This thesis concerns the mathematical modeling of transportation systems for improved decision support and analysis of transportation-related problems. The main purpose of this thesis is to develop and evaluate models and methods that exploit link flows. Link flows are straightforward to obtain by measurements or estimation methods and are commonly used to describe the traffic state. The models and methods used in this thesis apply mathematical optimization techniques, computer simulations, and probabilistic methods to gain insights into the transportation network under study and provide benefits for both traffic managers and road users. 

First, we present an optimization model for allocating charging stations in a transportation network to serve owners of electric vehicles. The model utilizes a probabilistic route selection process to detect locations through which vehicles may pass. It also considers the limited driving range of electric vehicles. The iterative solution procedure finds the minimal number of minimal charging stations and their locations, which provides a lower bound of charging stations to cover each of the considered routes. Second, we present a case study, in which we argue that stationary and mobile measurement devices possess complementary characteristics. In that study, we investigate how speed cameras and probe vehicles can be used in conjunction with each other for the collection of detailed traffic data. The results show that the share of successfully observed and identified vehicles can be significantly improved by using both stationary and mobile measurement devices. Third, we present a simulation model with the intent of finding the most probable underlying routes based on hourly link flows. The model utilizes Dijkstra's algorithm to find the shortest paths and uses a straightforward statistical test procedure to find the most significant routes in the network based on replicated movements of trucks. Finally, we investigate the possibility to study how the traffic flow in one location reflects the flows in the surrounding area. The statistical basis of the proposed model is built upon measured link flows to study the dispersion of aggregate traffic flows in nodes. By considering the alternative ways vehicles can travel between locations, the model is able to determine the expected link flow that originates from a node in a nearby region.

The results of the thesis show that the link flows, which are basic descriptors of the road segments in a transportation network, can be used to study a broad range of problems in transportation.

Traffic analysis is vital for enhancing the performance of transportation systems, where continuous evaluation of traffic states helps responsible road authorities detect and address issues. High-quality traffic data is key to analysis, as it aids in planning and investments. Traditionally, traffic data collection has been costly and limited. Nowadays, connected vehicles and mobile phones have transformed this process, enabling traffic data collection across large geographic regions without the need for dedicated measurement devices. The availability of large-scale and detailed traffic data allows for in-depth analysis using mathematical models. This thesis develops models to utilize available traffic data for transportation system improvements, aiming to enhance traffic conditions and road user experience. It utilizes data from link flows and travel times, applying models over large geographic areas. The thesis addresses transportation engineering issues through data-driven methods. The thesis proposes two methods for allocating electric vehicle charging stations using optimization and route sampling techniques. It introduces a new index for assessing travel time reliability. It shows how clustering analysis of descriptive travel time statistics can be used to detect different traffic states. Furthermore, this thesis presents a statistical model to estimate link flow propagation using measured link flow data, analyzing traffic influence across surrounding areas. The thesis also uses traffic simulation, focusing on combining speed cameras and probe vehicles for data collection and developing a model to identify probable routes based on hourly link flows. The thesis results highlight the importance of data-driven models in optimizing transportation systems and improving road user travel experiences.