Beneficios Netos

As may have been expected, a substantial amount of research has been performed on the effect that autonomous vehicles are expected to have on traffic flow . Perhaps the earliest examples of such studies are due to Varaiya [164] and Rao and Varaiya [127], who investigated the impact that vehicles equipped with autonomous intelligent cruise control would have on traffic flow. In these early studies, mathematical models were formulated in order to assess the effect of vehicle platoons (i.e. vehicles following each other at relatively close headways) on traffic flow, enabled by automatic adaptive cruise control. In order to estimate highway traffic flow in the presence of vehicles with automatic adaptive cruise control, Rao and Varaiya [127] proposed the relationship

q = _¯ 3600v ¯N

N (` + d)− d + ¯4, (3.34)

where v denotes the vehicle speed in m/s, ` denotes the average individual vehicle length, d denotes the average headway between vehicles within a platoon, ¯_{4 denotes the average distance} between platoons, and ¯N is the average size of a platoon. In this model formulation, the aver- age platoon size was determined according to a pre-specified platoon size distribution whereby vehicles would join a platoon based on a certain probability when they would find themselves within a specific distance from the platoon.

In another paper investigating the effects of adaptive cruise control on traffic flow along highways, Van Arem et al. [163] extended the approach of Rao and Varaiya [127] by including vehicle- to-vehicle communication in their modelling approach. Their approach was evaluated within the so-called MIXIC link-level mesoscopic traffic simulation modelling environment. In their simulation model, the vehicle following rules were adapted so as to model the effect that vehicles equipped with connected adaptive cruise control have on the highway throughput. Due to the fact that vehicles were now able to communicate, the reaction times were reduced from 1.4 seconds for human drivers to 0.5 seconds for connected vehicles, resulting in a reduction in the minimum allowable headway between connected vehicles.

In another simulation study into the effects of adaptive cruise control on highway traffic flow, Kesting et al. [69] designed an adaptive cruise control controller that would alter the cruise con- trol behaviour of a vehicle, based on the prevailing traffic conditions. A graphical representation of the controller is shown in Figure 3.11. The effectiveness of this controller in terms of altering the vehicle behaviour according to the prevailing traffic conditions was evaluated in the context of a microscopic traffic simulation model of a multi-lane highway exhibiting a single bottleneck at an on-ramp merge.

The influence of autonomous or connected vehicles on traffic flow stability and throughput was the focus of a study performed by Talebpour and Mahmassani [156]. They derived three differ- ent vehicle behaviour models in respect of acceleration and deceleration, according to different levels of vehicle connectivity capabilities. The first of these vehicle classes encompasses all ve- hicles that have no communication capabilities, as most of the vehicles currently on the roads. In the second class, vehicles that are communication-ready were modelled. This class encom- passes all vehicles which are equipped with the necessary infrastructure for vehicle-to-vehicle and vehicle-to-infrastructure communication, although connectivity between vehicles and/or infras- tructure cannot be guaranteed. Accordingly, four scenarios could be defined within this class: Active/inactive vehicle-to-vehicle communication and active/inactive vehicle-to-infrastructure communication. If both types of communication are inactive, the vehicle behaviour is the same as that of vehicles in class one, while if vehicle-to-vehicle communication is active, the car-following rules are updated, allowing for smaller headways between two successive vehicles. Vehicle-to-

the desired velocity Strategic lev el (∼ 10s .. .1 min)

Driving strategy matrix ACC parameter setting coefficients based on detected traffic situation Detection model

Autonomous identification of traffic situations by criteria and heuristics

Op erational lev el (∼ 0.1 s .. .1 s) Output data Calculated acceleration controls for engine and braking system Input data

Vehicle sensors provide vehicle velocity, distance rate

to leader and approaching

Adaptive cruise contoller (ACC) ACC operating mode Automated modification of ACC parameters

traffic situation depending on detected

Figure 3.11: An adaptive cruise control controller architecture. Adapted from Kesting et al. [69].

infrastructure communication allows drivers to receive information from traffic management centres (TMCs), such as real-time information on VSLs, route guidance or congestion warnings. The vehicle behaviour is, however, not adjusted when vehicle-to-infrastructure communication is active [156]. Finally, the third class of vehicles are fully autonomous vehicles. Reaction times for autonomous vehicles were assumed to be instantaneous, and minimum following distances were subsequently determined as a function of the vehicle deceleration capabilities and speed at which the vehicle is travelling. The effect that various percentages of either connected or autonomous vehicles have on the resulting traffic flow was subsequently evaluated in the context of a microscopic traffic simulation model of a simple hypothetical highway network consisting of a 3.5 mile segment with two lanes in the forward direction, and a single lane on-ramp which merges with the highway at the 1.75 mile mark.

