Vehicle automation and freeway ‘pipeline’ capacity in the context of legal standards of care

With the commercial rollout of increasingly-sophisticated vehicle-automation concepts, there is growing interest in the nature of potential impacts to various aspects of the transportation system, such as safety (Fagnant and Kockelman 2014; Kalra and Paddock 2016), parking (Zhang et al. 2015; Kong et al. 2016), pollutant emissions (Wadud et al. 2016), regulations (Smith 2014, Anderson et al. 2016; Gasser 2016), possible shifts from car-ownership to car-rental (Fagnant and Kockelman 2016), and how in-vehicle time is used (Malokin et al. 2015; Zmud et al. 2016).

This paper’s focus relates to the impacts of highly-automated cars (cf. SAE 2014) on traffic flow on mainline freeway segments. We consider operating regimes in which the automated vehicle’s (AV’s) longitudinal-control system makes and then implements control decisions regarding speed and following-distance-from-forward-vehicle without input from the vehicle’s occupant(s). In other words, this is a more highly automated concept than adaptive cruise control (ACC), in which a human driver makes an initial selection of speed and following distance, and the automated control system subsequently operates pursuant to this guidance. The kinematics of these two concepts are not fundamentally different, though the lack of guidance from a responsible human driver leads to distinctive issues of responsibility for vehicle operation (see “Conclusions” section).

This topic has been addressed by a number of earlier studies (cf. “Background” section); the original contributions of this research are as follows. First, ‘regular’ (i.e. non-emergency) freeway driving behavior is evaluated from the perspective of ‘defensive driving’; we document the current legal requirements for ‘defensive driving’ and subsequently employ them to specify and numerically test various plausible manifestations of this general approach. Earlier work (cf. Goodall 2014) has discussed the ethical issues of programming AVs’ behavior for circumstances where crashes are imminent (“crashing algorithms”); we build on prior work by Carbaugh et al. (1998) and Kanaris et al. (1997) in simulating car-following decision-making for mundane driving conditions which explicitly recognizes the potential for emergency conditions suddenly arising. Second, the kinematic parameters of the numerical analysis are derived from empirical field tests, and we take explicit account of uncertainty in braking-system performance to quantify the trade-off between crash-risk and capacity. We demonstrate that, under contemporary “Rules of the Road”, faithfully replicating the behavior (see “Human drivers’ degree of compliance with the ACDA Rule” section) of human drivers on a congested freeway could expose the manufacturers of automated-driving systems to a degree of liability¹ that they may find unacceptable, but reducing this risk would unavoidably reduce the capacity of the freeway network. Designers of automated control algorithms might be viewed less sympathetically than individual human drivers and be more attractive targets for litigation (as they might be seen to plausibly be able to pay out large claims for both actual as well as punitive damages).

The analysis we report in this paper is subject to several important limitations, including that the discussion of legal issues is based solely on American (U.S.) law (the consequent numerical calculations, however, are not specific to any particular jurisdiction). A second limitation is that the analysis focuses exclusively on mainline freeway segments; weaving, merging and diverging behavior are all left as topics for future research. Third, we consider only automobiles (leaving as future research needs the unique challenges posed by heavy vehicles, recreational vehicles, motorcycles, etc.) and for purposes of the numerical analysis we treat the kinematic parameters of automated cars as identical for all automated cars, whereas different manufacturers’ vehicle-control systems are likely to have distinctive properties (which are not currently knowable, due to both commercial confidentiality and the expectation of technological improvement in coming years). Fourth, the numerical analysis does not explicitly take account of the effects of uncertainty in automated vehicles’ sensor readings. Fifth, we focus exclusively on traffic streams of homogenous AVs; we leave issues of mixed human and AV traffic (including non-homogenous capabilities of AVs) for future research.

Throughout this paper, we employ the term ‘capacity’ to refer to the maximum throughput (vehicles per lane per hour) that can be sustained at a given free-flow speed. For human-driven cars, the standard model of traffic flow (TRB 2010) suggests that this value (1000 vehicles/lane/h at a 75 miles/h [121 km/h] free-flow speed) is much lower than typical quoted values of freeway-lane capacity, as it refers to maximum throughput at the free-flow speed, whereas typical quoted values (e.g. 2400 vehicles/h/lane, per TRB 2010) refer to maximum throughput across all speeds, which in the case of a freeway facility with a 75 miles/h [121 km/h ] free-flow speed is estimated by TRB (2010) to occur at 53 miles/h (85 km/h] (see “Fundamental diagram of ACDA-compliant automated car driving” section).

