Impact of Communications Delay on Safety and Stability of Connected and Automated Vehicle Platoons: Empirical Evidence From Experimental Data

Advances in communications and sensing technology have enabled the development of cooperative ITS technologies such as connected and automated vehicle (CAV) applications including adaptive cruise control (ACC) and cooperative adaptive cruise control (CACC) that could perform driving tasks with little human feedback. However, there are some key concerns and knowledge gaps regarding the impact of delay in communicated messages on CAV platoon safety and stability. This study contributes by analyzing the impact of delay while controlling for other factors on CAV platoon safety and stability using the concept of driving volatility. Real-world experimental data from a field test were used to examine the lead vehicle (LV) and following vehicles (FVs) behavior in a five-vehicle platoon with multiple scenarios by developing switching regime models. Results show that CACC reduces volatility in both LV and FVs compared to ACC system which can be attributed to the vehicular communication and motion synchronization of CACC. However, delay is observed to increase the likelihood of volatility and contribute to instability of platoons. FVs have more volatile behavior as compared to LV since the instability is transmitted through the string of the platoon. Further, Bayesian model reveals that a unit increase in delay is observed to increase the collision risk by 4%. Other confounding factors such as disengagement and ACC override contribute to higher volatility of platoon while the likelihood of high volatility in both LV and FVs decreases with increases in gap to the preceding vehicle. The risk of collision is expected to increase by 6.2% in response to a unit increase in disengagements. Likewise, ACC override increases the risk of collisions by 5.4%. These results have practical implications for considering delays in CAV performance analysis and for designing robust CACC algorithms with minimum delays in the future.


I. INTRODUCTION
The emergence of cyber physical systems (CPS) has given rise to the development of advanced cooperative The associate editor coordinating the review of this manuscript and approving it for publication was Eyuphan Bulut .
ITS applications for managing traffic congestion.Aggressive driving behavior of certain drivers create longitudinal waves in traffic, while stop-and-go waves from congestion cause phantom traffic jams on highways [1].Connected and automated vehicles (CAVs) are CPS applications that help in reducing these oscillations and phantom traffic jams VOLUME 11, 2023 within the traffic stream.Adaptive cruise control (ACC) may mitigate these oscillations by controlling the speed of a subject vehicle with respect to its preceding vehicle, but only with large headways.CAVs utilize communication between vehicles (V2V) and infrastructure (V2I) to create situational awareness of the surrounding traffic to form tight platoons through cooperative adaptive cruise control (CACC), which is an extension of ACC.
The basic purpose of longitudinal controllers like CACC is to safely follow preceding vehicles at fixed small headways.The CACC is required to guarantee stability of not only a single vehicle but the whole stream of vehicles within a platoon.CAV platoon safety and stability [2] depends on the relative position, speed and acceleration of the lead vehicle (LV) and following vehicles (FVs), which are dependent on reliable communication.Unfortunately, the communication medium is unpredictable and as the signal propagates through the medium, it experiences random fluctuations over time.Further, physical barriers (such as vehicles, bridges, and buildings) and frequency interference from communication networks and wireless devices may also create signal interference [3].These fluctuations and barriers ultimately cause time varying data rates and packet drops.Thus, there are three critical components of message transmission including delay, loss of packet or burst losses, and age of information (AoI).Delay refers to the time from the message/packet transmission to time of receipt and has several components.Loss or burst refers to drop of packets or undelivered messages during transmission.Such lost packets lead to unavailability of information about the positions of LV and FVs.In such cases, the controller uses the latest available information.The AoI [4] captures the knowledge freshness about the status of packets at the destination, i.e., the vehicle controller.It indicates the time gap between the current time and the available message generation time to the system with regards to the receiver's perspective.The paper will further focus only on delay and packet loses.These communications are based on Dedicated Short Range Communication (DSRC) that operates on 5.9 GHz at IEEE 802.11p and 1609 standards [5].Messages are broadcast from the infrastructure using roadside units (RSUs) to the onboard units (OBUs) of all other vehicles within a 300-500 m range.The delay is also dependent on multiple factors including obstacles in the communication path, channel congestion, and multiple packet drops [6].Thus, the actual delay observed will depend on various factors and may be higher than the recommended guidelines.
In case of packet drop or delay, the CAV may perform an erroneous action or degrade to ACC control, leading to instability of the platoon.This diminishes the benefits of platoon formation and leads to higher variation in driving regimes.The study of delay and its impacts within CAV is still an open topic and has not been studied extensively.A few studies [3], [7], [8], [9] have considered delay in CAV systems using simulation.However, the impact of delay on safety, stability and volatility in driving regimes using real field data has not been studied extensively.This study fills this knowledge gap about the impact of delay on variations in acceleration and deceleration regimes within CAV environment using large-scale field experimental data and application of switching regime models.

