Journal of Safety Research 51 (2014) 33–40

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A speed limit compliance model for dynamic speed display sign Anam Ardeshiri ⁎, Mansoureh Jeihani 1 Department of Transportation and Urban Infrastructure Studies, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA

a r t i c l e

i n f o

Article history: Received 14 June 2013 Received in revised form 2 February 2014 Accepted 19 August 2014 Available online 10 September 2014 Keywords: DSDS Speed limit Speed compliance Bayesian network

a b s t r a c t Introduction: Violating speed limits is a major cause of motor vehicle crashes. Various techniques have been adopted to ensure that posted speed limits are obeyed by drivers. This study investigates the effect of dynamic speed display signs (DSDSs) on drivers’ compliance with posted speed limit. Method: An extensive speed data collection upstream of, adjacent to, and downstream of DSDS locations on multiple road classes with different speed limits (25, 35, and 45 mph) was performed short-term and long-term after DSDS installation. Conventional statistical analysis, regression models, and a Bayesian network were developed to assess the DSDS’s effectiveness. Results’ conclusions: General compliance with speed limit (upstream of the DSDS location), time of day, day of week, duration of DSDS operation, and distance from the DSDS location were significantly correlated with speed limit compliance adjacent to the DSDS. While compliance with the speed limit due to the DSDS increased by 5%, speed reduction occurred in 40% of the cases. Practical applications: Since drivers were likely to increase their speed after passing the DSDS, it should be installed on critical points supplemented with enforcement. © 2014 National Safety Council and Elsevier Ltd. All rights reserved.

1. Introduction While variable message signs (VMSs) have been used for informational and advisory purposes in an intelligent transportation system (ITS) context, for example, to notify drivers about traffic conditions or hazards ahead, radar attachment allows the signs to detect and post vehicles' speeds (Garber & Patel, 1994). Radar-controlled VMSs are referred to as dynamic speed display signs (DSDSs). Usually aligned with the posted speed limit sign, the DSDS displays the approaching vehicle's speed as a reminder to the driver. DSDSs differ from variable speed limit (VSL) signs which show different speed limits at different times or locations (e.g., severe weather conditions, or work zones). The literature on the effectiveness of DSDSs in managing speed and improving traffic safety has reached differing conclusions for the short-term and long-term. Bloch (1998) stated that supplementing the DSDS with police enforcement significantly increased the sign's effectiveness for the short-term. However, average vehicular speeds were observed to return to pre-DSDS levels after four months in sharp horizontal curves and high-speed approaches of signalized intersections (Ullman & Rose, 2005). Although the DSDS decreased the mean speed for the first two weeks of operation, its effectiveness deteriorated over time, especially after removal (Cruzado & Donnell, 2009; Poulter & McKenna, 2005; Walter & Broughton, 2011; Walter & Knowles, 2008). ⁎ Corresponding author. Tel.: +1 443 885 4734; fax: +1 443 885 8324. E-mail addresses: [email protected] (A. Ardeshiri), [email protected] (M. Jeihani). 1 Tel.: +1 443 885 1873; fax: +1 443 885 8324.

http://dx.doi.org/10.1016/j.jsr.2014.08.001 0022-4375/© 2014 National Safety Council and Elsevier Ltd. All rights reserved.

Admitting the limited effectiveness of the DSDS long-term, Walter and Knowles (2008) proposed a DSDS rotation program to maintain and even improve safety gains. While some researchers used DSDSs as passive informational devices that simply displayed the road speed limit and the speed of passing vehicles (e.g., Bloch, 1998), others used them to warn speed violators via messages such as “excessive speed” and “slow down” (e.g., Garber & Srinivasan, 1998). Several researchers concluded that DSDSs had a considerable effect in work zones in reducing speeds higher than the speed limit (Garber & Patel, 1994; McAvoy, 2011). DSDSs have also demonstrated continuous positive effects in school zones (Ullman & Rose, 2005). Researchers have used hand-held lidar guns (Ullman & Rose, 2005), tubes and automatic traffic counters (Cottrell, Kim, Martin, & Perrin, 2006; Garber & Patel, 1994), or radar (Bloch, 1998) to collect and compare pre- and post-DSDS speed data. Data collection periods ranged from a few hours per day to a few weeks, weekdays only, or the entire week. Some researchers have used non-real traffic data, such as a driving simulator (McAvoy, 2011), to investigate the effect of DSDS on speed compliance. Statistical methods including F-test, t-test, ANOVA (Islam & El-Basyouny, 2013; Walter & Broughton, 2011), and linear regression models (Cruzado & Donnell, 2009; Ullman & Rose, 2005) were employed to conduct typical before/after DSDS speed analysis. Cottrell et al. (2006) used a standard normal density function to evaluate the effectiveness of speed humps and tables in speed limit compliance and found increase in compliance level in 14 of the 18 study sites. However, because past studies have mainly concentrated on speed comparison before and after DSDS to evaluate its effectiveness, the potential factors of speed compliance with DSDS have yet to be explored.

