In this paper a model and simulation results of integrated semiconductor passively modelocked ring lasers are presented. The model includes nonlinear effects such as two-photon absorption and a non-linear refractive index, a logarithmic gain-carrier relation, and concentration dependent radiative and non-radiative carrier recombination rates. The optical bandwidth of the system is controlled by a digital filter. The model has been used to simulate two geometries of ring modelocked lasers. The first is a symmetric design, where the two counter propagating pulses in the cavity experience the same amplification and absorption. The second is an asymmetric design where the differences for the two directions of pulse propagation are maximised. Simulation results showthat a symmetrical cavity shows a several times wider window for its operating parameters for stable modelocking.