II. LITERATURE REVIEW
A comprehensive literature review was conducted to analyze studies on the communication delay aspects of CAVs.CAVs have a huge potential to significantly improve transportation systems in terms of safety and operations [10], [11], [12], energy efficiency [13], and reduce phantom traffic jams [1].Upper and lower level control systems [14], [15] have been designed to improve traffic flow and stability.However, these CAV applications rely on some level of communication, and failures or delays in such communication can seriously affect the potential gains from these systems and may even lead to disruption of system operation.A few studies have incorporated communication delay aspects into their analysis to a certain extent using simulation approaches.Talebpour et al. [3] tested a speed harmonization application under perfect and delayed communication and observed that 25% of packets experienced delays of more than 1s.Zhao et al. [16] analyzed the influence of delays on vehicle platoons using simulations.They assessed the influence of random packet drops on the braking process.They observed that string stable behavior is still guaranteed with a small delay of 200ms.However, the behavior was unstable with crash occurrence when the delay was 1s.Ramyar and Homaifar [17] analyzed the influence of uncertainty in communication on CACC platoon formation and stability using simulation.They observed vehicle speed profiles to overshoot and string stability to reduce communication loss and delay.Further, they observed that the negative effects on string stability were dampened by larger time headways.Lei et al. [18] assessed the influence of loss in packet ratios, frequency of beacon, and time headways on CACC string stability within a simulation environment.String stability was observed to reduce with decrease in beacon frequency and decrease in packet loss.Likewise, they observed that for the same beacon sending frequency and packet loss ratio, the string stability improves with increasing time headway.Ling-Yun and Feng [19] studied automated vehicles for their string stability effects based on delay in communication.They took information delay into account for vehicle dynamics model and considered various combinations of predecessor and leader framework.Their simulation tests revealed string stability under delays, but with smaller control gains.However, PSF did not guarantee even weak string stability under delays.Another study [20] calibrated model parameters to simulate vehicle trajectories for car following and observed their model to reproduce ACC driving behavior with higher accuracy.Another study [21] proposes a framework for developing ACC or CACC control based on five layers for interaction with powertrain, traffic, fleet and infrastructure.
Several studies have considered communication reliability and delay from a theoretical and simulation perspective.Santini et al. [9] proposed a consensus-based controller for platooning that considered network losses and delays.Their simulation results showed their algorithm to be string stable under strong interference and delays.Another study [22] developed a cruise control algorithm based on an optimal control problem while considering stochastic delay.Simulation experiments showed the stability of the algorithm compared to existing algorithms.Santini et al. [23] proposed a longitudinal controller based on consensus for dynamic topologies such as joining, leaving and inclusion of vehicles in a platoon.The controller was tested using simulation considering communication loss and observed to be stable.Another study [24] proposed a platooning control strategy with consensus for communication based on fixed and switching topologies.Simulation experiments validated that their strategy was effective for position and speed.Giordano et al. [25] utilized a joint policy from the network and control perspective to design a cooperative platooning algorithm while considering errors arising due to packet loss.The system robustness to packet losses was validated using extensive simulations.Ploeg et al. [26] developed switching strategies for communication loss and delay such that the functionality of one vehicle look-ahead CACC was degraded to have a marginal increase in time gap.This helped in maintaining a string stable behavior that was verified through simulation experiments.Segata et al. [27] evaluated a scheduling algorithm for its impact on platooning control.Their simulation assessment showed bursts or packet losses to degrade the performance of cooperative driving or V2X networks.Wu et al. [28] proposed a controller for countering the effects of communication loss.Simulation and mobile robot experiments demonstrated the effectiveness of the controller compared to falling back to ACC.Luo et al., [29] examined the impacts of time delay, platooning intensity, and CAVs degradations when studying stability of CAVs in mixed traffic.Their simulation results verified the theoretical stability conditions and indicated that speed range becomes unstable and gradually increases with increasing time delay values.Yao et al., [30] analyzed CAV linear stability based on degradation and reaction time or perception delay of an on-board sensing system.Their simulation results showed that linear stability of heterogenous traffic increases with lower perception delay and traffic flow destabilizes with increasing reaction time.
Some studies have analyzed the performance of ACC and CACC systems on flow of traffic using experimental data.For instance, Ma et al. [31] used a five-vehicle platoon experimental data to test the performance of CACC.They observed CAV operation including platooning and merging to improve string stability and traffic capacity.Xiao et al. [32] used various market penetrations of CACC to compute the capacity at free flow and queue discharge bottleneck at merge section.Their results revealed that increased CACC penetration rate increases road capacity, however flow heterogeneity increased when switching between different modes.Stern et al. [1] analyzed autonomous control of vehicles for stop and go waves.Their data from circular track experiments showed that controlling a single vehicle can dampen the traffic waves.Some of the studies from grand cooperative driving challenge (GCDC), a competition for developing and testing automated and cooperative driving between European universities and research centers are also presented.Bayezit et al. [33] focused on the stability of a CACC algorithm designed for the GCDC.They tested the controller performance on A270 in the Netherlands.They observed the oscillations to disturb the string stability profile of vehicle motion.The disturbances from predecessors were amplified rather than being reduced.They attributed these performance issues to commands from high level controllers not being fulfilled fast enough by low level controllers due to the low bandwidth of the throttle control.Further, acceleration above 1.5 m/s 2 were not observed by the controller.Kianfer et al. [34] presented a time-domain based method for stability of CACC.Their receding horizon approach attenuated the preceding vehicle shockwaves.The controller was evaluated using two vehicles, a Volvo S80 and S60.Their experimental results showed the string stable behavior of the vehicles since the controller was never observed to amplify the acceleration of preceding vehicle.Kianfer at al. [35] also analyzed the performance of a CACC controller using field data from GCDC.They observed the CACC to be string stable and dampen the fluctuations in accelerations.Specifically, both speed and acceleration were tracked with respect to the LV, maintaining desired inter-vehicle distance.However, they observed some performance penalties in the position error.Another study [36] provides experimental observations from filed data collected from five ACC equipped vehicles.Their results highlight platoon instability.A recent study [37] presented car following experimental campaigns based on ACC with different conditions.
Most past studies [8], [17] have demonstrated the potential benefits of CAVs while a few studies have incorporated communication delay into their analysis and design of CACC systems using simulation [3], [7], [8].However, there is a knowledge gap in the literature regarding the use of data from real experiments to assess the impacts of delays on cooperative driving from the perspective of safety, stability, and volatility in driving regimes.Since failure or delay in such communication could have significant effects on the potential benefits of these systems and may even lead to disruption of system operation, it is imperative to analyze the impact of such delays on CAV safety and stability.This study provides a significant contribution by analyzing the impact of delay in transmitted messages on variations in acceleration and deceleration regimes within CAV environment through the use of real-world experimental data.

III. CONTRIBUTIONS AND SCOPE
CAVs offer potential to improve operations and safety, however there are some core challenges that need to be addressed.
While CAVs may help to improve traffic flow and reduce crashes resulting from human error, they might still experience technology-related failures and communication delays.A few past studies have incorporated communication related aspects into their analysis and CACC algorithms along with theoretical assessment, but utilizing field experimental data to evaluate the impact of delays in communicated messages and associated factors on platoon safety and volatility using a rigorous methodological approach is still an open issue.Thus, a knowledge gap exists in terms of utilizing sophisticated data science techniques for understanding the variation in platoon volatility of CAVs under delays in communicated messages and the effects of associated factors that contribute to unstable and volatile driving within a platoon.The major contributions include: • The paper contribution lies in utilizing sophisticated data science techniques to analyze field experimental data from platooning experiment to assess the impact of delay in transmitted messages on volatility and safety of lead and following vehicles within the platoon.The unique concept of volatility is utilized as a surrogate measure of flow stability and safety since volatility represents erratic movements in terms of acceleration and deceleration variations.
• The study leverages real-world CAV field test data using a switching regime and Bayesian framework to analyze the impact of delay in communicated messages on CAV safety and instability through the concept of volatility while taking unobserved heterogeneity into account.
• The study explains how the volatility and safety of leaders and followers within a platoon are affected by delays in communicated messages and associated factors while taking unobserved heterogeneity into account.Further, the relation between volatility and time to collision-based conflicts is analyzed while accounting for the effects of delay in communicated messages on conflicts.The volatility concept is relevant in this context since volatility identifies the abrupt and erratic changes in driving regimes, specifically accelerations and decelerations, which are leading indicators of traffic flow instability and safety.Highly volatile regimes with abrupt variations point towards an unstable driving profile.The authors emphasize that the goal of this paper is not to demonstrate string stable experiments, but rather to show how data science techniques could be utilized to infer patterns from field data.It is important to share the results of all field experiments related to cooperative driving with the research community since field experiments are rare.Since CAV technology is evolving rapidly, the insights gained from this real-world field data would be valuable for the future testing and deployment of CAVs.

IV. EXPERIMENTAL DESIGN
This section discusses the field experiment setup, system architecture, the controllers, the test track and the instructions provided to the LV and FVs.

