1. Modeling Freeway Crashes Using Lane-Specific Artificial Traffic Data
Dr. Zhi Chen (UW-Milwaukee)
Dr. Xiao Qin (UW-Milwaukee)

2. Outline Background Problem Statement Research Objectives Methodology
Case Study
Conclusions

3. Background
Traditional safety improvements, though effective, are reactive and restrictive.
With the aid of emerging technologies, proactive and flexible crash preventive techniques have rapidly progressed.
The changes in traffic flow observed from inductive loop detectors (ILD) present important cues to crash detection.
Real-time crash prediction models (RTCPM) have been developed to identify traffic conditions pertinent to crashes.
Traditional safety improvements are effective such as installing traffic signal at intersections and putting speed bumps on the ground. However, they are reactive because they are often implemented after crashes have happened. They are restrictive because they cannot adjust promptly to a changing traffic.
New technologies have emerged such as advanced traffic monitoring system, connected vehicles (CV. These emerging technologies have led to the development of dynamic and proactive crash prevention techniques.
Among various emerging technologies, inductive loop detectors (ILD) are widely used to monitor the traffic. ILD can record the changes in traffic flow which can be used to detect crash-prone conditions.
With real-time traffic data collected from inductive loop detectors (ILD) near the prospective crashes, real-time crash prediction models (RTCPM) have been developed to identify traffic conditions that could lead to the crash.
However, there are some issues in previous real-time crash studies.

4. Problem Statement
The ILD data, the primary data source of predictive analysis, are often compromised by the spatial and temporal consistency issues;
A big limitation in previous studies is that as the primary data source, the ILD data is compromised by two issues, spatial consistency and temporal consistency issues.
What are these two issues?

5. Spatial Consistency Issue
Unevenly Distributed
Close and Uniform
Distant and Uniform
The spatial issue is related to the layout of ILD stations.
Close and uniform layout is desirable, but it’s very rare in reality. Distant and uniform layout is also rare. The most common case is unevenly distributed spacings between stations.
The spacing between ILDs varies substantially from site to site. It leaves limited quality control on traffic data of crashes that occur between detectors. Therefore, questions arise regarding the consistency and transferability of findings in different studies.

6. Temporal Consistency Issue
Crash Prevention
Past 5-min Period
Future 5-min Period
Now
Hypothesized Crash Time
Here I present an example.
For crash prediction, this is the current moment, and what we have now is the data in the past 5-min period.
Because preventive actions may take extra time, we need to leave some buffer time. So we predict the crash risk 5 min from now and leave 5 min for taking preventive actions.
In crash modeling, we have two intervals, 5-10-min and 0-5-min before the crash. We can see that the past 5-min period corresponds to the 5-10-min period and the future 5-min period corresponds to the 0-5-min period.
Since we’re using past 5-min period to predict the crash risk, we need to use the 5-10-min period for crash modeling.
However, studies have shown that traffic data in 0-5-min period may be more associated with the crash occurrence.
Crash Modeling
5-10-min Period
0-5-min Period
Crash Time

7. Research Objectives
Have conducted predictive analysis using simulated traffic data from the output of traditional cell transmission models (CTM) to account for the spatial and temporal consistency issues of ILD traffic data (Chen and Qin, 2018);
Extend predictive analysis by using simulated lane-specific traffic data from a lane-specific CTM (LSCTM);
This study extends the previous study by using simulated lane-specific traffic data from a lane-specific CTM. I’ll give more details of these models very soon.

8. Data Sources Inductive Loop Detector (ILD) Traffic Data Crash Data
Regarding data sources, a sample of ILD traffic data and crash data are shown here.
This is 1-min ILD data. It records the volume, speed and occupancy of vehicles passing over the ILD in every 1-min interval.
This is crash data. The two most important pieces of information are the crash time and location. These two fields show the date and time of the crash, and these two fields show the latitude and longitude of the crash location.

9. Cell Transmission Model
Cell Transmission Model (CTM) is a macroscopic traffic simulation model proposed by Daganzo (Daganzo, 1994) based on solid traffic flow theory.
CTM can capture many important traffic phenomena including queue formation and dissipation as well as shockwave propagation.
CTM operates sufficiently with aggregated traffic data from detector stations.
Next I’ll introduce the cell transmission model (CTM).
CTM is a macroscopic traffic simulation model proposed by Dr. Daganzo based on very solid traffic flow theory.
It can capture many important traffic phenomena including queue formation and dissipation as well as shockwave propagation.
Compared with microscopic simulation models, CTM is more computationally efficient and easier to configure and calibrate. Moreover, aggregated data from ILD is sufficient for CTM to operate.

