Greatly needed improvements to rheological models of polymer fluids ca
n best be made by understanding and modifying a model on the molecular
level, where the physics governing real fluids are created. For this
purpose, stochastic simulations are an indispensible tool. The usefuln
ess of stochastic simulations for kinetic theory models are well-known
. In this paper, we show that the class of Rivlin-Sawyers, or K-BKZ, i
ntegral models is also subject to a molecular interpretation and can b
e simulated using stochastic techniques. We also illustrate how an exi
sting molecular model can be modified, resulting in better predictions
of viscoelastic behavior. For this we formulate a stochastic simulati
on of a reptation model modified to account for double reptation and t
ube-length fluctuations.