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We consider a mode-locked (ML) quantum-dot (QD) edge-emitting semiconductor laser consisting of a reverse-biased saturable absorber and a forward-biased amplifying section. To describe the dynamics of this laser, we use the traveling wave model taking into account carrier exchange processes between a reservoir and the QDs. A comprehensive parameter study is presented and an analysis of mode-locking pulse broadening with an increase of injection current is performed. The results of our theoretical analysis are supported by experimental data demonstrating a strong pulse asymmetry in a monolithic two-section QD laser.