Predicting STOP-Sign Compliance at All-Way Stop Intersections in Close Proximity to Signalized Intersections

STOP-signs (at unsignalized intersections) that are in close proximity to signalized intersections are often violated by drivers while “speeding up” to go through the upstream or downstream signalized intersection that have the green interval upon approach. It is thought that if the distance between the upstream or downstream signalized and the AWSC intersection is long, drivers usually comply with the STOP signs at the AWSC intersection. This research determined driver compliance rates (CRs) at All-Way STOP Control (AWSC) intersections that are in close proximity to upstream or downstream signalized intersections and, explored the existence of a relationship between CR and the distance between a pair of signalized and AWSC intersections. Thirty (30) isolated segments with combinations of signalized and AWSC intersections in the District of Columbia were selected for the study. Field data (traffic volumes) were obtained at each intersection in addition to observation of driver compliance with STOP signs at AWSC intersections via video playback. In all, 13,956 observations were made at 57 AWSC intersections in 2017. The study showed that lower CRs were observed at AWSC intersections that are in closer proximity to the signalized intersections. Thus, the shorter the distance from the existing AWSC to signalized intersections, the lower the CR (or higher violation rate). Based on the data obtained, a non-linear relationship between CR and distance between pairs of intersections was developed. From the model, to achieve a minimum compliance rate of 95% at an AWSC, an optimal distance of approximately 1,300 feet between the intersections

INTRODUCTION Most intersections in urban areas are either signalized or unsignalized (STOP or YIELD-Controlled). As a result road segments in such areas have a combination of both types of intersections. In order to ensure safety of drivers and pedestrians, it important for drivers to comply with traffic control devices. While compliance with traffic signals is relatively high, compliance with STOP signs is relatively low, especially for unsignalized intersections that are close to those signalized. Drivers often violate STOP signs in order to travel through the next signalized intersection that may have the green interval on approach.
This research explores the existence of a relationship between STOP sign compliance rate and the distance between an AWSC and a signalized intersection (downstream or upstream). Thirty segments with combinations of signalized and AWSC intersections in an urban area (Washington DC) were selected for this study. Each segment consisted of at least two signalized and one AWSC intersections. STOP sign compliance was observed via video playback during the off-peak period (10:00AM to 1:00PM) based on which the compliance rate (CR) at each AWSC intersection was then computed. A model was then developed to predict CR based on the distance between AWSC and upstream or downstream signalized intersections.
2. LITERATURE REVIEW Traffic flow interruptions are most likely to originate at or near intersections. Ideally, it is recommended that the minimum spacing for intersections in urban areas is 0.5 miles [1]. However, in some urban areas, intersections are much more closely spaced since there are often competing needs for providing land access. When access to an intersection is regulated by traffic signals or regulatory signs, it said to be controlled, while it is uncontrolled when access is regulated by the right-of-way rules. Controlled intersections are either signalized or unsignalized. Signalized intersections are controlled by traffic lights while unsignalized intersections are controlled by either STOP signs or yield signs. The STOP signs are installed either on the minor-roads only (Two-Way STOP control-TWSC) or on all approaches (All-Way STOP control-AWSC). Roadway networks in dense urban areas consist of combinations of signalized and unsignalized intersections which may affect throughput and may have safety implications. The Federal Highway Administration (FHWA) reported that since 2005, there has been a decline in the overall number of crashes that occur at or in close proximity to intersections [2]. Nevertheless, crashes at intersections are still a major concern for traffic authorities.  [5].
In 2017, Mahadiow investigated drivers' compliance at AWSC intersections in close proximity to signalized intersections. Drivers' compliance was observed at eight AWSC intersections that were at most 600 feet away to an upstream/downstream signalized intersection. Higher compliance rates were observed for vehicles which were heading towards the signalized intersections than vehicles moving away from the signalized intersections. The study further established a linear relationship between drivers' compliance and distance between the intersections [6].

