## 2 Literature Review  
Quantifying uncertainty in uncertain travel times is crucial and has wide-ranging applications, especially in logistics and route planning. The variability in travel time within distribution logistics is a consequence of the stochastic nature of numerous operational factors. This variability poses challenges for distribution and logistics firms, introducing uncertainty and associated costs. In [25], the authors conducted a comprehensive systematic review of the existing research on travel time reliability, with a specific focus on the assessment of the value associated with travel time reliability. Additionally, they undertook a meta-analysis to uncover the underlying factors contributing to variations in reliability estimates. Travel time uncertainty varies depending on congestion levels [6]. Congestion travel time levels have been considered by researchers. In [26], the authors examined how changes in congestion levels influenced the choice of departure time and they conducted an analysis of costs associated with uncertain travel times. In the study [27], the authors emphasized the relationship between travel time variability and congestion levels. To assess the value of travel time reliability, they developed a comprehensive modeling framework that incorporated trip scheduling, endogenous traffic congestion, travel time uncertainty, and pricing strategies. Hence, to quantify the value of travel time reliability, they integrated trip scheduling, endogenous traffic congestion, travel time uncertainty, and pricing strategies into one modeling framework. The common thread among the models developed in these research studies is that normal traffic flow conditions become unstable when uncertainties arise, especially during peak periods or when other incidents begin to deteriorate the typical traffic conditions. Hence, travel time uncertainty is frequently a result of traffic congestion, and, when congestion occurs, it amplifies the frustration experienced by road users. For the studies [28; 29; 30], it was important to model and understand the implications of travel time uncertainty on transportation systems. Additionally, studies of transportation networks have shown that travel time uncertainty is an important factor that influences traffic networks [30; 31; 32]. For example, in [31], it was observed that travelers place a greater importance on decreasing travel time variability than on reducing the total travel time for a specific journey. In [32], it was noted that deterministic traffic network models are inadequate for assessing traffic network performance. These models tend to magnify minor discrepancies in travel times while failing to adequately account for the substantial impacts of travel time uncertainty. In [30], it was determined that the loss in utility resulting from uncertainty is comparable in magnitude to the overall travel costs. The majority of the previous research concentrated on either the causes or the effects of travel time uncertainty. Considering the impacts of travel time uncertainty within traffic networks necessitates an explicit approach for quantifying and modeling this uncertainty. Hence, in comparison to previous studies in the literature, our objective is to model travel time uncertainty within the domain of distribution logistics. We aim to demonstrate the variability of travel time at different stages of congestion and during various peak times. To accomplish this, we employ an effective method for uncertainty quantification, namely, the collocation method. In addition, modeling uncertain travel times is crucial for real-world applications, especially in the context of routing optimization, where stochastic scenarios are commonly utilized to account for uncertainties between nodes [33].