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abuzwidahcrashriskanalysisdifferent2018.md

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category: literaturenote citekey: abuzwidahcrashriskanalysisdifferent2018 title: Crash risk analysis of different designs of toll plazas authors: "Abuzwidah, Muamer; Abdel-Aty, Mohamed" year: 2018 date: 2018-00-00 2018 doi: 10.1016/j.ssci.2018.02.024 publication: Safety Science url: "https://doi.org/10.1016/j.ssci.2018.02.024" zotero_key: U6P6IF8Z zotero_storage: 39EXXHR4 collections: transpordi_planeerimine folder: 001_artiklid/Road Safety Indicators firstAuthor: "Abuzwidah, Muamer"

status: converted

Contents lists available at ScienceDirect

Safety Science

journal homepage: www.elsevier.com/locate/safety

Crash risk analysis of different designs of toll plazas

Muamer Abuzwidaha,⁎ , Mohamed Abdel-Atyb

  • aDepartment of Civil and Environmental Engineering, University of Sharjah, Sharjah, United Arab Emirates
  • bDepartment of Civil, Environmental and Construction Engineering, University of Central Florida, Orlando, FL 32816-2450, United States

ARTICLE INFO

Keywords: Traditional toll plaza Hybrid toll plaza All-electronic toll collection And toll by plate Cashless toll Open road tolling Log linear

ABSTRACT

The Expressways (toll roads) offer a high level of service, and the Global Electronic Toll Collection market has exceeded the expectation. However, finding optimal designs for toll plazas is an issue with world-wide relevance, and this study makes a significant contribution towards this end. The main goal of this study is to examine for the first time the traffic safety impact of using different designs of the Hybrid Toll Plaza (HTP). In addition to that, this study helps understand the relationship between the crash frequency and several important crash-related factors and circumstances of these facilities. Crash data from a seven-year period was investigated, and a hundred mainline toll plazas in Florida were evaluated. The results of this study proved that there is a significant difference between the different designs of the HTP. And there is an indication that the majority of crashes occurred at diverge-and-merge areas before and after the plaza. Moreover, the results indicated significant relationships between the crash frequency and toll plaza types, annual average daily traffic, and driver-age. This study has also proved that the HTP and the All-Electronic Toll Collection (AETC) were associated with less number of crashes than the Traditional Toll Plazas by 44.7 and 72.6 percent, respectively. Also, one of the findings with interesting safety implications is the interaction between design type and percentage of prepaid transponder vs. manual payment users regarding crash rate. Overall, for those agencies who cannot adopt the AETC system, improving traffic safety at toll plazas should take a priority.

1. Introduction

The use of toll roads has risen dramatically in many countries around the world; and The Global Electronic Toll Collection market is valued at 5.42 billion U.S Dollar in 2014 and it is expected to reach 10.57 to 15.62 billion by 2022 growing at a CAGR of 9.16 to 12.71percent, (WISE GUY, 2017; MRR, 2017). In fact, the factors such as reduction in traffic congestion, low travel time, cashless travel facility and free flow of traffic are driving the Electronic Toll Collection (ETC) market growth (AB Newswire, 2017).

In the United States, there are many tolled road facilities; these facilities vary in type, size, ownership, and tolling systems deployed. Some of these facilities are private along with those owned and operated by various public agencies around the States (Yang et al., 2014). And even though toll roads offer high mobility benefits, traditional toll facilities may pose high traffic safety risk. Moreover, only a limited number of studies have explored the factors that affect safety at toll plazas.

The Transport Department of the Hong Kong SAR government conducted a trial traffic guidance scheme at the toll plaza of a busy road tunnel to improve traffic flow and traffic safety at this facility. A study by Wong et al. (2006) conducted an observational before-and-after study to assess the effects of the scheme. The results indicate that the trial scheme provided good guidance to drivers. Traffic safety was improved, and the travel time of auto-toll traffic improved in certain periods. Another study by Prasetijo et al. (2016) investigated the accidents at the toll plaza gates due to impacts of the vehicles with concrete crash barriers with results in damage and fatalities. The study conducted a simulation test for crash barrier Tensile Wire Fracture toughness system. The results show that the material for a new alternative crash barrier is likely to reduce the rate of death due to accident and damage with regards to road furniture and vehicles.

Valdés et al. (2017) evaluated the effectiveness of different electronic toll collection lane types, and how signage and queues affect safety and driver behavior and operations in toll plazas using driving simulator. The results showed that overhead signage configuration associated with the corresponding speed limits per lane was found to be significant in reducing the acceleration noise, thus reducing the potential for lane change related crash patterns. Also, female drivers tend to have a faster deceleration rate than male drivers in the toll booth approach zone. Moreover, no significant difference between genders on average running speed was found in basic tollway segment at the

E-mail addresses: mabuzwidah@sharjah.ac.ae (M. Abuzwidah), m.aty@ucf.edu (M. Abdel-Aty).

