Investigating the Impact of Automated Vehicles on the Safety and Operation of Low-Speed Urban Networks

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Introduction
Transportation networks face many challenges such as high travel times, trafc congestion, crashes, and environmental externalities such as emissions [1][2][3][4].Congestion is the root of other problems such as increased fuel consumption and increased travel time.For example, in 2021 American drivers lost an average of 36 hours per year due to trafc congestion [5].Meanwhile, the U.S. Department of Transportation's National Highway Trafc Safety Administration report [6] found that over twenty thousand people lost their lives in motor vehicle crashes in the frst half of 2021, up 18.4% over the frst half of 2020.Terefore, it is necessary to fnd solutions to improve the safety and decrease trafc congestion.
Due to the advancement of technology, it is predicted that automated vehicles (AVs) may help reduce congestion and improve safety [7][8][9].From a trafc fow viewpoint, AVs can beneft from smaller headway due to automation features [10,11].Tus, AVs are expected to have a positive efect on congestion mitigation.From the safety point of view, human error is a contributing factor in up to 90 percent of crashes [12,13], and AVs are believed to signifcantly reduce the risks and consequences of crashes [14][15][16][17][18][19][20].
Many studies have investigated the impact of AVs on trafc fow and safety in diferent environments and situations [11,16,[20][21][22][23][24][25][26].Some of these studies have explored the impact of AVs on fundamental diagrams (MFDs) and the capacity of transportation networks [10,27,28].On the other hand, others have investigated the safety impact of AVs based on safety measures [16,20,21,26,29].However, to our knowledge, no studies have yet investigated the impact of AVs on MFDs and safety simultaneously.Moreover, these studies have not explored the impact of AVs on macroscopic safety diagrams (MSDs) a concept introduced by Alsalhi et al. [30].MSDs share a conceptual foundation with MFDs, indicating that, like MFDs-which propose that trafc fow is a function of trafc density-MSDs can also apply this concept, making them essentially a function of density [30].Tus, generally, MSDs show the relationship between trafc conficts and density.However, given the conficts between speed, fow, and safety [31,32], it is not clear to what extent AVs can afect the conficts between fow and safety.
Tus, to fll these gaps, this study investigates the impact of AVs on network performance as measured through the simultaneous analysis of MFDs and MSDs.Te case study is a grid network with 50 km/h and 30 km/h speed limits.Te primary motivation for choosing a grid network as a lowspeed urban network is that the safety issues for intersections are crucial because many accidents occur at intersections.For example, 43 percent of trafc crashes involve intersections in the United States [33].Moreover, this study analyzes the impact of AVs on stop-and-go waves which are a common occurrence at intersections [20].Furthermore, this study presents a novel framework in which multiobjective optimization fnds a set of solutions in which trafc fows are high and the number of crashes remains low.At the end of this study, a comparison is made between urban speed limits based on the MFDs and MSDs.Te main contributions of this study are below: (1) Investigating the impact of AVs on trafc fow and safety simultaneously based on macroscopic and microscopic analysis.(2) Presenting a multi-objective optimization maximizing trafc fow while minimizing conficts.(3) Comparing two urban speed limits based on MFDs and MSDs in the presence of AVs.
Te remainder of the paper is organized as follows.Section 2 provides a review of previous studies on the efects of AVs on MFDs and safety.Te review highlights the unique contribution of this study.Section 3 presents the methodology for the study including the macrosimulation networks, car-following models, the method for generating MFDs and MSDs, safety analysis methods, and multiobjective optimization utilized.Section 4 displays the results obtained from the simulations.Finally, Section 5 presents the discussion and conclusion.

Literature Review
Te potential impact of AVs and connected and automated vehicles (CAVs) on trafc operations in road networks has been studied extensively.We do recognize the existence of a large body of work in this area, this review selects representative works for gap identifcation and discussion purposes.Te review is presented in two parts.First, we discuss key studies that have investigated the impact of AVs on trafc operations, focusing on trafc performance modeling at diferent scales under AV infuences.Second, we discuss studies that have addressed the issue of the safety impact of AVs.

