques can be generalized to non-exponential job sizes. In this paper
we show how simple monotonicity arguments can be used to prove global
attraction for a broad class of ordinary differential equations that capture
the evolution of mean field models with hyperexponential job sizes. This class
includes both existing as well as previously unstudied load balancing schemes
and can be used for systems with either finite or infinite buffers. The main
novelty of the approach exists in using a Coxian representation for the
hyperexponential job sizes and a partial order that is stronger than the
componentwise partial order used in the exponential case.
