Evalua ng the impacts of autonomous cars on the capacity of freeways in Brazil using the HCM-6 PCE methodology

Recebido: 13 de agosto de 2020 Aceito para publicação: 22 de abril de 2021 Publicado: 24 de agosto de 2021 Editor de área: Flávio Cunto ABSTRACT This paper analyses the factors that affect the impact of autonomous vehicles (AVs) on the capacity of a freeway in Brazil using an adapta:on of the HCM-6 procedure for truck PCE es:ma:on. A version of Vissim, recalibrated to represent traffic streams and AVs on Brazilian freeways, was used to simulate more than 25,000 scenarios represen:ng combina:ons of traffic (e.g., AV fleets, AV platoons, percentage of AVs and of heavy goods vehicles) and road (grades and number of lanes) characteris:cs. AV impacts on capacity were evaluated by means of the capacity adjustment factor (CAF) and a model to es:mate CAF from control variables was fiCed and validated. The results indicate increases of up to 30% in capacity with 60% of platooning-capable AVs. Sta:s:cal analyses show that the frac:on of AVs in the stream and the propor:on of platooning-capable AVs are the factors with the greatest impact on this increase in capacity.


INTRODUCTION
One of the attractions of autonomous vehicles (AVs) is the increase in capacity due to the more intensive use of traf ic lanes, and consequent improvements in the ef iciency of road operations (Zhao and Sun, 2013;Bierstedt et al., 2014). Various studies suggest that AVs will be able to improve traf ic low with a high level of penetration in traf ic streams and cooperation (VanderWerf and Miller, 2004;Shladover et al., 2012;Shladover, 2009). However, the effects of AVs on the capacity of freeways with a low and medium level of penetration are not yet well known (Milanes et al., 2014).
Understanding the impact of AVs in a wide range of motorway scenarios is of the utmost importance for concessionaires and public agencies responsible for motorway system operations. How to incorporate AVs when assessing the capacity and quality of service is an aspect that should be considered by managers, mainly for freeways that are under concession contracts and where the maintenance of a minimum quality standard is guaranteed under contract. In Brazil, as in many other countries, the quality of services is assessed by the Highway Capacity Manual (HCM), which still does not provide an instrument that includes AVs in the process, in its most recent edition, HCM-6 (TRB, 2016).
The present study is part of a broader project, which proposes a way to include AVs in quality-of-service assessments based on the HCM-6 passenger-car equivalents (PCE) method. This paper discusses the effects that different aspects of freeways, traf ic and AVs have on capacity. The impacts considered include: the type of AVs and their penetration rate; the maximum number of platooning vehicles; the number of lanes; the proportion of heavy goods vehicles (HGV) in the traf ic stream; and the length and magnitude of the slopes. In this study, a microsimulation software was used to generate synthetic vehicle low data. Based on the capacity of each scenario, the capacity adjustment factor (CAF) and a model for estimating the CAF value as a function of the simulation control variables were obtained.

