# Model-Based Dynamic Toll Pricing: An Overview
## 2 Overview of Dynamic Toll Price Definition Methods  
The dynamic tolling operations schemes currently in force in the managed lanes facilities in the United States are proprietary, and therefore not available to the public [63]. A notable exception is the algorithm employed to compute MnPASS dynamic toll is published [64]; MnPASS was one of the first managed lanes facilities to become dynamically tolled in 2005 [65] creating a congestion-free lane for both single occupancy vehicles whose drivers are willing to pay the toll and high occupancy vehicles [66]. During the morning and evening peak hours, the toll rate for a particular entry point of the MnPASS express lanes is a function of the maximum density downstream of the entry point: variations of this density define a specific variation of the toll based on lookup tables [64] with a 3-min tolling interval [13].  
Two operational objectives are identified for HOT lanes in [49]: (i) to keep free-flow conditions to ensure travel time reliability; and (ii) to maximize the tolled lanes' throughput in order to minimize the system's total delay. The most relevant methods for dynamic toll price definition explored in literature that we present in the remainder of this section are usually built to pursue one of these two objectives or a combination of both. We can say that control-based approaches are more focused on the former objective, while optimization algorithms usually pursue the latter or the maximization of another performance index of the tolled infrastructure. Figure 4 displays the distribution of the analyzed studies categorized by scope and main price definition method. We note that optimization (OPT) is the predominant price definition method, especially for studies regarding networks (NW) and tolled facilities (TF). For managed lanes studies (ML), which include also research concerning HOT lanes, express lanes and general toll lanes, control-based algorithms (C) are adopted in almost as many cases as optimization-based ones. We also stress that optimal control, which may be considered an application of both optimization and control theories, is implemented in two papers relating to managed lanes, one relating to network and one relating to toll facilities and we counted these algorithms in the control-based groups. Three approaches that are not attributable either to optimization or control theory, identified with label OTH, are employed for networks.  
\begin{table}
\begin{tabular}{c c l l l l l} \hline \hline
**Ref.** & **Year** & **Scope** & **Pricing Rule** & **Traffic Simulation** & **Driver Behavior** &
\begin{tabular}{l} **Recent** \\ **Technology** \\ \end{tabular} \\ \hline
[50] & 2012 & urb. NW & P control & macro (MFD) & binary logit & - \\  & & & & & agent-based & - \\
[51] & 2017 & large urb. NW & outflow-max. opt. & macro (MFD) & UE & - \\
[52] & 2013 & HOT lanes & P control & micro (CORSIM) & emb. in CORSIM & - \\
[53] & 2017 & toll roads & multi-obj. opt. & meso (DynusT) & - & - \\
[54] & 2016 & large NW & bottl. model [55] & meso & econometric DTC & - \\
[56] & 2017 & large NW & TTT-min. opt. & meso & econometric DTC & - \\
[57] & 2015 & toll vs. unt. fac. & various obj. opt. & delay operator (AD) & UE & - \\
[58] & 2015 & HOT lanes & TTTC-min. opt. & delay opertor (BPR) & time and price sens. & - \\  & & & TTT-min. opt. & & & \\
[59] & 2017 & urlb./na. rd NW & shifting obj. & - & - & big data mining \\
[6] & 2019 & urlb./na. rd NW & shifting obj. (adj.) & delay opertor (BPR) & binary logit & - \\
[12] & 2013 & HOT lanes & HOT infl-max. opt. & delay operator (AD) & VOT distr. (Burr) & - \\
[60] & 2013 & toll. vehic. NW & TTC\&TE-min. opt. & SRDC (DUE)[61] & SRDC (DUE)[61] & - \\
[62] & 2019 & HOT lanes & TDGP-min. opt. & delay operator (AD) & RF predictions & RF predictions \\ \hline \hline \end{tabular}
\end{table}
Table 3: _Cont._In what follows, Section 2.1 is dedicated to control-based algorithms and Section 2.2 to optimization-based approaches.