Impact of CAV Truck Platooning on HCM-6 Capacity and Passenger Car Equivalent Values

In Step 1, the flow-density plots of each scenario are created based on output from the VISSIM model. Following HCM-6 protocols, each scenario is simulated using a single run and the same seed number. There are nine volume levels (e.g., 240, 600, 1,200, 1,800, 1,920, 2,040, 2,160, 2,280, $\mathrm{2,400}\mathrm{veh}/\mathrm{h}/\ln$) in every run, and these correspond to volume-to-capacity ratios of 10%–100% based on an assumed theoretical capacity of $\mathrm{2,400}\mathrm{veh}/\mathrm{h}/\ln$. Each volume level consists of 1 h of vehicle loading to achieve a steady-state condition, 1 h of steady-state for data collection, and 1 h of vehicle unloading. As a result, the simulation period comprises a total of $27\mathrm{h}$ per scenario (e.g., 3 h per volume level × 9 volume levels). The scenarios are defined by a combination of the following factors:

In total, there are 91 scenarios for the passenger car–only flow condition (e.g., $13\mathrm{levels}\mathrm{of}\mathrm{grade}\times 7\mathrm{levels}\mathrm{of}\mathrm{distance}$) and 1,183 scenarios for the mixed-traffic flow condition (e.g., $13\mathrm{levels}\mathrm{of}\mathrm{truck}\mathrm{percentage}\times 13\mathrm{levels}\mathrm{of}\mathrm{grade}\times 7\mathrm{levels}\mathrm{of}\mathrm{distance}$). The VISSIM model output consisted of the space mean speed and the flow rate collected at each detector per $1\text{-}\min$ interval. These outputs are used to compute the hourly flow rate and density, at $1\text{-}\min$ averages, for each combination using Eqs. (1) and (2), respectively:where $q_{f,t,p,m,g,d,r}$ = flow rate for $f$ flow type at $t$ time interval, $p$ truck percentage level, $m$ truck composition level, $g$ grade level, $d$ distance level, and $r$ simulation flow-rate level based on $1\text{-}\min$ interval traffic volume recorded by the detector ($\mathrm{veh}/\mathrm{h}/\ln$); $V_{f,t,p,m,g,d,r}=1\text{-}\min$ interval traffic volume recorded by detector for $f$ flow type at $t$ time interval, $p$ truck percentage level, $m$ truck composition level, $g$ grade level, $d$ distance level, and $r$ simulation flow-rate level ($\mathrm{veh}/\min /\ln$); $k_{f,t,p,m,g,d,r}$ = density for $f$ flow type at $t$ time interval, $p$ truck percentage level, $m$ truck composition level, $g$ grade level, $d$ distance level, and $r$ simulation flow-rate level ($\mathrm{veh}/\mathrm{mi}/\ln$); ${\overline{v}}_{f,t,p,m,g,d,r}=1\text{-}\min$ interval space mean speed for $f$ flow type at $t$ time interval, $p$ truck percentage level, $m$ truck composition level, $g$ grade level, $d$ distance level, and $r$ simulation flow-rate level ($\mathrm{mi}/\mathrm{h}$).

The hourly flow-rate and density values populate the scatter plots for each scenario. There are 1,274 scatter plots in total. Each flow-density scatter plot for a given scenario contains 540 pairs of flow-rate and density values (e.g., $60\min \times 9\mathrm{volume}$ levels).