THEORETICAL FRAMEWORK AND PROPOSED APPROACH
While the concept of connected and autonomous vehicles is broad, in this study, the classi ication proposed by the CoExist project (Sukennik, 2018) will be used. CoExist de ines AVs as driverless automobiles, which are classi ied as: cautious, normal and all-knowing, depending on their driving behaviour. The cautious AV type behaves more cautiously than human-driven vehicles (HDV). The normal AV type behaves similarly to HDVs. All-knowing vehicles are platooning-capable AVs that have better awareness and predictive capabilities of manoeuvres and more cooperative behaviour (Sukennik, 2018).
The main impacts expected from AVs in the traf ic stream include: an increase in the maximum low, fewer lane changes, more homogeneous and stable low, and a reduction of traf ic jams (Calvert et al., 2017). AVs can travel with smaller headways and with variable spacing depending on the kind of vehicle travelling in front of them (Shi et al., 2019;Makridis et al. 2018;Martin-Gasullaet al., 2019). When connected, the AVs exchange information (such as: distance, speed, acceleration and failure events), allowing them to be safer and respond faster (Van Arem et al., 2006). All these characteristics result in an increase in road capacity (Mahmassani, 2016;Zhao and Sun, 2013); the size of this increment, however, differs in each study as it depends on the road's characteristics and the behavioural parameters used in the simulations since there is not yet a suf icient number of these vehicles in traf ic (Zhao andSun, 2013, Shi et al., 2019). Therefore, simulations that take into consideration the local traf ic characteristics are essential for more accurate analyses.
The reduction in lane change manoeuvres and the deterministic behaviour of AVs result in less con licts and more homogeneous traf ic (Strand et al. 2011, Gorter, 2015Papadoulis, 2019;Alkim et al., 2007). Therefore, the presence of AVs increases the space mean speed of the traf ic stream and reduces traf ic jams (Makridis et al., 2018). Although the different impacts of AVs have already been studied by and large, there is a lack of studies in the literature that address the combined effects of road characteristics, AV leet composition and AV platooning capabilities.
As AVs are still in the testing phase, it is expected that there will be a long period of coexistence between HDVs and AVs in low proportions and at different levels of automation on freeways (Mahmassani, 2016;Calvert et al., 2017;Shi et al., 2019). Thus, this research focuses on analysing the impacts on freeway capacity at levels of low and medium penetration of AVs in the traf ic stream.
This article reports on a broader study, whose aim is to propose incorporating AVs in the assessment of the quality of services on freeways and expressways in Brazil, based on the HCM-6 methodology for PCE estimation. In the proposed approach, the effect of AVs is treated in a similar way to that used to incorporate the effect of HGV on the quality of services: using an equivalence factor. In the case of HGV, HCM-6 adjusts the demand by (TRB, 2016, p. 12-33): where is the equivalent demand low rate (pc/h/ln); is the observed hourly volume (veh/h); is the peak hour factor; is the number of lanes; and is the adjustment factor for the HGV effect, which is calculated by (TRB, 2016, p. 12-34): where is a fraction of HGV in the traffic and an equivalence factor.
On HCM-6, the vehicle equivalent is calculated following a complex process which basically consists of (Zhou et al., 2019a;List et al., 2015): (1) obtaining low-density graphs for base traf ic (automobiles only) and mixed traf ic (cars+HGV); (2) obtaining the capacity adjustment factor ( ); (3) Adjusting the CAF prediction model; (4) estimating the CAF values for speci ic conditions; and (5) estimating the values for speci ic conditions of the road and traf ic. As the method calculates equivalents for the same capacity (List et al., 2015), HCM-6 de ines the capacity adjustment factor ( !" ) as the !" = !" #$%& ⁄ ratio between !" , the maximum mixed low (automobiles+HGV) and #$%& , the maximum low of cars. In the case of HGV, the value of !" is always lower than 1 and is used to obtain the equivalence factor of HGV through (Zhou et al., 2019b): The authors propose adapting the HCM-6 method using an adjustment factor ( ) ) for the presence of AVs in traf ic, which would be calculated using: where ) is the fraction of AVs in the low, and ) is an equivalence factor for the AVs. Therefore, the adjustment of the demand value is done by including an extra factor into Eq. 1: where the adjustment factor for the presence of AVs, ) , represents the effect of a particular set of traf ic stream (percentage of heavy vehicles, percentage of AVs and the composition of the AVs leet) and the road (number of lanes, magnitude and slope length, etc.) conditions in the same way that represents the effect of HGV for the speci ic conditions of the analysed stretch: fraction of HGV and magnitude and slope length (TRB, 2016;p. 12-34). This paper analyses the factors that affect the CAF on major freeways in Brazil and proposes a model for its prediction (stages 1 to 3 of the HCM-6 method); the estimate of the equivalence factor values ) for highways and expressways in Brazil will be addressed in another paper.

METHOD
This research is a prospective study, which uses synthetic data generated by simulations, as AVs are still in the testing phase. Brie ly, the adopted method can be described by the following steps: (1) obtaining the recalibrated microsimulation software to represent traf ic low on Brazilian freeways; (2) de ining the experiment and simulation scenarios; (3) generating synthetic data through simulations; (4) calculating the CAF for each scenario; (4) analysing the effect of controlled variables on CAF; (5) adjusting the CAF prediction model; and (6) validating the prediction model.
The synthetic data were obtained from simulations carried out in Vissim 2020, which is able to simulate AVs (Sukennik, 2018), where behavioural and vehicle performance parameters of automobiles and HGV were recalibrated to better represent the traf ic on Brazilian freeways (Bethônico et al, 2016;Carvalho and Setti, 2019). The following sections present the research steps.