Impact of AVs on Trafc
Flow.Te modeling of trafc fows is one of the key functions of trafc engineering [34].aggregate trafc fow modeling techniques.In particular, the MFDs have been studied and applied to network-level analysis, where an MFD relates the vehicle accumulation in a road network (e.g., the total amount or density of vehicles which refects "trafc state" or "level of congestion" of the network) to the trip completion rate (e.g., the amount of trips completed in the network which refects "level of service" or "efciency" of the network).
While the existence of MFDs was demonstrated in networks of conventional vehicles, further studies have investigated the properties of MFDs when other types of vehicles are available to users and operated in a shared space.For instance, Shelton [25] carried out a study using a multiresolution model and highlighted how the network capacity can be increased when the penetration rate of AV increases from 0% to 100%.Ghiasi et al. [22] proposed a Markov-chain-based analytical model, which estimated the change in headway when vehicles formulate platoons and analyzed the performance of trafc fow under variations in platooning and CAV penetration rates.Te research fndings revealed that the capacity could be increased when CAV penetration rate and platoon intensity increase in mixed trafc for freeway operation scenarios.
On a smaller scale, Martin-Gasulla et al. [24] carried out a study to investigate how CAVs can change the capacity at a signalized intersection.Tey identifed the importance of high penetration rates of CAVs for maintaining throughput.Liu and Fan [11] applied the Wiedemann car-following 2 Journal of Advanced Transportation model [49] for human drive vehicles (HDVs), which is calibrated using real data to evaluate CAVs efect on the capacity of a freeway.Tey also developed a revised intelligent driver model (IDM) to account for the features of CAVs.Teir analysis indicated that freeway capacity increased 85% when CAV penetration rate was 100% when operating in a 65mph (104 km/h) speed zone.Xiao et al., [28] examined the impact of cooperative adaptive cruise control (CACC)-equipped vehicles on the capacity and capacity drop at merging bottleneck based on CACC systems.Xiao et al. [28] found that the capacity of a merging section can be increased by nearly 60% when the penetration rate of CACC equipped vehicles is 100%.Initial attempts emerged at measuring the impacts of AVs on large-scale trafc operations, measured such as the road capacity of a network.For instance, Atkins [10] employed the Wiedemann 99 car-following model for a simulation-based analysis and showed that the inclusion of CAVs has a positive impact on capacity, e.g., the maximum fow observed on the MFDs is higher when the penetration rate of CAVs increases.Talebpour and Mahmassani [27] proposed a framework to evaluate the impact of CAVs and AVs on trafc fow.Te results based on MFDs suggested that throughput improves when the penetration rate of connected vehicles (CVs) and (AVs) increases; however, AVs were found to increase throughput more than CVs.
While many studies indicate that AVs will have a positive infuence on trafc efciency, other research suggests they may have a negative efect on trafc fow [50][51][52].Whether AVs have a positive or negative efect varies depending on a range of factors included their level of automation, the technologies incorporated into the AV, driving behavior, uptake, and permeation into the vehicle feet.Tis conjecture highlights the need for further research to understand the scenarios where AVs can have a positive infuence on trafc network performance, which can ultimately assist in guiding AV policy.

Impact of AVs on Trafc Safety.
AVs and CAVs have the potential to eliminate many common human errors (such as speeding and distracted driving) associated with crashes, as such, AVs are expected to improve safety substantially (Manivasakan et al., 2021, Zou et al. 2021).Many studies have attempted to estimate the reduction in crashes due to AVs.Tese studies have used diferent surrogate safety measures (SSMs) show to the extent to which AVs can improve trafc safety in diferent environments and under diferent driving conditions.
Investigating the benefts brought by AVs and CAVs is a classical and well-studied topic.For example, Virdi et al. [20] demonstrated the improved safety at intersections and highways as the CAVs were controlled under a so-called "Virdi CAV Control Protocol" in a mixed trafc fow environment.Te work illustrated that when the penetration rate of CAVs is over 80%, conficts could decrease substantially.Karbasi and O'Hern [23] tested an even higher penetration rate of 100% AVs and CAVs for intersection scenarios and found further reduction.Similar conclusions can be found in other studies as well, e.g., Papadoulis et al. [16] and Arvin et al. [21].Interestingly, the safety impact of AVs/CAVs is not always found to be positive.Papadoulis et al. [16] identifed that certain types of crashes did not beneft from the CAV operations; for example, an increased number of read-end conficts were observed.Tis is reasonable because the AVs/CAVs tend to operate at smaller headways, resulting in closed space between the vehicles and smaller TTC.In a large network where AVs/CAVs and HDVs operate in a shared space, the safety benefts or crash risks obviously are not spatially homogeneous.While it is important to identify where the black spots are located, there is a need to understand the system level of safety.Further research by Sinha et al. [17] evaluated the crash severity and rate of conventional vehicles in mixed feets with connected and automated vehicles.In addition, Dixit et al. [14] performed a safety and risk analysis of autonomous vehicles using computer vision and neural networks.
Generally, despite the studies using diferent approaches, methods, and road networks, the fndings show that AVs have the potential to improve safety and reduce congestion.However, most existing studies did not consider the correlation between safety and trafc congestion.It is sensible to examine the trafc-dependency feature of vehicle operation safety.Tis will be particularly useful for AV analysis, as it enables a holistic understanding of AV benefts and costs.Te challenge though, lies in the fact that high fow and low crash are too conficting objectives.To this end, there is the potential to identify a set of points where optimal trade-ofs can be made.Te frst work on this research direction was reported in Alsalhi et al. [30] who argued a relationship between crash risks and trafc density, namely, the macroscopic safety diagram (MSD).Interestingly, the MSD has a similar shape to MFDs but a higher "critical density" where the crash risk appeared to be the lowest (as compared to the MFD case, the maximum fow is achieved at its "critical density").Te MSD is a single mode model, not yet applicable for multi-modal trafc environment such as a mixed HDVs and AVs system.It is expected that AV-involved MSD will exhibit new patterns, given its unique operation characteristics.
To summarize, this paper aims to address some of the previous methodological limitations by examining the impact of AVs on MFDs and MSDs, identifying optimal operation solutions for safety-efciency trade-ofs, and ofering the relevant insights on policy indications.Concerning policy demonstration, this paper conducts a case study on the impact of infuencing speed limits in a road trafc network involving autonomous vehicles (AVs).

