# Model-Based Dynamic Toll Pricing: An Overview
###### Abstract  
In this paper, we review some of the most recent research regarding design, simulation, implementation and evaluation of dynamic tolling schemes. Analyzing the structure of the reviewed studies, we identify the common elements and the differences in the approaches chosen by different authors, presenting an overview of the methods for price definition and of the simulation techniques as well as a discussion on the newest technology applications in the field. Optimization revealed to be the dominant price definition method, while control-based algorithms are notably employed for managed lanes toll pricing schemes. Regarding traffic and driver behavior simulation we observed a great variety of solutions throughout the reviewed papers, with a prevalence of macroscopic models for the former and logit models for the latter. Still few papers include models for externalities quantification, while AI paradigms are gaining importance in the field. congestion management; dynamic toll pricing; control-based algorithms; optimization; driver behavior model; traffic model; externalities quantification 2021 12.2.2021 11.2.2021 12.2021 11.2.2021 12. To present a brief overview of the research efforts carried out worldwide on dynamic toll pricing, we evaluated the studies published to date. This analysis was based on the Scopus search engine (www.scopus.com (accessed on 3 May 2021)). The query string was written to find documents matching the keywords 'dynamic' AND 'toll' AND 'pricing' in the title, the abstract or the keywords. This query provided 209 references in all, spanning from 1992 to 2021. For comparison, we show the results of other query runs (Table 1), using different combinations in pairs of the same keywords. The analysis of the outcomes of the query indicates that dynamic toll pricing embraces a very diverse group of subject areas with a prevalence of engineering, social science, computer science and mathematics, as appears in Table 2. A classification of the documents by year, in Figure 2, suggests an overall increase of the research efforts on dynamic toll pricing during the last decades, with a peak of published documents in 2018. In this review, we will focus in particular on the research efforts carried out since 2008 when existing research on pricing algorithms for HOT operations was considered to be in its early stage [11]. Sorting of the documents by country (Figure 3) revealed that the USA and China are the countries that have contributed the most to the number of documents published on dynamic toll pricing. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Keywords** & **References** & **Years (Since)** \\ \hline dynamic AND toll AND pricing & 209 & 1992 \\ dynamic AND toll & 1503 & 1973 \\ dynamic AND pricing & 8894 & 1967 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of three different runs of the keywords search in title, abstract or keywords of documents on the Scopus search engine, characterized by different keywords combinations. Figure 1: Distribution of the analyzed dynamic toll pricing studies by scope. Figure 2: Evolution of the number of publications on dynamic toll pricing. In almost all approaches evaluated in this survey, the overall structure consists of a pricing strategy followed by a simulation study that evaluates the pricing strategy. This simulation study is carried out using a socio-technical model that combines a driver behavior model and a traffic flow model [12], with some papers also including quantification of traffic externalities.