The remainder of this paper is organized as follows: “Background” section contains a background discussion of the relevant literature and legal standards, “Methodology” section introduces the methodology, “Results” section presents the numerical results, and “Conclusions” section concludes the paper with a summary of findings and brief discussion of research needs.

A number of earlier studies have evaluated the impacts of vehicle automation on network capacity. The subsequent discussion focuses on impacts of automation on freeway-network capacity; readers interested in studies of automation on arterial networks are directed to Dresner and Stone (2008), Ferreira and d’Orey (2012), Li et al. (2014), and Le Vine et al. (2015, 2016).

The distinct concepts of connectivity (V2X communication) and automation (control by algorithm rather than human driver) are in practice closely intertwined in the literature, with various studies evaluating the interaction between them (cf. Kanaris et al. 1997; Vander Werf et al. 2002; Van Arem et al. 2006; Milanes and Shladover 2016; Motamedidehkordi et al. 2016; Zhou and Qu 2016; Asare and McGurrin 2016). For the purposes of this paper, however, the primary focus is on unconnected automation, in which each automated vehicle makes its own decisions on the basis of only line-of-sight information about its surroundings received from its own sensors. Whether other sources of information, specifically V2X communications, are received and disregarded (i.e. not considered trustworthy for decision-making purposes)—or simply not received—is treated as immaterial for the purposes of control decision-making. Whether AVs will be ‘self-directed’ or will rely on V2X communications to ‘direct their movement’ is noted by Glancy et al. (2016) as a major point of uncertainty.

In order to evaluate the impacts of automation on network capacity, a necessary starting point for comparison purposes is the existing set of models of human-driving behavior (Brackstone and McDonald 1999). Noteworthy models include the 2010 Highway Capacity Manual’s methodologies (hereafter referred to as “HCM-2010” (TRB 2010) and Wiedemann’s models of car-following behavior (Wiedemann 1974, 1999²), which are employed in the present paper, as well as models proposed by Gipps (1981), Yang and Koutsopoulos (1996), and Fritzsche (1994). Though the HCM-2010 model is the most widely used, none of these models is uniquely correct in describing the dynamics of traffic flow with human drivers; Brackstone and McDonald (2007, p. 1183) report that “providing clear unequivocal statements regarding car following and safety levels…is still far from straightforward”. Indeed, we demonstrate a wide divergence between the HCM-2010 and Wiedemann-1999 models in their analysis of human-driven traffic flow at freeway speeds (see “Fundamental diagram of ACDA-compliant automated car driving” section).

In analyzing the time gaps that human drivers leave behind the preceding vehicle, researchers have noted that humans regularly select time gaps that are much shorter than the values prescribed by standard advice (Brackstone et al. 2002; Friedrich 2016), with (Brackstone et al. 2002, p. 43) remarking that human drivers appear to “indulge in a certain amount of ‘educated risk taking’”. The reasons for such behavior are poorly understood; hypotheses include signaling of ‘fitness’ in the context of evolutionary biology (Skippon et al. 2012), or drivers simply making rational choices to accept the small risk of striking a lead vehicle in exchange for the benefit of arriving at their destination very marginally more quickly. Despite the fact that individual human drivers routinely select small time gaps that are apparently ‘unsafe’ when analyzed against standard kinematic criteria, and regardless of human drivers’ reasons for doing so, it appears unlikely that vehicle manufacturers would do the same in the design of automated-control algorithms. The software code would leave little doubt about the decision-making logic (in contrast to acknowledged human frailties when making split-second decisions³), and the archived stream of information from an automated vehicle’s on-board sensors would mean that the factual circumstances of a crash are also much less likely to be in dispute than in human-driver crashes for which the only evidence is physical and drivers’/eyewitnesses’ memories.