Methodology
To obtain extensive scenarios for the targeted AV impact analysis, this study carries out a simulation-based analysis.Te employed simulation, SUMO [55], is based on microscopic trafc fow models, i.e., the car-following models, which defne the driving behavior of HDVs and AVs.Six scenarios for AV penetration were considered with the percentage of AVs increasing market penetration rate (MPR) by 20% between 0% and 100%.Tis study performs a simulation on a grid road network that includes nine intersections.To generate MFDs based on simulation data, the Papageorgiou speed-density model [56] is used, and capacities, average speed, and critical densities based on diferent scenarios are determined.To investigate the safety impact of AVs, the time to collision (TTC) surrogate safety measure (SSM) is used to determine conficts between vehicles.MSDs are generated using a second-degree equation which is based on the relationship between conficts and densities.To fnd a set of solutions in which the fow is high and conficts are low, a multiobjective optimization based on the NSGA-II genetic algorithm is presented with the optimization based on minimizing the second degree equation and maximizing the network-level trafc fow.Te case study uses hypothetical demands to refect diferent degrees of congestion within a grid network.
Te methodology of this paper is presented in four steps.First is the microsimulation in which driver behavior of AVs and HDVs is defned.Te second step is generating MFDs which are based on simulation data and speed-density models.In the third step, safety analysis based on TTC is presented, and MSDs are constructed based on safety outputs.Te second-degree relationship between density and the number of conficts is also presented.In the last step, a multiobjective optimization problem is formulated, and the solution algorithm is introduced, in which based on the density-velocity model and the tertiary safety relationship, optimal points are found in which not only the fow is high but also the number of TTC incidents is low.

Microsimulation.
To defne the vehicle behavior of HDVs and AVs in microsimulation, a set of longitudinal and lateral equations based on car-following models and lanechanging models is required.Te SUMO simulator was used to simulate the driver behavior of HDVs and AVs in this study.Tis study uses the Weidmann model for HDVs and the intelligent driver model (IDM) for AVs to refect their distinct driving behaviors.Te Weidmann model was selected for its precise representation of human driving behaviors, while the IDM was chosen for AVs to showcase the benefts of automation in terms of safety and efciency.Parameters for both AV and HDVs are based on the study by Atkins [10].Te AVs parameters are based on the level IV defnition given by Atkins [10], meaning that the vehicles are operating without a human driver.
Te longitudinal driving behavior of HDVs was defned using the Wiedemann 99 car-following model.Based on the perceptions of relative speed and position changes by the following driver, Wiedemann's model determines the following driver's reactions, such as acceleration or deceleration [57].Four parameters of this car-following model are used to defne driving behavior at intersections.Te defnition of these parameters and the values used in this study are presented in Table 1.
To defne the AVs' longitudinal driving behavior, the intelligent driver model (IDM) car-following model, developed by Treiber et al. [58], was used.IDM calculates acceleration by measuring two ratios: desired velocity and actual velocity and desired headway and actual headway [11,23].Equations ( 1) and ( 2) show the calculation of acceleration: where a and a 0 are acceleration and maximum acceleration, v and v 0 are current speed and desired speed, respectively, δ is the acceleration exponent, s * (v, ∆v) is desired minimum headway, s 0 is current headway, T is the desired headway, b is deceleration, ∆v is the diference in speed between the lead and following vehicle.For AVs, the desired time headway is equal to 0.5 s, the minimum gap is equal to 0.5 m, and maximum acceleration is 3.8 m/s 2. , as reported by Atkins [10].Tis study used the SUMO simulator default lanechanging model called LC2013 [59] for both HDVs and AVs to capture lateral movements of vehicles and intersection movements.SUMO includes three lane-changing motivations: strategic, cooperative, and tactical lane-changing.For this study, strategic lane changing was used, which initiates lane changing when the vehicle fnds no connection between the current lane and the next lane on the route [29].

Quantifying the Network-Level Trafc Flow Operation:
Te Macroscopic Fundamental Diagrams.MFDs represent the relationship between fow, density, and speed and are often represented as fow density and speed-density diagrams.Te MFD presents information on trafc characteristics, such as the value of free-fow speeds and fow capacities.Te MFD can be used to distinguish between freefow and congested trafc conditions.Te relationship between fow, density, and speed is shown in the following equation: where Q i (p i ) is fow, p i is average density, and V (p i ) is speed (km/h).In this study, to generate MFDs from microsimulation data, a speed-density model is used.Te speed-density model is used because there needs to be a relationship between fow and density for a multi-objective optimization formulation.Terefore, by using the speeddensity model and substituting it into equation ( 3), a mathematical formula for the relationship between fow and density can be obtained.Tis study uses Papageorgiou speed-density model [56] which provides information such where v f is free-fow speed, p c is critical density, p is density, and a is the model shape parameter.By substituting (4) in (3), the relationship between fow and density is obtained.Tis study uses SUMO edge-based output data [59].In SUMO, edge-based data provide trafc metrics as outputs including average speed and density for each network edge at varying time intervals (e.g., every 60 seconds).A detailed description of this feature in SUMO is available in SUMO [59].To aggregate this data for the network and generate MFDs based on edge-based output data, the macrOutput.pytool was used [60].