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A. Ardeshiri, M. Jeihani / Journal of Safety Research 51 (2014) 33–40

Proposing a data aggregation approach, this study developed and calibrated a speed limit compliance model to predict the effectiveness of DSDSs based on important temporal–spatial predictors. Speed data upstream of, adjacent to, and downstream of DSDS were collected during a wide period before and after DSDS installation in three road classes. This enabled the study to investigate the effective time (shortterm and long-term) and the effective distance (downstream of and adjacent to the DSDS). By incorporating traditional statistical methods and soft models (Bayesian Network), the study identified the key factors and their sensitivity in drivers' speed limit compliance in response to DSDS.

BN parameter learning of the DSDS speed compliance model in this study, regression analysis was deployed to leverage the BN structure. Linear regression and categorical regression (CATREG) models were applied to the aggregated data to reveal the correlation among factors and their significance in a speed compliance model. Due to the categorical nature of the study data, CATREG was selected to extend conventional multiple regression to accommodate categorical variables. However, transformation to numerical values was required to develop a linear regression model. 3. Data collection and analysis

2. Methodology

3.1. Study data

This study initially performed conventional statistical tests to determine the significance of speed variation due to DSDS. The study methodology, however, is based on Bayesian network (BN) analysis to assess DSDS effectiveness and to develop a speed limit compliance model. The objective of BN analysis is to better identify the interactions among potential factors on speed compliance in the presence of DSDS. The BN approach has been recently applied in studies that involved uncertainty and complexity, for example, in transportation problems associated with classification (De Ona, Mujalli, & Calvo, 2011), forecasting (Xie, Lord, & Zhang, 2007), and decision-making (Ulengin, Onsel, Topcu, Aktas, & Kabak, 2007). BN is a powerful, directed graphical model derived from the Bayes rule on posterior simulation. Its nodes and links illustrate random variables, relationships among them, and conditional probability distributions for the states of each variable. The Bayes rule is used to predict a future event given a past event (Koski & Noble, 2009). BN provides an intuitive visualization of interactions among factors and also shows the results of changes to a variable on the question variable. Because a causal map is a visual representation, it provides better understanding of the system than conventional analysis tools. The BN's learning algorithm employs a training dataset that is derived from actual events. The final, learned BN can be used for policy scenario analysis. BN construction has two major steps. The first step is designing the network topology or the arrangement of the nodes in the network. This is a key step because BN structure should imply a realistic causeand-effect relationship among variables. BN structure design can substantially benefit from the integration of conventional statistical methods. Past studies have demonstrated that such a combination produces a pure BN with a precise estimate. Xu, Donohue, Laskey, and Chen (2005) demonstrated that the integration of expert judgment with statistical methods improved BN accuracy to estimate delay propagation in aviation systems. Jin, Wang, and Qi (2010) utilized a BN model to estimate speed data using volume and occupancy from single-loop detectors: the study further asserted that the BN is more accurate than the conventional methods. The second step in BN construction is parameter learning; it determines each node's conditional probability table given the data and the topology of the network. It is based on the application of minimax criterion to minimize error-rate classification (Koski & Noble, 2009). While the Netica (2011) software package was employed for

This study used digital traffic counters for speed data collection, including box and tubes. Three corridors with speed limits of 25 mph, 35 mph, and 45 mph were selected. Table 1 summarizes the physical features of the three sites studied in this research. As presented by counter code in Table 1, counter 1 was installed 200 ft (60 m) upstream of, and counter 2 was installed adjacent to the DSDS locations for all three sites. No merge or diverge points between the two counters ensured an even traffic flow. While all three sites were used to evaluate the effectiveness of DSDS in general, site 1 was selected to test the effective duration and distance of the DSDS because it is a relatively long stretch without entrance/exit. Hence, counter 3 was installed 1,100 ft (335 m) downstream of the DSDS to measure the distance effect. If drivers reduced their speeds due to DSDS, it was likely that they increased their speeds at a certain distance from the DSDS. Furthermore, after three months of constant DSDS operation at this site, additional data were collected at the upstream and adjacent locations to evaluate the long-term effectiveness of the DSDS. It is noteworthy that, prior to DSDS installation, speed was measured at site 3 at the hypothetical installation location to control for the preexisting conditions. Each data set contained a 10-day average of continuous speed data. Fig. 1 depicts the mean speeds by time and distance for the three study sites. Because DSDS targets drivers who exceed the speed limit, speeds much below the posted speed, such as those during congestion period, are not normally influenced by DSDS. Therefore, data records associated with very slow speeds (overall less than 10% of the whole dataset) were eliminated from the analysis. For a detailed description of study data collection process refer to Jeihani, Ardeshiri, and Naeeni (2012). 3.2. Statistical tests Conventional statistical tests of the collected speed data assessed the significance of speed variations before and after DSDS installation, and when it was installed, before and after observation (upstream, adjacent, and downstream the DSDS location). With respect to the large sample size of speed data, it was assumed that any two sets of data were drawn from populations with normal probability distributions. Consequently, the difference between the two speed distributions had a normal distribution. The t-test addressed mean differences, knowing

Table 1 Sites and DSDSs' physical features. Site number & name

1—Perring Pkwy. 2—Hillen Rd. 3—Fenwick Ave.