A. SYSTEM ARCHITECTURE
The system architecture for the test vehicles and infrastructure elements consists of multiple components and is shown in Figure 2 [31].These components include: • A proprietary longitudinal controller comprising electronic control units (ECUs) to allow vehicle motion and braking control in automated manner by integrating with the existing ACC controller.
• Basic safety messages (BSMs) reception and transmission enabled by Dedicated short range communications (DSRC) on board unit (OBU).
• A real time computing platform known as d-Space Micro-Autobox II controller (MAB), providing commands to the longitudinal controller, which is assessed through a MATLAB/Simulink library.
• A secondary Linux based in-vehicle controller integrating with MAB and gathering vehicle measures and operating the algorithm.
The field tests were conducted with the Cooperative Automation Research for Mobility Applications (CARMA) fleet of the Saxton Lab, as shown in Fig. 3.These vehicles operate on a robot operating system (ROS) [31], which enables custom algorithms to be implemented and executed within each vehicl's module.The user selects the plugins at the software startup that are initiated in the vehicle's Linux PC.The speed profile for the vehicle is generated by the cooperative motion planning performed by the enabled plugins.The plans for vehicle maneuvers are executed after going through several sanity checks for trajectory, speed limits etc. during validation.A fleet of Cadillac 2013 SRX are utilized for CARMA hardware.The stock ACC is overridden by a drive-by-wire system that sends throttle and brake commands to the CAN bus.The CARMA platform generates speed commands on the Linux PC [39], that are forwarded to a control module in real-time using a loop of proportional-integral derivative (PID) controller.
The CARMA platform utilizes a combination of fusion of GPS sensors, wheel sensors and inertial measurement using pinpoint device to generate accurate estimates of vehicle altitude and location in real time.These prevail even during occlusions causing GPS satellite drops or other issues.The stock forward-facing radar [39] sensor is utilized by the CARMA platform by connecting with the forward object CAN bus.The Linux PC and sensor fusion system receives data from these sensors [39].The high-speed CAN bus also provides vehicle speed data and status of ACC.The CARMA platform also provides the ability to communicate with the internet during vehicle motion using networking hardware.The vehicl's DSRC communications to and from the Linux PC are enabled by a Cohda OBU.

B. EXPERIMENTAL TEST TRACK
This study utilized data from field tests conducted by Federal Highway Administration (FHWA) [40] in collaboration with Volpe Center for a platooning proof of 128552 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.concept based on CACC and ACC (https://data.transportation.gov/Automobiles/Test-Data-of-Proof-of-Concept-Vehicle-Pl atooning-B/wpek-zziu).The field tests were conducted on a 4.5-mile test track at Aberdeen Center in Maryland.A fleet of five Cadillac SRX vehicles were equipped with CACC controllers, with variations of LV and FVs used for conducting the field tests.The test track geometry includes grades, lane markings, width, and curvature that are like a typical US highway.The test track was designated with geolocations called waypoints that were used to send target speeds to LVs, and the LV used these geolocations and global positioning system (GPS) to adjust its CACC parameters accordingly.A diagram of the test track along with the waypoints is provided in Figure 3.A test run was considered complete when the test vehicle traveled from the first waypoint to the last waypoint along the track.A test run was considered valid when no errors were identified during the performance or execution of commands in any of the systems.The target speeds were configurable during the drive runs, although they were defined prior to the start of each run.Typically, the test was considered complete with three valid runs within a total of ten runs in a group, otherwise it was suspended.

C. PLATOONING
The platooning algorithm utilized for the field testing originates from [41] and [42] and was extended by Bujanovic [43], [44].The algorithm allows the selection of the platoon leader dynamically in the event of communication between two or more vehicles.While the control topology remains the same during a specific experiment for a platoon to remain stable, thresholds are defined for rare cases where differences in time gap between followers necessitate dynamically changing the leader while forming a new platoon.For instance, the followers join the platoon with the first vehicle as a leader, while monitoring the follower's headway.The leader changes to any of the two immediate followers if the time gap between the followers is less than a defined threshold j l = 0.4s.Likewise, if the time gap is greater than an upper threshold limit of j h = 3s, the leader changes to the second vehicle between the two followers.
The algorithm operates in intra-platooning, approaching and inter-platooning modes along with ACC.In the Intra-Platooning mode, the algorithm determines the command speed for the subject vehicle (n) to achieve a desired headway.In this process, the subject vehicle will use the information from all the predecessors' vehicles.The vehicle (n) estimates the disturbances downstream after communicating with predecessors and minimize their impact by dynamically adjusting the weight assigned to each predecessor vehicle.The command speed is given by equation (1).
The variable t indicates the current time and t indicates the time for communication range.The variable x j represents the jth vehicle position, x n indicates the subject vehicle position, ẋn represents the subject vehicle speed, ẋj indicates the jth vehicle speed.xn indicates the subject vehicle command speed,t h,j,n indicates the headway between the subject and jth vehicle.π n denotes the current platoon context, and k 1 and k 2 denotes the controller constants to be tuned.The values could range from 0.05 to 0.08 depending on the controller.The premise behind the absolute weight is that the vehicle (n) communicates with the downstream vehicles and monitors their headway (i.e., vehicle j and j + 1 for all j < n).The variable w j,n (π n ) is the relative weight since it takes the absolute weight α j,n (π n ) into account, which is assigned by the subject vehicle to every vehicle in the platoon.The absolute weight for vehicle j assigned by the vehicle (n) has inverse relation to jth and j + 1 follower headway.Readers interested in further details about the weight assignment and the controller, are encouraged to refer to [43] and [44].
Further, when the vehicle (n) has a lead vehicle and the platoon capacity has not reached, then the subject vehicle will use the approaching mode given by equation (2).
The lead vehicle for vehicle (n) is given by the subscript N, p ap and d ap are the approaching mode constants, the headway between vehicles within the platoon is given by t d and ẋd,n represents the subject vehicle speed.
Further, the inter-platooning mode is utilized if the platoon in front has already capacity.The subject vehicles receive information from the downstream vehicles during this mode but it is not required to used it to maintain CACC.The subject vehicle speed in this mode is given by equation (3).
where p p and d p are constant of the platooning controller, t p denotes the required headway between platoons.
Likewise, the simplified ACC controller is provided in equation 4, which is based on errors in distance and speed.
where, g 1 s the host and preceding vehicle's position difference gain, g 2 is the host and preceding vehicle's speed difference gain, t h is the ACC controller's desired time gap (s).The speed profile for the following vehicles is selected based on LV or based on vehicles in proximity.
The speed advisory and position of every preceding vehicle is received by each vehicle in the platoon during CACC operation.The advisory for the target gap is sent to both LV and FVs, which helps in speed adjustment within the platoon.
For the field experiment, a target time gap t h of 1.2s was  utilized for the ACC mode while a target gap t h of 1.1s was chosen for the CACC mode.The different time gaps help with smooth transition between the CACC and ACC modes and creating string stable behavior.Thus, for t h below 1.2s, the CACC mode is activated.Further, ACC requires higher time headway and was unstable at lower t h .Thus, different t h values were utilized for CACC and ACC.The acceleration and deceleration limits for the ACC mode were set lower at 0.25 m/s 2 (compared to the limits of 1.0 m/s 2 and 2.03 m/s 2 for the CACC mode) to enable ACC to maintain a stable platoon.It is worth noting that the ACC controller responds with a significant delay as compared to the CACC, which leads to a minimum undershoot during the speed changes.Thus, ACC has to constantly catch up or slow down with respect to the LV and higher acceleration or deceleration limits lead to abrupt braking and acceleration.For deceleration maneuvers with similar rates, ACC brakes harder as opposed to the CACC controller, which shows a gentle response.Thus, the limits were kept lower for ACC to allow for smoother transitions.

