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Publication Number: FHWA-RD-03-050

Surrogate Safety Measures From Traffic Simulation Models

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7. Algorithms for Surrogate Measures of Safety at Intersections

This section summarizes the proposed surrogate measures of safety and the algorithms required to derive the suggested surrogate measures from microscopic traffic simulation models. This section has three main subsections:

  1. Description of conflict event situations to be evaluated at intersections.
  2. Definition and description of the data required to be collected from the simulation models to compute the surrogate measures.
  3. Proposed step-by-step descriptions of the algorithms for collecting the surrogates from a simulation model.

Conflict Event Descriptions

Observable situations (in the simulation) that can indicate the relative safety of different traffic intersection designs are conflict events. Conflict events occur between two vehicles that are on a collision course, but do not collide because of evasive action (by either one or both of the vehicles). These events can either occur in a particular single location in time and space – a conflict point – or during a range of times and locations – a conflict line (45). Figure 10, an elaboration of the figure from (45), illustrates both conflict line and point concepts. In all discussions of this report, travel is assumed to be according to the North American standard – vehicles travel on the right-hand side of the roadway.

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Figure 10. Conflict point and lines.

Crossing Flows—Conflict Point Events

As shown in the figure, conflict points (notations 1, 2, 7, and 8) occur at the crossing of:

  • Left turn by the westbound traffic onto the minor street conflicting with the eastbound traffic.
  • Left turn by the minor approach traffic onto the main street to travel westbound.
  • Crossing movement by the minor traffic proceeding straight across conflicting with the traffic going both eastbound and westbound.

These conflict points model the potential for angle collisions due to the acceptance of a gap that is too small by the encroaching traffic. The corresponding conflict events for other travel directions are not shown, but are also possible.

Merging Crossing Flows—Conflict Line Events

Conflict lines (notations 3 and 4) occur at the crossing of:

  • Left turn by the minor-street traffic conflicting with the westbound traffic.
  • Right turn by the minor-street traffic conflicting with the eastbound traffic.

These conflict lines model the potential for rear-end collisions (or angle collisions from the rear) due to the acceptance of a gap that is too small by the encroaching traffic. The corresponding conflict events for other travel directions are not shown, but are also possible.

Adjacent Flows—Lane-Changing Conflict Line Events

Conflict lines (notation 6) denote rear-end events where the leader vehicle changes lanes abruptly in front of the follower vehicle, requiring the vehicle in the adjacent lane to brake to avoid collision. The corresponding alternative lane changes from outer lanes to inner lanes, as well as the occurrence in the other travel directions, are not shown, but are also possible.

Following Flows—Rear-End Conflict Line Events

Conflict lines (notation 5) denote rear-end events where the leader vehicle makes a right (or left [not shown]) turn causing the following vehicle to decelerate to avoid a collision. Additional conflict lines are possible for other travel directions, but are not shown in the figure.

Collision Types Not Represented in the Surrogate Measures

All of the conflict events represented in the surrogate measures are those that occur because of normal driving behaviors that are observable and possible to be modeled in a computer simulation. Some collisions that are not included here are sideswipe collisions, head-on collisions, and swerve-out-of-lane collisions. Some discussion of each of these categories is presented in the next subsections.

Sideswipe Collisions

A vehicle in the process of changing lanes strikes an adjacent vehicle in the side because it:

  1. Accepts the gap too early.
  2. Does not see the vehicle because of obstructions.
  3. The vehicle struck has made its own maneuver simultaneously with the lane-changer, e.g., enters the link from a driveway.

Head-On Collisions

Would only be represented in the intersection model as a vehicle inadvertently crossing the centerline. This is not modeled in current simulation codes.

Swerve-Out-of-Lane Collisions

Much like a head-on collision, vehicles making a right turn from a minor approach onto the major street might veer into the opposing lanes if their speed were too high to make the turn. This is not modeled in current simulation codes.

Pedestrian Collisions

Simulation of pedestrians’ movements, awareness of pedestrians by vehicles, and vehicle-pedestrian interactions are not as well developed as vehicle-vehicle model components in available traffic simulation models (i.e., car following, lane changing, gap acceptance, etc.). Only a percentage of conflict events between pedestrians and vehicles are because of "normal" driving and pedestrian behaviors (jaywalking and mid-block pedestrian crossings are not typically modeled). Also, sight-distance restrictions and driver distractions play a large part in conflict events between pedestrians and vehicles, and pedestrian movements can cause rear-end conflicts between two approaching vehicles as well. These elements are not modeled in current traffic simulations, but should be an important part of future work in traffic simulation modeling. If the interactions between pedestrians and vehicles can be improved in future simulations, the extension of the concepts presented in this report should be easily extendable to conflict events between pedestrians and vehicles.