Number of lanes

3 3 1

Speed limit

45 35 25

DSDS size⁎

Large Small Small

⁎ Small: 8 in × 15 in (20 × 38 cm2); large: 1.5 ft × 3 ft (46 × 91 cm2). ⁎⁎ DSDS in operation.

Before installation

Counter 2 – –

Short-term after installation⁎⁎

Long-term after installation⁎⁎

Upstream

Adjacent

Downstream

Upstream

Adjacent

Counter 1 Counter 1 Counter 1

Counter 2 Counter 2 Counter 2

Counter 3 – –

Counter 1 – –

Counter 2 – –

A. Ardeshiri, M. Jeihani / Journal of Safety Research 51 (2014) 33–40

50

45mph

47.6

47.1

48.3

46.2

48.4

45

Mean speed (mph)

35mph 25mph

48.8

35

38.3

40

35.4 35 30 25

21.7

21.5

20 15 Location: Time:

Adjacent Before installation

Upstream Adjacent Downstream Short-term after installation

Upstream Adjacent Long-term after installation

Fig. 1. Average speeds by time, DSDS location, and road class.

the variances. An F-test determined the equality of variances. The research questions are summarized in Table 2, where S is the mean speed. Each test was conducted on the relevant available data and the results of this analysis are extended in Table 3. Hypothesis I determines whether the mean speed decreased by observing the sign a short term period after the DSDS installation. According to the F-test results, since F-values are greater than the F-critical for all sites at 5% significance, the variances were unequal. Conducting the t-test for unequal variances, t values were greater than the critical one-tail t at 5% significance for all three sites. HI0 was rejected, and we concluded that the mean speed adjacent to the DSDS was significantly less than the upstream speed a shortterm period after the DSDS installation for the three road classes. However, according to hypothesis II, DSDS lost its effectiveness after three months of operation and drivers did not decrease their speeds by observing them in DSDS. Therefore, the continuous presence of DSDS appeared not to be effective in the long term. The results of hypothesis III, in line with hypothesis II, invalidated the long-term effect of DSDS presence on the road. It indicated that the mean speed adjacent to the DSDS after three months was not less than the mean speed immediately after the DSDS installation. On the other hand, according to hypothesis IV, the mean speed upstream of the DSDS after three months of operation was less than the mean speed shortly after installation. This pattern contradicted the findings of the former two hypotheses and indicated an indirect effect of DSDS on (especially familiar) drivers' speed choices during its long-time operation. Based on hypothesis V, the mean speed adjacent to the DSDS shortly after installation was less than the pre-installation speed, which confirms the short-term effect of the DSDS. Lastly, hypothesis VI indicated that short term after the DSDS installation the mean speed downstream of the DSDS was not less than the mean speed

upstream and it undermined the continuing effect of DSDS over a long stretch of site 1. The confounding results of DSDS effectiveness analysis over time in this section (hypotheses II, II, and IV) and lack of control groups for evaluating the effect of distance (similar to hypothesis V) necessitate performing a more rigorous analysis to reveal the role of DSDS on drivers' speed choices. 4. Speed compliance model 4.1. Data aggregation More than 110,000 valid speed records (upstream of, adjacent to, and downstream of DSDSs) were collected for an average of 10 days of DSDS operation at each site. Due to the technical limitation of the pneumatic tube and vehicles' changing lanes along the study approach, it was impractical to track individual vehicles crossing the study's mileposts. Thus, an aggregate method was pursued. Aggregation could be based on an equal number of vehicles (n) passing a section, or based on equivalent periods of time (t). In the former approach, platoons of n vehicles might pass during various time intervals. In the latter approach, different vehicular volumes represent each t interval and make adjustment necessary to attain an equal impact of every speed record in the model. The first aggregation approach was selected because it better illustrated the behavior of each unit, although it was selected with caution that the time intervals did not cause major inconsistency in the traffic pattern. The mean speed was calculated for every 50 consecutive vehicles (i.e., n = 50). This procedure shrank the database to 2,210 aggregated mean speed values, with each value representing 50 observations. This is to say that the aggregated records of all three sites were integrated into one dataset for modeling purposes.

Table 2 Hypotheses tests and decisions. Hypothesis test

Hypothesis of interest (Ha)

Decision on H0

(adjacent) (upstream) HI0: S short-term ≥ S short-term

Short term after installation, the average speed adjacent to the DSDS is less than those upstream.

Reject

Long term after installation, the average speed adjacent to the DSDS is less than those upstream.

Fail to reject

The mean speed adjacent to the DSDS decreased after three months of DSDS operation.

Fail to reject

The mean speed upstream of the DSDS decreased after three months of continuous DSDS operation.

Reject

The mean speed adjacent to the DSDS decreased a short term after DSDS installation.

Reject

Short term after installation, the average speed downstream of the DSDS is less than those upstream.