10. Traffic Evolution in CTM
This figure shows how the traffic evolves in CTM. A roadway segment is divided into multiple cells, and the traffic in each cell changes based on the number of vehicles in the cell, the entering flow, number of vehicles that enter the cell and the leaving flow, number of vehicles that leave the cell.

11. Traffic Flow in Lane-Specific CTM (LSCTM)
Difference from traditional CTM (Pan et al., 2016):
Heterogeneous traffic across lanes;
Lane-change activities.
In this study, we use a extended version of CTM, lane-specific CTM (LSCTM).
This figure shows the traffic flow in LSCTM. A cell includes several lanes.
For lane m, m-1 is its left lane and m+1 is its right lane. Traffic flow from one lane can travel into the same lane and its adjacent lanes of the next cell.
In traditional CTM, all lanes in the same cell operate together and have homogenous traffic across lanes.
But in LSCTM, each lane operates independently.
Therefore, the traffic is heterogenous across lanes, and lane-change activities can be modeled in LSCTM.

12. Lane-Change Model: probability and key variables
Discretionary lane-change (DLC): to gain speed advantage only
Mandatory lane-change (MLC): to reach the target turning point (e.g., off-ramp, accident, lane drop)
Two lane-change types are modeled in LSCTM: discretionary lane-change (DLC) and mandatory lane-change (MLC).
DLC is executed to gain speed advantage only, and MLC is executed to reach the target turning point, for example, to exit the off-ramp, avoid the lane blockage due to accidents or accommodate the lane drop.
There are several crucial components of LSCTM.
The lane-change probability varies by type. The DLC probability is related to speed difference between two lanes.
The MLC prob. Depends on the distance to the turning point. There are two important distances, xr is the remote distance and xc is the critical distance
Before reaching Xc, the MLC probility increases as it approaches the turning point until the prob. Becomes 1 when the car passes Xc as the MLC is very urgent.
Whether DLC and MLC can be made depends on the required gap size and actual gap size in the target lane. And required gap size varies by the distance from xr and xc.

13. Merge and Diverge of Traffic
Received Demand
Sending
Demand
The LSCTM needs to consider the merge and diverge of traffic in different lanes.
One lane in one cell can receive the straight-moving traffic from the same lane and lane-change traffic from its adjacent lanes in its previous cell.
And the traffic in it would diverge into its connected lanes in the next cell.

14. Case Study
A 4.15-mile corridor on I-94; 113 crashes and 2,260 non-crash cases (1:20 ratio) in ;
Real-time ILD traffic data from stations; and weather information.
The corridor was divided into mi cells with 42 virtual detector stations
Lane-specific fundamental diagram is calibrated with filed data
Parameters were set based on previous literatures (Laval & Daganzo, 2006; Pan et al., 2016; Yang & Koutsopoulos, 1996)
First, the study site is a 4.15-mile corridor on I-94 in Wisconsin.
The crash dataset includes 113 crashes that happened on this corridor in , and 2,260 non-crash cases were collected to achieve a 1:20 crash to non-crash ratio.
Crash cases are traffic conditions before the crash occurrence, while non-crash cases are normal conditions that are not associated with crashes.
Real-time traffic data was collected from seven ILD stations along this corridor.

15. Candidate Variables Traffic variables: Non-traffic variables: Upstream
Average and standard deviation of flow, speed, and density at upstream and downstream virtual stations that are 0.2-mile away;
Traffic state:
Non-traffic variables:
Presence of horizontal curve, on-ramp, off-ramp
Weather factors: snow, rain
Upstream
Free-flow
Congested
Downstream
Free-flow (FF)
Bottleneck front (BN)
Back of queue (BQ)
Congestion (CT)
Candidate variables used to develop crash models include traffic variables and non-traffic variables.
Traffic state is determined by upstream and downstream traffic. There are four traffic states, FF, BN, BQ, CT.

16. Results Variable Description Estimate Standard Error P-value Intercept
-4.154
0.380
<0.001 BN
State: Bottleneck
2.208
0.611 BQ
State: Back of queue
1.042
0.506
0.040 CT
State: Congestion
3.305
0.766
FF× AvgDenu
Average upstream density
0.043
0.015
0.004
FF× Snow
Snow indicator
1.088
0.493
0.027
BQ× StdSpdd
Standard deviation of downstream speed
0.133
0.049
0.007
CT× AvgDenu
0.008
0.035
CT× AvgSpdd
Average downstream speed
-0.034
0.011
0.003
This table shows the modeling results. We can see that different traffic states present different contributing factors.

17. Conclusions
The lane-specific CTM (LSCTM) is able to simulate lane-specific traffic data by considering heterogenous traffic across lanes and lane-change activities;
Lane-specific simulated data by LSCTM based on a uniform and close station layout did not provide better prediction performance compared to physical data from unevenly distributed stations;
It still presents a viable alternative to utilizing macroscopic traffic simulation for safety analysis and evaluation.