Table 1 summarizes earlier studies that have evaluated the impacts on freeway capacity of automated vehicles operating with only line-of-sight information. Various methodologies have been employed, including both bespoke kinematic analysis and adaptation of car-following models of human-driving used in standard traffic-microsimulation software.

This study builds on a body of research originating in the 1990s into rear-end-collision warning and avoidance systems. Ervin et al. (1998) develop a simulation framework of adaptive cruise control (ACC) to investigate the empirical frequency of short-following-distance episodes and either human intervention or crash occurrence. Galler and Asher (1995) similarly present a control algorithm for incorporating V2V communications in automated car-following; both Ervin and colleagues and Galler/Asher focus on safety metrics rather than capacity impacts. Farber (1994, 1995) reports similar studies, conducted as part of the REAMACS project. Carbaugh et al. (1998) evaluate the trade-offs between safety (defined by crash frequency and severity) and capacity on the basis of a requirement not to strike a leading vehicle. Carbaugh and colleagues evaluated kinematics in a similar manner to the present study, however they assumed emergency-braking by all vehicles at their maximum physically-achievable rate. By contrast, the present study considers a range of braking concepts for both the leading-vehicle/stationary-object (e.g. the ‘weak’ and ‘strong’ interpretations of the Assured Clear Distance Ahead doctrine described later in this section) and following vehicle (e.g. occupant-comfort considerations, at the boundary between ‘normal’ and ‘emergency’ braking, and during wet driving conditions). As with the findings reported by Kanaris et al. (1997), Carbaugh and colleagues also do not quantify the trade-off between safety and capacity in the systematic manner (in order-of-magnitude increments up to a 1 in 1,000,000 risk) of the present paper, nor do these studies address the speed-flow relationship of AVs in congested-flow conditions (i.e. the fundamental diagram of traffic flow, cf. TRB 2011).

General limitations of earlier studies are that either: (1) the requirement to avoid striking a leading vehicle or previously-obscured object is not explicitly taken into account, or (2) deceleration concepts are specified in a narrower manner than in the present paper, or (3) properties of congested-flow conditions are not addressed.

Standard advice to human drivers is to “drive defensively”; this generally includes both anticipating unexpected behavior by other drivers and selecting an appropriate following distance behind a forward vehicle, though the specific advice offered varies both qualitatively and quantitatively in terms of what is a “safe” gap. New York, for instance, advises drivers to select a two-second gap, whereas Florida advises four seconds (NYS DMV 2015; Florida DHSMV 2015). Texas also advises four seconds, and explicitly instructs motorists that “you should always be able to stop within the distance you can see ahead of your car (Texas DPS 2014, p. 48).

The Assured Clear Distance Ahead doctrine is the common law manifestation of the Defensive Driving concept; it requires a vehicle operator to “regulate his speed so that he can stop within the range of his vision” (Pearson 2005, p. 333).⁴ Buchwalter et al. (2016, Automobiles and Highway Traffic, Sect. 1115) report that “Most jurisdictions follow the rule that a collision between a preceding and a following motorist gives rise to a presumption of negligence on the part of the following motorist, whether the preceding vehicle is moving, stopped, or stopping.”

The Sudden Emergency doctrine qualifies the ACDA criterion; Sudden Emergency generally excuses a driver from negligence in the case of striking a vehicle, object, or person which has unexpectedly and suddenly moved laterally or vertically⁵ into their trajectory (Pearson 2005). For instance, “A motorist driving at a reasonable speed and obeying the rules of the road is generally not liable for injuries to a child who darts in front of the vehicle so suddenly that the motorist cannot avoid injuring the child, as where a child darts out from behind other vehicles that were stopped in traffic, directly into the path of the vehicle, and there was no evidence that [the] driver was driving too fast” (Buchwalter et al. 2016, Automobiles and Highway Traffic, Sect. 498). Similar logic has been found applicable in the circumstance of one vehicle abruptly changing lanes to place itself directly in front of another vehicle’s trajectory (Decker v. Wofford 1960), though the presence of stationary and reasonably expected road features (e.g. the crest of a hill limiting sight lines) has been held to not warrant application of the Sudden Emergency exception (Coppola v. Jameson 1972).