Fail to reject

(upstream) HIa: S (adjacent) short-term b S short-term

HII0: S long-term (adjacent) ≥ S long-term (upstream) (upstream) HIIa: S (adjacent) long-term b S long-term (adjacent) HIII0: S (adjacent) long-term ≥ S short-term (adjacent) HIIIa: S (adjacent) long-term b S short-term (upstream) HIV0: S (upstream) long-term ≥ S short-term (upstream) HIVa: S (upstream) long-term b S short-term (adjacent) HV0: S (adjacent) short-term ≥ S before (adjacent) HVa: S (adjacent) short-term b S before

HVI0: S (downstream) ≥ S (upstream) short-term short-term b S (upstream) HVIa: S (downstream) short-term short-term

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Table 3 Details of statistical tests for the six hypotheses. t Stat.b

Hypothesis

Site

Location

Mean speed

Variance

Observations

F

Fcriticala

I

1

UpstreamS AdjacentS UpstreamS AdjacentS UpstreamS AdjacentS UpstreamL AdjacentL AdjacentS AdjacentL UpstreamS UpstreamL AdjacentB AdjacentS UpstreamS DownstreamS

47.57 47.10 38.31 35.42 21.72 21.50 46.15 48.36 47.10 48.36 47.57 46.15 48.83 47.10 46.15 48.25

71.07 47.17 25.42 9.46 36.61 28.86 21.32 28.40 47.17 28.40 71.07 21.32 61.08 47.17 21.32 52.56

22,101 20,822 36,688 35,306 4643 5032 28,020 27,629 20,822 27,629 22,101 28,020 111,616 20,822 28,020 32,631

1.507

1.023

2.687

1.017

1.268

1.048

0.751

0.980

−52.38

1.661

1.022

−22.02

3.334

1.021

22.59

1.295

1.018

32.67

0.406

0.981

−41.74

2 3 II

1

III

1

IV

1

V

1

VI

1

a b S L B

6.417 93.15 1.891

One-tail test with α=0.05. tcritical = 1.645 at α = 0.05. Short-term after installation. Long-term after installation. Before installation.

4.2. Explanatory variables Ten categorical variables were defined in this study to explain the environmental, spatial, and temporal conditions, as well as an aggregate of speed responses to create a behavioral model. Table 4 classifies variables into four groups and describes the categories (states) associated with each. The first three groups are naturally independent, while the last group of variables constitutes drivers' speed choices that could be explained by the former groups. The number of scenarios within any variable's probability table in BN is determined by the variable's number of states multiplied by the number of states of its parent nodes. To ensure that each scenario's conditional probability table could be elicited from the data, the number of states in each node was minimized to produce fewer scenarios. Aggregate speed records were divided into weekday and weekend groups because they represent different driver behaviors. Furthermore, peak and off-peak quantities were obtained from the actual diurnal distribution of collected traffic counts on a daily basis to develop the Time (of day) variable. Effective Time is an inherent continuous measure representing the number of days that the DSDS was in operation. It was discretized into four categories for modeling purposes: the fourth group represented the long-term effect (i.e., three months after installation). While the first speed detector is always set upstream of the DSDS, Effective Distance represents the location of the second speed detector: adjacent to or downstream of the DSDS. Three speed-specific variables were defined to explain the research questions. Speed “compliance” variables were not considered dichotomous (i.e., compliance vs. noncompliance) since a speed value slightly above the speed limit is not

Table 4 Variable description for speed compliance model. Variables

Group

States

Day Time Speed limit Lane number Size Effective time Effective distance Speed alteration Compliance upstream Compliance adjacent

Date

Weekend/weekday Peak/off-peak 25/35/45 (mph) 1/3 Small/large 1~2/3~7/8~12/ N 12 (days) Adjacent/downstream Decrease/constant/increase LSL/L107SL/L115SL/H115SL LSL/L107SL/L115SL/H115SL

Road DSDS

Speed and compliance

necessarily noncompliance; instead it may be due to normal speed noise or inaccuracy of speed measurement with traffic counters. Hence, four speed compliance levels were specified as follows: (i) (ii) (iii) (iv)

Less than the speed limit (LSL). Up to 7% above the speed limit (L107SL). Between 7% and 15% above the speed limit (L115SL). More than 15% above the speed limit (H115SL).