U-Turn-Related Collisions

U-turn maneuvers and the associated conflicts are somewhat difficult to represent in simulation models. Such a maneuver can create a point conflict event (crossing in front of oncoming traffic in the leftmost lane to U-turn into the rightmost lane) and/or merging line conflict event (crossing in front of oncoming traffic to U-turn into the same lane as oncoming traffic).

There could also be the case where the U-turning traffic strikes a vehicle turning right (or vice versa). Such conflict events would either involve the U-turner or the right-turner braking to avoid the collision, depending on how the gap-acceptance procedure in the simulation model deals with right-of-way during a U-turn. U-turn conflict event statistics would only be available in simulation models that implement them explicitly and the representation of U-turns would be two separate conflict events—a crossing conflict point for a vehicle in the lane closest to the median and a conflict line event for a vehicle approaching in the lane that the vehicle enters upon completing the U-turn.

Summary

Even though these conflict types listed in this section are not represented, the majority of crashes that occur at intersections are covered by the conflicts that are represented in the simulation models. As shown in table 13, not being able to represent sideswipes and head-on conflicts will only have a small effect on estimating the total potential collisions. For example, in the first column, at urban, four-leg intersections, 83 percent of all collisions are angle, rear-end, pedestrian, and "other unknown," not including sideswipe and head-on collisions. The "other unknown"events are typically single-vehicle crashes (e.g., run-off-road, striking fixed objects) that are not measurable in this project.[2]

Table 13. Percentage of total intersection crashes made up of angle, rear-end, and pedestrian collisions (other and unknown percentages in parentheses).

Intersection Type

Two-Way Stop-Controlled

Signalized

Urban

Rural

Urban

Rural

3-Legs

64 (+8)

45 (+6)

72 (+8)

66 (+10)

4-Legs

69 (+14)

62 (+6)

78 (+8)

76 (+7)

 

Unrepresented Evasive Maneuvers

In addition to neglecting the above collision types, the conflict points and lines illustrated in figure 10 also do not represent the capability of the reacting vehicles to perform the following countermeasures to avoid conflict events:

  • Change lanes or swerve.
  • Accelerate.
  • Proactively decelerate or change lanes (i.e., defensive driving behaviors that a certain class of drivers learn from experience with a particular location).
  • Abort maneuvers.

Significant Unrepresented Conflict Event Contributors

The simulation models are only approximations to behavior in the real world. The hypothesis of the surrogate measures approach proposed here is essentially that some large percentage of undesirable behaviors (i.e., conflict events) are because of the geometry and/or signal timing of the intersection. Notable effects that are important contributors to conflict events and crashes, which cannot be modeled (yet) in traffic simulations include:

  • Obstructions to visibility such as overhanging trees and shrubs, sharp corners, utility poles, bus stops, etc.
  • Lighting deficiency or difficult lighting conditions such as sunrise and sunset.
  • Snow, rain, blowing dust, standing water, poor drainage design.[3]
  • Lack of adequate signage, location and readability, interpretability of signs.
  • Noise level inside and outside of the vehicle.
  • Driver distractions inside and outside of the vehicle (cell phones, rubber-necking, etc.).
  • Special conditions such as reversible lanes during particular times of the day that are location-specific (and come as a surprise to drivers that are new to an area— "unintentional scofflaw behavior").
  • Red-light violations and other traffic scofflaw behavior.

Conflict Point

The conflict point represents a fixed location in space where the crossing flow intersects with the flow proceeding straight through the intersection. In simulations where the crossing path is fixed, i.e., the turning vehicles always enter the receiving link in the same lane, this point would not change for each through lane. Where there are several paths available to the turning vehicle, then there would be several conflict points defined. This would be the case if there is a driveway or intersection at which the turning vehicle wishes to make a right turn shortly downstream (and the simulation models this).

It might be useful for the simulation model to pre-process the locations of these conflict points at the beginning of the simulation and store them in a data structure for each intersection. This would eliminate re-computing the conflict points for each evaluation of a crossing maneuver.

The time line of a conflict point event is illustrated in figure 11. The top curve represents the time-space trajectory of the crossing vehicle. The bottom curve represents the time-space trajectory of the through vehicle. While these curves are represented as continuous, smooth functions in the following figures, in a traffic simulation, the vehicle time-space trajectories are actually a set of straight lines between time steps. As the number of time steps per second increases, the curves become closer and closer approximations to a smooth curve (assuming the update equations and functions used by the traffic simulation are applicable at any time step resolution).

The times t1 through t5 are defined as follows:

  • At time t1, the crossing vehicle enters the encroachment area (i.e., starts to turn left).
  • At time t2, the through vehicle realizes that a collision might occur and begins braking to avoid the collision.
  • At time t3, the corner of the rear bumper (either right or left rear corner, depending on the travel direction) of the crossing vehicle leaves the encroachment point.
  • At time t4, the through vehicle was projected to arrive at the conflict point if the vehicle continued at the same speed and trajectory before it started braking.
  • At time t5, the through vehicle actually arrives at the conflict point.