Glancy et al. (2016) posit that AV manufacturers may face “design-defect claims in which a particular programming choice associated with an accident is attacked as defective” (p. 39). Though ACDA is the generally-applied standard relevant to longitudinal vehicle control by human drivers, in practice it raises three major pragmatic issues relating to automated operation.

The first of these issues is that, notwithstanding their obligations under the ACDA rule, human drivers routinely violate it in the exercise of normal driving behavior. Leibowitz et al. (1998) document, for instance, that strict adherence to the ACDA criterion would require human drivers of automobiles to travel no faster than approximately 20 miles/h (32 km/h) at nighttime on unlighted roads (regardless of roadway functional class), in order to be able to stop in time to avoid a ‘dark-clad pedestrian’. Despite traffic speeds at night exceeding 20 miles/h (32 km/h) on much of the unlighted road network, as well as posted speed limits far in excess of this speed, courts have attributed negligence to drivers not observing the ACDA rule at nighttime (cf. Mantz v. Continental Western Insurance Company 1988; Dranzo v. Winterhalter 1990). A fundamental tension arises from the fact that holding automated vehicles to the ACDA standard at all times could result in driving that is more conservative than human driving, which would tend to reduce capacity.

The second issue is that ACDA generally requires vehicle operators to avoid colliding with both the vehicle ahead (the ‘weak’ ACDA interpretation) as well as stationary objects (the ‘strong’ ACDA interpretation). If the following vehicle strictly observes the ACDA requirement to be able to “stop within the range of his vision”, the vehicle must avoid striking a possible stationary object⁶ in the travel lane (e.g. a moderate-sized piece of road debris) which only becomes ‘within the range of his vision’ once the leading vehicle (which blocks the forward line of sight) has passed over the foreign object. We show (see “Results” section) that imposing this ‘requirement on AVs would result in large decreases of roadway capacity as measured by vehicles-per-lane-per-hour.

The third pragmatic issue with rigid application of ACDA is that, even in cases where striking an object would not be negligent, the manufacturer may nevertheless wish to instruct the vehicle to drive more conservatively than the minimum legal standard. The designer may, for instance, plausibly view a heightened degree of occupant-safety as a marketing advantage. Under current law, the only apparent limitation to conservative driving behavior in most jurisdictions are statutes that prohibit ‘impeding’ the flow of traffic, and that such laws typically provide explicit exemption for slowing “when necessary for safe operation” (New York Vehicle and Traffic Law, Section 1181; cf. also California Vehicle Code Section, 22400a).

While courts have generally held that the operator of an automobile following another vehicle “must handle the automobile in recognition of the superior rights of the traveler in front” (Naffky 2012, Sect. 734), the operator of the following vehicle “may assume that the preceding vehicle is being driven with care and caution, will use every precaution to avoid being struck in the rear by following vehicles, [and] will give timely warning, by an appropriate signal, of his or her purpose to stop, or decrease the speed of the car, or to turn” (Naffky 2012, Sect. 735). The obligation of the leading vehicle to signal when turning or braking has historically referred to visual indications, but may in the future be broadened to include electronic V2X messaging. In the case of visual turning/braking indicators, the leading vehicle’s operator generally bears responsibility for signaling their maneuver (Naffky 2012, Sect. 698), rather than whether the following vehicle’s operator receives and processes the signal correctly (Naffky 2012, Sect. 703). This is a minor distinction in the case of plainly-visible visual indicators (brake lights and turn signals), however in the case of V2X electronic messaging there is the novel possibility of data packets being successfully transmitted by the leading vehicle but failing to be received by the following vehicle (Bergenhem et al. 2014). A following vehicle would also quite reasonably place superior trust in the condition of its own sensing/processing equipment in comparison to the sensing/processing/V2V-signaling equipment of other vehicles on the road.⁷ Whilst the forward driver owes a duty of care to the following vehicle (Naffky 2012, Sect. 734), the following vehicle’s lack of visibility beyond the vehicle ahead prevents it from knowing whether circumstances ahead of the forward vehicle have presented a sudden emergency that requires the forward vehicle to brake. Given that there is very little private benefit (in terms of travel time savings) to the occupants of a following vehicle from following closely behind the leading vehicle and potentially large costs (in the form of crash risk for which some combination of the following vehicle’s manufacturer and/or occupant would be liable), it appears prudent, under prevailing technology and rules of the road, for vehicles in a traffic stream to make control decisions on the basis of information from their own line-of-sight sensing.