⁎ Corresponding author.

beginning of the experiment.

Saad et al. (2017) explored some of the factors that affect driving behavior and safety at toll plaza. This study assessed driving behavior using a driving simulator. They found that drivers experiencing the open road tolling (ORT) have safer driving behavior than those who use the tollbooth. Van Dijk et al. (1999) studied toll plaza in twofold: to configure the types of toll booths with multiple payment functionalities (cash, credit cards, and electronic payment); and to determine the number of toll booths for each type. The model was also used to validate the spacing, safety, and accessibility of the toll plaza. A hybrid approach of simulation and queueing theory were used in this study. The study showed that fewer toll booths were needed when different payment systems were separated, as a combination of different payment systems at one toll booth would substantially enlarge the variability of service times. This variability appeared to dominate the 'inefficiency' of separate toll booths which may seem counterintuitive. Consequently, the initial design had to be completely redesigned. Overall, none of these studies evaluate or simulate the impacts of using different designs of the toll plazas on traffic safety.

The literature also showed that different toll collection systems have been adopted by different toll agencies around the world with no uniform standard (Mohamed et al., 2000; Schaufler, 1997). The most common toll collection systems can be summarized as follows:

Traditional Toll Plaza (TTP); this design requires vehicles to rapidly decelerate, navigate through different fare transaction options, and then accelerate and merge with traffic (Miami-Dade Expressway, 2017; McDonald and Stammer, 2001; Abuzwidah and Abdel-Aty, 2015). These confusing maneuvers constitute safety challenges and form high risk locations on toll roads.

Hybrid Toll Plaza (HTP); this system retrofits existing tollbooths with express open Electronic Toll Collection (ETC) lanes. This design is allowing more than 81 percent of the vehicles in Florida to travel at full speeds using electronic transponders or license plate recognition technology in an open road environment with fewer diverge and merge maneuvers before and after the toll plaza. The HTP design combines either express Open Road Tolling (ORT) lanes on the mainline and separate traditional toll collection to the side, or traditional toll collection on the mainline and separate ORT lanes to the side (FTE, 2017). However, the HTP is widely deployed by many toll authorities such as in Florida, Illinois, New Jersey, and many other states.

All-Electronic Toll Gantry or All-Electronic Toll Collection (AETC); this system is completely barrier-free that replaces all tollbooths with regular express ETC lanes to change the toll plaza to be similar to regular segments. The AETC system allows driving straight through an open road without needing to change lanes, stop the vehicle, or even slow down to pay a toll. The payment will be done automatically, instantly and accurately by using the automatic toll collection transponder known as prepaid transponder (FTE, 2017).

Past studies and the current data have indicated that certain locations at the TTP and HTP are more likely to experience traffic crashes than the regular segments on the expressway. In April 2006 in Washington, D.C., investigators for the U.S. National Traffic Safety Board (NTSB) revealed that the most dangerous locations on the highways are toll plazas. In the same year, the NTSB reported that 49 percent of all crashes on expressways in Illinois occurred at toll plazas, and three times as many people died in them as in crashes on the rest of the same roadways. Also, 30 percent of all crashes on the Pennsylvania Turnpike happened at toll plazas and 38 percent of all collisions on New Jersey toll highways are toll plaza incidents (NTSB, 2017). An older study (Mohamed et al., 2000) found that about 32 percent of the total crashes that occurred on the Orlando expressway system were located at the Traditional Toll Plazas.

However, there are some obstacles to the use of the AETC systems in many countries around the world, and that because these systems require good arrangements between the tolling agencies and the department of motor vehicles, as well as the law enforcement and the regulations. These regulations and arrangements are needed to identify and bill drivers who do not have the prepaid transponder.

Although the use of the HTP and AETC systems has demonstrated measured improvements in traffic operations and environmental issues, the question is: What if we cannot apply the AETC? What are the alternative solutions? The answer was either adopting the HTP design or improving the current situations of the TTPs and it was proved that some simple and quick treatments could improve safety at TTP (Sze et al., 2008).

For example, Wong et al. (2006) evaluated the effects of a traffic guidance scheme for auto-toll lanes on traffic safety at TTP and they found that the overall lane-changing rate decreased significantly by 23 percent and the pooled conflict count decreased sharply by 44 percent, also the crash count decreased sharply by 38 percent. A better option however is to apply the HTP design and that also has some safety issues and there is a lack of research that compares and evaluates the different designs of the HTP, especially nowadays many agencies are adopting the HTP design without a uniform design standard.