Quantifying the Network-Level of Crash Risks: Te
Macroscopic Safety Diagram.In dynamic urban networks, MSDs aim to explore the possible relationship between safety performance (e.g., the likelihood of a multi-vehicle rear-end collision) and operational performance (e.g., trafc conditions at that time) [30].Tis study uses MSDs to show the relationship between the number of conficts and density.
Before explaining the MSDs, it is necessary to defne the defnition of the confict based on safety measures.In this study, TTC is used to determine conficts.If two vehicles followed their current path and maintained their current speed, TTC would be the remaining amount of time before a collision occurred [61,62].In the SUMO simulator, SSM device output [59] is used to generate conficts based on TTC safety measures.SSM devices generate outputs including type of conficts, positions of vehicles, and TTC value.In the SSM device, the TTC is calculated in the following two ways: where x i−1,t is the leader position at the time t, v i−1,t is the leader speed at the time t, x i,t is the position of the following vehicle and v i,t is the speed of the following vehicle at the time t, L i−1,t is the length of vehicle at the time t.(5) calculates rear-end collisions, and (6) calculates merging and crossing conficts.Tis study uses two diferent TTC threshold values for HDVs and AVs.Te TTC threshold is used to identify potential conficts, i.e., when maneuvers occur below the threshold value.Te TTC threshold value for HDVs is 1.5 s which has been suggested in previous studies [16,20,63].Previous research has demonstrated that the minimum gap for AVs is one-third of the minimum gap for HDVs, and as such a TTC threshold of 0.5 s was selected [20].
Based on safety and density outputs, MSDs were generated using a nonlinear regression to ft a simple seconddegree polynomial model to the simulation data which present the relationship between conficts and density: where PC is the number of potential conficts and a and b are the equation parameters.Critical density associated with maximum conficts is obtained by fnding the roots of the equation (7).Te critical confict point (CCP) is obtained by substituting the critical density into (7), which has been shown in the following equation: where CCP is the peak confict in a period and CD is the critical density associated with maximum conficts.Similar to MFDs, ( 7) is necessary because there needs to be a relationship between the number of conficts and density for a multiobjective optimization formulation.

Te Efciency-Safety Trade-Of through a Multiobjective
Optimization.As mentioned before, there is a contradiction between fow and crashes in that the probability of a crash increases as the fow increases and moves towards the capacity of the road [30].Terefore, there is a trade-of between fow and safety.Terefore, it is essential to pursue a multi-objective optimization approach that identifes scenarios where both the fow-to-capacity ratio is maximized and the confict-to-maximum-confict ratio is minimized, ensuring an optimal balance between trafc efciency and safety.In this study, there are two objective functions.Te frst objective function is (7) (this equation is called f 1 (p i ) for optimization) which shows the relationship used for generating MSDs.Tis equation must be minimized to reduce conficts.Te second objective function is shown as follows: Equation (10) shows the relationship for generating MFDs.Tis equation must be maximized to reach the capacity.However, in this study, use a minimizing function, so we use -f 2 (p).Tus, the generic formula for the current study problem optimization is presented in the following equation: where P critical is critical density associated with the fow, α and β are weights of objective functions.Tese weights can vary between 0 and 1 so that 0 shows the least importance and 1 shows the highest importance.Tese weights help decision makers to fnd their optimal points based on different strategies and the importance of each objective function.Tis optimization model includes a critical constraint to avoid choosing a zero-density value when safety is prioritized (b � 0), which would unrealistically eliminate conficts by not allowing any vehicle presence.To ensure practicality and efciency, the model operates within a density range from 33% to 100% of the critical density, avoiding both the impractical extremes of zero density and full jam density.Tis approach guarantees the model uses at least a third of the road capacity, balancing road usage effciency and safety considerations.Tis study uses a nondominated sorting genetic algorithm (NSGA-II) algorithm to fnd the optimal points.NSGA-II was developed by Deb et al. [64] which by using a Pareto dominance relationship, the rank of solutions is determined using a fast, nondominated sorting algorithm those with a higher rank survive and are selected to reproduce [65].Pareto fronts are a set of optimal solutions in a space of objective functions in multiobjective optimization problems (MOOPs) that are not dominant over each other but are best compared to the rest of the solutions [66].As a result of its robust elitist strategy, focus on nondominated solutions, quick running speed, and diversity preservation mechanism, NSGA-II is uniquely competitive [67].To explain the NSGA-II procedure, some steps are needed.In the frst step, assume the initial population called P t with the size of N. In the second step, after evaluating objective function and performing crossover and mutation on P t, a new population is created called Q t [68].In the third step, the population that consists of P t and Q t is called R t , so the nondominated sorting is done on R t .At each stage, it selects the nondominant members and places them on one front and removes them from the population, placing the rest of the population on the next front in the same way.Tese steps continue until the entire population is on diferent fronts (F 1 , F 2 , F 3 , . . ..) and this process is based on the Pareto front concept that the Pareto front consists of compromises that are acceptable for all objectives [67,68].Te fourth step is calculating the crowding distance for members that are nondominant with each other.Solutions with larger crowding distances are preferred in this approach, which is determined by the average distance between two solutions along each of the objectives [65,68].In the ffth step, a tournament is used to select the population members for the next generation based on their rank and crowding distance called P t+1 [67,68].Until the stopping criteria are met, the procedure continues.In this study population size, maximum generations are equal to 20 and 100, respectively.Figure 1 shows the procedure of NSGA-II.

