# Comprehensive Review of Traffic Modeling: Towards Autonomous Vehicles
## 5 Traffic Flow Models
### Macroscopic Models
#### 5.1.2 Network Models
A real solution can be between these two variants. The fourth area, marked by number 4, corresponds to congestion at the inlet and both outlets. The arrows can go to the point of the capacities of both outlets or one of two capacities, similar to the second and third areas. Figure 10: Solution for diverged node with two outlets: (**a**) input capacity less than the sum of the output capacities; (**b**) input capacity more than the sum of the output capacities. Areas: 1—free flow (green), 2 and 3—congestion at the inlet and at one of the outlets (rose), 4—congestion at the inlet and both outlets (red). Figure 9: Solution for a merge node with two inlets. Areas: 1—free flow (green), 2 and 3—congestion in the output road and in one of the input roads, 4—congestion at the outlet and both inlets (rose). As traffic networks become more intricate, involving multiple inlets and outlets, the complexity of modeling increases significantly. Early solutions to these complex intersections were proposed by researchers [142; 143], laying the groundwork for more sophisticated models that integrate merges and diverges into a unified framework. [PERSON] et al. [144] analyzed a generic class of first-order node models for simulating traffic flows, while [PERSON] and [PERSON] [145] introduced an approach to the macroscopic first-order modeling of traffic at complex urban intersections. These contributions have advanced the theoretical understanding of traffic dynamics at intersections, particularly in urban environments. [PERSON] et al. [146] investigated dynamic network models where congestion manifests as queueing behind bottlenecks, further contributing to the understanding of how congestion propagates through networks. Their work, along with that of [PERSON] and [PERSON] [147], who utilized a parallel computing framework for large-scale transportation simulations, underscores the importance of computational methods in handling the complexity of modern traffic networks. [PERSON] et al. [148] proposed a traffic control strategy for multiple intersections, introducing the concept of a \"super intersection\" where vehicle movements are coordinated across closely connected intersections. This innovative approach aligns with the increasing need for integrated traffic management solutions in urban areas, where intersections must be managed collectively rather than in isolation. [PERSON] et al. [149] developed a solution framework for estimating multiclass dynamic demands for the origin and destination in large networks, which is applicable to a wide range of vehicular data. Their framework is particularly relevant for urban planners and traffic engineers tasked with managing demands in increasingly congested cities, where an accurate demand estimation is crucial for effective traffic management. Further advancements in intersection modeling include [PERSON] et al. [150], who proposed a multi-agent-based cellular automata model for simulating intersection traffic control. Their model incorporates car-following and lane-changing rules tailored to different traffic scenarios, providing a detailed and dynamic approach to traffic simulations. [PERSON] et al. [151] introduced a cooperative framework to address the scheduling of connected and automated vehicles (CAVs) at unsignalized intersections, where lane-changing behavior is permitted. This framework is particularly relevant in the context of emerging autonomous vehicle technologies, which require new models and approaches to ensure an efficient and safe traffic flow. Finally, [PERSON] et al. [152] proposed a two-level solution framework that combines dedicated intersection deployment schemes with intelligent traffic assignment algorithms based on artificial bee colonies. This multi-level approach represents a significant step forward in optimizing traffic flow in mixed environments that include both traditional and connected automated vehicles.