Overall, to the best of our knowledge there were no studies evaluated the safety impacts of using different design of Hybrid Toll plazas (Fig. 1). Therefore, the main goals are the following:

  • 1. Cover the urgent need of assessing the traffic safety impacts of using different designs of the HTP. It is worth mention that many agencies want to adopt Design 2 (Fig. 1) and that because it just requires adding separate ORT lanes to the side without touching the existing main-line toll plazas.
  • 2. Investigate the relationship between crash frequency and the crash related variables such as geometric characteristics, toll plaza types, traffic volumes, and driver-age.

2. Methodology

2.1. Safety Performance Functions (SPFs)

Data from the reference group are used to estimate a safety performance function (SPF) that relates crash frequency of the sites to their traffic and geometrical characteristics. Generally, a safety performance function (SPF) is a crash prediction model, which relates the frequency of crashes to traffic (e.g., annual average daily traffic) and the roadway characteristics (e.g., number of lanes, width of lanes, width of shoulder, etc.). There are two main types of SPFs in the literature: (1) full SPFs and (2) simple SPFs. Full SPF is a mathematical relationship that relates both traffic parameters and geometric parameters as explanatory variables, whereas simple SPF includes annual average daily traffic (AADT) as the sole explanatory variable in predicting crash frequency on a roadway entity. It is worth mentioning that the calibrated Crash Modification Factors in the Highway Safety Manual are based only on the simple 'SPF' (Abdel-Aty et al., 2014). Therefore, a series of SPFs were developed in the first part of this study using Negative Binomial Regression Models.

2.2. Negative binomial regression model

Crash data have a gamma-distributed mean for a population of systems, allowing the variance of the crash data to be more than its mean (Shen, 2007). Suppose that the count of crashes on a roadway section is Poisson distributed with a mean λ, which itself is a random variable and is gamma distributed, and then the distribution of frequency of crashes in a population of roadway sections follows a negative binomial probability distribution (Hauer, 1997). Count data is usually modeled using a Poisson distribution; the main characteristic of the Poisson distribution is that its mean is equal to its variance. Several studies found that a negative binomial distribution fits crash frequency data better (Brown et al., 2006) (Abdel-Aty and Radwan, 2000). The Negative Binomial (NB) is similar to a Poisson distribution, though its

Fig. 1. Different designs of the Hybrid Toll Plazas (Source: (Google Earth)).

variance is greater than its mean (Agresti, 2002). The NB model can be used to estimate crashes at locations, such as toll plaza segments (Chang, 2005).

Eq. (1) presents the NB probability distribution function.P (yi) ∼ Negbin (λi, k):

$$\frac{\Gamma(1/k+y_i)}{y_i!\Gamma(1/k)} \left(\frac{k\lambda_i}{1+k\lambda_i}\right)^{y_i} \left(\frac{1}{1+k\lambda_i}\right)^{1/k}$$ (1)

Where,

y = number of crashes on a certain location at a certain period, λ= Expected number of crashes on a certain location at a certain period

k = over-dispersion parameter.

The NB estimation equation is given as follows;

$$Log\lambda_i = log(EV_i) + (\beta_0 + \beta X_i + \varepsilon_i).$$ (2)

where λi is the estimated number of crashes at location i; β is a vector of explanatory variables, and EVi is the exposure variable which is included in models as an offset term to account for unequal exposure to crashes along toll plazas. Count models such as NB need a mechanism to deal with different exposure scenarios. For example the Annual Average Daily Traffic (AADT), or expected number of crashes, can be included as an exposure offset term in NB models (Chen, 1997). By offsetting the exposure, the response variable becomes the log crash frequency at a certain location. εi is the term adjusting for over dispersion. It is an error term due to a combination of variables omitted from the model and pure randomness. Maximum Likelihood Estimation (MLE) is used to estimate the coefficients of the explanatory variables and the over dispersion parameter. The goodness of fit of the NB model is measured by analyzing the over dispersion parameter.

2.3. Log-Linear model

Past studies and current data have indicated that certain locations at toll plazas are more likely to be more risky than regular segments on the expressway. However, to the best of our knowledge there were no studies that investigated the association between traffic crashes and toll plaza types, AADT or driving maneuver variables among various age groups.

A log-linear model is a generalized linear model for Poisson-distributed data; it specifies how the size of a cell count depends on the levels of the categorical variables for that cell. The nature of this specification relates to the association and interaction structure among the variables (Christensen, 1990; Abdel-Aty et al., 1998). The log-linear model describes the association and interaction patterns among a set of categorical variables (Knoke, and Burke, 1980). The estimates of parameters resulting from the model can be converted to estimate the odds ratio between variables. The formulation of a log-linear model with three variables and two-way interactions is as follows:

$$log m_{ijk} = \nu + \lambda_i^x + \lambda_j^y + \lambdak^z + \lambda{ij}^{xy} + \lambda{jk}^{yz} + \lambda{ik}^{xz}$$ (3)

Where:

Log mijk = log the expected frequency of cell in which:

x = i, y = j, z = k;

υ overall effect = .

