A nonlinear delay differential equation model for passive mode-locking in semiconductor lasers, seeded with parameters extracted from the gain and loss spectra of a quantum dot laser, is employed to simulate and study the dynamical regimes of mode-locked operation of the device. The model parameter ranges corresponding to these regimes are then mapped to externally-controllable parameters such as gain current and absorber bias voltage. Using this approach, a map indicating the approximate regions corresponding to fundamental and harmonically mode locked operation is constructed as a function of gain current and absorber bias voltage. This is shown to be a highly useful method of getting a sense of the highest repetition rates achievable in principle with a simple, two-section device, and provides a guideline toward achieving higher repetition rates by simply adjusting external biasing conditions instantaneously while the device is in operation, as opposed to re-engineering the device with additional passive or saturable absorber sections. The general approach could potentially aid the development of numerical modeling techniques aimed at providing a systematic guideline geared toward developing microwave and RF photonic sources for THz applications.