Results
In this study, a grid network that includes nine intersections was used to determine the impact of AVs on MFDs and MSDs.Each link in the network is 400 meters and bidirectional.Two speed limits were assessed 50 km/h and 30 km/h.Te multiobjective optimization was performed on the 50 km/h speed limit, and the 30 km/h speed limit was used to compare the impact of the speed limit on MFDs and MSDs in presence of AVs.All trafc lights had a 90-second cycle time with a 43 second green phase, a 43 second red phase, and a 4 second yellow phase.Four turning movements were allowed at each intersection: straight, left turn, right turn, and U-turn.Te grid network was routed randomly using Randomtrip.py(SUMO's built-in tool).Randomtrip.py in SUMO benefts from the period option which gives in the opportunity to control the trafc value and determine the rate of vehicle insertion in the network.By using this option, this study frst generates vehicles randomly until there is congestion in the network.After this time, the rate of period option was reduced to reduce the number of vehicle insertions smoothly to eliminate congestion.Te network generated by random trips was more homogeneous and fexible when compared to a grid model with fxed routes [29].Te duration of simulations is 1200s, and the data have been aggregated based on 1 min time intervals.In order to avoid gridlock, this study does not allow density to exceed 70 vehicles per kilometer, and the aggregated data has been ignored in each simulation where density exceeds 70 vehicles per kilometer.In our study, we conducted trafc simulations across various scenarios; each scenario was repeated 20 times to ensure data reliability and account for variability, thereby enhancing the robustness of our fndings.Figure 2 shows the grid network.Tis scenario was considered high trafc demand; low and medium trafc demand are also presented in Section 4.5.Te maximum density of low and medium demand is 18 veh/km and 45 veh/km, respectively.2 shows the statistical analysis of Papageorgiou speed-density model [56].Where v f is free-fow speed, p c is critical density, a is the model shape parameter, and R 2 , the goodness of ft measure.For each penetration rate R 2 is more than 0.98, demonstrating that the model provides a strong estimate of the relationship between speed and density.

6
Journal of Advanced Transportation Te results presented in Table 3 shows that AVs increase critical density (P c ) by up to 63% when the MPR of AVs is 100%.Moreover, Figure 3 show the impact of AVs on average speed, capacity, and MFDs.Te results confrm that AVs increase average speed and capacity by up to 21% and 59%, respectively.However, AVs have diferent efects depending on the penetration rate.When the MPR of AVs is 40%, the impact of AVs on MFDs is small with capacity, P c , and average speed improving by 8%, 4%, and 6% respectively.
However, when MPR is 60%, AVs improve capacity, P c and average speed 17%, 20%, and 13%, respectively, which shows that when AVs become the dominant fow, the efect of the AVs becomes more signifcant.In addition, when MPR is 100%, AVs increase capacity, P c , and average speed 36%, 34%, and 7%, respectively, compared to when MPR is 60%.
To discuss the impact of AVs on MSDs, Table 4 shows the results of the statistical analysis of the MSDs model.R 2 values confrm that second-degree polynomial model can accurately estimate the relationship between conficts and density.Table 4 includes information about the impact of AVs on CCP and CD.Table 3 shows that AVs can increase CD up to 31%.Also, Figure 4 illustrate that AVs reduced conficts and CCP up to 80% and 75%, respectively.Tus, these changes confrm that AVs can improve the safety situation of urban networks substantially.Journal of Advanced Transportation It can be seen that AVs can improve MFDs and MSDs when AVs are dominant fow.However, at low penetration rates AVs are not expected to have a signifcant impact on MFDs and MSDs and that signifcant benefts are only achieved once penetration rates exceed 40%.

Time-Space Trajectory of HDVs and AVs.
Based on disaggregated analysis, Figure 5 show trajectories (timespace) of each penetration rate.Tese trajectories show the whole network trajectories in a specifc time period.Figure 5 shows when the penetration rate of AVs is increased the trafc jams are reduced substantially.Figure 5(a) shows the trajectory when MPR is equal to zero and all the vehicles are HDVs it can be realized that the stop-and-go waves are propagated backward from the intersection as a result of abrupt accelerations and decelerations.Stop-and-go waves reduce the passing speed of vehicles at intersections, thus decreasing the trafc throughput and increasing the chances of a collision [69].Figures 5(b)-5(f ) illustrate that when the penetration rate of AVs increases the stop-and-go waves decrease substantially.Tus, it can be concluded that AVs have the potential to increase fow and speed and decrease trafc jams.Tese fgures confrm macroscopic results based on MFDs and MSDs results.

Te Resulting Trade-Of between Capacity and Risk via the
Multiobjective Optimization.In this section, the results of multi-objective optimization based on NSGA-II are presented.For this study, α and β are equal to 1. Te value of α and β show the importance of each objective function in (10) and they can be changed based on the decision-makers trafc management strategy.Figure 6 shows the Pareto front solution using NSGA-II for diferent MPRs.Tese points are nondominance points among all possible solutions which are equal to the population size for each MPR.In addition to the values of α and β, Pareto front points represent alternative optimal points that decision-makers could choose based on their desired road network management strategy.Tus, this optimization method gives the decisionmakers the opportunity to obtain their desired results based on diferent strategies in two ways.First, decision-makers can change the values of α and β based on the importance of each objective function.Second, decision-makers can choose their desired point from Pareto front points based on the diferent trafc management strategies.
To explain the importance of these points, assume a scenario.In this scenario, the values of α and β are set to 1, and we aim to select one point from each MPR to investigate to what extent these points can help to fnd a point in which not only the fow is high but also the number of conficts is low.Tus, the main strategy is maintaining high fow and reducing conficts.Table 4 shows the points that we selected from Pareto front points based on the above-mentioned main strategy.Generally, these points (new capacity and new CCP in Table 4) show that by reducing the trafc capacity by 10 to 12 percent, the number of maximum conficts at the capacity point can be reduced from 21 to 27 percent, and in the case of CCDs from 21 to 30 percent.Te points are a good indication of the main strategy that the selected points are the points where the fow is high, and the number of conficts is low compared to the maximum number of conficts.It is worth noting that the use of these points and values of α and β varies according to diferent strategies, and the fow can be reduced more than the stated amount to further reduce crashes.Moreover, it should be noted that these optimal points can be changed based on other strategies.For example, these fndings seek to fnd points that are in the range of 8 to 12 percent reduction in fow, and subsequently seek the efect of this reduction in fow in reducing conficts.

