We present a time-domain travelling-wave model for the simulation of passive mode-locking in quantum dot (QD) lasers; accurate expressions for the time varying QD optical susceptibility and the QD spontaneous emission noise source are introduced in the 1-D wave equations and numerically described using a set of infinite-impulse response filters. The inhomogeneous broadening of the density of states of the whole QD ensemble as well as the homogeneous linewidth of each QD interband transition are properly taken into account in the model. Population dynamics in the QD, quantum well, and barrier states under both forward and reverse bias conditions are modeled via proper sets of multi-population rate equations coupled with the field propagation equations. The model is first applied to the study of gain and absorption recovery in a QD semiconductor optical amplifier under both forward and reverse bias conditions. Simulations of passive mode-locking in a two-section QD laser are then performed as a function of the bias parameters. Gain and absorption dynamics leading to the generation of mode-locking pulses is described. The onset of a trailing-edge instability at low currents is observed and fully explained in the framework of the described model.