Compliance Upstream implies general compliance behavior with the speed limit neutral to DSDS effect, while Compliance Adjacent implicates speed limit compliance due to DSDS. Speed Alteration indicates the change in speed before and after DSDS observation (upstream and adjacent speeds respectively). The states' frequencies for these three variables are presented in Fig. 2. As shown in the left-side graph, there was a noticeable counterclockwise rotation in the speed limit compliance quadrilateral, where the major shift due to DSDS was from L115SL to L107SL. In fact, drivers in the two highest speed clusters (L115SL and H115SL) considerably reduced their speeds. 4.3. Regression analysis To determine the level of association between the predictors and the response variable, two regression models were developed and the results are presented in Table 5. Independent variables listed in this table are the variables introduced earlier in Table 4: Compliance Adjacent (to DSDS) is the dependent variable in both models. Categorical variables were scaled as ordinal (such as Speed Alteration and Effective Distance) or nominal (such as Day and Time) to conduct a standard linear regression model; however, they were inserted into the CATREG with their original values. Compliance variables were coded as 0 to 3 denoting LSL to H115SL, respectively, implying lower compliance rates with speed limit for higher values of the variable. Standardized coefficients (betas), t-statistics, and p-values were computed for the linear model. Betas, F-statistics and p-values, and importance, and tolerance are reported for the CATREG. The F test for each factor is contingent on the other regressors and indicates how exclusion of a variable weakens the whole model, when all other variables are kept in the model (Meulman & Heiser, 2010). While variables' coefficients can interpret their importance in the model, they cannot explain the full impact of each predictor and the inter-relationships among them. Importance shows the relative contribution of any single predictor to the regression. Tolerance determines the inter-correlation between

A. Ardeshiri, M. Jeihani / Journal of Safety Research 51 (2014) 33–40

LSL 50%

Compliance Upstream

40%

Compliance Adjacent

37

Speed Alteration

30% 20%

25%

10% H115SL

L107SL

0%

47%

Decrease

29%

Constant Increase

L115SL Fig. 2. Frequencies of states for the three speed-related variables.

predictors and ranges from zero, the lowest contribution to the model, to one, which is fully independent from other predictors (Meulman & Heiser, 2010). The two models achieved a comparative goodness-of-fit according to R2 and significance of independent variables. Because speed limit and lane number demonstrated significant multicollinearity, the former was excluded in the linear model. Both received zero tolerance in the CATREG. The high tolerance of Time and DSDS size indicated that they cannot be predicted by other variables. DSDS size was relatively trivial in CATREG and showed a confounding positive coefficient in the linear regression. Because Speed Alteration had the highest importance, it appeared with equal coefficients and p-values in both models. Significant positive coefficient of Compliance Upstream indicated that a higher general compliance with the speed limit led to a higher DSDS compliance. Although Effective Distance had a high tolerance, it was not judged to be significant in either of the models. Interestingly, while Effective Time appeared with significant negative coefficient in the linear model, it had a positive coefficient in the CATREG with low importance. Similar to the study by Islam and El-Basyouny (2013), Day and Time had consistent significant signs in both models, indicating higher speed compliance rates for off-peak weekdays, though they were not very important in the CATREG. 4.4. Bayesian network (BN) 4.4.1. BN construction A BN is normally initiated based on the causal relationship of the effective variables to disclose how a complex system functions (Ulengin et al., 2007). In a BN graph, nodes and links represent the variables and the relationship among them. Correlations among

explanatory variables and the effect of each variable on the final node are important factors. The initial BN topology in this research was developed based on regression analysis results and then complemented using trial and error to attain the best model fit. In a BN, two nodes can be connected directly or indirectly via one or more mediator node(s). The coefficients, importance, and tolerance of regression assisted in determining the directness or indirectness of the relationships between the predictors and the target node (Compliance Adjacent). Two levels of proximity to the target node were set in the graph. Speed Alteration, Compliance Upstream, and DSDS size were laid as the first-hand nodes, and the other six predictors were laid as the secondary nodes due to either low importance or less-significant coefficients in the regression models. Unlike regression analysis where the interdependency of two predictors results in the exclusion of either of them, they can coexist in the BN with direct connection (e.g., lane number and DSDS size). However, nonessential links were eliminated to shallow the network and to avoid the over-fitting problem. The structure of the final BN network is displayed in Fig. 3, while the conditional probability tables of each node present the node's states as belief bars. 4.4.2. BN validation Performance evaluation ensures that a predictive model performs appropriately. The aggregate speed data were randomized into two subsets for training and for testing the network. Eighty percent of the data (including 1,768 aggregate records) was randomly selected among all sites for the learning process to calibrate the BN model using an expectation–maximization algorithm. The calibrated model was used to predict the probability distribution of the target node for the remaining 20% of the dataset (442 records), and then the predicted values were compared to the observed values. Table 6 presents the

Table 5 Regression results for linear and CATREG compliance models. Independent variables

Linear regression

CATREG

Standardized coefficient (β)

t (sig.)

Standardized coefficient (β)

F (sig.)

Importance

Tolerance

Day Time Speed limit Lane number DSDS size Effective time Effective distance Speed alteration Compliance upstream R2 F (sig.)