Impact of AVs in
Low-Speed Limit Environments.In this section, the impact of AVs on MFDs and MSDs is presented.In Section 4.1, the speed limit was set to 50 km/h.In this section, the speed limit is 30 km/h.Using the Papageorgiou speed-density model [56] and second-degree polynomial model, MFDs and MSDs are generated.Te statistical results of the two models confrm that the two models can accurately generate MSDs and MFDs.Appendix A presents the statistical results of the two models in detail.Figure 7 shows the impact of AVs on MFDs, capacity, and average speed.Te impact of AVs on capacity is steadily increasing at each MPR, so that at each penetration percentage greater than 20%, the capacity increases by approximately 10%.Te average speed results show that when the MPR is less than 60%, AVs do not have much efect on the average speed, but when the MPR reaches 60% and above, the average speed increases more dramatically.Figure 8 also shows the efect of AVs on MSDs, CCP, and total conficts.Tis fgure shows that when the MPR is less than 40%, the total number of conficts and the CCP change very slightly.But when the MPR moves to 60% and above, the impact of AVs on the total number of conficts and CCP increases.In general, the results show that for a dramatic change in the CCP, the average speed and the number of conficts need to be dominated by AVs, but AVs increase capacity more continuously and signifcantly in low MPRs than the CCP.Moreover, Figure 9 shows the trajectory for each penetration rate.Like the 50 km/h scenarios, in the 30 km/h scenario, AVs have the ability to reduce stop-and-go waves and they can increase capacity and speed and decrease congestion and collisions.Tese results are in line with macroscopic results based on MFDs and MSDs results.

Impact of Speed Limits on AVs Efect on MFDs and MSDs.
To compare the impact of speed limits on capacity, CCP, and total conficts Figures 3, 5, and 10 must be compared.Tese fgures can be interpreted in two ways.First, a comparison is made between speed limits when there are only HDVs in the network.In this condition, the capacity in the 50 km/h speed limit condition is 10% higher than the 30 km/h speed limit condition, while the total conficts and CCP when the speed limit is 50 km/h are 15% and 18% higher than the 30 km/h speed limit condition.Tus, choosing the best speed limit varies based on the importance of safety or fow.Second, a comparison is made between speed limits when there are AVs in network.When the speed limit is 50 km/h, AVs increase capacity and average speed up to 59% and 21%, while at speed limits of 30 km/h, AVs increase capacity and average speed up to 46% by 17%.In addition, when the speed limit is 50 km/h, AVs reduce the total number of conficts and AVs up to 80% and 75%, while when the speed limit is   up to 80% and 79%.Generally, it can be realized that the impact of AV on capacity and average speed is more prominent in 50 km/h speed limit than in the 30 km/h speed limit, and AV's efect on safety is similar for both speed limits.
To compare the impact of AVs on MSDs and MFDs under diferent speed limits in detail, Figure 10 shows the impact of AVs on average speed, capacity, CCP, and total conficts.Figure 10(a) confrms that AVs have a positive impact on CCP under the 50 km/h speed limit and 30 km/h speed limit.Based on the two-way ANOVA, the results show that there is no signifcant diference between the impact of AVs on CCP under two speed limits (p � 0.31).Te 50 km/ h speed limit condition did not meet the normality assumption of AVONA.Tus, the Kruskal-Wallis test, which is the nonparametric equivalent to the ANOVA, has been performed on the CCP change percentages for the two speed limits (50 km/h and 30 km/h).Te test yielded a p value of approximately 0.810 which confrms that there is no signifcant diference between the impact of AVs on CCP under two speed limits.
Figure 10(b) illustrates when MPR is under 80%, the impact of AVs on capacity under 30 km/h is more than 50 km/h speed limit situation but when MPR is between 80% and 100%, the impact of AVs on capacity under 50 km/h speed limit is more than 30 km/h speed limit, so that when MPR is 100, the impact of AVs under 50 km/h speed limit is 24% more than when the speed limit is 30 km/h.Nevertheless, based on Table 5, the ANOVA analysis result shows that there is no statistically signifcant diference between the impact of AVs on capacity in the 50 km/h speed limit scenario compared to the 30 km/h speed limit (p � 0.86).Figure 10(c) shows that AVs have more impact on average speed under the 50 km/h speed limit.However, although Table 5 results show that the impact of AVs on average speed is signifcant (p � 0.01), it seems it is not sensible to compare the average speed under the diferent speed limits because it is obvious that the average speed under the 50 km/ h speed limit is more than the average speed under the 30 km/h speed limit.Figure 10(d) confrms that AVs under the 50 km/h speed limit have a more positive impact on total confict reduction in each MPR compared to the 30 km/h speed limit.Table 6 results for total conficts show there is a statistically signifcant diference between the impact of AVs on total conficts under the 50 km/h and 30 km/h speed limits (p � 0.03).Figure 10(e) illustrates that the impact of AVs on CD in a 30 km/h environment is more signifcant than in a 30 km/h environment when MPR is under 80, but because p value is 0.23 diferences between the two speed limits' results are not signifcant.Figure 10(f ) shows that in some MPRs, the impact of AVs on P c in 30 km/h is more signifcant than 50 km/h environment, and vice versa.Although, based on Table 5 results, diferences between the two speed limits' results are not signifcant (p � 0.13).It is worth mentioning that Table 5 confrms that the impact of all MPRs based on all metrics on two speed limits is signifcant.

