Analysis and comparison of traffic flow models: a new hybrid traffic flow model vs benchmark models

Background This paper compares a hybrid traffic flow model with benchmark macroscopic and microscopic models. The proposed hybrid traffic flow model may be applied considering a mixed traffic flow and is based on the combination of the macroscopic cell transmission model and the microscopic cellular automata. Modelled variables The hybrid model is compared against three microscopic models, namely the Krauß model, the intelligent driver model and the cellular automata, and against two macroscopic models, the Cell Transmission Model and the Cell Transmission Model with dispersion, respectively. To this end, three main applications were considered: (i) a link with a signalised junction at the end, (ii) a signalised artery, and (iii) a grid network with signalised junctions. Results The numerical simulations show that the model provides acceptable results. Especially in terms of travel times, it has similar behaviour to the microscopic model. By contrast, it produces lower values of queue propagation than microscopic models (intrinsically dominated by stochastic phenomena), which are closer to the values shown by the enhanced macroscopic cell transmission model and the cell transmission model with dispersion. The validation of the model regards the analysis of the wave propagation at the boundary region.

A Density-Based and Lane-Free Microscopic Traffic Flow Model Applied to Unmanned Aerial Vehicles

In this work, we introduce a microscopic traffic flow model called Scalar Capacity Model (SCM) which can be used to study the formation of traffic on an airway link for autonomous Unmanned Aerial Vehicles (UAVs) as well as for the ground vehicles on the road. Given the 3D trajectory of UAV flights (as opposed to the 2D trajectory of ground vehicles), the main novelty in our model is to eliminate the commonly used notion of lanes and replace it with a notion of density and capacity of flow, but in such a way that individual vehicle motions can still be modeled. We name this a Density/Capacity View (DCV) of the link capacity and how vehicles utilize it versus the traditional One/Multi-Lane View (OMV). An interesting feature of this model is exhibiting both passing and blocking regimes (analogous to multi-lane or single-lane) depending on the set scalar parameter for capacity. We show the model has linear local (platoon) and asymptotic linear stability. Additionally, we perform numerical simulations and show evidence for non-linear stability. Our traffic flow model is represented by a nonlinear differential equation which we transform into a linear form. This makes our model analytically solvable in the blocking regime and piece-wise analytically solvable in the passing regime. Finally, a key advantage of using our model over an OMV model for representing UAV’s flights is the removal of the artificial restriction on passing via only adjacent lanes. This will result in an improved and more realistic traffic flow for UAVs.

A new heterogeneous traffic flow model based on lateral distance headway

Based on a density gradient model proposed recently by Imran and Khan, a new heterogeneous traffic flow model considering time and lateral distance is proposed. The type and stability of the equilibrium solution of the model are discussed by using the differential equation theory, and the global distribution structure of the trajectory in the phase plane is analyzed. In addition, the density wave stability conditions and saddle-node bifurcation conditions of the model are studied, and the solitary wave solutions of the KdV equation in the metastable region are derived by using the reduced perturbation method. The numerical results show that the new model cannot only reproduce the spatiotemporal oscillation phenomenon when walking and stopping, but also describe the sudden change behavior of traffic near the critical point of saddle-node bifurcation. It is shown that the model can reproduce some complex traffic phenomena qualitatively.