Each scatter plot is used to identify the capacity value for a given scenario. Note that in the HCM-6, capacity is defined as the 95th percentile of the maximum $1\text{-}\min$ average flow rate for the given scenario (Dowling et al. 2014a, b; Yang 2013). To the authors’ knowledge, this is the first time that the HCM has used an aggregation level other than $15\min$ to calculate a traffic-flow metric. Therefore, care must be taken in comparing the capacity values found in the HCM-6, and by definition in this paper, with other published capacity values that are based on larger aggregation levels. The simulated capacity for each of the 1,274 scenarios is calculated using Eq. (3). Note that if the 540 observations from each scenario were ordered from smallest to largest, the 95th percentile value would be the 513th largest observation:where $C_{f,p,m,g,d}$ = capacity for $f$ flow type at $p$ truck percentage level, $m$ truck composition level, $g$ grade level, and $d$ distance level ($\mathrm{veh}/\mathrm{h}/\ln$); $P95$ = 95th percentile; and $q_{f,t,p,m,g,d,r}$ = flow rate for $f$ flow type at $t$ time interval, $p$ truck percentage level, $m$ truck composition level, $g$ grade level, $d$ distance level, and $r$ simulation flow-rate level, based on sixty $1\text{-}\min$ interval traffic volume recorded by detector ($\mathrm{veh}/\mathrm{h}/\ln$).

To illustrate, Fig. 3 shows a graph of flow rate versus density for the passenger car–only flow, 3% grade, and 1.61 km ($1.0\mathrm{mi}$) distance scenario. It may be seen that the relationship between flow rate and density is linear. Using Eq. (3), the definition of the HCM-6 EC-PCE methodology, the capacity is found to be $\mathrm{2,260}\mathrm{veh}/\mathrm{h}/\ln$.

Fig. 4 shows the flow-rate versus density graph for the same conditions as Fig. 3 but for the mixed-traffic flow condition and a 20% truck percentage. It may be seen that at low density, the relationship between flow-rate and density is linear. A breakpoint occurs at approximately 25 veh/mi/ln, and the capacity value is estimated to be $\mathrm{1,780}\mathrm{veh}/\mathrm{h}/\ln$.

In this step, the CAFs for each scenario are calculated using the simulation results from Step 1. These are calculated for the mixed-flow and passenger car–only scenarios using Eqs. (4) and (5), respectively. These equations use the capacity of each scenario obtained from the flow-density scatter plots from Step 1:where ${\mathrm{CAF}}_{2,p,m,g,d}$ = capacity adjustment factor for mixed flow at $p$ truck percentage level ($P=13$), with $m$ the truck composition level ($M=3$), $g$ the grade level ($G=13$), and $d$ the distance level ($D=7$); ${\mathrm{CAF}}_{1,0,0,g,d}$ = capacity adjustment factor for auto-only flow at $g$ grade level ($G=13$) and $d$ distance level ($D=7$); $C_{2,p,m,g,d}$ = capacity for mixed flow at $p$ truck percentage level, with $m$ truck composition level, $g$ grade level, and $d$ distance level ($\mathrm{veh}/\mathrm{h}/\ln$); and $C_{1,0,0,g,d}$ = capacity for auto-only flow at $g$ grade level and $d$ distance level ($\mathrm{veh}/\mathrm{h}/\ln$).

To illustrate, consider the scenario defined by mixed flow ($f=2$), 20% truck percentage ($p=5$), $30/70$ SUT/TT truck composition ($m=1$), $+3\%$ grade ($g=10$), and 1.61 km ($1.0\mathrm{mi}$) distance ($d=4$). Note that the passenger car–only and mixed-traffic scatter plots for this situation were shown in Figs. 3 and 4, respectively. Using Eq. (4) the CAF for this situation (${\mathrm{CAF}}_{2,5,1,10,4}$) is 0.788 ($\mathrm{1,780}/\mathrm{2,260}$). This calculation is repeated for the other 1,273 scenarios using either Eq. (4) or Eq. (5), as appropriate for the given flow type.

