## 1 Introduction
Precisely capturing and forecasting travel time variations is essential in multiple domains, including transportation planning, traffic management, and logistics. Many research endeavors have focused on tackling uncertainties and developing approaches to improve the precision and effectiveness of uncertainty quantification (UQ). UQ tools have been applied in numerous studies to evaluate and mitigate risks effectively. In [9; 10], the authors proposed a model that utilizes uncertainty quantification to address risks associated with the customs supply chain. This model employs the moment matching method and takes into account the seasonality of illicit traffics at five different sites in Morocco. In the study [11], uncertainty quantification methods for differential equations were utilized to predict and simulate the transmission of influenza within the setting of a boarding school. In [12], the researchers developed an uncertainty quantification model to assess and manage the risks related to atmospheric dispersion. They utilized five different techniques to depict and analyze uncertainties, encompassing the probability theory, the interval analysis, the fuzzy approach, the mixed probabilistic-fuzzy approach, and the evidence theory. Stochastic uncertainties, which result from the inherent unpredictability of natural events, can originate from two primary sources: sampling uncertainty or measurement uncertainty [13]. Epistemic uncertainties, on the other hand, originate from gaps in information or knowledge about these events and may have various causes, such as data limitations, uncertain parameters, algorithmic ambiguities, or methodological uncertainties [13]. In [14], the authors introduced a model to predict and model epidemic risks, employing uncertainty quantification (UQ) techniques. They explored two specific methods, namely, the collocation method and the moment matching method. These methods were applied in the context of studying the epidemic risk associated with SARS-CoV-2 in Morocco, serving as an illustrative example. In the humanitarian logistics context, uncertainty quantification (UQ) holds a significant importance. This is primarily because disasters typically exhibit a substantial degree of uncertainty. For example, for flooding, UQ helps in the making of informed decisions, particularly when it comes to predicting disasters [15]. One of the fundamental approachesfor uncertainty quantification (UQ) is the Monte Carlo simulation (MCS), which has been widely employed in various fields. The basic principle of the MCS involves repeatedly sampling input parameters from their respective probability distributions and propagating them through the model to obtain a distribution of output responses. By generating a large number of samples, the MCS can capture the full range of possible outcomes and provide statistical measures. The computational cost associated with the Monte Carlo simulation (MCS) can be a challenge due to the need for a large number of samples. This requirement can make the MCS computationally prohibitive [16]. The Latin hypercube sampling (LHS) technique offers potential improvements in uncertainty quantification. This sampling approach has been shown to provide better accuracy [17]. However, it is important to note that the LHS does have its limitations, as pointed out by [18]. In this context, a promising approach known as the polynomial chaos expansion (PCE) emerged. The PCE allows for the representation of random variables as multivariate series of Gaussian variables [19; 20; 21; 22]. The representation of random variables follows the concept of a Hilbert basis, with approximation achieved by truncating the representation at a specific level. This approach has demonstrated significant advantages over traditional methods such as the Monte Carlo simulation (MCS) and the Latin hypercube sampling (LHS), offering lower computational costs and an increased efficiency.