Factors influencing non-compliance at signalized intersections
Non-compliance is not limited to only unsignalized intersections. In 1986, Gordon and Robertson studied the cause of driver noncompliance at twelve (12) signalized intersections in the Washington, D.C., metropolitan area.
The study further sought to define a relationship between noncompliance, intersection operational characteristics (traffic volumes) and roadway features such as number of approach lanes, traffic signal location, intersection jurisdiction and primary land use. Violations were observed for vehicles making left, through and right turn movements at the intersections. About 380 observations were made at each intersection. The results showed that higher violations occurred at intersections with low traffic volumes. Also, most violations occurred during the off-peak periods. The highest number of violations was recorded for vehicles making right turn at intersections where right turn on red is permitted. Violating drivers usually failed to come to a complete stop before turning right. Fewer vehicles were observed making through and left turn movements on red signal. Overall, an average of 1.25 violations occurred for every 100 vehicles entering an intersection [7]. In 2010, Elmitiny investigated how certain variables affect a driver's decision to stop or go on a red-light, at signalized intersections. The variables used included distance of the vehicle from the STOP bar, approach speed, yellow interval entry time, whether the vehicle was in the lead or following position, lane position, and vehicle type. The study intersection was located on a high-speed corridor located in a suburb in Central Florida. Data was collected using a threecamera-video-based system which recorded drivers' behavior associated with traffic signal change. A total of 1,292 vehicle observations were made. The results of the statistical analysis showed that the speeds of vehicles significantly affected drivers' decision to stop or go. Vehicles which approached the intersection at higher speeds were more likely to violate the red light. Also, the probability of a stop decision increased as the distance of the vehicle from the STOP line increased. Drivers within 280 feet to 320 feet from the intersection had probabilities of both stop and go decisions close to 50%. This implies that vehicles within this interval showed the largest variability in their decision to stop or go during the yellow interval. Also, 90% of red-light-violators were within the 210 feet to 480 feet range of the intersection [8].
In 2013, Chuanyun et al also examined the contributing factors affecting compliance of traffic signs and signals. The study concluded that at signalized intersections, incoming drivers are usually puzzled whether to speed up or slow down when the traffic signal changes from green to yellow. If they are far from the traffic signal, they tend to speed through the intersection and this may lead to a traffic signal violation. If they suddenly slow down, it may result in rearend collision [9].

Countermeasures for Traffic Control Signals and STOP Sign Violations
Various measures have been tested to mitigate the violation of traffic signals and STOP signs. In 2009, Rice and Polanis showcased low-cost plans to improve safety at four STOPcontrolled intersections in Winston-Salem, North Carolina. Various measures were taken to improve visibility and pavement markings at the intersections. These included the replacement of existing 24-inch STOP signs with 30-inch STOP signs, installing "STOP AHEAD" signs before the STOP signs, and providing double yellow centerlines and stop bar pavement markings. This treatment reduced crashes by 56.7% and improved throughput [10].
Recently, advanced techniques including the use of infrastructure and vehicle-based collision avoidance systems are being implemented to increase compliance, thereby improving safety. These systems utilize roadway sensors, processors, warning devices, roadside-vehicle communication devices and other informational and warning devices to provide driving assistance to road users. Currently, connected vehicle-based approaches are being proposed to improve safety at intersections. These technologies enable the real-time sharing of vehicle data such as position, speed and acceleration [11]. The body of literature suggests that the factors which affect violations of STOP signs mainly include traffic volumes on the major roadway and socio-demographic and physical attributes such as gender, age, number of passengers, as well as the presence of law-enforcement. Also, though the literature shows that distance between CR at an AWSC intersection varies based on the distance to an adjacent signalized intersection, the existence of a non-linear relationship between CR and the distance between a pair of signalized and AWSC intersections is yet to be explored. This research therefore seeks to examine the existence of such a relationship by analyzing data collected over a wider range of locations than previous research.

Selection of Study Segments
A total of thirty (30) segments located on arterial and collector roads were selected in the District of Columbia for this study. Each segment consists of at least two signalized intersections and one AWSC intersection. The segments are such that no two signalized intersections are successive with at most two AWSC intersections in between. A typical segment configuration is presented in Figure 1.

Data Collection
Field data collection was conducted at the thirty (30) selected segments on typical weekdays (Tuesday, Wednesday and Thursday) from April 2017 through December 2017. In the event that road maintenance or construction was ongoing at any of the intersections, the data collection was deferred until it was completed. The data collection was conducted via video recordings. Video recording cameras were installed at the STOP controlled intersections which are adjacent to the signalized intersections. The video recordings were conducted on typical weekdays (Tuesday, Wednesday and Thursday) over a twelve (12) hour duration from 6:30 AM to 6:30 PM. The following data/information associated with intersection traffic operations were obtained:

a. Vehicular Volumes
The volume of vehicles travelling upstream or downstream toward the signalized intersections during the off-peak period from 10:00AM to 1:00PM, were extracted from video playbacks. The volume counts were conducted using JAMAR count boards which were downloaded and processed.