The CAFs for all 1,274 scenarios are shown in Fig. 5. The $x$-axis represents the scenario number. Each specific scenario number is calculated using Eq. (6) and is a function of the truck percentage, grade, and distance. There were 14 truck percentage values (including 0%), and these are shown at the top of Fig. 5. The thinnest line in the background represents the simulated CAFs from this paper and the lower thick line the estimated CAFs obtained in the original HCM-6 research. The blue line will be discussed in Step 4. For a given truck percentage, the CAFs for grade and grade distance are shown in order. The general form is a flat straight line for the negative and zero grade scenarios, followed by decreasing CAF values for the positive grade values:where $n$ = scenario number; $p$ = ordinal number of truck percentage level ($p=1,2,\dots ,P$ indicates a 2%–100% truck percentage); $P$ = total levels of truck percentage, $P=13$; $g$ = ordinal number of grade level ($g=1,2,\dots ,G$ means –6% to 6% grade); $G$ = total levels of grade, $G=13$; $d$ = ordinal number of distance level (level of detector location) ($d=1,2,\dots ,D$ means $0.40–8.05\mathrm{km}$ ($0.25–5.00\mathrm{mi}$); and $D$ = total levels of distance (detector location), $D=7$.

All else being equal, a greater CAF value indicates a higher capacity of the freeway segment. A visual analysis suggests that there is a good match between the estimated CAF values from the two sources. This closeness will be examined statistically in the next section. Note that the CAF values from the HCM-6 are fairly stable while the simulation values tend to have considerable variability. This difference will be explained in the following section.

Because of the inherent variability of the CAF results from the simulation, the HCM-6 developers chose not to use the simulated CAF values directly. Instead, they calibrated a regression model that related the simulated CAF values to the truck percentage, grade, and distance parameters. The goal was to lessen the variability in the CAF results.

The CAF values from Step 2 are used as input, and statistical regression techniques are used to calibrate the model. The nonlinear regression model used in the HCM-6 are shown in Eqs. (7)–(11) (Dowling et al. 2014b; Zhou et al. 2019; Zhou 2018):where ${\mathrm{CAF}}_{2,p,m,g,d}$ = capacity adjustment factor for mixed flow at $p$ truck percentage level, $m$ truck composition level, $g$ grade level, and $d$ distance level; ${\mathrm{CAF}}_{1,0,0,g,d}$ = capacity adjustment factor for auto-only flow at $g$ grade level and $d$ distance level (this value is assumed to be 1); ${\mathrm{CAF}}_{2,p,m}^{T_a}$ = capacity adjustment factor for truck percentage effect for mixed flow at $p$ truck percentage level and $m$ truck composition level; ${\mathrm{CAF}}_{2,p,m,g,d}^{G_a}$ = capacity adjustment factor for grade effect for mixed flow at $p$ truck percentage level and $m$ truck composition level; ${\mathrm{CAF}}_{2,p,m}^{{\mathrm{FFS}}_a}$ = capacity adjustment factor for free-flow speed effect for mixed flow at $p$ truck percentage level and $m$ truck composition level; ${\rho }_{2,p,m}^{G_a}$ = coefficient for capacity adjustment factor for grade effect for mixed flow at $p$ truck percentage level and $m$ truck composition level; ${(p_s)}_p$ = truck percentage at $p$ truck percentage level (between 0 and 1); $p^{*}$ = threshold of truck percentage for calculating coefficient for capacity adjustment factor related to grade with default value 0.01; ${(g_s)}_g$ = grade at $g$ grade level (between $-0.06$ and 0.06); ${(d_s)}_d$ = distance of grade at $d$ distance level (mi); ${\mathrm{FFS}}_1$ = free-flow speed for auto-only flow ($\mathrm{mi}/\mathrm{h}$); ${\alpha }_{1_{2,m}}^{T_a}$, ${\beta }_{1_{2,m}}^{T_a}$ = parameters for capacity adjustment factor for truck percentage effect; ${\gamma }_{2,m}^{G_a}$, ${\theta }_{2,m}^{G_a}$, ${\mu }_{2,m}^{G_a}$, ${\alpha }_{2,m}^{G_a}$, ${\varphi }_{2,m}^{G_a}$, ${\eta }_{2,m}^{G_a}$, ${\beta }_{2,m}^{D_a}$, ${\alpha }_{2,m}^{D_a}$, ${\varphi }_{2,m}^{D_a}$ = parameters for capacity adjustment factor for grade effect; and ${\mu }_{2,m}^{{\mathrm{FFS}}_a}$, ${\rho }_{2,p,m}^{{\mathrm{FFS}}_a}$, ${\beta }_{2,m}^{{\mathrm{FFS}}_a}$, ${\varphi }_{2,m}^{{\mathrm{FFS}}_a}$ = parameters for capacity adjustment factor for free-flow speed effect.