GENERATING SYNTHETIC DATA
This section describes how synthetic traf ic low data were obtained using the Vissim software.

Simula on Model
The network used (Table 1) consists of three segments. The irst one is 4 km long, it is lat, and allows vehicles to reach the segment under study in a stable way. The data are collected in an intermediate link which is 8 km long, where the slope and number of lanes vary according to the scenario. Five sensors, installed at 500, 1000, 2000, 4000 and 8000 m from the beginning of the link, are used to collect the data. Positioned in this way, the sensors can simulate ive different lengths of the gradient without needing to change the total length of the road in each simulation. The exit segment is 2 km long and has a slope of −2%. The time-step of the simulations was adopted as 5 updates/second to obtain the best combination between the most realistic results and computational performance (PTV, 2019). Conventional automobiles, i.e., human-driven vehicles (HDVs) were simulated using parameters from the Wiedemann-99 model, previously calibrated for typical highways in the state of São Paulo (Bethônico et al., 2016). Recalibrated parameters are those related to the carfollowing (CF) and lane-changing (LC) models and to the desired speed. The Table 1 provides parameter values for the CF and LC models used in this study and compares them to the Vissim default values. The "HDVs" column contains the recalibrated values (Bethônico et al., 2016) and the "cautious", "normal" and "all-knowing" columns contain the recalibrated values in the CoExist project (Sukennik, 2018). The desired speed distribution for HDVs was recalibrated to better represent Brazilian drivers' behaviour based on data collected from a one-hour video of a freeway, recorded in the off-peak period. The space mean speeds were obtained using a method based on computer vision (Marcomini and Cunha, 2018). Only passenger cars travelling under low rates below 500 veh/h/ln (TRB, 2016; p. 12-27) and headways higher than 8 seconds in relation to the vehicle in front (Al-Kaisy and Durbin, 2011) were included in the sample, making a total of 205 cars. The desired speed distribution for HDVs, shown in Figure 2, was obtained from the cumulative frequency observed for this sample. The distribution obtained indicates that the studied stream has vehicles that are slower than those in the distribution adopted as default by Vissim. The recalibrated parameters for HGV performance were obtained from a previous study (Carvalho and Setti, 2019) and include: maximum and desired acceleration functions, cumulative weight and power functions, and dimensions. These parameters were input into the software for four categories of HGV that characterise leets of HGV that travel on freeways in São Paulo state (Carvalho and Setti, 2019).
Simulated AVs are automobiles of three types: cautious, normal and all-knowing -, / and 0 , respectively. Each type of AV represents a different behaviour and V2V communication level; therefore, they have different calibration parameters, as well as distinct observation and cooperation capabilities (Table 1). For example, while and / are able to see only the vehicle in front of them and do not form platoons, 0 monitors up to 8 vehicles ahead and presents cooperative behaviour during lane changes and has the ability to form platoons (Sukennik, 2018). The default values of Vissim were used for the parameters related to the formation of AV platoons: maximum distance of 250 m to start a platoon; and 0.6 second headways and a minimum distance of 2 m from the platoon.
All AVs were simulated using deterministic, rather than a stochastic operation. The desired speed for AVs was de ined as the speed limit of ± 2 km/h. The headway of the 0 depends on the vehicle in front. In order to maintain smaller headways, these vehicles have an increase in the acceleration factor, de ined as 105% for the / and 110% for the 0 . These characteristics make the 0 vehicle an AV with cooperative behaviour. This con iguration for the three types of AVs enables us to evaluate the effect of the behaviour of AVs on capacity and, consequently, on the equivalence factor.

