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Studying the uncertainty of traffic flow takes significant importance for the transport planners because of the variation and fluctuation of temporal traffic flow on all links of the transport network. Uncertainty analysis of traffic flow requires identifying and characterizing two sets of parameters. The first set is the link choice set, which involves the Origin-Destination pairs using this link. The second set is the link choice probabilities set, which includes proportions of the travel demand for the Origin-Destination pairs in the link choice set.For this study, we developed a new methodology based on Monte Carlo simulation for link choice set and link choice probabilities in the context of route choice modeling. This methodology consists of two algorithms: In the first algorithm, we used the sensitivity analysis technique the variance-based method to identify the set of Origin-Destination pairs in each link. In the second algorithm, we used a Gaussian process based on the Maximum Likelihood framework to estimate the link choice probabilities. Furthermore, we applied the proposed methodology in a case study over multiple scenarios representing different traffic flow conditions. The results of this case study show high precision results with low errors' variances.The key contributions of this paper: First, the link choice set can be detected by using sensitivity analysis. Second, the link choice probabilities can be determined by solving an optimization problem in the Maximum likelihood framework. Finally, the prediction errors' parameters of traffic assignment model can be modeled as a Gaussian process.

Forecasting of traffic flow in the traffic assignment model suffered to a wide range of uncertainties arising from different sources and exacerbating through sequential-stages of the travel demand model. Uncertainty quantification can provide insights into the level of confidence on the traffic assignment model outputs, and also identify the uncertainties of the input Origin-Destination matrix for enhancing the forecasting robustness of the travel demand model. In this paper, a systematic framework is proposed to quantify the uncertainties that lie in the Origin-Destination input matrix. Hence, this study mainly focuses on predicting the posterior distributions of uncertainty Origin-Destination pairs and correcting the biases of Origin-Destination pairs by using the inverse uncertainty quantification formulated through Least Squares Adjustment method. The posterior distributions are further used in the forward uncertainty quantification to quantify the forecast uncertainty of the traffic flow on a transport network. The results show the effectiveness of implementing the inverse uncertainty quantification framework in the traffic assignment model. And demonstrate the necessity of including uncertainty quantification of the input Origin-Destination matrix in future work of travel demand modelling.

Uncertainty can be found at all stages of travel demand model, where the error is passing from one stage to another and propagating over the whole model. Therefore, studying the uncertainty in the last stage is more important because it represents the result of uncertainty in the travel demand model. The objective of this paper is to assist transport modellers in perceiving uncertainty in traffic assignment in the transport network, by building a new methodology to predict the traffic flow and compare predicted values to the real values or values calculated in analytical methods. This methodology was built using Monte Carlo simulation method to quantify uncertainty in traffic flows on a transport network. The values of OD matrix were considered as stochastic variables following a specific probability distribution. And, the results of the simulation process represent the predicted traffic flows in each link on the transport network. Consequently, these predicted results are classified into four cases according to variability and bias. Finally, the results are drawn into figures to visualize the uncertainty in traffic assignments. This methodology was applied to a case study using different scenarios. These scenarios are varying according to inputs parameters used in MC simulation. The simulation results for the scenarios gave different bias for each link separately according to the physical feature of the transport network and original OD matrix, but in general, there is a direct relationship between the input parameter of standard deviation with the bias and variability of the predicted traffic flow for all scenarios.