This paper adopted the same form of the nonlinear model [i.e., Eq. (7)] as was used in the HCM-6. The parameters were estimated using a generalized reduced gradient (GRG) approach. This is a nonlinear optimization method that uses an iterative process to optimize a target value. In this paper, the target goal was to minimize the sum of squared errors between the simulated CAFs from Step 2 and the estimated CAFs from the nonlinear regression model. A detailed description of the method can be found elsewhere (Lasdon et al. 1974). Note that the original research did not mention the optimization technique that was applied to find the best estimates of the model parameters.

Table 3 shows the values of the parameters in the CAF model for the original research and for this paper in Rows 1 and 2, respectively. It may be seen that the estimators between both cases are very similar. It is hypothesized that the small differences found are due to the different versions of the simulator.

In this step, the CAFs for the mixed flow scenarios (${\mathrm{CAF}}_{2,p_s,m_s,g_s,d_s}$) are estimated for the specific conditions listed in the HCM-6. The parameters of interest are truck percentage $p_s$, grade $g_s$, and distance $d_s$. These estimated CAFs are obtained using Eq. (7) based on the calibrated parameters shown in Table 3 (Row 2).

Fig. 6 shows a scatter plot of the estimated CAF value from the original HCM research as a function of the estimated CAF value from this paper. There are a total of 1,274 points or comparisons in this figure. It may be seen that the approach adopted in this paper resulted in a linear relationship with a very high $R^2$ value of 0.99. Fig. 5 shows a direct comparison between the CAF values calculated in this paper (upper thick line) and the CAF values from the HCM-6 (lower thick line). Not surprisingly, the CAF values are generally in agreement. It was concluded that using a VISSIM 9 model for passenger cars and a VISSIM 20 model for mixed traffic allowed for an accurate estimation of the HCM-6 values.

Fig. 6 also shows the relationship between the HCM-6 CAF values and the values obtained if all the simulation data were obtained from VISSIM 20. While the relationship is generally linear, there is considerably more scatter, as evidenced by the mean absolute percentage error (MAPE) value of 8.2%. In addition, the VISSIM 20 CAF results tended to underestimate the CAF values used in the HCM-6. This is why a combination of VISSIM 9 and 20 was used in this paper. Because VISSIM 20 limits lane changing for vehicles traveling at the same speed, it is hypothesized that this adversely affected the passenger car–only simulations (PTV 2019a). With respect to mixed-traffic conditions, this is not as critical as the vehicle characteristics create more lane changing opportunities. This also illustrates a danger in using simulation models for national design guides without adequate controls, such as clearly defining simulation logic and parameters (Hendrickson and Rilett 2017; Rilett 2020).

In the last step of the methodology, the EC-PCEs ($\mathrm{EC}-{\mathrm{PCE}}_{2,p_s,m_s,g_s,d_s}$) at specific conditions of truck percentage $p_s$, grade $g_s$, and distance $d_s$ are calculated using Eq. (12):where $\mathrm{EC}-{\mathrm{PCE}}_{2,p_s,m_s,g_s,d_s}$ = EC-PCE for mixed flow at truck percentage $p_s$, truck composition $m_s$, grade $g_s$, and distance $d_s$; ${\mathrm{CAF}}_{2,p_s,m_s,g_s,d_s}$ = capacity adjustment factor for mixed flow at truck percentage $p_s$, truck composition $m_s$, grade $g_s$, and distance $d_s$; and $p_s$ = truck percentage (between 0 and 1).