Conflict points also occur at the intersection of a flow from a right- or left-turning vehicle that proceeds in the same direction as the conflicted vehicle, but in a different lane. This situation can only be evaluated in simulations where the entering path can vary by lane. For example, in the real world, many maneuvers of this type occur on purpose by drivers that want to accept a particular gap of the size required to enter the flow, but that gap size was not available in the closest lane, because of the acceleration needed by the entering vehicle to avoid an approaching vehicle in that lane. A smaller size gap could be accepted, however, if the entering vehicle crosses in front of the approaching vehicle and begins accelerating in the adjacent lane (no vehicle is approaching in the adjacent lane, or the approaching vehicle in the adjacent lane is farther away). Thus, a conflict point event can occur when the driver crosses the first lane to enter the second one and begins accelerating. This occurs even if the driver then re-enters the crossed lane after the approaching vehicle has passed.

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Figure 11. Conflict point diagram.

Conflict Line

The conflict line represents a region of space where a preceding vehicle conflicts with a following vehicle in the same lane. This can be true of:

  • Vehicle entering the lane from a cross street in front of a vehicle proceeding straight.
  • Vehicles traveling in the same direction when the leader decides to turn left or right abruptly.
  • Vehicles changing lanes in front of another vehicle, causing braking by the follower to maintain a safe following distance.

The latter two cases are described in the "rear-end conflict line" situations in the next section. The spatial regions of conflict lines are not fixed locations because they depend on the acceleration/deceleration characteristics of the particular vehicles involved in the conflict and the behavior of the driver model, i.e., how early or late the driver uses a turn signal. Thus, each conflict line will have to be computed for each conflict event.

A timeline of a conflict line event for a vehicle turning from a minor approach onto the main street in front of a vehicle progressing straight through the intersection is illustrated in figure 12. The topmost curve represents the time-space trajectory of the leading vehicle (turning from the minor street). The bottommost curve represents the time-space trajectory of the following vehicle (vehicle already traveling on the main street). The times t1 through t9 are defined as follows:

  • At time t1, the leading vehicle enters the encroachment area (i.e., starts to turn left into the same lane as the follower).
  • At time t2, the following vehicle realizes that a collision might occur and begins braking to avoid the collision.
  • At time t3, the next time step of the simulation is reached and state variables for each vehicle are updated.
  • At time t4, the leading vehicle stops accelerating, reaching its intended travel speed.
  • At time t5, the following vehicle is projected to have arrived at the first encroachment point if it had continued at the same velocity as before it started decelerating.
  • At time t6, the leading vehicle arrives at a maximum conflict evaluation distance downstream from the starting point.
  • At time t7, the following vehicle is projected to have arrived at the second encroachment point if it had continued at the same velocity as at the second time step of the conflict line time period.
  • At time t8, the following vehicle reaches the first encroachment point of the conflict line.
  • At time t9, the following vehicle reaches the maximum conflict distance point.

The reference maximum downstream distance (shown as the horizontal dotted line across the top of the figure) is required for computation of surrogate measures similar to the post-encroachment time. In a pathological case, the measures could continue to decrease far down the link, and thus the minimum would continue to be recomputed even though the conflict event is not severe enough to be stored as a valid event. This is discussed further in the sections on computation of surrogate measures for conflict lines and rear-end conflict lines.

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Figure 12. Conflict line example.

Rear-End Conflict Line

Rear-end conflict lines are a slightly different conflict line situation. This is because either the leader or the follower could be the "encroaching party" in the generation of the near-miss collision event (or both). Consider that:

  • The leader may fail to signal a turn soon enough or decelerate or turn suddenly while the follower was initially at a safe following distance.
  • The follower may be following too closely to react to an adequate signal indication or at a safe braking speed.
  • Both may be true.

In any case, the braking done by the following vehicle is the indicator of the need to check for a rear-end conflict event. Recall also that we are seeking a linkage between rear-end conflict event frequency and differences in geometric or operational policies between intersection designs. It will be interesting to learn if the frequency of rear-end conflict events is influenced by geometric and/or phasing differences of intersection designs in the next phase of the surrogate safety measures project.

A timeline of a rear-end conflict line event for a vehicle turning off of the main street onto a minor street in front of a vehicle progressing straight through the intersection is illustrated in figure 13. The topmost curve represents the time-space trajectory of the following vehicle (continuing straight). The bottommost curve represents the time-space trajectory of the leading vehicle (turning off of the road). Note that in this figure, the vehicles are traveling in the opposite direction to the vehicles in the example figures 11 and 12. The times t1 through t8 are defined as follows:

  • At time t1, the leading vehicle starts to decelerate to turn off of the main street.
  • At time t2, the following vehicle realizes that a collision might occur and begins braking to avoid the collision.
  • At time t3, the next time step in the simulation begins and the state variables of each vehicle are updated.
  • At time t4, the following vehicle is projected to have reached the first encroachment point if it had continued with the same velocity as before beginning deceleration.
  • At time t5, the following vehicle is projected to arrive at the next conflict evaluation point in the rear-end conflict line (where the leading vehicle was located at time t3) if it had continued with the same velocity as at time t3.
  • At time t6, the next time step in the simulation is reached and the state variables for each vehicle are updated.
  • At time t7, the leading vehicle leaves the main street, turning off the road.
  • At time t8, the following vehicle is projected to have reached the point where the leading vehicle was located at time t6.

