I. INTRODUCTION
Nowadays traffic congestion in extra-urban areas is a major problem. The cost of congestion is related both to the waste of time due to the increasing travel time that drivers spend on the roads and the higher amount of fuel that is consumed in the presence of congestion. This also has implications for the environment due to the high amount of pollutant emissions. Various methods to control the traffic flow with the aim of reducing congestion, minimizing travel times, fuel consumption and emissions have already been proposed. Among them, the Mainstream Traffic Flow Control (MTFC) by means of Variable Speed Limits (VSL) is a method that on the basis of available traffic and weather conditions, computes the optimal value for the speed limit and communicates its value to drivers by using posted signs. Among others, in [1] MTFC concept was introduced with VSL-posts and in [2] it was applied by means of connected/automated vehicles. VSLs have been demonstrated to be effective and beneficial for the traffic flow but they presents two main drawbacks. First, traditional VSLs require ad hoc infrastructure, as stationary detectors to estimate the current traffic state and variable message signs to communicate the speed limit. Moreover, the impact of VSLs is very sensitive to the level of driver compliance to the posted speed limits. The compliance rate has been proved to be very low especially when dealing with familiar routes. For instance, an experimental study was reported in [3], where participants were familiarised with a particular route and then the displayed speed limit was changed. The experiments showed that most of the driver after passing all signs were still unaware that the speed limit had changed. The expected increasing number of CAVs introduces the chance to avoid the drawbacks of standard VSL by using vehicles as actuators. Among all the available VACS, Vehicle to Vehicle (V2V) and Vehicle to Infrastructure (V2I) communication systems are suitable to be used as sensors for gathering traffic state data and as actuators to impose variable speed limits to other vehicles, by in-vehicle actuation of traffic control commands. A great research effort has been accomplished in recent years in order to model the presence of VACS in traffic flow. One of the main problem is that currently there is not yet a sufficient traffic-level penetration of VACS that allows to have real data for validation and calibration purposes available. Moreover, changes in users driving behaviors introduced by VACS and their impact on traffic are still under investigation [4]. Studies on new modeling and simulation tools for VACS are carried out with both microscopic and macroscopic approaches. Macroscopic models have the advantage to be computationally less demanding and the computational burden does not increase with increasing number of vehicles in the highway. In this papers CAVs are modeled as moving bottlenecks (MB). Some recent works have already investigated this direction. In [5] a coupled PDE-ODE system consisting of the scalar conservation law of the Lighthill-Whitham-Richards (LWR) model [6] [7] and of an ordinary differential equation accounting for the trajectory of the MB was presented. The influence of the MB on the surrounding traffic flow was expressed as an inequality constraint on the flow and the speed of the MB was controlled in [8] aiming to get a reduction of the fuel consumption. In [9] a modelling framework representing traffic scenarios with platoons of trucks was introduced by using a micro-macro extension of the METANET model [10]. In [11] a new model extending the discrete first-order Cell Transmission Model (CTM) [12] was proposed where VACS-equipped vehicles are seen as MB and modeled by modifying the free-flow speed. The speed of the MB was assumed as control variable and controlled by means of a feedback controller to reduce the error of the density with respect to a reference value. A different extended CTM model including MB has been presented in [13] where a control strategy for traffic jam resolution was also applied. The drawback of first-order traffic flow models is that they are not able to capture the capacity drop phenomenon, i.e. the reduction of the discharge flow from a bottleneck that is empirically observed. In this paper the model presented in [11] is further extended to take the capacity drop into account and a different control approach is used. Moreover, the speeds feedback control applied in [11] is replaced and enhanced by a MPC approach that aims to reduce the travel time spent on the highway. Section II reports the model, Section III tackles the capacity drop problem and introduces the extension used for its modeling. Section IV describes the implemented control and Section V shows the simulations results.