D. PLATOON FORMATION
The platoon was formed between the LV and FVs for all scenarios.The tests consisted of three scenarios [40]: 1. ACC alone.
2. Hybrid ACC mode and CACC mode 3. CACC mode These scenarios are shown in Figure 4.The DSRC communication occurs only within the third scenario with all CACC vehicles.The ACC only scenario had both LV and FVs in ACC mode.The FV speed was set higher than the LV.All vehicles within the group maintain speed and car following through sensors.The hybrid mode had CACC in LV and ACC mode in FVs.The blue arrow in scenario 2 represents CACC communication for the first LV and is a representation of I2V CACC, which receives a reference target speed from the waypoints.Thus, the LV operates using CACC speed and acceleration limits.LV is controlled automatically to match the set speed, so the LV speed is more stable, which also makes it easier for the FVs to stabilize their speeds.However, the FVs operate on ACC control and maintain speed and following distance by only considering the information it receives from its sensors.The CACC mode, where all vehicles are in CACC is a representation of V2V CACC and was used to govern vehicle following within the platoon in the third scenario.The target speed was used to control the LV while the time gap mode was utilized for the FVs via dedicated short-range communication (DSRC) commands.
The FVs communicate with each other while they also receive information from the LV.The CACC mode utilizes communication between vehicles within the platoon, which helps in assessing the impact of delay in communicated messages on CAV stability and safety.ACC is utilized in studying the impact of transitions between modes and differences in speed profiles shown by ACC override.

1) INSTRUCTIONS FOR LV DRIVING
The following instructions [40] were provided to the LV driver.
1.The LV driver was instructed to accelerate in response to the target speed at a rate of 2.5-3.5 m/s 2 to ± 6 mph on test conductor's cue.They were asked to turn the ACC system on prior to the Waypoint while keeping the vehicles centered in the outside lane.2. The LV driver was instructed to perform the following applicable actions as they crossed the Waypoint, while keeping the LV centered in the outside lane.
a) Set the ACC speed manually to the target speed in the ACC mode.b) Engage CACC during the hybrid or CACC type setting.
3. The LV driver was instructed to continue remaining centered in the outside lane as the vehicle approached the next Waypoint and the vehicle speed stabilized under brake and throttle controls.4. The LV driver was advised to avoid potential collisions during testing based on the test drivers' perception of unsafe test conditions by manually taking evasive actions such as braking, steering, or accelerating.ACC or CACC are disengaged by brake application, while automatic controls are overridden by throttle activation.

2) INSTRUCTIONS FOR FV DRIVING
The following instructions were provided to the FV drivers: 1.The FV driver was instructed to accelerate in such a way as to keep a 20-30m gap as the LV begins to accelerate.Turn on the ACC system after reaching a speed of 25 mph.2. The FV driver was asked to perform the following applicable actions within 1-3 seconds of the LV passing the Waypoint: 3. The FV drivers were instructed to stay at the center of the outside lane as the vehicle approached the next waypoint and the vehicle speed stabilized under brake and throttle controls.An auto time-gap was activated to control FVs at this stage since each vehicle followed the preceding vehicle.
The FV driver was advised to avoid a potential collision during testing based on the test drivers' perception of unsafe test conditions by manually taking an evasive action such as braking, steering, or accelerating.ACC or CACC are disengaged by brake application, while automatic controls are overridden by throttle activation.The drivers were recommended to swerve to an alternate lane on the inside or outside depending on the driver's position in the platoon and number of FVs engaging in evasive maneuvers.