Similar to the conflict line situation, the rear-end conflict line situation requires a reference maximum downstream distance (not shown in figure 13) to terminate calculations of the measures such as the minimum TTC. Otherwise, the minimum TTC could be calculated as zero. This will be discussed further in future sections.

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Figure 13. Rear-end conflict line example.

Summary of Conflict Points, Lines, and Rear-End Lines

Conflict points define the situations where a crossing vehicle interrupts the progress of another vehicle, but the vehicles only interact at a specific point in space. Conflict lines describe the situations where two vehicles interact in the same lane for a period of time. Algorithms for calculating the surrogate measures of safety for these event types are specified in the next section.

Surrogate Measures Definitions

The surrogate measures that are suggested to be collected for each conflict event (point, line, and rear-end line) that occurs during the simulation are:

  1. TTC.
  2. PET.
  3. Initial DR.
  4. Maximum of the speeds of the two vehicles involved in the conflict event (MaxS).
  5. Maximum relative speed of the two vehicles involved in the conflict event (DeltaS).
  6. Starting and ending latitude and longitude – for conflict points (conflict point location [CPL]) and conflict lines (conflict line starting point [CLSP], conflict line ending point [CLEP]).

The approach suggested here is to collect all of the relevant data on all of the individual conflict events that occur for a particular scenario. The role of the SSAM software is to help the analyst process this list of conflict event data into meaningful information about the surrogate safety of the intersection scenario.

Severity of Conflict and Severity of Resulting Collision

The size of the surrogates TTC, PET, and DR are intended to indicate the severity of the conflict event. This measures how likely a collision would result from a conflict, such that:

  • Lower TTC indicates higher probability of collision.
  • Lower PET indicates higher probability of collision.
  • Higher DR indicates higher probability of collision.

MaxS and DeltaS are used to indicate the likely severity of the (potential) resulting collision if the conflict event had resulted in a collision instead of a near-miss, such that:

  • Higher MaxS indicates higher severity of the resulting collision.
  • Higher DeltaS indicates higher severity of the resulting collision.

Using the mass of the vehicles involved in the conflict, the MaxS and DeltaS values could also be used to calculate momentum values and get a better estimate of the severity of the resulting collision. This would reflect the fact that heavier vehicles can cause more damage than lighter ones. One must be careful, however, since the mix of the traffic stream is an input variable to the simulation. The analyst could reduce the incidence of high-consequence conflict events by reducing the proportion of heavier vehicles in the traffic mix.

Nevertheless, it is important to determine both the severity of the conflict and the severity of the resulting collision. A location with many conflict events of a severity exceeding the thresholds for TTC, PET, and DR, but that are of low severity on the DeltaS and MaxS scales, may not have as high an interest for the analyst in terms of ranking or selecting intersections for safety improvements or further analysis. The resulting crashes in such a case would be more likely to be property damage only when MaxS and DeltaS are low. Locations that may experience fewer total conflict events with very high resulting potential severity (i.e., higher probability of resulting in injury and fatality crashes) are probably of more interest to analysts and engineers deciding how to prioritize safety upgrades among a number of candidate locations.

The next subsections identify the surrogate measures TTC, PET, DR, MaxS, and DeltaS on the conflict point, conflict line, and rear-end conflict line diagrams and specify a procedure for calculations of each.

Surrogate Measures for Conflict Points

Figure 14 illustrates the definitions of the surrogate measures for a conflict point on the same diagram as shown in figure 11.

Time To Collision

TTC is defined uniquely for a conflict point as t4–t3. This is the difference between the encroachment end time of the turning vehicle and the projected arrival time of the through vehicle with the right-of-way at the conflict point if the vehicle had continued at the same speed as at the time of initial deceleration to avoid collision.

Post-Encroachment Time

PET is defined uniquely for a conflict point as t5-t3. This is the time between the departure of the encroaching vehicle from the conflict point and the arrival of the vehicle with the right-of-way at the conflict point.

MaxS

MaxS is first defined for each vehicle independently as the maximum speed of the vehicle between the times t1 and t5. Then the maximum of those two maximum values for each vehicle is recorded as the MaxS value for the conflict point event.

DeltaS

DeltaS is first defined for each time slice (from the beginning to the end of the conflict event) as the difference between the velocity of the two conflicting vehicles. Then the maximum of those DeltaS values for each time slice would be recorded as the DeltaS value.

