## 4 Eco-Driving Strategy for Connected Vehicles
### Numerical Modelling  
Numerical modeling is a commonly used tool for evaluating the performance of new eco-driving and eco-routing algorithms. The reason why it has become popular is that it allows researchers to assess the efficacy of these strategies or algorithms without the need for actual field experiments, which result in great savings of both study time and cost. However, its results are typically less precise and dependable than those obtained through laboratory testing or on-road experiments. However, when novel eco-driving strategies are proposed in any case, two significant scenarios are typically considered: freeways [42; 43], and signalized intersections on urban roads [44; 45; 46; 47]. Since the first scenario is beyond the scope of this thesis, we will focus on investigating the literature that covers the second scenario. There are numerous dynamic eco-driving models currently available, which vary in their design, formulation of the problem solution (including mathematical formulation, interacting modules, input space, and others), and the energy and traffic models used to connect the eco-driving service to energy and dynamics [48]. In the early models of dynamic eco-driving, the fuel-optimal speed trajectory was estimated and advised using the equipped vehicle's dynamic status, location information, and SPaT data. For instance, [PERSON] et al. [49] proposed arterial velocity planning, which aimed to maximize the probability of encountering a green light when approaching a signalized intersection. Building on this concept, [PERSON] et al. [44] expanded on the model to determine energy-efficient (de)acceleration profiles based on remaining green/red time and distance from the vehicle to the intersection. Despite the aforementioned models considering similar inputs for fuel-optimal velocity estimation, they employ varying methodologies to process the inputs, and all of their assumptions are based on the assumption of no interference from other surrounding vehicles. Therefore, to account for the impact of other surrounding traffic factors, the concept design of the eco-driving strategy was adjusted to consider queue discharge information and the status of the preceding vehicle. Therefore, in order to implement the advice speed in actual complex traffic conditions, the authors [50] proposed the Predictive Cruise Control (PCC) model, which minimized travel time under both free-flow and stop-and-go traffic conditions while providing energy-efficient (de)acceleration strategies. In addition to traffic signal and preceding vehicle factors, Queue Length Estimation (QLE) techniques, which are based on commonly installed induction loop sensor systems, helped the predictive speed assistance system, which showed fuel savings of 8-11% [51]. Similar research can be found in [52; 53; 54]. Although V2I technology has simplified the process of acquiring real-time SPaT information on signalized intersections with pre-timed signal control, obtaining precise future SPaT data remains challenging due to variations in pre-timed traffic signals and traffic environment fluctuations. To tackle this issue, the probabilistic signal timing approach has been developed, which utilizes real-time SPaT data and historical average timing data for each signal status [55]. For example, the Green Light Optimized Speed Advisory (GLOSA) has been implemented for fully and semi-adaptive traffic lights, thereby leveraging empirical signal and detector data as a solution [56], while, from the vehicle control perspective within the transportation system, the eco-driving problem for Connected and Autonomous Vehicles (CAVs) has been formulated as a data-driven, chance-constrained robust optimization problem. DP has been applied to solve this optimization problem to enhance the controller's robustness when dealing with uncertain signal timing, regardless of random variable distribution [57; 58].