In this paper we study the influence of random noise on route to chaos followed by directly modulated laser diode as we found that is more complex than just a Feigenbaum sequence. We have already shown that when the laser is modulated at twice its resonance frequency and the modulation index is increased, a period tripling stable solution coexists with the Feigenbaum sequence for certain values of the modulation index, giving rise to hysteresis loops and chaotic bifurcations. This coexistence gives the noise a relevant role in determining the dynamic behavior. We have studied the route to chaos of the laser diode when the random noise fluctuations are introduced in the model. For this study, we have used three different numerical methods. We have employed a single step fourth order Runge- Kutta algorithm, which has been commonly used in previous studies, and its results have been compared to those provided by two stochastic integration methods: Euler- Maruyama and a stochastic Heun method. In all three cases, the behavior evolves from the single periodic response through period doubling, period quadrupling and period tripling in accordance with recent experimental studies, showing that in the route to chaos, the period doubling sequence is effectively truncated due to random noise. The reason for the truncation is found in the nearby coexisting period three solution. Nevertheless, the Runge-Kutta algorithm smoothes off the random noise fluctuations, probably due to its large correlation time.