Te Impact of Diferent Levels of Congestion on Trafc
Flow and Safety.Tis section explores the efect of AVs on trafc fow and safety under diferent levels of congestion.Tis study applied three diferent demand levels including low, medium, and high trafc demand.In low demand, the trafc situation is at an uncongested level which means that the network is far from reaching capacity.In medium trafc demand, the network reaches its capacity, but it is not highly congested.In high trafc demand, the network is highly congested, and there is gridlock on some links in the network.Te previous sections' results were based on the high trafc demand.Generating diferent levels of demand in the network is applied using Randomtrip.py in the SUMO simulator.Tis build tool gives you this opportunity to defne diferent levels of demand based on tunning a parameter called period.
To evaluate the trafc fow and the safety impact of AVs at diferent levels, the total number of conficts, average speed, maximum fow, and maximum number of conficts per time interval are used.Te reason that capacity and CCP are not used is that in the low trafc demand, the network cannot reach capacity and CCP.Figures 11 and 12 show the results of diferent levels of congestion for the 50 km/h and 30 km/h speed limits.Te maximum trafc fow results for both speed limits illustrate that with an increase in MPR and an increase in demand, the maximum fow increases.Also, the results show that as MPR increases, the diference between the maximum and average demand fow increases.Based on total conficts and maximum conficts results for two speed limits, as the MPR increases and demand decreases, the number of total conficts and maximum conficts reduces.However, the important point is that in contrast to the high congestion level when MPR is low, the number of total conficts and maximum conficts decreases which means that in low-and medium-demand situations, AVs can reduce conficts even at lower rates of penetration.Moreover, the results of average speed based on two speed limits demonstrate that as the MPR increases, the average speed increases for all congestion levels but as demand increases, the average speed decreases.Te reason is that when the demand increases from low to high, density increases, and consequently, the average speed decreases.Generally, the results show that AVs within the two speed limits and diferent congestion levels have the potential to improve trafc fow and decrease the risk of collision.
Tables 5 and 7 summarize the results of the two-way ANOVA of the impact of AVs on key trafc parameters for the two diferent speed limits at low and medium demand levels, respectively.Te statistical data for high demand scenarios were addressed previously and are recorded in Table 6.Tis analysis for both demand levels shows that, similar to the fndings for high demand, the MPR has a signifcant impact on all metrics assessed.In low-demand conditions, the infuence of AVs on maximum fow and total conficts does not show a statistically signifcant diference with two speed limits, while their impact on maximum conficts and average speed does show a signifcant Journal of Advanced Transportation   diference with two speed limits.In contrast, for medium demand, the efect of AVs on maximum fow shows a signifcant diference for both speed limits, but their impact on other metrics does not reveal a signifcant diference with two speed limits.