Initial Deceleration Rate

Deceleration is the evasive action taken by the subject vehicle to avoid the collision. The initial DR would be a useful measure to indicate the potential severity of the conflict event. Acceleration and DRs should be available directly from the simulation model at each time step. On figure 14, the initial DR is the second derivative of curve B at time t2.

Location of the Conflict Point

Noting the latitude and longitude of the conflict point event can indicate particular locations that are risk areas.

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Figure 14. Surrogate measures on conflict point diagram.

Computational Algorithms—Conflict Points

Trigger Condition: Crossing vehicle decides to accept a gap and perform crossing maneuver in front of vehicle with right-of-way. The following situations include conflict points:.

  • Left turn from side street to opposite direction of travel to the right-of-way vehicle.
  • Left turn from opposing direction of vehicle with right-of-way onto side street.
  • Right turn from side street into lane on left-hand side of vehicle with the right-of-way.
  • Left turn from side street to lane on right-hand side of vehicle with the right-of-way in the same direction of travel as the vehicle with the right-of-way.[4]

1.Record:

1.1. Current time step, t1.

1.2. Starting lane number of the encroaching vehicle.

1.3. Approach number of the encroaching vehicle.

1.4. Approach number of the right-of-way approach.

1.5. For a signalized intersection, traffic signal head indications (green, yellow, red) of all approach directions.

2. Compute the conflict point (latitude, longitude) for each lane crossed by the encroaching vehicle based on the projected path to the exiting lane number.

3. Record the CONFLICT POINT LOCATION (CPL) for each lane.

4. For each lane in the opposing direction crossed by the encroaching vehicle, identify:

4.1. Vehicle closest to the encroaching vehicle in that lane.

5. At each time step until the vehicle clears the conflict point for each lane, record for the crossing vehicle:

5.1. Vehicle speed.

5.2. Vehicle latitude and longitude.

5.3. Vehicle acceleration.

5.4. Driver behavior parameters.

6. Record time t3 that encroaching vehicle (rear bumper) clears the conflict point.

7. At each time step until the right-of-way vehicle clears the conflict point for its lane, record for the right-of-way vehicle:

7.1. Vehicle speed.

7.2. Vehicle latitude and longitude.

7.3. Vehicle acceleration.

7.4. Driver behavior parameters.

7.5. Traffic signal head indications (green, yellow, red) of all approaches impacted by the conflict event.

8. Record clearance time t5 of right-of-way vehicle from the conflict point for all vehicles with the right-of-way.

9. For the data recorded for each vehicle with the right-of-way, determine whether the vehicle had a deceleration event.

9.1. If previous step is true, determine whether the deceleration event was because of normal reaction to yellow/red.[5]

9.2. If reaction was not because of normal reaction to yellow/red, determine earliest time of deceleration of that vehicle.

10. Record INITIAL DR.

11. Record time t2.

12. Compute the projected arrival time at the conflict point of the right-of-way vehicle using the velocity at time t2 assuming no deceleration.

13. Record as time t4.

14. Compute TTC as t3-t2. Store as TTC.

15. Compute PET as t5-t2.

16. For each time step between t1 and t5, record the difference in the speed values of the encroaching vehicle and the vehicle with the right-of-way.

16.1. Find the maximum difference of the speed differential and store as DeltaS.

16.2. Find the maximum speed of encroaching vehicle between t1 and t5. Store as Max-s_encroaching.

16.3. Find the maximum speed of the right-of-way vehicle between t1 and t5. Store as Max-s_row.

16.4. Find the maximum of Max-s_encroaching and Max-s_row. Store as MaxS.

17. Determine whether the event has a significantly small enough TTC to be a valid conflict event.

17.1. If TTC < TTC_upper_limit (user determined parameter, e.g., 1.5 s), keep event.

17.2. Otherwise, do not store event data.

Surrogate Measures for Conflict Lines With Merging Flows

Figure 15 illustrates the definitions of the surrogate measures for a conflict line with a merging vehicle from a side street entering the flow in front of a vehicle with the right-of-way.

Time To Collision

As shown in figure 15, TTC is defined at each time step during the conflict line event. This begins when vehicle A begins braking to avoid the collision. At each time step, calculate the time that it would take vehicle A to reach the current location of vehicle B if its velocity remained unchanged from the start of the time period. The minimum of these TTC values is recorded as the TTC for the conflict line event. If the TTC values begin to increase after the first TTC calculation, the first value will be the minimum. If the TTC values begin to decrease, the values must continue to be calculated until they begin to increase. The value at the inflection point is the minimum TTC. If the TTC values begin to decrease and continue to decrease until the leader vehicle leaves the roadway or a maximum reference distance is reached, the minimum TTC value is recorded as the TTC value at the end of the conflict line event.