Simulated scenarios
In order to evaluate the impact of AVs on different traf ic conditions, the experiment considers a large number of scenarios combining controlled variables, shown in Table 2.
The Autonomous variable represents the total percentage of AVs in the low, whose maximum value was set at 60%, as AVs are not expected to reach levels close to 100% of the low in the near future (Calvert et al., 2017). Traf ic streams containing only HDVs are base low for a given scenario and traf ic streams containing HDVs and AVs are mixed lows for that scenario. The AV leet could comprise different proportions of AV types. In this experiment, 9 compositions were established with different proportions for each type of AV, as shown in Table 3, in such a way that the sum of proportions of + / + 0 always totalled 100%. (¹) Percentages such as AV1 + AV2 + AV3 = 100%, as shown in Table 3 The characteristics related to the road were also controlled in the simulation scenarios. The scenarios were created using different numbers of lanes on the freeway segment (2, 3 and 4), as well as the gradient magnitude, which can be 0%, +2% and +4%. These variables are relevant in this study as they affect the quality of service on freeways with a high number of heavy vehicles, as is the case in Brazil (Carvalho and Setti, 2018). Moreover, the literature does not show studies that address the effect of slopes on traf ic streams with AVs.
The combinations of control variables to provide a total number of 5103 scenarios, of which: 567 were scenarios without AV platoons ( irst 3 AV combinations in Table 3, 7 levels of proportion of AVs in the stream, 3 levels of traf ic lanes, 3 levels of ramps, and 3 levels of percentage of heavy vehicles) and 4536 were scenarios with AV platoons (6 remaining AV combinations, 7 levels of proportion of AVs, 4 levels of platoon size, 3 levels of traf ic lanes, 3 levels of ramps, and 3 levels of percentage of heavy vehicles). The time chosen for the simulation was 90 minutes: 30 minutes for warming-up and the remaining time for data collection. Each scenario was simulated 5 times, with approximately 50%, 60%, 75%, 90% and 100% of the maximum possible low in the stream, which was previously set. 75% 50% 25% 25% 25% 25% 0% 0% 0% 23 5 (normal) 25% 50% 75% 50% 25% 0% 75% 50% 25% 23 6 (all knowing) 0% 0% 0% 25% 50% 75% 25% 50% 75% Considering that the large number of scenarios to be simulated and the method used for calculating the values used in HCM does not foresee replications of the simulations to generate synthetic data (Zhou et al., 2019b), it was initially decided to evaluate the need for replications of the simulations. As empirical results indicate that the number of replications required depends on the variable analysed and that, in some cases, one or two replications are suf icient (Fries et al. 2014), 6 scenarios were simulated with 9 replications (different random seeds). The scenarios that were chosen randomly for this analysis correspond to the following conditions: 30% of heavy vehicles; level road; two traf ic lanes; 50% of AVs, in three different compositions 4, 5 and 6 ( Table 3) and capable of forming platoons of up to two AVs; and four distances travelled in the link (500, 1000, 2000 and 4000 m).
For each of the replications, the CAF values and their averages were calculated. Then, those values were normalised (Table 4) in such a way that the average would become equal to 1. Considering this, the variation of the values obtained for CAF can be evaluated in relation to the average for all 54 cases. By observing the last line of Table 4, it can be seen that the greatest variation observed between the normalised average (1.00) and the CAF normalised values was 3.6%. This variation margin can be considered small for an exploratory study such as this one. Thus, considering the computational costs involved in the replication of the simulations and the time available for this research, it was decided to reproduce the procedure used for calculating the equivalence factors of HCM (Zhou et al., 2019b), where no replications were made.
In total, the generation of synthetic data required 25,515 simulations, which were carried out automatically using a program written in Python that prepared the input iles for the Vissim simulation and collected the results from each simulation.

