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The emergence of connected and automated vehicles technology is beneficial in the enhancement of traffic flow performance, in particular, traffic stream stability and roadway capacity. However, the reliability of the shared information among vehicles is usually negligible in the existing systems. In this paper, a stochastic traffic flow model was developed under connected environment to reveal the impact of information reliability on traffic stream, and the analytical study was conducted by applying the expansion of the Fourier mode. The results showed that the reliability of information is closely related to the vehicular stream stability. The modified Korteweg–de Vries (mKdV) equation was obtained by using the nonlinear analysis approach. Consequently, the analytical solution of the derived mKdV equation was attained, which could describe the observed congestion phenomena. Furthermore, the impact of information reliability on traffic flow was verified under two connected scenarios: first, the impact of stochastic available information on the stability of traffic system was investigated, and second, the influence of time interval of reliable information lasted on traffic flow dynamics was explored, wherein the reliable information followed a discrete uniform distribution.