An early attempt at controlling highway traffic flow by means of providing direct instructions to autonomous vehicles is due to Baskar et al. [11]. In this implementation, the traffic flow was assumed to consist only of autonomous vehicles, which may receive direct instructions from the roadside TMC. Another assumption was that all vehicles travel in platoons, and that, as such, the dynamics of all the vehicles within a platoon could be described by the lead vehicle of that platoon. Any action carried out by the leader of the platoon would thus also be performed by all of the follower vehicles in the platoon. These actions involved the speed at which the platoon should travel, the lane in which the platoon should travel, and the time at which a platoon should enter the highway from an on-ramp. An MPC approach was adopted with the aim of determining these actions for each of the platoons present within the simulated environment, such that the total time spent in the system by all vehicles would be minimised. The objective

of the MPC approach was then to minimise J_TTS= `=0 X N<sub>sim</sub> (n(`) + qm(`) + q0(`)) TTTS, (3.35)

where J_TTS denotes the total time spent by all vehicles in the system over the course of the entire simulation period, n(`) denotes the number of vehicles present in the simulation model at the start of control interval `, qm(`) denotes the number of vehicles entering the simulated

area along the mainline during the control interval ` and qo(`) denotes the number of vehicles

entering the simulated area from an on-ramp during the control interval `. Here qm(`) may be

negative in the case where there are more vehicles leaving the simulated area than there are vehicles entering the simulated area from the mainline during control interval `. The constraints incorporated in their formulation ensure that sufficient space is available for an entire platoon to change lanes, and that sufficient space is available for an entire platoon to enter the highway traffic flow from an on-ramp. This formulation was implemented in a MITSIM [177] inspired traffic simulation model within MATLAB. The MPC optimisation problem was solved using the pattern search method [7] available within the patternsearch command incorporated in the Genetic Algorithm and Direct Search Toolbox in MATLAB.

Although the presence of autonomous vehicles was not assumed, Schakel and Van Arem employed vehicle-to-infrastructure communication in order to develop an in-car advice algorithm, based on which drivers of “connected” vehicles would receive specific advice regarding lane choice, speed and following distance [141]. The architecture of the system is illustrated in Figure 3.12.

Loop detector data Floating car data Driver advice Advice algorithm Traffic state prediction

Traffic Management Centre

Figure 3.12: Overview of an in-car advisory system. Adapted from Schakel and van Arem [141].

As may be seen in the figure, a combination of loop detector and floating vehicle data are employed to generate an estimation of the current traffic flow, as well as a prediction of the traffic flow that a connected vehicle is likely to encounter downstream of its current location. This traffic state prediction is the input to the advice algorithm. The algorithm is based on two principles of traffic flow. The first is the so-called acceleration advice principle. According to this principle, drivers are encouraged to maintain short, but safe, headways at the end of a congested traffic zone. The basis for this advice is the principle that the capacity drop due to congestion is mainly due to the fact that drivers only accelerate once the actual headway is larger than the desired headway [141]. Thus, by maintaining a shorter headway, the effects of the capacity drop may be reduced. The second component of the advice algorithm is the so-called distribution advice principle. It has been shown that drivers do not fully utilise all highway lanes once traffic breakdown occurs [73]. The aim of the distribution advice principle then, was to redistribute traffic flow more evenly across the lanes, thereby utilising the available highway capacity more effectively [141]. Based on these two principles, drivers were given three distinct types of advice, namely speed advice (i.e. drivers are advised on the speed at which they should be travelling), headway advice (i.e. drivers are advised on the following distance they should maintain), and