FACTORS THAT AFFECT THE CAPACITY ADJUSTMENT FACTOR
The CAF was calculated for all simulated traf ic streams. The capacity was de ined as the low rate of the 95 th percentile of the low of each scenario, which was obtained from time intervals of 5 minutes of observation, as stipulated in HCM-6 (Dowling et al., 2014). Figure 3(a) shows an example, where one scenario without AV results in a capacity of 1692 veh/h/ln; Figure 3(b), shows that the capacity increases to 1878 veh/h/ln when the stream has 60% of AVs.
In this section the factors that affect the are analysed. The CAF is the ratio between the capacity of the mixed low (conventional vehicles and AVs) and the capacity of the base low where ! is the CAF for scenario i; !, !" is the capacity (vehic/h) for the mixed low scenario i; !,#$%& is the capacity (vehic/h) for the base low in scenario i. The histogram of the values found for , shown in Figure 4(a), presents an asymmetric distribution whose average is 1.077 and the variance is 0.003 ( = 22005, as the sample excludes the repeated base scenarios). As expected, this asymmetry is due to the larger number of observations greater than 1, since in most simulated scenarios there was an increase in the capacity, given that the AVs are able to maintain smaller headways than those of conventional vehicles. The boxplot in Figure 4(b) indicates an increase in the variance as the proportion of AVs in the stream increases.
The simulated scenarios resulted in CAF values between 0.95 and 1.30. The maximum value represents a 30% increase in the capacity and was obtained in a scenario with a high proportion of 0 , platooning-capable AVs. On the other hand, the lowest value was observed in scenarios with only 10% of non-platooning AVs. In these scenarios, the CAF values were between 0.95 and 1.10. The CAF values, aggregated by the type of leet and proportion of AVs in the low ( Figure  5), lead us to conclude that the higher the connectivity of the AVs, the higher the value (combination 9 has 75% of platooning-capable AVs); it can also be observed that the level of penetration of the AVs implies an average increase in the values. The analysis of the effect of the parameters on the capacity was carried out using the , which represents the impact of the AVs on the capacity. Welch's one-way ANOVA showed a major effect of the penetration of AVs (Autonomous) on the capacity: (6, 21998) = 54669.09; C < 0. 05; and E = 0.77. The boxplot in Figure(b) indicates that the impact of AVs on the capacity increases as the level of penetration increases. To test this hypothesis, as there is not variance homogeneity in the samples corresponding to each level of penetration (0%, 10%, ..., 60%), the Games-Howel post-hoc test and Hochberg's GT2 test were used. The results show that the average of the values for each penetration level were signi icantly different from each other (G = 5%), indicating that a 10% increase in the level of AV penetration contributes to an increase in capacity.
The factorial ANOVA was used to verify whether the control variables (Table 2) affected the values. The results (Table 5) indicate that for G = 5%, all control variables have a signi icant irst order effect, except for the slope length -which can be explained as the performance of AVs is not affected by the slope. This table also shows that the second order effects were signi icant (C < 0.05), except for the second-order interaction Autonomous×Distance.
The I² values show that the most important factors are the level of AV penetration and their capacity to form platoons. Interaction graphs were used to investigate the interaction between the main effects on the average value. The graphs in Figure 6 represent these interactions, comparing the results for the lows where there is predominance of platooning-capable AVs ( 0 ) with the lows where there is predominance of platooning-incapable AVs ( and / ). Figure 6(a) shows that the rises as the fraction of AVs increases in both cases, although more markedly with the predominance of AV3 in the low and that, in this case, there is a relation with the percentage of HGV.
An analysis of the comparisons between scenarios with different leets, shown in Figure 6, shows that all the factors analysed have little in luence on streams with a predominance of platooning-incapable AVs. In streams with a predominance of 0 , these factors have a different behaviour. The graph in Figure 6(a) shows that increasing the percentage of HGVs reduces CAF; the graph in Figure 6(b) indicates that for scenarios with more than 30% of AVs, the more lanes there are, the smaller the increase in CAF, a phenomenon also observed in the literature (Xiaobao and Ning, 2007). Figure 6(c) suggests that steep gradients (4% or more) affect CAF more than level segments (2% or less), while the graph in Figure 6(d) indicates that the gradient length has no effect on CAF and the graph in Figure 6(e) shows that the size of the platoon has no impact on CAF, except for the scenario with a high rate of AVs. In scenarios with a predominance of 0 and 60% of AVs, scenarios with smaller maximum platoon length generated higher CAF values.

Predominance of AV1 and AV2
Predominance of AV3

MODEL TO ESTIMATE VALUES FOR THE CAPACITY ADJUSTMENT FACTOR
In HCM-6 (TRB, 2016, p. 26-6;Zhou, Rilett and Jones, 2019b), the CAF values are obtained using regression models. However, these models are complex, with parameters that are dif icult to interpret and cannot be observed in a traf ic stream. In order to overcome these limitations, we propose a model for estimating the which, can easily evaluate the effect of each parameter and covers all simulated scenarios.