The numerical analysis of this study subsequently implemented ACDA-compliant driving behavior via a kinematic model. We then perform comparisons with capacity values calculated from the HCM-2010 (TRB 2010) and Wiedemann-1999 (PTV 2011) models of human driving behavior, and also draw on empirical “Naturalistic Driving” data from two sources (TRB 2013; USDOT 2016) to characterize additional dimensions of human-driving behavior. These tasks are described in this section.

Equations 1 and 2 present the minimum requirement for ACDA-compliant driving behavior, based on the fundamental equations of motion. Equations 1 and 2 are expressed in terms of headway (the time gap between the front of the leading vehicle and the following vehicle) and following distance, respectively:

Notation is described in Table 2; the derivation of Eqs. 1 and 2 can be found in the Appendix of Le Vine et al. (2016). Capacity (\(C_{v}\)) at free-flow speed \(v\) is the maximum throughput of vehicles at the specified speed; it is calculated by taking the reciprocal of the minimum headway value.

We note that a single value of velocity is specified for both \(veh_{l}\) and \(veh_{f}\) (a pair of leading and following vehicles) to represent both vehicles having the same initial speed under conditions of uncongested flow. Separate notation (\(a_{l}^{ - }\) and \(a_{f}^{ - }\)) is shown, however, for the rates of deceleration. These are the rates of deceleration that would govern in case of \(veh_{l}\) initiating emergency braking without advance warning and \(veh_{f}\) responding by also braking. We present results under various assumptions for \(a_{l}^{ - }\) and \(a_{f}^{ - }\).

The sources of empirical parameter values for automated vehicles are presented in Table 3. A particularly important assumption is the value of \(t_{lag,f}\): the maximum possible amount of elapsed time that \(veh_{f}\) assumes can take place between \(veh_{l}\) and \(veh_{f}\) initiating emergency braking. Shladover (1997) points out that it is “very difficult” (p. 14) to select uniquely correct values for \(t_{lag,f}\), with (Bierstedt et al. 2014, p. 22) noting that “the exact operating characteristics of automated vehicle technologies are proprietary and unknown”. This is due to multiple interacting factors including commercial sensitivity on the part of automotive manufacturers, and improvement over time in sensing/processing/actuating capabilities. For the purposes of this study, we generally specify \(t_{lag,f}\) to be 0.4 s, though we test (in Scenario #8) the effect of an arbitrarily-small latency value. The specification of 0.4 s is greater than the 0.2 s of latency described in Anderson et al. (2013), which is predicated on ideal lighting and weather conditions; we selected a larger value in order to account for the fact that an automated vehicle cannot know in advance with certainty whether or not lighting and environmental conditions will be optimal at the moment that circumstances abruptly change and emergency braking is required. A conservative amount of processing time also enables multiple sensor observations to be processed before initiating emergency braking. Limit false positives is an important consideration, particularly if the specified deceleration rate of emergency braking is sharp enough to be uncomfortable or dangerous for the AV’s unsuspecting occupants (e.g. if the deceleration could cause a hot beverage in the AV to spill onto an occupant).

We employ VISSIM software (PTV 2011) to implement the Wiedemann-1999 car-following model which we use (in addition to HCM-2010) as a descriptor of humans’ driving behavior on freeways. Where we report results from the Wiedemann-1999 model, they are on the basis of a 60-min analysis period, which is preceded by a 15-min ‘warm-up’ period. The network consisted of a single-lane freeway-class road segment five km (3 mi) in length, with 0% grade and no horizontal or vertical curves. All vehicles were defined to be ‘cars’, with identical ‘desired speeds’. Demand was specified (at 3000 veh/h) to be comfortably in excess of capacity for human drivers; capacity conditional on speed was calculated by measuring achieved flow for different ‘desired speeds’. The numerical results we present are averages across ten simulation runs for each desired speed.