presence of autonomous and connected vehicles, Roncoli et al. [136] formulated an optimal control problem with the aim of providing optimal metering rates, VSLs and lane change advice. The basis of this optimal control approach was a macroscopic lane-based cellular transition model (CTM) [135]. In this formulation, RM is applied in the conventional way, by directly regulating the inflow of traffic onto a highway from an on-ramp by means of a traffic light. Thus, no autonomous capabilities, vehicle-to-infrastructure or vehicle-to-vehicle communication are required or assumed for the RM implementation. For VSL control, sufficient penetration of autonomous or connected vehicles is assumed, where sufficient is defined as the number of vehicles required to enforce a speed limit on all vehicles, even if this speed limit is only assigned to a limited number of vehicles [136]. It is therefore assumed that the new VSL is imposed on the entire traffic flow at a specific link during every control time step. For the LA component of the optimisation problem, an intermediate algorithm is employed. This algorithm receives as input the optimal lateral flows between lanes, together with the probability for random lane changes by human-driven vehicles and the probability that a vehicle will exit the highway system at an off-ramp. The intermediate algorithm then determines an appropriate number of autonomous vehicles which should receive a lane-change command such that the optimal lateral flows may be achieved [136]. The aim of the optimal control approach is to determine the optimal metering rate for every on-ramp within the study area, the optimal VSL to be applied at each highway segment and the optimal lateral traffic flows of every highway segment, all based on a piecewise- linear fundamental diagram of traffic flow. Furthermore, the optimal control interval lengths for each of these control measures were also determined by the optimisation model. The objective function to be minimised comprised seven terms, three of which were linear, while the four remaining terms were quadratic. The first, and most important, of these terms represented the total time spent in the system by all vehicles during the entire control period. The second and third terms were penalty terms, introduced to avoid the build-up of impractically long on-ramp queues, and impractically large numbers of lane change manoeuvres, respectively. Finally, the four quadratic terms were introduced to either penalise variation in control variables from one time step to the next, or from one segment to the adjacent downstream segment [136]. The underlying CTM and the optimal control approach were implemented in MATLAB, while the Gurobi optimisation solver was employed for solving the quadratic programming problem. The above-mentioned optimal control approach by Roncoli et al. [135, 136] was refined and implemented by Roncoli et al.[137] in the context of a hierarchical MPC control structure with the aim of enabling the optimal control problem to be solved in an online manner. A graphical illustration of the structure of this hierarchical control structure may be seen in Figure 3.13. The purpose of the adaptation and prediction layer is to process the data obtained from roadside traffic sensors, as well as the data collected from autonomous vehicles, and subsequently generate a traffic demand forecast for the duration of the following control interval. This traffic state estimation, as well as the predicted traffic demand, is then provided to the optimisation layer. In the optimisation layer, the optimal control problem outlined above, as formalised by Roncoli et al. [136], is solved. Due to the fact that the optimal control problem is solved in the context of a link-based macroscopic traffic simulation model, while the hierarchical MPC approach was implemented within a microscopic traffic simulation model, a local control layer was introduced. The function of the local control layer is to translate the optimal macroscopic densities, as determined in the optimisation layer, to physical speed limit values and red phase times for the

Adaptation and prediction layer Optimisation layer Motorway system Optimal control results Application layer

Local control layer Optimal control actions Local control actions Applied control actions T raffic measuremen ts

Traffic state estimation Predicted demand Other

Parameters

Figure 3.13: A hierarchical MPC control structure with distributed controllers in the presence of autonomous vehicles. Adapted from Roncoliet al. [137].

MTFC and RM components respectively. This is achieved by employing the target densities suggested by the optimal control layer as set points for several local feedback controllers, which then determine suitable red phase times and VSLs in order to achieve these set target densities [137]. I-type feedback controllers, such as those employed in ALINEA and the MTFC controller by M¨uller et al. [105], are employed for this purpose in the hierarchical MPC control structure. The VSLs to be applied are then determined as

vi,j(t) = vi,j(t− 1) + Kv[ˆρi+1,j(t)− ρi+1,j(t)] , (3.36)

where vi,j denotes the speed limit applied at lane j of segment i, ˆρi,j denotes the target density

set point for lane j of segment i, ρi,j denotes the measured density at lane j of segment i, and

Kv denotes the integral gain of the controller. The same controller structure is employed for

the RM component as the optimal control layer specifies target densities for the merge sections, which the controller aims to achieve. Finally, the application layer serves the purpose of applying the lane changing actions suggested by the optimal control layer, as well as the VSL and RM actions suggested by the feedback controllers within the simulation model. As stated above, this hierarchical MPC approach was implemented in the context of a simplified microscopic highway network comprising a 5 km stretch of a three-lane highway with a single on-ramp at 3.5 km, implemented within the AIMSUN microscopic traffic simulation software.

Perraki et al. [120] applied the hierarchical MPC framework of Roncoli et al. [137] in the con- text of a real-world case study of the A20 highway connecting Rotterdam and Gouda in the Netherlands. This case study model was also implemented within the AIMSUN microscopic traffic simulation software. While an improvement of 17.7% in respect of the total time spent in the system by all vehicles was recorded, several shortcomings were also pointed out. In this implementation, the control actions were carried out under the assumption that all vehicles are equipped with vehicle automation and communication systems, while different vehicle types (such as passenger vehicles, delivery vehicles or trucks) were not considered. It is expected that

component of the hierarchical MPC framework of Roncoli et al. [137], is another area of research within the broader field of autonomous driving which has received a significant amount of at- tention [34]. This is demonstrated in the work of Rempe et al. [129], Bekiaris-Liberis et al. [14], Fountoulakis et al. [38] and Roncoli et al. [134]. The aim in all of these studies was to generalise information obtained from individual vehicles (regarding their immediate traffic surroundings) in order to form a reliable picture of the state of traffic flow in general. Typically, the aim then was to employ this new-found, real-time traffic information in order to be able to better con- trol traffic flow and even prevent congestion, as illustrated by the fact that most of the control approaches presented above make use of traffic flow predictions in one way or another.