Calibra on of the K2L predic on model
The model used to estimate the value was obtained by multiple linear regression, whose independent variables are listed in Table 2, except for the distance travelled on the slope, which does not in luence the CAF, and the fraction of type 2 AVs (AV2). The AV2 variable was excluded from the model because it presents a high correlation with AV3 (M = 0.697) and a low correlation with CAF (M = 0.029), which is explained by the similarity of the behaviour parameters between / and HDVs.
The model obtained is statistically signi icant:  Table 6 summarizes the model itting results. The standardised coef icients (Table 6) show that the variable with the highest predictive power is AV, which is compatible with the factorial ANOVA results. The 0 and variables, which represent the bene icial effect of the AV platoons on capacity, have positive coef icients. From the variables that have negative signs, which reduce the capacity, it should be noted that the increase of (AVs with excessively conservative behaviour) in the traf ic stream reduces the capacity, as well as the proportion of HGV. Figure 6(a)-(c) show the deleterious effect of increasing O, , and in . Table 6 also shows that the predictors do not present signi icant collinearity as the tolerance statistics were higher than 0.1 and the variance in lation factor (VIF) is less than 10.  (Table 3): combination 9, with a higher percentage of 0 , platooning-capable AVs; combination 1, in which predominates; and combination 4, a middle ground. Table 7 summarises the controlled variables used in the validation. The validation was carried out comparing the values observed for the validation sample against the values estimated using the model in Equation 7. Figure 7(a) shows the relation between the observed and the estimated values (the band represents a tolerance margin of 4%), whereas Figure 7(b) shows the proportion of correct answers in the model in Equation 7. Figure 7(b) shows that 74% of the values predicted by the model were within the 4% error margin, compared to the observed values. Figure 7(c) and Figure 7(d) show that the model has a better ability to predict the CAF value for scenarios with a higher proportion of type 3 AVs and produces larger errors in scenarios where type 1 AVs predominate.
The quality of the estimates was evaluated using the mean normalised error (MNE), mean absolute error (MAE), normalised root mean square error (NRMSE) and the correlation coef icient (M).
The observed and estimated values presented a high correlation (M = 0.724) and a low value of systematic errors, V = 0.019. As V = 0.032 and OVW = 0.040, indicating that the error in the CAF prediction is 3% to 4%, on average. Additionally, the standard deviation of the observed values X Y#% = 0.048 is very close to the standard deviation of the estimated values, X Z[\ = 0.051, which indicates that the dispersions of the two sets are similar. The low error values demonstrate a good accuracy of the model, within the limits of the simulated values for the independent variables.

FINAL CONSIDERATIONS
The aim of the research reported here was to analyse the impact of AVs on the capacity of major freeways in Brazil, using a recalibrated version of Vissim to represent typical automobiles and HGV typical of Brazilian freeways. The capacity was obtained using the HCM-6 method and a wide range of control variables was used. The ANOVA results indicated that the larger the fraction of AVs in traf ic, the larger the capacity and that the factors that most impact the capacity increase are the fraction of AVs in the traf ic and the proportion of platooning-capable AVs in the AV leet. The results of the interaction graphs suggest that the AVs platoons increase capacity and that the platoon maximum size does not affect the capacity for AV penetration levels up to 50%. However, in scenarios with 60% of AVs in which platooning-capable AVs predominate, smaller platoons provide a signi icantly higher capacity than platoons with many AVs. For low levels of AV penetration (up to 30%), the number of traf ic lanes does not in luence capacity; for AV fractions above 30%, the capacity decreases as the number of traf ic lanes increases. This occurs because a higher number of lanes leads to more lane changing manoeuvres (TRB, HCM p. 13-5), reducing the density and, consequently, the capacity. Correct answers (%)

Tolerance margin
A CAF prediction model was adjusted using multivariate regression and its validation demonstrated a good performance of estimates, with mean errors of 3% to 4% of the CAF. Although a high rate of correct answers was obtained, the model may not be as precise for scenarios that are different from those simulated; therefore, it is suggested that future research uses simulations with different scenarios, different AV behaviours, inclusion of autonomous HGV and other characteristics of freeways.
The results indicate that AVs would increase the capacity of freeways in Brazil, and that the impact would be proportional to the fraction of AVs in the traf ic. The research demonstrated that AVs with cooperative behaviour and greater V2V communication capabilities would lead to a greater increase in capacity, of up to 30% from the base capacity. These results are important for road system planning, freeway operation companies and future research in this area. However, it must be emphasized that these results are highly dependent on the microsimulation model adopted (Vissim); another model might produce different results.