V. DATA DESCRIPTION
This paper used data from the experimental tests conducted with CACC equipped vehicles as described in the aforementioned section.A total of 600,000 observations collected at a frequency of 20 Hertz from 72 tests were utilized in this study.The data collected includes information on vehicleto-vehicle communication (V2V), as well as variables on standard driving such as speed, acceleration, and position collected through CAN Bus and GPS.Further, variables on driving behavior including gap from preceding vehicle and disengagement from CACC mode through brake application, variables related to vehicular motion such as ACC override were also utilized in this study.
Of particular interest is the delay of messages transmitted through DSRC.Some packets are expected to be dropped during transmission (known as burst loses), which also leads to increases in delay.During loss of packets, the information about the position and speeds of LV and FVs is not available, and the controller awaits the new packet's arrival.The effects of these losses are also included in the overall delay.However, the impact of packet loss has not been assessed separately.The concept of AoI referenced in the introduction, which captures the difference between the current time and the available message generation time has not been considered in the analysis.While messages between vehicles are broadcasted through BSMs to provide position, speed, and location awareness to surrounding vehicles, these cannot be retransmitted.However, the initial target speed communicated to the LV through DSRC can be retransmitted in case of packet loss.The initial target speed was communicated to the LV using DSRC while the data acquisition module communicates the LV information to the FVs using DSRC.The GPS clocks within the systems were synchronized through the Precision Clock Synchronization Protocol [45], [46] before starting the experiments.The process involves a master slave hierarchy and sending message from master to slave, and slave to master for identifying offsets as a difference of message receipt time and precise sending time.The offset is then used to correct the slave clock time.This process helps to avoid clock drift and achieve a uniform time across clocks.
The delay depends on various factors including distance between antennas, number of transmitters, obstacles in the communication path, and packet drops [6].The increase in distance between receiver and transmitter antenna increases propagation delay assuming line of sight transmission.This is commonly the case in platooning.The propagation delay represents the time taken for the first bit of signal to propagate from the transmitter to the receiver.The propagation delay is a function of distance of the signal within the medium to the actual propagation speed of the signal within the medium.The propagation path loss or delay increases with both frequency and distance and signal strength falls off with distance over the transmission medium.Further, the packet drops rate increases with vehicle traversing a grade.Hoque et al. [6] observed a burst of packet losses with changing altitude between vehicles in an urban environment.They tested vehicles traversing uphill and downhill grades with different speeds (30 mph, 34 mph, 39 mph, and 42 mph) and observed burst of packet losses.Thus, reliability of V2V decreases with variations in altitude due to significant packet losses.Likewise, the placement of DSRC inside or outside the vehicle influences the communication range of transmission.Hoque et al. [6] conducted a set of experiments and observed that placement of DSRC inside the vehicle reduces the communication range since the packets have to propagate through the windshield and other interior obstructions.Further, placement of DSRC on the roof top was observed to improve the communication range.A denser environment is also expected to have an influence on delays.Thus, the vehicle's ability to receive reliable messages decreases with increasing vehicles in range of communication.This may be attributed to packet collisions and increase congestion on the wireless medium.This transmission process in general includes three delay components a) propagation delay, which is the time for the signal transmission from sender to receiver, b) transmission delay, which is the time for the sender to transmit and receiver to receive the packet, and c) queueing delay, where messages wait to be sent.The delay in this paper involves transmission and propagation delay.A unique ID is assigned to each message and time stamp is recorded while the message is transmitted and then the time stamp is recorded at the receiving end.Considering an initial time T 1 , the source (RSU) transmits a data packet p 1 to the LV.Using sequential difference recovery (SDR) for end-to-end communication in Figure 5 [47], time T 0 1 is attached to the data packet.This packet is forwarded towards the receptor or LV.At time T2, the packet is successfully received and timestamp T 0 2 is recorded.The end-to-end delay for the packet p 1 is estimated as the difference of recorded timestamps provided in equation 3. Likewise, the end-to-end delay of packets transmitted between LV and FVs is also calculated.Thus, the distribution of observed communication delay (d) from the empirical data is provided in Figure 6.
The data for each test were processed to extract observations within 300 sec.A moving average method [48] was used to smooth the data.An example profile of the smoothed data is provided in Figure 7.The acceleration was derived from smoothed speed data, which eliminated the difference between acceleration values estimated from raw and smoothed data.GPS measurements are widely used in the literature [39], [49], [50], [51] for speed assessment since they have a low error rate 1 of ≤0.006 m/sec over any 3-second period.The sensors used in these experiments, however, are based on the fusion of multiple sensors involving dual GPS receivers, wheel speed sensors, and inertial sensors that generate real-time position, orientation, speed, and location information, providing accurate measurements for speed profiles.Thus, measurements provided by fusion of these sensors remain available even during events of momentary satellite drops, occlusion, or other issues.Several variables are used in the modeling approach including communication delay (measured in seconds) as a main factor, and other control factors including disengagement (dummy variable), gap to the preceding vehicle (s), acceleration (m/s 2 ), and ACC override (dummy variable).The descriptive statistics are provided as follows.The speeds and accelerations were used to estimate performance measures of volatility.The communication delay represents the delay in communication as measured by the difference in the time stamp of speeds from the time the messages were transmitted to the time of receipt.It has a mean of 0.02, standard deviation of 0.0244, mode of 0.0053 and maximum of 0.082.Further, given the max observed value of 0.082 s, the distribution is within the safe range and do not cross the 0.1s boundary for safety critical situations or the least stringent boundary of 1s.The dummy disengagement variable shows driver disengagement through the application of brakes.The test drivers are advised to disengage the CACC and ACC system based on their perception of unsafe outcomes.Thus, the test driver may disengage when they perceive that driving in the autonomous mode may lead to an unsafe outcome.However, the condition leading to disengagement may or may not necessarily be unsafe since it's based on the perception of test driver.The mean value is 0.1, standard deviation is 0.28, and the maximum value is 1, which indicates a disengagement.The gap to the preceding vehicle indicates the gap between the host or subject vehicle and the preceding vehicle.The mean value is 0.63, standard deviation is 0.59, and the 1 https://www.gps.gov/systems/gps/performance/accuracy/128556 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.maximum is 2. The acceleration variable has a mean of 0.203, standard deviation of 0.61, and maximum of 0.44.The ACC override (dummy) variable represents the override to the ACC mode based on an increased gap.The test driver has the ability to override the system set speed.The driver uses the throttle to override in hybrid mode when the leading CACC increases speed based on target guidance and the gap for the subject ACC increases.Thus, to close the gap with the LV, the ACC override is used.The mean value is 0.17, standard deviation is 0.14, and maximum is 1, which indicates override.
The time-speed graphs of sample tests for the three scenarios are presented in Figure 8 (a-c).These example plots are based on single run and provided for the sake of demonstration.The plots show that the vehicles platoon well together and FVs remain stable during constant speeds in hybrid and CACC scenarios.With ACC, some instability arises towards the end of the acceleration and deceleration phase.The FVs in ACC begin decelerating gradually in response to LV deceleration, while all FVs overshoot at the end of deceleration.The FVs in CACC (Figure 8c) show a much more rapid response to LV deceleration at the beginning of the deceleration phase.Only FV1 and FV4 overshot during the deceleration period of 150s-180s and during the acceleration period of 230s-245s.FV1 and FV4 show higher amplification compared to FV2 and FV3 and represent unstable response during this period.The FVs in CACC also stabilize more rapidly than those in ACC at the end of deceleration.Thus, CACC FVs take less convergence time for speed adjustment with respect to the LV, which may be attributed to the stable LV speed produced by automatic control of the LV.Further, the FVs in CACC (Figure 8c) follow the LV much more closely than FVs in ACC throughout the acceleration phase.The sharper slope of LV's time-speed diagram in Figure 8-c reveals that the vehicles have a higher acceleration rate in CACC mode, and FVs can follow the LV as opposed to the ACC mode.The acceleration settings in a hybrid LV were kept lower to enable ACC FVs to follow the LV due to their response delay, however the FVs in ACC still lagged LV speed.Further, the FVs in CACC stabilize well at the end of acceleration phase.Thus, the CACC mode operates more smoothly as compared to the ACC mode.It is worth mentioning that this performance is dependent on the design of specific controllers implemented in vehicles.

VI. MODELING APPROACH
The study contributes by analyzing real-world experimental data to show the impact of delays in communicated messages and associated factors on CAV platoon stability and safety.This section discusses measures of volatility and the modeling approaches of switching regime and Bayesian framework.

A. PERFORMANCE MEASURES
The study used performance measures of volatility for assessing the impact of communication delay on stability of the CAV platoon and variations in driving regimes.

Volatility Measures:
The volatility concept is a surrogate for flow stability and safety risks due to its representation of erratic movement of vehicles in three dimensions.Mathematically, volatility is the deviation calculated over a time period, showing how spread out the driving regimes of acceleration-deceleration are around the mean.The safety, stability and variation in driving regimes of CAVs under the tested scenarios were analyzed using volatility [52].Coefficient of variation and absolute deviation of the mean and were utilized as two major indicators of volatility [10], [52] in this study and their definitions are provided below.The proactive nature of volatility measures makes them significant since these indicate risky vehicle maneuvers including maneuvers with jerks, which may lead to safety critical events.Their availability prior to the occurrence of safety critical events makes them leading indicators of safety and stability.The mean and standard deviation ratio indicates the coefficient of variation.This represents the relative dispersion in equation 6.
where S.D. indicates deviation, and x provides the mean value for acceleration-deceleration and speed.The difference in average value of each of the speed or acceleration observations from the mean is provided by absolute deviation, given by equation 7.
where x indicates the acceleration or speed values, the number of observations are n.

Time to Collision:
Traffic conflicts are defined by [51] as ''When vehicle movement of remains unchanged as they approach each other, and there is a collision risk.''The premise behind using surrogate safety is that conflicts provide a proactive approach to safety risk assessment and have a comparable mechanism to crashes.Time to collision (TTC) measure for conflicts is given by equation (8).
where TTCn(t) represents the TTC value of vehicle n at time t, x is the vehicle position, vn represents vehicles velocity and Kn−1 represents preceding vehicle length.The conflicts indicate crash likelihood.TTC threshold of 1s and 2s were used to identify the relative risk of CAVs [38].

