In this paper, a theoretical model is used to investigate the lasing spectrum properties of InAs-InP(113)B quantum dot (QD) lasers emitting at 1.55 mum. The numerical model is based on a multipopulation rate equations analysis. Calculations take into account the QD size dispersion as well as the temperature dependence through both the inhomogeneous and the homogeneous broadenings. This paper demonstrates that the model is capable of reproducing the spectral behavior of InAs-InP QD lasers. Especially, this study aims to highlight the transition of the lasing wavelength from the ground state (GS) to the excited state (ES). In order to understand how the QD laser turns on, calculated optical spectra are determined for different cavity lengths and compared to experimental ones. Unlike InAs-GaAs QD lasers emitting at 1.3 mum, it is shown that a continuous transition from the GS to the ES is exhibited because of the large inhomogeneous broadening comparable to the GS and ES lasing energy difference.