Data Analysis
A compliance rate (CR) analysis was conducted to obtain parameters for further statistical analyses. The CR for each of the selected AWSC intersections that were in close proximity to the upstream or downstream signalized intersections were computed using the following equation:

Compliance Rate = VC/TV 100
Where VC = Number of vehicles in compliance, i.e., those that completely stopped before proceeding through the intersection, and TV = Total number of vehicles going through the intersection on the same approach

Statistical Analysis
Descriptive statistics such as the mean, median, and standard deviation, were computed for CR and distance between successive signalized and unsignalized intersections located within the selected segments of study.

Model Development
To determine whether there exists a relationship between the distance between an AWSC intersection and an upstream or downstream signalized intersection, and the compliance rate (CR), a non-linear model was determined to assume the following form: CR= Compliance Rate (%).

D = Distance between signalized and AWSC intersections (ft)
The value k0 is the model constant and k1 and k2 are the model coefficients with an associated error of ε [ε ~ N (0, σ 2 )]. The form of the model was the result of several data transformations since the data was determined not to follow the normal distribution. A scatter plot of CR and D showed no issue with heteroscedasticity.

Statistical Analysis
The summaries of the descriptive statistical analysis for the CR, and distance between successive signalized and unsignalized intersections located within the selected segments of study were computed and are presented in Table  1. The reported descriptive statistics are the mean, median, standard deviation and 95% confidence interval. From the table, it can be observed that the mean compliance rate was 69.84 %, with a standard deviation of 10.53%. The highest and lowest observed compliance rates were 92.27 % and 55.00 % respectively. Also, the mean distance between consecutive signalized and unsignalized intersections was 461.15 feet with a standard deviation of 169.82 feet. The highest and lowest distances measured were 885 feet and 142 feet respectively.

Model Development
An analysis was conducted to determine the existence of a relationship between the distance between an AWSC intersection and signalized intersection and the CR. A model was then developed to predict the CR based on the distance. The model was assumed to take the form: The results in Table 2 show the estimates of the model coefficients. The coefficients k0, k1 and k2 were estimated to be 99.99, -66.90 and -0.002 respectively. Also, the R 2 value of 0.738 shown in Table 3 indicates that the model explains a high percentage (73.8%) of the variance in the data.

Model Tests Residual Plots
For a statistically significant model, the residuals would approximate the random errors that establish the relationship between the explanatory variables and the response variables. Therefore, if the residuals appear to behave randomly, it suggests that the model fits the data well. Figure  2 is the residual plots for the model. The plot shows evenly distributed random plots, which confirms that the model appears to fit the data set well. Thus, it can be concluded that the model adequately predicts compliance rate based on the distance between successive AWSC and signalized intersections.

DISCUSSION
The study focused on improving compliance at AWCS by attempting to develop a model that could define the optimal distance of AWSC intersections from signalized intersections that could result in a relatively high rate of compliance. The study used 30segments that had AWSC intersections and signalized intersections upstream or downstream. The compliance observations were conducted via video playback for data compiled over a 6-months period. Other field data collected include traffic volumes entering the AWSC intersections and the distance between the upstream and/or downstream signalized intersections and the AWSC intersections. In all 13,956 compliance observations were made. In addition, the minimum and maximum distances between the AWSC intersections and the signalized intersections were respectively 142 feet and 885 feet. The maximum compliance rate was determined to be approximately 92% and the minimum was 55%. A model was then developed that predicts the compliance rate based on the distance from the upstream/downstream signalized intersection. The model had an R 2 value of 74%. The model also had a margin of error of 6.1%. Based on this study, it can be concluded that the closer the AWSC intersection is to the upstream/downstream signalized intersection, the lower the CR. From the model, it can be deduced that to attain a CR of 95% at an AWSC intersection, it should be approximately 1,300 feet away from the upstream or downstream signalized intersection. Drivers generally tend to "speed through" AWSC intersections if the signalized intersection on approach has a green interval, thereby violating the STOP sign.

CONCLUSIONS
The study revealed that there exists a strong relationship between the CR at AWSC intersections that are adjacent to signalized intersections and the distance between the two intersections. Lesser CR were reported at AWSC intersection with shorter distances to the next signalized intersection. In addition, the proposed model has a high explanatory power on the observed data. The model can therefore accurately predict the CR at AWSC intersections based on the distance between the AWSC and adjacent signalized intersections in Washington DC. This model may not be applicable to other jurisdictions since driver behavior in Washington DC may differ from other urban jurisdictions. The study used 30 segments with different functional classifications and with distances of AWSC intersections less than 1,000 feet from next signalized intersections. Thus, future work may include validation of the model using field data, development of CR models for specific functional classification segments and including segments that have AWSC intersection distances of more than 1,000 feet from the next signalized intersections. 7. ACKNOWLEDGEMENT