1) SWITCHING REGIME MODEL
The study utilized a switching regime [11] framework for modeling the impact of delay on LV and FV behavior.The difference in LV and FV behavior within the CAV platoon leads to self-selection bias [11] and all factors that influence the behavior of these two groups [11] may not be observed.This impacts the output from the causal relationship [11] of factors leading to stable and unstable platoons and self-selection between leader and follower.The switching part is applicable for correcting bias for LV and FVs since both behave differently.The difference in response of LV and FVs to delays in communicated messages leads to selection effects 128558 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply. in the LV and FV behavior if not properly accounted in the model and may lead to difference in causal relationship of factors leading to stable and unstable platoon.This approach accounts for difference in behavior of LV and FVs by estimating correction factors and helps in identifying the causal relationship between factors that influence the behavior of LV and FVs individually.Additionally, unobserved heterogeneity [11], [53] may exist due to variation in parameter effects and non-observability of all factors that may influence the relationship between delay and LV and FVs stability.The application of a switching regime [11] modeling framework takes care of selection into two regimes of LV and FV and unobserved heterogeneity bias.The model [11], [53] initially estimates correction terms for selection into each of the two regimes and heterogeneity correction.The model uses these corrections as variables.The probit regression is first used in the selection [53] as provided in equations 9 and 10. and where y i represents [9] the LV or FVs selection within the platoon.
y * i denotes the latent response to selection [9], θ is the variable effect coefficient, k i is explanatory variable row vector and ε d i is the unobserved variables error term, which is normally distributed.The θ in equation 10 is used to estimate Mills ratio (inverse) or selection correction [9].
The equations for the outcomes uses the correction terms as explanatory variables [9], [53] within the switching regime model [9].The LV volatility and FVs volatility outcomes are estimated by equations 13-14.
where y 1 i and y 0 i represent the response variables [9], X i represents the vector of explanatory variables including delay, disengagement, and ACC override, etc, and β represents the coefficients.λ 1 (k i θ) and λ 1 (−k i θ) are the correction 128560 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
terms [9].n i represents the vector of residuals from the regression, The unobserved variables errors (ε 1 i and ε 0 i ) [9] are provided in equation ( 15) with ε d as normal distribution assumption.

2) BAYESIAN POISSON-LOGNORMAL MODEL
A Bayesian Poisson lognormal model was utilized to model the impact of delay on CAV stability while accounting for the relation of the risk of collision and volatility.The modeling approach was considered since it captures the overdispersion in count data.The Bayesian framework was utilized to account for heterogeneity (unobserved) arising due to influence of factors that cannot be observed in the data.Due to non-observability of all factors influencing CAV stability, omitted variable bias arises [54].This leads to unobserved heterogeneity in the relationship between the impact of delays and associated factors on LV and FVs.This unobserved heterogeneity leads to variation and erroneous estimates for the effects of observed correlates and delay on platoon stability.The use of appropriate statistical techniques can reveal microscopic driving decisions and their impact on CAV safety and stability.Considering the ordinal nature of crash conflicts, relevant count data models were estimated [55].Crash conflicts were used as dependent variables while delay and volatility measures were used as independent factors in Bayesian Poisson regression models.
Assuming n denotes the number of crash conflicts, then the probability of n conflicts for Poisson regression is given by: where λ n i is a Poisson parameter for observation i = 1,2, . . .N .
(E n i ) is the probability in equation 16 while ln(λ n i ) is the log-link function of a set of explanatory parameters [55].
To account for overdispersion in unmeasured heterogeneity, a Poisson lognormal model was used.The model assumes the crash conflicts are independently distributed as shown in equation (18), while the unobserved heterogeneity is considered as shown in equation (19).The term exp (λ i ) in equation (19) indicates random effect multiplication.
The Bayesian estimation fuses prior beliefs (from prior distributions) with the available evidence (through the likelihood function).These are utilized to generate posterior distributions of parameters to be estimated which are then used to generate inferences.The prior beliefs were generated from a sub-sample of data treated as historical data.The distribution for priors was selected based on the type of variable, either fixed or random.The fixed parameters have a constant effect and their distribution do not change while random parameters have a variable effect over time and non-constant distribution.The use of flat prior for random parameters causes posterior density to be improper.Thus fixed parameters were assigned flat priors while semi informative priors (β ij ∼ Normal(1, 100 2 )) and (σ 2 ij ∼ Normal(0, K )) were utilized for random parameters to account for the random nature.This is a commonly used method [57] The informative priors were estimated for random parameters' (σ ) standard deviation while K serves as the uniform density's upper limit.An iterative process was used for crafting the limits by starting at smaller value and moving in increments to observe failure of convergence or no improvement in Bayesian based Information Criterion (BIC).This inference method is in accordance with other studies.
The prior distribution was used to derive the distribution (posterior) by the Gibbs Sampler method [51] and used to estimate β ij and σ 2 ij .The method utilizes Monte-Carlo based Markov chain (MCMC) simulations.The method involves repeated samples generation until they converge to the target posteriors.A subsample of draws [51] was discarded as burn-in after testing convergence.A total of 100,000 draws with 50,000 burn-in were used.The convergence was satisfied [58] when a value of less than 1 was observed for the Brooks-Gelman-statistic. Further, the 95% Credible Interval (Bayesian) were used to test significance of parameters [51].The model fit and performance [58] was tested using the Deviance Information Criterion (DIC).This is a generalization (Bayesian) of the Akaike Information Criterion.

VII. RESULTS AND DISCUSSION
The assessment of delay's impact on CAV platoon stability is provided.The analysis is performed from a volatility, and safety perspective.The performance metrics or dependent variables in Tables 1-2 include volatility in acceleration and deceleration that were estimated from acceleration and deceleration profiles in section VI.Likewise, the performance metrics in Table 3 are represented by the conflicts estimated from speed and following distances collected from the experiments as shown in section VI.Further, communication delay serves as the main factor in the switching regime model and indicates the impact of unit increase of delay on probability of increase or decrease in volatile behavior of lead and following vehicle within the platoon.Likewise, the delay variable serves as the main factor in the Bayesian model representing the influence of unit increase in delay on the probability of occurrence of conflicts.Further, the model variables (disengagement, gap to preceding vehicle, ACC override) serve as confounding factors to account for their influence on the performance metrics of volatility and safety risk in driving regimes, thus representing the true impact of delay on the dependent variable.The consideration of confounding factors within the models helps to account for heterogeneity changes that are observed or unobserved as explained in the modeling approach.The estimated marginal effects indicated probability outcome change in percentage.The marginal effects are estimated for dummy variables by specifying a unit change from base conditions while for continuous variables, a change of one standard deviation is specified.The value of 'coeff' in the Tables indicates the expected change or impact of each variable in terms of probability response on the volatility and safety, while the p-value indicates the statistical significance of the variable.