The estimated EC-PCEs as a function of the HCM-6 EC-PCEs are shown in Fig. 7. It may be seen that the relationship is approximately one to one with an $R^2$ value of 0.997 and a MAPE of 3.9%. It was concluded that the simulation approach adopted in this paper can (1) replicate the current HCM-6 values using the HCM-6 assumptions, and (2) be used to model the effect of CAVs on capacity and PCE values using the same HCM-6 approach. Also shown in Fig. 7 is the relationship between the HCM-6 EC-PCE values and the estimated EC-PCE values if only VISSIM 20 were used. While linear, the fit is not nearly as good, as evidenced by the MAPE value of 18.3%.

The 91 passenger car–only scenarios and their associated flow-density plots were developed using VISSIM 9, as described previously. Next, the flow-density plots were developed for the 1,183 CAV scenarios using VISSIM 20. From these plots the HCM-6 capacity, defined as the 95% maximum flow rate using $1\text{-}\min$ aggregation, was identified. These capacities were then used in Step 2 to calculate the CAF values of the CAV condition for each of the 1,274 combinations.

For illustrative purposes, Fig. 8 shows the flow-density curve for the baseline CAV condition for the same conditions as in Fig. 4. It may be seen that the breakpoint occurs at a higher density value (e.g., $30\mathrm{veh}/\mathrm{h}/\ln$). In addition, the CAV capacity (e.g., $\mathrm{2,080}\mathrm{veh}/\mathrm{h}/\ln$) is approximately 10% higher than the equivalent non-CAV capacity (e.g., $\mathrm{1,780}\mathrm{veh}/\mathrm{h}/\ln$). It is hypothesized that the higher capacity occurs due to the deployment of CAV truck platoons in the traffic stream, which vehicles have shorter headways and reduced stochasticity compared to non-CAVs.

In the original HCM-6 research, a nonlinear regression model was used in Step 3. The form for the HCM-6 analytical model was based on kinematic and resistance equation–related vehicles ascending and descending different grades (Dowling et al. 2014b). A heuristic optimization approach was used to calibrate the model where the goal was to identify the model that minimized the error between the simulated CAFs and the estimated CAFs. The parameters of these equations were optimized using an Excel spreadsheet. The final model consisted of a combined grade and distance effect parameter, a free-flow speed effect parameter, and truck percentage effect parameter (Dowling et al. 2014b; Zhou 2018) as shown in Eqs. (7)–(11).

In this paper, the same model structure was assumed. However, the truck percentage effect (${\mathrm{CAF}}_{2,p,m}^{T_a}$) parameter could not be calibrated to an acceptable level. Therefore, it was decided to use four parameters to model this effect. No changes in model format were performed for combined grade and distance effect (${\mathrm{CAF}}_{2,p,m,g,d}^{G_a}$) and free-flow speed effect (${\mathrm{CAF}}_{2,p,m}^{{\mathrm{FFS}}_a}$). The statistic that was used to assess model fitting was the standard error of the regression ($S$), as shown in Eq. (13). The advantage of the $S$ metric is that it can be applied for both nonlinear and linear models, in contrast to the $R^2$, which is only valid for linear models (Spiegelman et al. 2011):where $S$ = standard error of regression; SSE = sum of squared errors; $N$ = number of observations; and $P$ = number of parameters in model.

Seven potential models that attempted to capture the truck percentage effect were analyzed as shown in Table 2. The HCM-6 model, shown as Model 1, is a power function with two parameters. It had an $S$ value of 0.0578. Model 4, which is a polynomial model, had an $S$ value that was approximately a sixth of the size of Model 1. This model was chosen because it had a low $S$ value and fewer parameters compared with other models. Once the final model structure was chosen, the same approach as in the HCM-6 methodology was adopted to find the best estimators for the parameters of the nonlinear regression model.

Figs. 9(a and b) show the simulated CAF value versus the estimated CAF values for the original HCM-6 model formulation and the revised model formulation, respectively. It may be seen that the revised model formulation performed much better at predicting the CAF value for a given scenario, as evidenced by the linear relationship shown in Fig. 9(b) and the very high $R^2$ statistic of 0.971.