18. Thank you!

19. Fundamental Diagram

20. Weights of Movements
DLC
MLC
Straight-moving 1

21. MLC Rule

22. Density Evolvement
Overall Density
MLC Demand Density

23. Loop Detector Data for Crash Modeling8 1
Upstream Station
Downstream Station 7 5
Based on the crash time and location, the related ILD data can be collected for crash modeling.
the nearest upstream and downstream ILD stations can be determined. The downstream means the direction of the traffic flow, and upstream means the opposite direction.
and the traffic data from those stations before the crash occurrence can be used to develop the crash prediction model. … 8

24. Lane-Change Probability
DLC
MLC
There are several crucial components of LSCTM.
This figure shows that this car is driving in Lane beta at time step k with speed. The speed in the adjacent lane, Lane m, is X.
There are two important distances, xr is the remote distance and xc is the critical distance.
The lane-change probability varies by type. The DLC probability is related to the difference in the speed of the subject lane and target lane. For example, the DLC prob. From L2 to L3 is only related to the difference between v2 and v3.
The MLC prob. Depends on the distance to the turning point. Before reaching Xc, the MLC probility increases as it approaches the turning point until the prob. Becomes when the car passes Xc as the MLC is very urgent.

25. Lane-Change Required Minimum Gaps
Available Gap
DLC
Whether one car can successfully make the lane change depends on its required minimum gap and available gap in the target lane.
First, the available gap in the target lane is the average available space within one cell after excluding the total spaces occupied by vehicles in that cell.
The minimum gap for DLC is only related with the speed difference between the yellow car and two read cars, and it does not change over distance.
On the opposite, the minimum gap for MLC changes over space. Before reaching the remote distance, the MLC is not urgent the minimum gap is same as that for DLC. After that, the MLC is moderately urgent and the size decreases as the driver is willing to accept smaller gaps. After reaching the critical distance, the MLC is very urgent, and the deriver is even willing to accept a very small gap.
Then these gaps are normalized by the vehicle length, where Lp is the length of a passenger car.
MLC

26. Sending Demand DLC MLC Straight-moving
Based on the lane-change probability, the sending demand can be obtained. Note that if the required minimum gap for DLC or MLC is larger than the available gap, then there would be no DLC or MLC demand.
Straight-moving

27. Weighted Traffic Demand
Straight-moving
Flow Demand
DLC Demand
MLC Demand
DLC Weight
MLC Weight
Since DLC and MLC requires larger gaps than the straight-moving traffic, normalized gaps are assigned as the weights of the DLC and MLC demand and a weighted traffic demand is obtained.

28. Actual Received Demand
DLC
MLC
Then actual received demand of Cell I, lane m can be calculated by these formulas.
Then the traffic of each cell can evolve.
Straight -moving

29. Data A 4.15-mile corridor on I-94 in Wisconsin;
113 crashes and 2,260 non-crash cases (1:20 ratio) in ;
Real-time ILD traffic data from stations; and
Historical weather information.
First, the study site is a 4.15-mile corridor on I-94 in Wisconsin.
The crash dataset includes 113 crashes that happened on this corridor in , and 2,260 non-crash cases were collected to achieve a 1:20 crash to non-crash ratio.
Real-time traffic data was collected from seven ILD stations along this corridor.
Historical weather information was also collected.

30. Prediction Performance
Model
Area Under Curve
LSCTM (Model V)
0.66
Physical (Model P)
0.81
Lane-specific simulated data by LSCTM based on a uniform and close station layout did not provide better prediction performance compared to physical data from unevenly distributed stations, possibly due to inaccurate simulated traffic data as many parameters were not fine-tuned with field data.
Despite this, this study still presents an alterative method to apply macroscopic traffic simulation for safety analysis and evaluation.

31. References
Chen, Z., & Qin, X. (2018). A novel method for imminent crash prediction and prevention. Accident Analysis & Prevention.
Daganzo, C. F. (1994). The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B: Methodological, 28(4),
Laval, J. A., & Daganzo, C. F. (2006). Lane-changing in traffic streams. Transportation Research Part B: Methodological, 40(3),
Pan, T., Lam, W. H., Sumalee, A., & Zhong, R. (2016). Modeling the impacts of mandatory and discretionary lane-changing maneuvers. Transportation Research Part C: Emerging Technologies, 68,
Yang, Q., & Koutsopoulos, H. N. (1996). A microscopic traffic simulator for evaluation of dynamic traffic management systems. Transportation Research Part C: Emerging Technologies, 4(3),