−0.044 0.029 – 0.170 0.257 −0.075 −0.037 0.756 0.236 0.524 302.70 (0.000)

−2.24 (0.025) 1.93 (0.054) – 7.98 (0.000) 15.40 (0.000) −3.47 (0.001) −1.64 (0.101) 29.98 (0.000) 9.90 (0.000)

−0.057 0.039 0.540 −0.310 −0.001 0.046 −0.004 0.751 0.273 0.549 205.85 (0.000)

8.71 (0.003) 6.80 (0.009) – – 0.01 (0.93) 3.77 (0.052) 0.04 (0.84) 903.3 (0.000) 124.1 (0.000)

0.015 0.002 0.503 −0.281 −0.001 0.042 −0.001 0.861 −0.141

0.559 0.933 0.000 0.000 0.769 0.361 0.499 0.330 0.354

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A. Ardeshiri, M. Jeihani / Journal of Safety Research 51 (2014) 33–40

Fig. 3. BN model for speed compliance adjacent to DSDS.

calibration and validation results of the BN model derived from the training and test sets, respectively, and overall evaluates the predictive power of the BN model based on four criteria. The error rate indicates the percentage of false predictions. The three scoring rules (logarithmic loss, quadratic loss, and spherical payoff) were computed based on the actual belief levels of node states, not just the state with the highest probability, to evaluate model efficiency and classification ability (Morgan & Henrion, 1990). The logarithmic loss and quadratic loss vary from zero to infinity, with zero as the best fit. Spherical payoff varies from zero to one, in which one indicates the best fit. Eq. (1) shows the formulation of these rules (Netica, 2011), where M is the mean function over all cases, Pc is the estimated probability of the true state, and Pj is the estimated probability of jth state when there are n states for the question node. The results demonstrated a strong consistency between the calibration and validation, endorsing no evidence of over-fitting. The results also asserted that the BN model can be used for sensitivity analysis of the different components of drivers' speed compliance.

Logarithmic loss ¼ M ð–Ln P c Þ  Xn 2  P Quadratic loss ¼ M 1−2P c þ j¼1 j ffi  rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xn 2  Spherical payoff ¼ M P c = P j¼1 j

ð1Þ

4.4.3. Sensitivity analysis BN can identify how the DSDS effectiveness would change when the value of each node changed. Table 7 summarizes the computed sensitivities for each node in the proposed BN. The variables were ranked according to their level of impact on Compliance Adjacent based on two parallel criteria of mutual information and percentages. Mutual

Table 6 BN Model's goodness-of-fit. Criteria

Train set

Test set

Error rate Logarithmic loss Quadratic loss Spherical payoff

31.1% 0.671 0.422 0.754

33.0% 0.720 0.448 0.739

information, also called entropy reduction, is the anticipated reduction in uncertainty of a random variable due to another random variable. For random variables of X and Y, the mutual information of I(X; Y) is a measure of dependency as Eq. (2) (Cover & Thomas, 2006), where p(x, y) is the joint probability function. I ðX; Y Þ ¼

X x;y

pðx; yÞlog

pðx; yÞ pðxÞ pðyÞ

ð2Þ

Table 7 also presents the detailed effect of the four important variables (Speed Alteration, Compliance Upstream, Effective Time, and Speed Limit) on the final node while controlling for other variables. Due to the interdependency between the Size and Speed Limit, the former was excluded from further discussion. Hereafter, base case refers to the probabilities presented in Fig. 3, which indicates that adjacent to the DSDS location, 25.5% of the sample was LSL, 49.6% was L107SL, 20.4% was L115SL, and 4.5% was H115SL. Speed Alteration was divided into three states: decrease, constant, and increase. According to Table 7 and the base case's speed profiles, when all drivers decreased their speed after observing a DSDS, the probability of LSL increased from 25.5% to 41.3% and the probability of L107SL slightly increased from 49.6% to 54.5%. As expected, the probabilities of L115SL and H115SL decreased dramatically. This finding demonstrates that even immediate speed reduction due to DSDS does not result in a generic compliance with the speed limit: nearly 59% drove higher the speed limit. When the vehicles' speeds remained constant, the probabilities of the two extreme states of LSL and H115SL decreased and the probabilities of L107SL and L115SL increased. When drivers increased their speed by observing a DSDS, as expected, the probabilities of lower speed groups (LSL and L107SL) dropped and the probabilities of higher speed groups (L115SL and H115SL) increased. According to the Compliance Upstream variable, for drivers with speed LSL prior to the DSDS observation, the probability of LSL after observation was approximately double the base case (48.8%) and the probability of L107SL was half of the base case (27.9%). Since only 48.8% of the LSL group maintained their speed below the speed limit, it can be argued that the remaining 51.2% ignored the DSDS; however, some might raise their speed to meet posted speed due to the close adjacency of the DSDS and speed limit sign. The cumulative results indicated that among drivers in L107SL group, 29.2% increased their speeds—to L115SL (27.5%) or to H115SL (1.7%) and only 16.9% slowed down to LSL.

