# Macroscopic Traffic-Flow Modelling Based on Gap-Filling Behavior of Heterogeneous Traffic
## 6 Conclusions and Future Work  
In heterogeneous traffic conditions, the drivers tend to fill the gaps between the vehicles in front, irrespective of the lane-discipline, causing extreme interactions between the vehicles. This unique behavior results in severe disturbances within the traffic stream, which is why the driver behavior leading to it must be characterized.  
In this paper, a new macroscopic traffic-flow model based on the gap-filling behavior of heterogeneous traffic was proposed. In the first part of this study, a driver's anticipation term was derived that explains the gap-filling behavior in heterogeneous traffic. This anticipation term is derived by developing analogies of traffic parameters with gas parameters, using the Effusion model of the gases. Then, a model for heterogeneous traffic was proposed by replacing the constant driver's anticipation term in the PW model with the derived model for the gap-filling behavior. The second part of this study comprised the numerical approximation of the proposed model, using the Roe Scheme. Finally, in order to observe the behavior of the proposed model, it was numerically simulated in MATLAB for three different types of road conditions: straight road with ingress traffic, straight road with no ingress traffic, and ring road or circular road. The results of the proposed model were further compared with those of the PW model. The PW model results in negative velocities and violates the upper velocity bound, as well. Moreover, the PW model does not significantly reflect the effect of the bottleneck introduced in initial conditions. On the other hand, the proposed model addresses the shortcomings of the PW model, attains robust and realistic results, and does not exhibit unrealistic velocities. It can be concluded that, unlike the PW model, the proposed model produces results that better simulate the expected reality, owing to the effect of the bottleneck which is projected backwards at other time instants in the form of a propagated shockwave.  
For future research, an extension of this study would include the calibration and validation of the proposed model with real traffic data before it could be practically implemented. Moreover, it is planned to develop a new methodology in order to introduce different traffic conditions in the simulations of the macroscopic traffic-flow models. These traffic conditions may include active bottlenecks, traffic signals, intersections, and mergers. The authors are also planning to use different velocity distributions within different macroscopic traffic-flow models and then further comparing the results.  
M.U.K., conceptualization, methodology, software, formal analysis, data curation, visualization, and writing--original draft preparation; S.S., methodology, software, formal analysis, visualization, and writing--review and editing; M.L.N., validation, resources, project administration, funding acquisition, and writing--review and editing; R.R., project administration and review and editing. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.