Discussions
Tis study investigated the impact of AVs on MFDs and MSDs, and more specifcally, it investigated the networklevel capacity, average speed, critical density, critical confict point, critical density associated with maximum conficts, and crash risk as a result of diferent levels of AV integration and operation.Tis study has some key features which distinguish it from other studies.First, there are many studies that have investigated the impact of AVs on capacity and MFDs [10,11,22,24,25] or safety [16,20,21,26,29].However, none of these studies have explored the impact of AVs on MFDs and MSDs simultaneously, and there is no study that has examined the impact of AVs on MSDs.Te results of this study show that AVs can improve capacity, critical density, and average speed which is in line with previous studies [10,11,22,24,25].Also, the results show that AVs can reduce conficts substantially which is in line with previous studies [16,20,21,23], and AVs can reduce CCP and CD signifcantly.Te important result is to quantify the network-level impact of the AVs, measured with the MFDs and MSDs, under variations in market penetration rate.When AVs dominate the fow, the impact of AVs on MFDs and MSDs is substantial compared to when HDVs are the dominant fow.Tis is a positive confrmation that the longer-term beneft of AVs to trafc operation can be substantial for the road network, though in the short term only marginal efects in crash reductions or network capacity improvements are expected (due to low presence).For urban road networks with typical grid structures such as the one used in this study, the lower-level threshold of market penetration for notable improvement is found to be 40%.Te notable improvement of a penetration rate higher than 40% is primarily due to the fact that when penetration rates are high, the interaction between AVs and HDVs is low, and the dominant fow is AVs.Terefore, improvement in a higher penetration rate is made more signifcant.Some studies have shown that the percentage of automated vehicles will be at least 30% by 2040 and 100% after 2050 [70][71][72][73].Tus, reducing congestion and improving safety with AVs is not a farfetched policy but a feasible policy and achieving 40% of this penetration rate can be achieved within the next few decades, so we can hope for a reduction in congestion and safety problems with AVs.It is worth mentioning that logically, there should be an upper-level threshold exceeding which the magnitude of operation improvement becomes marginal.Te results of space-time   Te results show that AVs have the potential to increase the average speed across the network.Even when the mode share of the AVs is not high and distributed sparsely, there is still the beneft of "moving more efciently" for the entire network.While it is promising to see that increasing speed is coupled with reducing conficts, higher speeds of vehicles are associated with increased crash risk and severity, particularly for other modes of transportation, especially vulnerable road users [74][75][76].In cases of more than moderate increase in average speed (for example, "moderate increase" can be some percentage over an average speed limit that is estimated from the MSD), warnings should be given to the driving assistant or control systems so that the systems can activate the emergency responses in various scenarios proactively.
Te MSDs show that until the capacity and the critical density are reached, there is no common beneft between fow (i.e., network efciency) and conficts (i.e., network safety).Te applied multiobjective optimization is demonstrated to be useful to identify some suboptimal sets of operation points.For example, on average, these suboptimal operation solutions see a drop in capacity of 10 to 12 percent, Journal of Advanced Transportation while they see a more drastic reduction in the number of maximum conficts from 21 to 27 percent and in CCDs from 21 to 30 percent.While the numbers are network-specifc, such operation concepts are rarely discussed in literature, and they provide alternatives and mobility targets for the operators.Potentially, another dimension that could be incorporated into the analysis is variable speed limits and even dedicated lane allocations to further increase the beneft of having AVs in the system.Tis, however, requires more efcient algorithms to handle real-time implementation (the complexity of the optimization problem of a fow-safetyspeed limit trade-of is extremely high).
With regard to speed limits, this study demonstrates the benefts of AVs operating in low-speed limit trafc environments.Our results indicate that the change in speed limit has a minor impact when the network has only HDVs (the number of conficts and capacity has a 15% and 10% negative diference, as speed limit drops from 50 km/h to 30 km/h).However, when there are only AVs in the network, the operation improvement is signifcant compared to the HDV-only scenario, aligning with the research's fndings on safety and efciency carried out by Lu et al. [77].Moreover, this study investigated the impact of AVs on trafc fow and safety based on diferent congestion levels.Te results confrmed that at all congestion levels, AVs improved trafc fow, increased average speed, and demonstrated that AVs can improve safety, even at low MPRs.
Te fndings of this study show that the presence of AVs has the potential to reduce the dilemma between mobility efciency and safety.Based on this study and literature, AVs, given their control features, ofer the advantages of increasing average speed, reducing conficts, and increasing capacity at a network-wide scale [10,16,20].In addition, to balance the mobility goals, this research provided a multiobjective optimization-driven tool which can help users identify the optimal trade-ofs between the objectives.Tis multiobjective optimization-driven tool allows city planners and network operators to develop dynamic strategies based on current infrastructure or trafc management priorities.
Tis study includes some limitations that future studies could seek to address.Tis study makes several assumptions regarding how AVs operate.For example, it assumes that AVs follow AVs and HDVs with the same driving behavior.As more information becomes available about AV technology, these behaviors can be more accurately simulated which could infuence the fndings.
An important element of this study was the demonstration of how AVs can infuence MSDs and MDFs; however, the network used for analysis was simplistic.Furthermore, this study focuses on a grid network where each road has a single lane in each direction, which means the efects of AVs lane-changing behaviors are not examined in this research.Future studies are encouraged to explore grid networks with multiple lanes in each direction to better understand how AVs' lane-changing actions might impact trafc fow and safety.Beyond this, studies could consider real-world urban networks under diferent congestion levels, while broadening the optimization modeling by considering additional factors such as GHG emissions or air pollution to provide a more holistic view of the impacts of AVs.

Figure 3 :
Figure 3: Impact of AVs on capacity, MFD, and average speed (speed limit � 50 km/h).(a) Flow-density diagram.(b) Change of capacity and average speed.

Figure 4 :
Figure 4: Impact of AVs on CCP, MSD, and total conficts.(a) MSD.(b) Impact of CAVs on CCP and total conficts.

Figure 10 :
Figure 10: Comparison between impact of AVs on average speed, capacity, total conficts, and CCP under two speed limits.(a) Impact of CAVs on CCP reduction.(b) Impact of CAVs on increment of capacity.(c) Impact of CAVs on increment of average speed.(d) Impact of CAVs on total conficts reduction.(e) Impact of CAVs on increment of CD (%).(f ) Impact of CAVs on increment of PC (%).

Table 1 :
[56]emann 99 car-following parameters.fowspeed and critical density (the point at which the fow reaches its highest value).Te following equation shows the Papageorgiou speed-density model[56]relationship:

Table 4 :
Results of new capacity and CCP.

Table 5 :
Statistical analysis of impact of AVs on diferent metrics in two speed limits (low demand).

Table 6 :
Statistical analysis of impact of AVs on diferent metrics in two speed limits.

Table 7 :
Statistical analysis of impact of AVs on diferent metrics in two speed limits (medium demand).

Table 11 :
Second-degree polynomial model statistical analysis results.