Numerical models based on rate equations are used to study carrier dynamics in the two lowest energy levels of an InAs/InP (113)B quantum dot (QD) system. Two different theories are presented, one based on a cascade-relaxation model and the other using an additional efficient carrier relaxation. The comparison between these two theoretical approaches leads to a qualitative understanding of the origin of the two-state lasing in 1.55 mum InAs/InP (113)B (QD) lasers. In order to investigate the QD laser dynamics, numerical results for the turn-on delay of the double laser emission are also presented and discussed