Post-Encroachment Time

Similar to the TTC, the PET must be recorded as the minimum PET over the conflict line duration. Two PET values are illustrated in figure 15. At each time step, the location of the leading vehicle must be recorded until the vehicles are no longer on a collision course (speed of vehicle B has dropped to zero) or the maximum conflict distance has been reached or the leading vehicle leaves the lane of the following vehicle. For each location recorded for the leading vehicle, the PET is calculated as the time difference between the arrival of the leading vehicle at that location and the arrival of the following vehicle at that location. The minimum PET is then selected from the PETs calculated for each location as the PET recorded for this conflict line event. For the situation shown in figure 15, the minimum PET that would be recorded is PET-1.

MaxS

Similar to the conflict points, MaxS is first defined for each vehicle independently as the maximum speed of the vehicle between the times t1 and t9 (or the time when the vehicles are no longer on a collision course). Then the maximum of the two maximum values for each vehicle is recorded as the MaxS value for the conflict line event.

DeltaS

Identical to the calculation for DeltaS in conflict point events, the DeltaS for conflict line events is first defined for each time slice (from the beginning to the end of the conflict event) as the difference between the velocity of the two conflicting vehicles. Then the maximum of those DeltaS values for each time slice would be recorded as the DeltaS value.

Initial Deceleration Rate

Initial DR is the second derivative of curve A (following vehicle) at time t2. It should be a state variable stored by the simulation model and directly available to be recorded.

Location of the Conflict Line

Noting the latitude and longitude of the start and ending points of the conflict line event can indicate particular locations that are risk areas. Where the conflict stops could be a number of points in the time line. For simplicity, we choose the ending point as the location of the following vehicle where the minimum PET is recorded. The beginning location is the starting point of the encroachment. The resulting line represents the risk area of the conflict occurrence.

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Figure 15. Surrogate measures on conflict line diagram.

 

Computational Algorithms—Conflict Lines for Merging Flows

Trigger Condition: Crossing vehicle decides to accept a gap and enter traffic in same lane as vehicle with right-of-way. The following situation are included in conflict line events:

  • Left turn from side street to same direction of travel as the vehicle with the right-of-way.
  • Right turn from side street into same lane as vehicle with the right-of-way.
  • Vehicle from adjacent lane changing lanes into the current lane in front of vehicle with the right-of-way.

1. Record:

1.1. Current time step, t1.

1.2. Starting lane number of the encroaching vehicle.

1.3. Approach number of the encroaching vehicle.

1.4. Approach number of the right-of-way vehicle.

1.5. For a signalized intersection, traffic signal head indications (green, yellow, red) for all approach directions.

1.6. Vehicle mass values.

1.7. Vehicle ID numbers.

2. Compute the first conflict location (latitude, longitude) for the lane entered by the encroaching vehicle.

3. Record the CONFLICT LINE STARTING POINT (CLSP).

4. For the lane entered by the encroaching vehicle, identify:

4.1. The vehicle closest to the encroaching vehicle in that lane (this vehicle is designated as the right-of-way vehicle).

5. At each time step, until the encroaching vehicle reaches the maximum conflict distance, record for the encroaching vehicle:

5.1. Vehicle speed.

5.2. Vehicle latitude and longitude.

5.3. Vehicle acceleration.

5.4. Driver behavior parameters.

6. At each time step, until the encroaching vehicle reaches the maximum conflict distance, record for the right-of-way vehicle:

6.1. Vehicle speed.

6.2. Vehicle latitude and longitude.

6.3. Vehicle acceleration.

6.4. Driver behavior parameters.

6.5. Traffic signal head indications (green, yellow, red) for all approaches impacted by the conflict event.

7. For the data recorded for the vehicle with the right-of-way, determine whether the vehicle has a deceleration event.

8. If yes, determine whether the deceleration event was because of a normal reaction to yellow/red.[6]

9. If reaction was not because of a normal reaction to yellow/red, determine earliest time of deceleration of that vehicle.

10. Record INITIAL DR.

11. Record time t2.

12. For each time step t between t2 and t9, compute:

12.1. The projected arrival time at the location of the leading vehicle by the right-of-way vehicle using the velocity at time t assuming no deceleration. Record as time t_arrival.

12.2. Compute TTC(t) as t_arrival – t.

12.3. Determine the location in the list of locations for the leading vehicle that the right-of-way vehicle has just passed. Store the time of passage at that location as t_previous.

12.3.1. If no locations have been passed by the following vehicle yet, continue.

12.3.2. Or else, record the PET(t) as t_previous – t.

12.4. Record the difference in the speed values of the encroaching vehicle and the vehicle with the right-of-way as DELTA SPEED(t).

12.5. Record the maximum speed of the two speed values of the encroaching and right-of-way vehicles as MAX SPEED(t).

12.6. Check:

12.6.1. If TTC(t) < TTC(t-1),

12.6.1.1. Save TTC = TTC(t).

12.6.2. If PET(t) < PET(t-1),

12.6.2.1.Save PET = PET(t).