In this section we present numerical results for mainline-segment freeway capacity (vehicles per lane per hour) in the presence of automated vehicles, on the basis of the criteria specified in “Methodology” section.

This research highlights a fundamental tension, namely that human drivers are in principle held to the ACDA standard but routinely violate it in practice, and this ‘negligent’ driving tends to increase traffic-moving capacity (i.e. to lower congestion). We demonstrate that, even if ACDA is deemed to be applicable for AVs as it is for human drivers and V2 V signaling is deemed unreliable for the purposes of selecting following distances, large gains in freeway capacity are nevertheless possible. A requirement, however, is that the occupants of automated cars must be placed at risk of deceleration at or near their vehicle’s maximum physically attainable rate, which places limits on the cabin configuration of automated cars and the types of activities that their occupants can perform while traveling. While V2 V signaling could in principle allow even greater capacity, this would require a level of trust in others that is not reflected in current rules of the road.¹⁶

An additional tension is that cars following one another closely on a freeway provides benefits mainly to upstream vehicles, in the form of decreased congestion. The occupants of the vehicle performing the close following, however, receive little in the form of direct benefit (time savings) and bear a higher risk of being held liable for striking the vehicle ahead in the traffic stream. Circumstances in which there is a systematic mismatch between the distribution of benefits and costs to public and private actors can result in suboptimal outcomes, however; this is a classic collective action problem (Ostrom 2015).

We now conclude this paper with a brief discussion of research needs for the next phase of the research agenda.

First, this research highlights the need for a program of testing the emergency braking capabilities of AVs. There is also a need to confirm through field testing whether or not the kinematic parameters employed in this paper will continue to be valid. The empirical degree of error-correlation between the braking rates of a leading and a following vehicle is a further issue in need of further enquiry; this study’s assumption of independence (see “Capacity calculations under uncertainty, with various thresholds of crash risk” section) is likely to be conservative. Given that the consequences of unconnected automation could include substantial gains or losses of capacity on the publicly-owned freeway network, there appears to be a case for public dissemination of the full technical results, which would of course need to be balanced against the commercial interests of AVs’ manufacturers.

Second, further research is needed into the traffic flow properties of ACDA-compliant AVs in congested conditions. The analysis presented here does not account for possible ‘shockwave’ phenomena in traffic streams of automated vehicles, which is complex for two reasons. The ‘shockwave’ phenomenon in human-driven traffic streams is itself neither “well-understood” nor “accurately modeled in existing models” (Yeo and Skarbadonis 2009, both quotes from p. 99). Different manufacturers’ AVs will also likely operate in idiosyncratic ways, though for reasons of commercial sensitivity and the absence of large fleet sizes (100 s of vehicles) available for on-road testing, there is limited evidence today on which to base reliable conclusions. Therefore, researchers using simulation methods would need to make operational assumptions of parameters for which much less knowledge currently exists in the public domain, in comparison to the set of assumptions made in the kinematic model presented in this paper.

Third, the ACDA rule is not the only plausible standard for ‘reasonable’ operation of automated vehicles; research is needed into both the various interpretations of ACDA (‘strong’ vs. ‘weak’) and alternatives to ACDA. For instance, a government may reach a considered conclusion that the benefits from increased capacity (and avoided costs from postponing/canceling planned road-widening projects) of non-ACDA-compliant operation of automated vehicles outweigh the marginal costs of a heightened risk profile, and may therefore plausibly define manufacturers’ duty of care to permit (or require) more aggressive driving behavior than ACDA permits.¹⁷ Glancy et al. (2016) note the possibility of ‘safe harbor’ legislation or regulation that could provide manufacturers a defense against liability on the basis of satisfying a safety standard set by policymakers. Even if such policies are enacted by neither legislation nor regulation, Anderson et al. (2016) note that it is likely that AV manufacturers will argue in court that the ‘reasonableness’ standard in allocating liability should consider AVs’ societal cost–benefit analysis (which the authors expect to be demonstrably favorable), whereas plaintiffs in AV crashes may by contrast be incentivized to argue that ‘reasonableness’ is to be determined on the basis of a narrower cost–benefit analysis limited to the specific component of the AV-driving algorithm that governed the vehicle’s behavior proximate to the crash. If, however, the ACDA criterion as it is applied to human drivers is treated as the relevant criterion for AVs’ operation, guidance will be needed regarding whether AVs driving on limited-access freeways may/should/must interpret the ACDA criterion ‘weakly’ or ‘strongly’. Also, any departure from the ACDA criterion in the interest of maximizing capacity (or in locations where it cannot be guaranteed, such as on weaving segments of freeways) would require in-depth analysis to determine whether chain-reaction collisions can be avoided when an initial crash occurs in a traffic stream of vehicles that are not operating in ACDA compliance and, if not then how the costs of the crash are allocated.¹⁸ Shladover (1997) studied the problem of sub-ACDA-compliant spacing, highlighting the fact that in AV platoons with very close headways any crashes would be relatively low-energy impacts (because there is little distance for differential rates of deceleration to lead to large speed differences), however in the process of longitudinally forming a platoon there is unavoidably a point at which ACDA compliance is impossible but the headway has not yet become small enough to ensure a low-energy crash.