A. CAV VOLATILITY AND STABILITY
Figures 9-11 show how delay affects the temporal volatility of CAVs estimated from mean absolute deviation of speeds.The volatility was estimated for a delay of 0.04s and 0.08s, as opposed to a base case of 0s delay.The delay changes with time, thus a single value of delay was not used within one period.Rather, two ranges of delay were used to screen a spectrum of performance for those ranges to collect 100s of driving profile.The volatility was estimated for a delay of 0.04s and 0.08s, as opposed to a base case of 0s delay.The Figures represent 100s of driving profiles that had up to 0s, 0.04s and 0.08s delay in communication.In practice some delay is expected.However, signals with negligible delay in the range of <0.00005s were considered equivalent to zero.For the hybrid case which involves both ACC and CACC, the ACC does not involve communication, and thus there is no communication delay for ACC.Further, we used two example cases of 0.04s and 0.08s delay and screened the data based on ranges of delay less than or equal to 0.04s and 0.08s.The 100s driving selected accounts for a total of 25 runs with delay starting up to a maximum value in the range of 0.04s and 0.08s.The performance corresponding to delays less than or equal to 0.08s is included in the range of 100s driving, while the performance for delay less than or equal to 0.04s delay constitute hybrid cases involving ACC and other lower values that make up the 100s driving profile.The values are based on an average of 25 test runs (grouped together by common conditions).The total run numbers are reduced for these specific cases since delay was different between run numbers and 0s in ACC cases.This assessment examines the influence of delay on LV and FV behavior.The concept of volatility is used as a surrogate measure of flow stability and safety since volatility represents erratic movements in terms of acceleration and deceleration variations The effects of delays from transmission to reception are analyzed based on the volatility in terms of fluid or abrupt flow of LV and FVs.This section explains how changes in delay influence the volatility and instability of a platoon including its leader and followers.The ACC portion of the hybrid case is represented in Figure 9, the CACC portion of the hybrid scenario is represented in Figure 10, and Figure 11 represents the CACC scenario.The results from Figure 9 indicate that the baseline case shows negligible volatility or variation in driving regimes with no communications delay producing an average volatility value of 1.02m/s.Figure 10 reveals that increasing the communications delay to 0.04s has a slightly higher impact on the volatility and instability of the CAV platoon, with an average volatility of 1.5m/s.A more pronounced effect is observed with further increases in delay to 0.08s, resulting in average volatility of 2.1m/s as shown in Figure 11.The trend is thus consistent with lower delay leading to less volatile driving and higher delay leading to highly volatile driving and unstable behavior.The difference is observable in the response of followers, specifically FV3 and FV4 which show highly volatile behavior in response to increasing delay in Figure 10-11.The overall impact observed on volatility, however, is marginal given the small delay considered in the example cases.Both LV and FVs are observed to respond with highly volatile behavior to increases in communications delays.The FVs show more variations in driving regimes as represented by higher volatility compared to the LV as the delay propagates within the platoon from LV to FVs.The 0.08s delay case represents an average increase of 2% in volatility over the 0.04s delay case for the LV, while the volatility of FV increases by an average of 3.2%.Thus, the impact is more pronounced as the messages are received by each of the FVs.This may be attributed to the fact that when information is transmitted, vehicles farther from the LV have not received or changed its state in response to the LV information as suggested by [8].Inherent delay in propagation of information along the string may be responsible for the increase in volatility.The overall impact is concerning from both the LV and FV perspective and poses risk of collision since the effect is amplified within the platoon.

B. VOLATILITY IN ACCELERATION AND DECELERATION
The section explains how real-world field test data of CAVs can be leveraged using data science techniques including a switching regime and Bayesian framework to assess the relationship between volatility and communications delay while accounting for the impact of additional confounding factors and unobserved heterogeneity.
Tables 1-2 show the results for the switching regime model.The results further reveal how the delay from both LV and FVs impacts the stability and volatility of the CAV platoon.The modeling reveals the individual impact of delay and associated control factors within LV and FVs.This is important since variation in communication and other factors from LV and FVs can have differing impacts on the platoon stability and performance.Thus, the overall effects on volatility and safety performance of platoons are a combination of multiple factors, and not considering these control factors will lead to biased estimates by underestimating or overestimating the effect of communication delay on volatile driving.The delay is therefore used as the main factor to analyze its impact on safety and volatility of platoons while other variables 128562 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.such as disengagement, ACC override, and gap to preceding vehicle are used as control factors to account for observed heterogeneity.
The results reveal that delay in communication of both LV and FVs produce instability in the CAV platoon.The increase in delay leads to a higher propensity for variation in acceleration and deceleration.The relative comparison shows a higher volatility with increased delay in LV communication as compared to FVs communication.This is intuitive since followers rely on the LV driving profile, and delayed communication about speed changes or position can result in delayed responses from FVs as the instability propagates through the FVs within the platoon.Low or high variations in acceleration and deceleration are significant as they indicate fluid or jerky flow of traffic, which can result in instability in the platoon and serious concerns from safety perspective.
While the main focus of this analysis is on the delay variable, it is important to control for other confounding factors to avoid omitted variable bias [54], [59].Thus, the control factor of disengagement is also observed to increase the volatility in both acceleration and deceleration.The finding is intuitive since a driver's manual disengagement will require more reaction time to respond to external events.The human driver may not be able to maintain constant headways, which could result in highly volatile driving with abrupt variations.While disengagement occurs as an evasive action based on the perception of the test driver to take manual control, i.e., the roadway conditions or vehicle maneuvers deemed dangerous or safety critical by the test driver but may not necessarily be unsafe.Thus, disengagement is not necessarily related to system failure, and it is imperative to control the effects of this variable on driving volatility.
Likewise, the time gap to preceding vehicle is also found to be a significant control factor affecting the volatility of the CAV platoon.Specifically, higher time gaps to the preceding vehicle show a reduction in the propensity of volatility in acceleration for the FVs.A safe time gap is required for safe longitudinal operation.While this gap is preferred to be minimized to improve vehicular throughput, measures of ride comfort such as jerks, vehicle performance capabilities including maximum and minimum acceleration, and other safety considerations impose additional constraints and bounds.Thus, the finding is in agreement with past studies [60], [61] that observed saturation of throttle and brake rates at smaller time gaps results in instability of platoon with higher variations and lower comfort in the tail of platoon.A recent study [62] also quantified the impact of response time on flow stability.
The variable of ACC override also shows a higher propensity for increases in volatility in acceleration and deceleration of CAV platoon.The instability in terms of volatility in acceleration and deceleration increases for both LV and FVs.The test driver uses a manual override of target speed to catch up with the LV in response to an increase in LV speed, which will cause a sudden jerk and increase variations in driving regimes, thus influencing volatility.The CACC mode   allows smaller reaction time due to continuous communication and cooperative coordination of speeds as opposed to ACC, allowing more stable performance.

C. RELATION BETWEEN TIME TO COLLISION-BASED CONFLICTS AND VOLATILITY
This section explains how the safety of leaders and followers within a platoon are affected by delays in communicated messages and associated factors while taking unobserved heterogeneity into account.These results also clarify the relation between volatility and time to collision-based conflicts while accounting for the effects of delay in communicated messages on conflicts.
Although the previous section reveals the impact on volatility in acceleration and deceleration and traffic instability, it is imperative to analyze the impact of volatility on the risk of collisions since higher variations in driving profiles are expected to increase the chances of rear end collisions.The results in Table 3 are provided for the fixed parameter and hierarchical random parameter models.It should be noted that communication delay is used as a main contributing factor with measures of volatility to analyze their impact on crash risk while disengagement and ACC override act as control factors.
The hierarchical model clearly outperforms the fixed parameter model, as shown by parameter effects and a lower DIC value.Table 3 shows that an increase in delay results in a higher risk of rear end collisions.Marginal effects in Figure 12 reveal that a 1% increase in delay increases 128564 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.collision risk by 4.2%.This is expected since increased delay in messages transmitted within the platoon would require vehicles to respond faster to maintain safe headways.The volatility measures also indicate a strong influence on collision risk.The impact of an increase in mean absolute deviation of acceleration on traffic conflicts reveals a higher risk of rear end collisions.Marginal effects indicate a higher risk of collision by 3.5% for a unit increase in the volatility measures.These provide better insights about CAV stability and driving profile since instability is at a minimum when the acceleration-deceleration profile is constant and there is a minimum variation in speed.These findings reveal a non-constant speed profile for the platoon.Likewise, disengagement is observed to cause instability and lead to higher risk of rear end collisions.Marginal effects reveal an increase in collision risk of 5.8% when a disengagement occurs.
This again indicates highly variable speeds and accelerationdeceleration profiles for the platoon.Disengagements are not related to system failure since the test driver disengages based on their perception of unsafe driving conditions or vehicle maneuvers, which may not be safety critical in reality.Further, the ACC override also shows a higher risk of collision.The propensity for collision risk increases by 4.5% for a unit increase in ACC override as indicated by marginal effects.The ACC override occurs in hybrid mode when the test drivers in ACC followers override the target speed in response to increases in LV speed.The sudden transition towards ACC with manual override of target speed requiring higher reaction time than CACC contributes to instability of platoon, which may increase the risk of collision.

