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In this paper, a model is presented for the simulation of integrated passively mode-locked InP-InGaAsP ring laser systems that include active components such as an amplifier and saturable absorber, and passive components that can be frequency dispersive. These dispersive components can have a complex frequency dependence, such as arrayed waveguide gratings (AWGs). The model is a lumped-element model that is used as a design tool for developing integrated femtosecond pulse sources with internal dispersion control. Simulations based on an InP/InGaAsP amplifier and absorber show the possibility of laser designs that are able to generate pulses with pulse durations down to 300 fs in the 1550-nm wavelength range. The designs are based on femtosecond laser systems in bulk and fiber optics that are published in the literature. The femtosecond laser sources presented here can be realized using existing InP-InGaAsP active-passive integration technology.