Fourth, there is a need to quantitatively establish the safety/efficiency tradeoffs in the context of AVs’ control. The fact that kinematic parameters cannot be known a priori with certainty means that there is no combination of car-following distance and speed that could completely eliminate the possibility of striking the leading vehicle. Therefore, research that rigorously exposes, in numerical terms, the specific safety/efficiency tradeoffs (extending from the initial analyses that we report in “Capacity calculations under uncertainty, with various thresholds of crash risk” section) would enable manufacturers to design algorithms for which it can be demonstrated that the anticipated benefits exceed the anticipated costs (cf. the discussion in LaValley [2013] of the precedent established in United States v Carroll Towing [1947]¹⁹ to determine whether a party has performed an adequate duty of care).

Fifth, the fact that maximum throughput for AVs is calculated to occur at much lower speed (26 miles/h [42 km/h]) than for human drivers is a novel speed/capacity tradeoff that requires further research. This tradeoff is an undesirable system-level property because it introduces a new type of tension between two of the principal objectives of the transportation network.

Sixth, there is a general need to establish the circumstances under which V2X messages can be regarded as trustworthy and complete, and hence actionable for safety–critical decision-making. For instance, it is unclear at present how liability would be allocated in case of the failure of a leading vehicle’s V2V signaling to be received and processed by a following vehicle.²⁰

Seventh, research is required to establish which person or entity is responsible in the event of non-ACDA-compliant driving by an AV, and how this may depend on circumstance. In circumstances where a human driver has made an informed selection of a speed and headway combination that is not ACDA-compliant and then instructed their vehicle to mimic this behavior in automated mode, it may be that the human driver bears some degree of responsibility in the event of a rear-end crash while in automated-driving mode. In this context, it is noteworthy that at least one designer of automated vehicle control algorithms (Urmson et al. 2015) has proposed a ‘learning period’ during which a human driver drives their automated car, while the vehicle ‘learns’ the human’s driving style which it subsequently aims to mimic. In such a set of circumstances, the designer of the control algorithm might assert that the end user is at least partly liable in case of a rear-end crash while in automated mode, by claiming that the end user gave instructions to not follow the ACDA rule by not himself/herself having driven in an ACDA-compliant manner during the learning period. If, however, the owner/occupant of an automated car has never given instructions (or anything that can be construed as ‘instructions’) to an automated car regarding driving style, it may be more likely that liability for failing to comply with ACDA would rest with the manufacturer.

Eighth, this research is intended to provide support for transportation planners simulating the effects of AVs in regional travel-demand models. Therefore, there is a need to adapt the volume-flow relationships we report here (e.g. Fig. 2) into curves analogous to the volume-delay curves employed in travel demand models. This research would ideally involve algorithms that account for spillback during periods of oversaturated demand.

From the earliest days of vehicle automation, it has been recognized that “the most effective (and proactive) method to control costs related to liability is through careful product design and careful system operation” (Stevens 1997, p. 344). It is the authors’ hope that this research will assist researchers, designers and policymakers in understanding the degree of care required in automated cars’ operation, and the attendant consequences for traffic flow.