# Model-Based Dynamic Toll Pricing: An Overview
## 3 Overview of Simulations
### Externalities Quantification  
Drivers are responsible for additional costs imposed upon other users and society, such as congestion, accidents, pollutants emissions and noise. These costs, called externalities, can be internalized through road charging [4]. As referred in Section 2.2, social welfare improvement, and maximization are among the objectives of dynamic pricing schemes, thus, together with the quantification of travel times, which is usually done through traffic assignment and reflects congestion, some studies include models for the quantification of other externalities.  
Vehicular pollutants emissions include carbon dioxide (CO\({}_{2}\)), nitrous oxides (NO\({}_{x}\)), volatile organic compounds (VOC), carbon monoxide (CO), and particulate matter (PM\({}_{10}\)) [105; 106]. The emission may be estimated through emission factors (in gram/km), as in [107], or modeled in function of traffic conditions. Emission models are classified by [60] into three categories: microscopic, macroscopic and mesoscopic. In microscopic approach, the emission rates \(e_{i}(t)\) of single vehicles \(i\) (in gram/m/s), are modeled as a function of the vehicular velocity \(v_{i}(t)\) (in km/h) and, possibly, acceleration \(a_{i}(t)\) (in m/s\({}^{2}\)), as in (17):  
\[e_{i}(t)=f(v_{i}(t),a_{i}(t)), \tag{17}\]  
while in macroscopic emission models, the average emission rate \(\bar{e}(t)\) (in gram/m/s) on a road segment is expressed as a function of the average density \(\bar{p}(t)\) in (veh/km) and average velocity \(\bar{v}(t)\) (in km/h) in that segment as in (18):  
\[\bar{e}(t)=g(\bar{p}(t),\bar{v}(t)). \tag{18}\]  
Finally, mesoscopic models combine elements of the two previous approaches.  
In [86], carbon dioxide emissions are quantified through a microscopic model as a velocity function only. In [108], emission rate is calculated at a macro level as a function of average segment velocity and vehicle type.  
A noise emissions model is presented in [109]: noise emission levels are calculated on a macro level for each road segment due to traffic volume, heavy-duty vehicles share and maximum speeds. A grid of receivers is considered for calculating noise impression levels, which allow the quantification of the noise damages to be internalized.  
The authors of [110] recently observed that when more than one externality is considered for marginal cost pricing, there exist correlation between the externalities, and it should be taken into account with proper correction factors.  
Not only are externalities considered for dynamic toll schemes design, but they are also part of evaluation criteria, as in the Benefit-cost analysis of variable pricing projects in [105; 106].  
Figure 6: The distribution of the analyzed studies sorted by driver behavior model.  
In summary, in this section we have presented the main components of the traffic simulation frameworks adopted in literature, grouping them into traffic models (Section 3.1), driver behavior models (Section 3.2) and externalities quantification models (Section 3.3). We now briefly discuss the most recent technology applications in the dynamic toll pricing field.