Table 3 shows the model parameters that were used to calculate the estimated CAFs using Eqs. (7)–(11) for each scenario. Row 1 corresponds to the HCM-6 research, Row 2 to the HCM-6 replication described earlier, and Row 3 to the CAV base case described earlier.

Once the regression models were calibrated in Step 3, the CAFs were then estimated. A comparison of the estimated CAFs for the CAV condition (base case) and the estimated CAFs for the non-CAV condition (e.g., HCM-6 results) are shown in Fig. 10. The increasing line represents the CAV condition and the decreasing line the non-CAV condition. The scenario number (horizontal axis) is given by Eq. (6) and corresponds to a particular combination of truck percentage, grade, and distance that was used to compute the corresponding CAF. For the non-CAV condition, the CAF values decrease as truck percentage increases, and this decrease is at a fairly linear rate. In contrast, for the CAV condition the CAF values increase as the percentage of trucks increase. For truck percentages of less than 10%, the CAF values are similar to the HCM-6. It is hypothesized that this occurs because there are fewer opportunities for truck platoon formation. Interestingly, when trucks are 100% of the vehicle stream, the CAF values are approximately 10.5% higher than the CAF for passenger cars. That is, a traffic stream with 100% CAV will have a higher vehicle flow rate than a traffic stream with 100% passenger cars. Taking as reference the truck percentage interval from 10% to 100% (Scenarios 274–1,274), the CAF values for the CAV condition are, on average, 41.0% higher (ranging from 0.1% to 176.5%) than those of the non-CAV condition.

Similar to the HCM-6, the EC-PCE values were estimated for 10 levels of truck percentage (i.e., 10%–100% in 10% increments), grade (i.e., 0%, $+3\%$, and $+6\%$), and distance [i.e., 0.8 km ($0.5\mathrm{mi}$), 1.61 km ($1.0\mathrm{mi}$), and 2.42 km ($1.5\mathrm{mi}$)]. Fig. 11 shows the corresponding EC-PCE values as a function of truck percentage for the three levels of grade and three levels of distance for both the CAV condition (base case) and the HCM-6 values. The solid line represents the CAV EC-PCE values and the dotted line the HCM-6 (e.g., non-CAV) EC-PCE values. The EC-PCE values were calculated using Eq. (12). Note that any specific condition within the explored range of truck percentage, grade, and distance that were considered in the HCM-6 methodology can be computed using the model parameters provided in Table 3. On average, the EC-PCE values for the CAV condition are 34.3% lower than those of the non-CAV condition, indicating that the CAV technology lessens the impact of heavy trucks on traffic operations.

For both the CAV and non-CAV conditions, the maximum EC-PCE values occur at a truck percentage of 10%. These values range from 2.0 to 4.5. In general, as the grade and distance increase, so does the EC-PCE. For higher truck percentages, the EC-PCE values for the non-CAV condition tend to decrease as truck percentages increases until the 30% value is reached. After this point, the EC-PCE values tend to increase at a decreasing rate with truck percentage. In general, the EC-PCE ranges from 2.0 to 4.5 for the non-CAV condition. In contrast, for the CAV condition the EC-PCE decrease at a decreasing rate as percentage of trucks increase. As would be expected from the earlier analysis, as the truck percentage approaches 100% the EC-PCE value approaches 1.

In summary, the CAV technology increases the capacity for a given scenario, all else being equal, and this results in correspondingly lower EC-PCE values. The increase in capacity for a given scenario is a function of the grade, grade length, and percentage trucks in the scenario. It should be noted that this comparison is for trucks equipped with CAV technology. It is hypothesized that if passenger cars also had CAV platoon technology, then the capacity increase shown in Fig. 11 would be even greater. However, it is unclear how the EC-PCE values would change without a detailed simulation study, which is beyond the scope of this paper.