We consider a mode-locked quantum-dot 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 quantum dots. 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 quantum dot mode-locked laser