The travel-time flow relationship is not always increasing in nature, it is very difficult to predict precisely. Traditional method fails to replicate this unique conditions. Until millennium, although various researchers and practitioners have given much attention to develop travel-time flow relationships, the advancement to improve travel-time flow relationships was not substantial. The knowledge about the travel-time flow relationship is not commensurate with or parallel to the advancement of new knowledge in other fields. After millennium, most investigators did not devote enough attention to create new knowledge, except for application and performance evaluation of the existing knowledge. Therefore, it is necessary to provide a new theoretical and methodological advancement in travel-time flow relationship. Consequentially, this research proposes a new methodology, which considers stochastic behavior of travel-time flow relationship with probabilistic Bayesian statistics and logistic growth mapping techniques. This research moderately improves the travel-time flow relationship. The unique contribution of this research is that the proposed methods outperforms the existing traditional travel-time flow theory, assumptions, and modeling techniques. The results shows that the proposed model is considerably a good candidate for travel-time predictions. The proposed model performs 36 percent better and accurate travel-time predictions in compared to the existing models. Furthermore, travel-time flow relationship need capacity and free-flow speed estimations. Traditionally, practice of capacity estimation is mostly practical, subjective, and not steady-state capacity. Therefore, a robust and stable capacity-estimation method was developed to eliminate the subjectivity of capacity estimation. The proposed model shows robust and capable of replicating steady-state capacity estimation. The free-flow speed estimation should relate to the traffic-flow speed model while the density is zero. Therefore, this research investigates the existing deterministic speed-density models and recommends a better methodology in free-flow speed estimation. This research presents how the undefined practice of free-flow speed selection can be sensitive. Additionally, finding suitable concurrent travel-time data and traffic volume is crucial and very challenging. To collect concurrent data, this research investigates and develops several technologies such as crowdsource, web app, virtual sensor method, test vehicle, smartphone, global positioning system, and utilized several state and local agencies data collection efforts. Keywords: Travel-Time Flow, Travel-Time Delay, Volume-Delay Function, Travel Time, Origin-Destination Survey, Travel Demand Model, Travel Data Collection, Transportation Survey, Internet Sensor, Crowdsourcing, Virtual Sensor Method, VSM, Transportation Planning, GPS, Smartphone, Loop Detector, Travel -Time Prediction, Travel-Speed Prediction, TDM, Bayesian Inference, Logistic Growth Function.