# Model-Based Dynamic Toll Pricing: An Overview
###### Abstract
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ref.** & **Year** & **Scope** & **Pricing Rule** & **Traffic Simulation** & **Driver Behavior** &
\begin{tabular}{c} **Recent** \\ **Technology** \\ \end{tabular} \\ \hline
[13] & 2009 & managed lanes & P control & delay operator (PQ) & binary logit & self-learning \\
[11] & 2008 & HOT lanes & PWcontr. & micro (VISSIM) & binary logit & - \\
[14] & 2018 & managed lanes & PWcontr. op. gains & micro (VISSIM) & agent-based & - \\
[15] & 2014 & managed lanes & PWcontr. op. gains & micro (VISSIM) & agent-based & - \\
[16] & 2015 & managed lanes & PWcontr. op. gains & micro (VISSIM) & binary logit & - \\
[17] & 2016 & HOT lanes & PD control & macro (LWR-based) & binary logit & - \\
[18] & 2016 & MM up. NW & PI control & macro (MFD) & agent-based & - \\
[19] & 2018 & LS NW & PI control & macro (MFD) & C-logit & - \\
[20] & 2014 & HOT lanes & PI control & macro (LWR) & binary logit & - \\
[21] & 2015 & HOT lanes & PID control & micro (Paramics) & agent-based & - \\
[22] & 2018 & HOT lanes & PD control & macro (LWR-based) & binary logit & - \\
[23] & 2016 & HOT lanes & cascaded control & micro (VISSIM) & VOT dist. (Gauss.) & - \\
[24] & 2017 & toll lanes & optimal control & queuing theory & binary logit & - \\
[25] & 2018 & toll lanes & optimal control & queuing theory & binary logit & - \\
[26] & 2018 & LS system & optimal control & discretized model & UE & - \\
[27] & 2008 & freeways & optimal control & micro (Paramics) & emb. in Paramics & - \\
[28] & 2013 & toll facilities & revenue-max. opt. & linear function & binary logit & - \\
[29] & 2015 & tolled route & revenue-max. opt. & micro (CORSIM) & VOT dist. (Weib.) & - \\
[30] & 2019 & managed lanes & revenue-max. opt. & micro (MITSIM) & path-size logit & - \\  & & & & meso (DynaMIT) & & \\
[31] & 2011 & HOT lanes & throughp.-max. opt. & macro (CTM [32]) & binary logit & self-learning \\
[8] & 2013 & HOT lanes & av.flow-max. opt. & macro (CTM [32]) & binary logit & self-learning \\
[33] & 2015 & toll. NW (D2D) & bi-objective opt. & UE & UE & - \\
[34] & 2014 & transp. NW & syst.cost-min. & delay operator & VOT dist. & - \\
[35] & 2009 & general NW & bi-level opt. & UE & UE & - \\
[36] & 2018 & two-layer NW & bi-level opt. & macro (MFD) & UE & - \\  & & & & micro (VISSIM) & \\
[37] & 2019 & NW & bi-level opt. & DUE & DUE & - \\
[38] & 2012 & NW & bi-level opt. & DUE & DUE & - \\
[39] & 2016 & NW (D2D) & Markov DP & Markovian & path-size logit & - \\
[40] & 2018 & managed lanes & Markov DP & macro (CTM) & VOT distr. (disc.) & - \\
[41] & 2018 & managed lanes & Markov DP & macro (CTM) & agent-based & MA RL \\
[42] & 2020 & express lanes & Markov DP & macro (CTM) & MC binary logit & deep RL \\  & & & & MC decision route & \\
[43] & 2013 & LS MM NW & game theory & delay oper. (ABM) & Nash Equilibrium & - \\
[44] & 2014 & HOT lanes & game theory & delay operator (AD) & VOT distr. (log-n.) & - \\
[45] & 2014 & HOT lanes & multi-obj. opt. & delay operator (AD) & VOT distr. (log-n.) & - \\
[46] & 2012 & managed lanes & revenue-max. opt. & macro (TAT) & binary logit & - \\
[48] & 2015 & HOT lanes & opt. (any objective) & macro (CTM) & binary logit & - \\
[49] & 2020 & HOT lanes & throughp.-max. opt. & delay operator (PQ) & MN logit & - \\  & & & & UE VOT distr. & \\  & & & & & general lane-choice & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: A list of the main reviewed studies described by reference (Ref. ), year of publication, scope, main pricing rule principle, traffic simulation basis, driver behavior model and recent technology application. We included in the table also some studies which do not give a complete pricing scheme, but are limited to the presentation of some tool which can be combined with other models in order to obtain a complete pricing scheme. The following abbreviations are adopted in this table: AD = Arrivals-Departures, adj. = adjustable, av. = average, bottl. = bottleneck, CTM = Cell Transmission Model, D2D = Day-to-day, discr. = discrete, distr.