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Table 7 Sensitivity of compliance adjacent with respect to other variables. [Variable] State [Speed alteration] Decrease Constant Increase [DSDS size] [Compliance upstream] Less than speed limit Speed range: 1–1.07 of speed limit Speed range: 1.07–1.15 of speed limit Higher than 1.15 of speed limit [Effective time] 1 to 2 days 3 to 7 days 8 to 12 days More than 12 days [Speed limit] 25 35 45 [Lane number] [Effective distance] [Time] [Day]

%LSL

%L107SL

%L115SL

%H115SL

41.3 10.6 21.1

54.5 60.5 19.0

4.2 27.7 39.8

0.0 1.2 20.1

48.8 16.9 20.6 21.6

27.9 53.9 57.6 50.5

17.0 27.5 16.5 21.8

6.3 1.7 5.3 6.1

34.1 28.2 24.5 18.2

48.6 54.5 50.9 40.8

14.0 15.2 21.0 31.2

3.3 2.1 3.6 9.8

53.1 24.1 24.4

30.7 43.4 49.0

11.7 16.3 22.9

4.5 6.2 3.7

However, only 5.3% of the L115SL group increased their speed (to H115SL) and 78.2% decreased (to LSL or L107SL). On the other hand, 93.9% of the H115SL group decreased their speeds due to DSDS and 6.1% maintained their high speeds. Overall, the speed profile of those driving 15% higher than the speed limit was not considerably different from the base case. The drivers presumably either ignored the sign or did not notice it. According to the Effective Time variable, there is a systematic decline in speed limit compliance as the DSDS duration increases. During the first week of DSDS operation, the probability of LSL was higher than the base case, the probability of L107SL was similar to the base case, and the probabilities of L115SL and H115SL were considerably less than the base case. After a week, the probability of LSL was less than the base case and the probability of L115SL rose higher than the base case. However, the probability of H115SL exceeded the base case only after 12 days, which represented the long-term DSDS installation. This emphasized the gradual deterioration of the DSDS effectiveness over time. For the speed limit of 25 mph, the probability of LSL was double the base case, while the probabilities of the other three groups exceeding the speed limit were lower than the base case. For the speed limits of 35 mph and 45 mph, the probability configuration of the four speed ranges was consistent with the base case. Overall, it appears that the compliance rate with the speed limit is relatively higher on roads with lower posted speeds, though having only one sample in each road class precludes generalizing this finding. 5. Summary and conclusions This study evaluated drivers' compliance with the speed limit in the presence of DSDS by collecting speed data upstream of, adjacent to, and downstream of DSDSs on three road classes with different speed limits (25, 35, and 45 mph) for an average 10-day period. The statistical tests of the mean speeds before-and-after indicated that the DSDS is an effective short-term tool for short distances. Additional analytical methods— linear and categorical regression models and Bayesian networks—were utilized to discover the associations among various factors on speed limit compliance in response to the DSDS. To this end, the recorded speeds for every 50 successive vehicles were aggregated for modeling purposes to overcome the impracticality of tracking individual vehicles across the study sites. Treating compliance as a continuous behavior, it

Mutual info.

Percent

0.2636

15.8

0.0987 0.0716

5.90 4.28

0.0412

2.46

0.0175

1.04

0.0085 0.0080 0.0002 0.0001

0.51 0.48 0.01 0.01

was categorized into four groups of less than the speed limit, up to 7% above, between 7% and 15% above, and more than 15% above the speed limit. The regression results revealed that speed changes due to DSDS, upstream speed limit compliance, time of day, and day of week had a significant effect on speed compliance adjacent to the DSDS in both model structures. However, due to interdependency of speed limit, number of lanes, DSDS size, and time period after DSDS installation, they failed to appear with consistent sign and significance in the two models. To better disclose the interactions among such factors, a BN speed compliance model complemented the regression analysis. The BN sensitivity analysis provided a comprehensive interpretation of the important factors in speed compliance. When there was a decrease in all cases' speed, the probability of driving below the speed limit adjacent to the DSDS was 41.3% and the cumulative probability of driving below 1.07 times of the speed limit was 95.8%. While even an instant speed reduction due to the DSDS did not result in full speed limit compliance, this finding argues that driving slightly above the posted speed does not trivialize DSDS effectiveness. The BN model also revealed that 51.2% of cases with average speeds below the posted speed upstream of the DSDS increased their speeds adjacent to the DSDS. In this case, DSDS might act as a reminder to some to raise their speed to meet the posted speed. Alternatively, the DSDS size and location might undermine its effectiveness. DSDSs located on the right/left sides of the road may fail to communicate with drivers from farther lanes. Utilizing separate signs for each lane similar to VMSs mounted on overhead structures may minimize the effect of the number of lanes. The BN structure was mainly based on road-specific invariants. Although a restricted sample size (three sites representing three road classes), lack of information on drivers' attitudes and socioeconomic characteristics, inherent limitations with the aggregation method, and the effect of other unmeasured site-specific features prevented generalizing the study's findings, the results provided a general overview of the important factors and the level of sensitivity of each on the speed compliance behavior in the presence of the DSDS. In addition, time of day (peak hours vs. off-peak) and day of week (weekdays vs. weekends) appeared to be less significant compared to the road-specific variables. Overall, the DSDS is effective when it is utilized as a temporary solution for a limited amplitude as its effectiveness reduces with time, and drivers are likely to increase their speed after passing the DSDS. Therefore, DSDSs should be installed on critical points, where the probability

