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A self-consistent rate equation model is presented to investigate the influence of carrier relaxation on the modulation response of 1.3 m InAs–GaAs quantum dot lasers. In this model, the carrier dynamics in GaAs barrier, relaxation pathways, and the phonon- and Auger-assisted relaxation are considered. The dependence of 3 dB bandwidth on the relaxation time and relaxation pathway is discussed. It is shown that carrier relaxation via less energy level has better carrier confinement and higher 3 dB bandwidth. The improvement of bandwidth by tunnelling injection QD structure is investigated from the point of view of relaxation pathway. The different effects of tunnelling into ground state and excited state on the 3 dB bandwidth are analyzed. The enhanced carrier relaxation by p-type …