12.6.2.2.Save CONFLICT LINE ENDING POINT (CLEP) = Lat, lon of follower at t.

12.6.3. If MaxSpeed(t) > MaxSpeed(t-1),

12.6.3.1.Save MaxS = MaxSpeed(t).

12.6.4. If DeltaSpeed(t) > DeltaSpeed(t-1),

12.6.4.1.Save DeltaS = DeltaSpeed(t).

12.6.5. If velocity of right-of-way vehicle = 0, stop.

13. Record TTC.

14. Record PET.

15. Record CLEP.

16. Record MaxS.

17. Record DeltaS.

18. Determine whether the event has a significantly small enough TTC to be a valid conflict event.

18.1. If TTC < TTC_upper_limit (user-determined parameter, e.g., 1.5 s), keep event.

18.2. Otherwise, do not store event data.

Surrogate Measures for Rear-End Conflict Lines

Figure 16 illustrates the definitions of the surrogate measures for a conflict line during a rear-end event. Rear-end events describe those conflict lines that occur specifically when the two interacting vehicles are already in the same lane.

Time To Collision

As shown in figure 16, TTC is defined at each time step during the conflict line event. This begins when vehicle A begins braking to avoid the collision. At each time step, calculate the time that it would take vehicle A to reach the current location of vehicle B if its velocity remained unchanged from the start of the time period. The minimum of these TTC values is recorded as the TTC for the conflict line event. If the TTC values begin to increase after the first TTC calculation, the first value will be the minimum. If the TTC values begin to decrease, the values must continue to be calculated until they begin to increase. The value at the inflection point is the minimum TTC. If the TTC values begin to decrease and continue to decrease until the leader vehicle leaves the roadway or a maximum reference distance is reached, the minimum TTC value is recorded as the TTC value at the end of the conflict line event.

Post-Encroachment Time

Similar to the TTC, the PET must be recorded as the minimum PET over the conflict line duration. Two PET values are illustrated in figure 16. At each time step, the location of the leading vehicle must be recorded until the vehicles are no longer on a collision course (speed of vehicle B has dropped to zero) or the maximum conflict distance has been reached or the leading vehicle leaves the lane of the following vehicle. For each location recorded for the leading vehicle, the PET is calculated as the time difference between the arrival of the leading vehicle at that location and the arrival of the following vehicle at that location. The minimum PET is then selected from the PETs calculated for each location as the PET recorded for this conflict line event. For the situation shown in figure 16, the minimum PET that would be recorded is PET-1.

MaxS

Similar to the conflict points, MaxS is first defined for each vehicle independently as the maximum speed of the vehicle between the times t1 and t9 (or the time when the vehicles are no longer on a collision course). Then the maximum of the two maximum values for each vehicle is recorded as the MaxS value for the conflict line event.

DeltaS

Identical to the calculation for DeltaS in the conflict point events, the DeltaS for the conflict line events is first defined for each time slice (from the beginning to the end of the conflict event) as the difference between the velocity of the two conflicting vehicles. Then the maximum of those DeltaS values for each time slice would be recorded as the DeltaS value.

Initial Deceleration Rate

The initial DR is the second derivative of curve B (following vehicle) at time t2. It should be a state variable stored by the simulation model and directly available to be recorded.

Location of the Conflict Line

Noting the latitude and longitude of the starting and ending points of the conflict line event can indicate particular locations that are risk areas. Where the conflict stops could be a number of points in the time line. For simplicity, we choose the ending point as the location of the following vehicle where the minimum PET is recorded. The beginning location is the starting point of the encroachment. The resulting line represents the risk area of the conflict occurrence.

Click to view alternative text

Figure 16. Surrogates identified on rear-end line diagram.

Computational Algorithms—Rear-End Conflict Lines

Trigger Condition: Vehicle B is following vehicle A in the same lane. The following situations are included in rear-end conflict line events:

  • Vehicle A turns left from the main travel direction in front of the following vehicle B.
  • Vehicle A turns right from the main travel direction in front of the following vehicle B.
  • Vehicle A performs unexpected sudden braking to avoid collision and/or react to red/yellow.

1.Record:

1.1. The current time step, t1.

1.2. Lane number of the vehicles.

1.3. Approach number of the vehicles.

1.4. Intended movement of vehicle A (left, right, diagonal).

1.5. For a signalized intersection, traffic signal head indications (green, yellow, red) for all approach directions.

1.6. Vehicle mass values.

1.7. Vehicle ID numbers

2.Compute the first conflict location (latitude, longitude) for the leading vehicle.

3.Record CLSP.