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A. Ardeshiri, M. Jeihani / Journal of Safety Research 51 (2014) 33–40

of crashes is high or safety is very important (e.g., work zones or school zones), and should be supplemented with speed enforcement. Acknowledgments The authors would like to thank the Morgan State University's National Transportation Center (DTRT06-G-0045) for its funding support and continued encouragement of student participation in research projects. The authors also thank Baltimore City's traffic division for facilitating tube installation on the streets. References Bloch, S. A. (1998). A comparative study of the speed reduction effects of photo-radar and speed display boards. Proceeding of the annual meeting of the Transportation Research Board, Washington, DC. Cottrell, W. D., Kim, N., Martin, P. T., & Perrin, H. J., Jr. (2006). Effectiveness of traffic management in Salt Lake City, Utah. Journal of Safety Research, 37(1), 27–41. Cover, T. M., & Thomas, J. A. (2006). Elements of information theory (2nd ed.). New York, NY: John Wiley & Sons. Cruzado, I., & Donnell, E. T. (2009). Evaluating effectiveness of dynamic speed display signs in transition zones of two-lane, rural highways in Pennsylvania. Transportation Research Record: Journal of the Transportation Research Board, 2122, 1–8. De Ona, J., Mujalli, R. O., & Calvo, F. J. (2011). Analysis of traffic accident injury severity on Spanish rural highways using Bayesian networks. Accident Analysis & Prevention, 43(1), 402–411. Garber, N. J., & Patel, S. T. (1994). Effectiveness of changeable message signs in controlling vehicle speeds. Virginia transportation research council, report: FHWA/VA-95-R4, Charlottesville, VA. Garber, N. J., & Srinivasan, S. (1998). Effectiveness of changeable message signs in controlling vehicle speeds: Phase II. Virginia transportation research council, report: VTRC-98R10, Charlottesville, VA. Islam, M. T., & El-Basyouny, K. (2013). An integrated speed management plan to reduce vehicle speeds in residential areas: Implementation and evaluation of the silverberry action plan. Journal of Safety Research, 45, 85–93. Jeihani, M., Ardeshiri, A., & Naeeni, A. (2012). Evaluating the effectiveness of dynamic speed display sign. National transportation center research report. Morgan State University. Jin, S., Wang, D., & Qi, H. (2010). Bayesian network methods of speed estimation from single-loop outputs. Journal of Transportation Systems Engineering & Information Technology, 10(1), 54–58.

Koski, T., & Noble, J. M. (2009). Bayesian networks, an introduction. United Kingdom: John Wiley & Sons, Ltd. McAvoy, D. S. (2011). Work zone speed reduction utilizing dynamic speed signs. Working paper, report: 01353750. University of Ohio. Meulman, J. J., & Heiser, W. J. (2010). IBM SPSS categories 19. SPSS Inc. Morgan, M. G., & Henrion, M. (1990). Uncertainty: A guide to dealing with uncertainty in quantitative risk and policy analysis. U.S.: Cambridge University Press. Netica (2011). Version 5.02. Vancouver, Canada: Norsys Software Corp. Poulter, D., & McKenna, F. (2005). Long-term SID report. University of Reading project report for Royal Borough of Kingston. Ulengin, F., Onsel, S., Topcu, Y. I., Aktas, E., & Kabak, O. (2007). An integrated transportation decision support system for transportation policy decisions: The case of Turkey. Transportation Research Part A, 41(1), 80–97. Ullman, G. L., & Rose, E. R. (2005). Evaluation of dynamic speed display signs. Transportation Research Record: Journal of the Transportation Research Board, 1918, 92–97. Walter, L., & Broughton, J. (2011). Effectiveness of speed indicator devices: An observational study in South London. Accident Analysis & Prevention, 43(4), 1355–1358. Walter, L. K., & Knowles, J. (2008). Effectiveness of speed indicator devices on reducing vehicle speeds in London. Published project report 314. Transport Research Laboratory. Xie, Y., Lord, D., & Zhang, Y. (2007). Predicting motor vehicle collisions using Bayesian neural network models: An empirical analysis. Accident Analysis & Prevention, 39(5), 922–933. Xu, N., Donohue, G., Laskey, K. B., & Chen, C. (2005). Estimation of delay propagation in the national aviation system using Bayesian networks. Presented at 6th USA/Europe air traffic management research and development seminar, Baltimore, MD. Anam Ardeshiri is a doctoral candidate in the Department of Transportation and Urban Infrastructure Studies at Morgan State University. He received his Master's degree in Transportation Planning and Engineering and his Bachelor's degree in Civil Engineering from Sharif University of Technology, Tehran, in 2007 and 2004 respectively. He has five years of experience in the private sector and has been working as research assistant in six projects funded by state and federal agencies. Mansoureh Jeihani is an associate professor in the Department of Transportation and Urban Infrastructure Studies at Morgan State University. She has work experiences in both private and public transportation agencies before joining Morgan State. She has a multidisciplinary background, a PhD degree in Civil (Transportation Systems) Engineering and a Master's degree in Economics from Virginia Tech, a Master's in Socio-economic Systems Engineering from IRPD, and a Bachelor's degree in Computer Engineering from Iran National University. Dr. Jeihani is interested in different research areas such as transportation planning, intelligent transportation systems, and traveler behavior. She has published 40 papers and conference proceedings.