VIII. COMPARISON WITH RESULTS FROM PAST STUDIES
The conclusions and findings from this research were also compared with past studies that considered communication delays and their impacts on cooperative driving, as shown in Table 4.It is worth mentioning that each study uses a different set of performance measures for their assessment, which makes a direct comparison difficult.However, the overall goal of assessing stability is the same, thus the general trends towards increasing stability are compared.
Luo et al. [29] was selected as one of the studies for comparison since that evaluation assessed the impacts of time delay on stability of CAVs in mixed traffic within simulation.Their simulation results verified the theoretical linear stability conditions and indicated that increases in time delay from 0.1 to 0.4 increased perturbations in speed in the range of 5m/s, which indicates instability of platoons.In comparison, our findings utilize volatility measures estimated from speed kinematics to assess stability and show that the volatility of LV increases by 2% under communications delay while the volatility of FVs is observed to increase by 3.2%, representing instability of platoon.Another study [23] proposed a longitudinal controller based on consensus for dynamic topologies of a platoon while incorporating communication loss.They used speed profiles as measures of assessment and observed their controller to be stable under small delays.Followers were observed to experience slight disturbances with increases in speed from 100km/h to 115km/h and revert to normal speeds with time.These findingsare also comparable to our field experiments showingan increase in volatility of LV and FVs by 2% to 3.2% resulting from increasing delay.Wu et al. [28] proposed a controller for countering the effects of communication loss and compared its performance to ACC with communication loss in simulation.They assessed stability performance based on speed profiles and inter-vehicle distance.They observed increases in disturbance with communication loss and fall back to ACC with inter-vehicle distance increasing in the range of 1m.The performance measure is not directly comparable to our measure of volatility from field experiments, however both show instability and increase in spacing error contributes to abrupt increases in speeds.Our assessment, however, also considers the influence of other confounding factors along with delay on stability of platoons.Another study [19] analyzed linear stability of automated vehicles under delays in communication.They considered various combinations of predecessor and leader frameworks within a simulation.They observed delay in communication to result in instability, shown by increase in inter-vehicle spacing error of followers.This performance measure is also not directly comparable to our measure of volatility, however both show instability and our assessment also considers the influence of other confounding factors.Zhao et al. [16] analyzed the influence of communications delays on linear stability of vehicle platoons using simulations.They observed that delay in the range of 20ms to 200ms lead to unstable behavior, shown by abrupt increases in speed by 2.5m/s to 3m/s with possibility of crash occurrence.The findings are comparable to our results from field experiments showing increase in volatility by 2% in LV and 3.2% in FV from delay, meaning 2% to 3.2% higher variations in speeds and accelerations.

IX. CONCLUSION AND IMPLICATION
CAVs can potentially improve transportation systems' performance.Past studies have analyzed the impact of various CAV applications on traffic operations and safety, however there is a knowledge gap regarding the impact of delay in transmitted messages on CAV platoon safety and stability.This study fills this knowledge gap by studying the effects of delay on platoon safety and stability using the volatility concept as a surrogate measure using real-world experimental data.
Large-scale experimental data collected for testing of CAV applications (ACC and CACC) were utilized in this study.Measures of driving volatility were calculated to analyze the impact of delay and associated factors on CAV safety and stability using a switching regime framework.The results reveal that CACC improves platoon safety and stability by reducing volatility in both LV and FVs compared to ACC system.This is expected due to the vehicular communication and motion synchronization of CACC.However, delays are observed to increase the likelihood of volatility and contribute to instability of CACC platoon.FVs behave more volatile compared to LV since the instability is transmitted through the platoon string.A unit increase in delay is observed to increase the likelihood of collision risk by 4.2%.Other confounding factors such as disengagement and ACC override contribute to higher volatility of platoon while the likelihood of high volatility in both LV and FVs decreases with increase in gap to the preceding vehicle.The likelihood of risk of collision is expected to increase by 5.8% in response to unit increase in disengagements.Likewise, ACC override increases the likelihood of risk of collisions by 4.5%.
These results have implications for considering delay and associated factors in the design and analysis of CAV systems due to their safety critical nature.The study reveals that starting with a delay of 0.04s in communication, instability within the platoon is observed, which causes both LV and FV to have more volatile behavior.Likewise, the risk of collision is also observed to increase relative to increase in delay within the platoon.Thus, for future safe integration of CAVs in the existing traffic environment, the effects of delay and associated factors need to be properly considered so that the expected collision risk could be avoided.These results would, therefore, provide guidance to researchers and system designers for incorporating the effects of delay within CAV simulation studies to provide a more realistic assessment of different CAV applications.Furthermore, robust CACC algorithms could be designed by incorporating communication delays.In addition, modifying CACC algorithms such that the effects of ACC override and manual disengagements are minimized could enable more stable CAV profiles, resulting in lower volatility and improving the net gains from these systems in terms of throughput and safety.The results provide insight from real-world driving however, these are limited to the scenarios and conditions specific to the experimental tests.Field tests are highly valuable; however, it is currently not feasible to conduct CAV field tests with larger fleets and multiple scenarios due to the limited availability of such instrumented vehicles.Future studies could focus on testing with multiple platoons as more CAV fleets become available and utilize multiple scenarios including mixed traffic, weather and traffic conditions.Further, the driver's response to such automated systems and analysis of their trust level could also be a valuable future research direction.

FIGURE 1 .
FIGURE 1. System architecture for the experiment.

FIGURE 2 .
FIGURE 2. Fleet of CARMA vehicles in the field experiment at the Aberdeen Center [40].

FIGURE 4 .
FIGURE 4. Field test scenarios for CAVs, (arrow in legend indicate direction of traffic).
a) Assign minimum gap to gap setting and set 65 mph as ACC speed during hybrid or ACC-only setting.b) Engage CACC during CACC-only type testing.

FIGURE 5 .
FIGURE 5. Communication delay calculation, (blue bars in the transmissions and reception indicate a single packet).

FIGURE 9 .
FIGURE 9. Volatility (measured as mean absolute deviation of LV and FVs under base case (0s delay).

FIGURE 10 .
FIGURE 10.Volatility (measured as mean absolute deviation) of LV and FVs under (up to 0.04s delay).

FIGURE 11 .
FIGURE 11.Volatility (measured as mean absolute deviation) of LV and FVs under (up to 0.08s delay).

TABLE 1 .
Switching regime model for volatility in acceleration.

TABLE 2 .
Switching regime model for volatility in deceleration.

TABLE 3 .
Bayesian estimation of crash conflicts under communication delay.

FIGURE 12 .
Influence of parameters on stability and safety performance.

TABLE 4 .
Comparison with results from the literature.