4.For the leading vehicle, identify:

4.1. The vehicle closest to the encroaching vehicle in that lane (this vehicle is designated as the following vehicle).[7]

5. At each time step, record for the leading vehicle, until the leading vehicle:

  • Reaches the maximum conflict distance,
  • Performs the turning maneuver, or
  • Comes to a complete stop,

    5.1. Vehicle speed.

    5.2. Vehicle latitude and longitude.

    5.3. Vehicle acceleration.

    5.4. Driver behavior parameters.

6. At each time step, until the leading vehicle reaches either of the conditions in the previous step, record for the following vehicle:

6.1. Vehicle speed.

6.2. Vehicle latitude and longitude.

6.3. Vehicle acceleration.

6.4. Driver behavior parameters.

6.5. Traffic signal head indications (green, yellow, red) of all approaches impacted by the conflict event.

7. For the data recorded for the following vehicle, determine whether the vehicle had a deceleration event.

7.1. If yes, determine whether the deceleration event was because of normal reaction to yellow/red.[8]

7.2. If reaction was not because of normal reaction to yellow/red, determine earliest time of deceleration of that vehicle.

8. Record INITIAL DR.

9. Record time t2.

10. For each time step t between t2 and t9, compute:

10.1. The projected arrival time at the location of the leading vehicle by the following vehicle using the velocity at time t assuming no deceleration.

10.2. Record as time t_arrival.

10.3. Compute TTC(t) as t_arrival – t.

10.4. Determine which location in the list of locations for the leading vehicle that the following vehicle has just passed.

10.5. Store the time of passage at that location as t_previous.

10.5.1. If no locations have been passed by the following vehicle yet, continue.

10.5.2. Or else, record the PET(t) as t_previous – t.

10.6. Record the difference in the speed values of the leading vehicle and the following vehicle as DeltaS(t).

10.7. Record the maximum speed of the two speed values of the leading and following vehicles as MaxS(t).

10.8. Check:

10.8.1. if TTC(t) < TTC(t-1),

10.8.1.1.Save TTC = TTC(t).

10.8.2. If PET(t) < PET(t-1),

10.8.2.1. Save PET = PET(t).

10.8.2.2.Save CLEP = Lat, lon of following vehicle at t.

10.8.3. If MaxSpeed(t) > MaxSpeed(t-1),

10.8.3.1.Save MaxS = MaxSpeed(t).

10.8.4. If DeltaSpeed(t) > DeltaSpeed(t-1),

10.8.4.1.Save DeltaS = DeltaSpeed(t).

10.8.5. If velocity of following vehicle = 0, stop.

11. Record TTC.

12. Record PET.

13. Record CLEP.

14. Record MaxS.

15. Record DeltaS.

16. Determine whether the event has a significantly small enough TTC to be a valid conflict event.

16.1. If TTC < TTC_upper_limit (user-determined parameter, e.g., 1.5 s), [9] keep event.

16.2. Otherwise, do not store event data.

Summary

Surrogate measures from simulation models are proposed to estimate the comparative safety effect of different intersection alternatives. Definitions and computational algorithms for surrogate measures were presented in this section for:

  • Conflict points.
  • Conflict lines with vehicles merging into the same lane.
  • Conflict lines for vehicles following one another in the same lane.

The surrogates TTC and PET measure the severity of the conflict event and the MaxS, DeltaS, and DR measure the severity of the potential collision that would ensue if, in fact, the vehicles collided. Conflict points have unique definitions of TTC and PET. Conflict lines and rear-end lines require a search for the minimum TTC and PET over the duration of the conflict event (e.g., for all locations on the conflict line). The next section specifies what the event file output from the simulation models could look like to support surrogate safety analysis.


[2] The percent of crashes that are coded as "other" and "unknown" crashes are shown between parentheses (12). back

[3] Some representation of snow and rain can be included by modifying the driver behavior parameters—desired following distance, speed, reaction times, and vehicle performance variables. However, representation of reduced visibility, skidding, etc. could not be modeled adequately by modifying behavior parameters. back

[4] Note that multiple combinations of A through D can occur in the same maneuver. back

[5] The braking of the right-of-way vehicle could be incidental to the gap acceptance of the encroaching vehicle. In the real world, this is quite common with drivers that anticipate the onset of yellow by watching the DON’T WALK indications change from flashing to solid. back

[6] See previous footnote. back

[7] Terms of "encroaching" and "right-of-way" are replaced with "leading" and "following" since, in a rear-end conflict event, the fault can be placed on either driver, or both (failing to signal and/or following too closely). back

[8] As with footnotes 3 and 4, the following vehicle could react to the signal indication independent of closely following the leading vehicle and create a conflict event that is because of behavioral parameters alone. Some combination of phasing strategy and geometry must contribute to the frequency of rear-end conflict events for a valid comparison between alternatives. back

[9] Automated intelligent cruise control (AICC) research (84) indicates that humans remain safe in high-speed car-following experiments at a TTC of 3.5 s without warning systems and 2.6 s with warning systems. (85) has reported lower critical TTC values at intersection approaches of 1.5 s, primarily because of the slower speeds (49). back

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