λ = effect due to the i level of x; i x th

λ = effect due to the j level of y; j y th

λ = effect due to the k level of z; k z th

λ = interaction of x at the i level and y at the j level; ij xy th th

λ = interaction of x at the i level and z at the k level; ik xz th th

λ = interaction of y at the j level and z at the k level. jk yz th th

For instance, when the model contains the term λij xy, which is the effect due to the interaction of x being at level j, it also contains λi , the effect due to the ith level of x, and λj , the effect due to the jth level of y. A reason for including lower-order terms is that the statistical significance and practicable interpretation of a higher order term depends on how the variables are coded. Since this model contains an X–Y twofactor term, it permits association between X and Y, controlling for Z. It also permits an X–Z association, controlling for Y, and a Y–Z association, controlling for X (Abdel-Aty et al., 1998). By using Eq. (1) for two

cells, the log odds logit can be determined. And it helps understand how the independent variables affect the response variables (especially the toll plaza types); the logit models are constructed according to the response variables as follows:

$$\begin{split} \log(m{ijk}/m{i1k}) &= [\nu + \lambda{i}^{x} + \lambda{j}^{y} + \lambda{k}^{z} + \lambda{ij}^{xy} + \lambda{jk}^{yz} + \lambda{ik}^{xz}] \ &- [\nu + \lambda{i}^{x} + \lambda{j}^{y} + \lambda{k}^{z} + \lambda{ij}^{xy} + \lambda{jk}^{yz} + \lambda{ik}^{xz}] \ &= [[\lambda{j}^{y} - \lambda{i}^{x}] + [\lambda{ij}^{yy} - \lambda{ij}^{xy}] + [\lambda{jk}^{yz} - \lambda{ik}^{yz}]] \end{split} \tag{4}$$

Thus, for instance, in Eq. (4), we are modeling the log of the odds that y = j instead of y = 1, when x = I and z = k.

3. Data description

Different tolling systems are expanding on the Florida expressways. In the past decade, many toll agencies converted their Traditional Toll Plaza s to either Hybrid Toll plaza or all-electronic toll collection system.

Multiple sets of data maintained by Florida Department of Transportation (FDOT, 2017) were used in this study including: Crash Analysis Reporting (CAR) system, Roadway Characteristics Inventory (RCI) system, TranStat IView aerial mapping system, and Financial Project Search Database. Moreover, Google Earth and the publication reports of Florida Turnpike and Central Florida Expressway Authority (CFX, 2017) were used to verify the toll plazas' characteristics. A hundred mainline toll plazas located on approximately 750 miles of toll roads in Florida were selected. Crash data from seven-year period (2007–2013) were investigated. Crashes that occurred within the influence areas (1 mile before and 0.5 mile after the centerline of the mainline toll plaza (MUTCD, 2017)) were extracted from the crash database and data in the period when toll plazas were being upgraded in addition to six months after were excluded from the analysis.

4. Analysis and results

4.1. Part I: Comparison between different designs of the Hybrid toll plaza

Data from 60 Hybrid Toll Plazas (HTP) were used in this approach and crash data from a seven-year period was investigated. Fig. 1 shows different designs of the Hybrid Toll Plazas; Design 1 (D1) combines express Open Road Tolling (ORT) lanes on the mainline and separate traditional toll collection to the side; while Design 2 (D2) combines traditional toll collection on the mainline and separate ORT lanes to side.

A series of Safety Performance Functions (SPFs) using Negative Binomial (NB) models were fitted to establish the relationships between traffic and roadway characteristics, and crash frequency at the vicinity of HTPs. Exploratory modeling indicated that the crash frequency is not significantly associated with traffic direction, number of entry and exit ramps, and distance to entry and exit ramps.

Table 1 shows the parameter estimates of the final model. Only log Annual Average Daily Traffic (AADT) and the type of design came out to be significant with the expected signs. The coefficient of AADT has a

Table 1 Estimates of Coefficients for Different designs of the HTP.

| Negative Binomial | | |----------------------------------------------------|--| | Analysis of Maximum Likelihood Parameter Estimates | |

Crash type Injury level Parameter Estimates Pr > ChiSq AIC
All All Intercept
Log AADT
Design type*
Dispersion		 −16.755
1.883
0.169
0.113		 < 0.0001
< 0.0001
0.0433		 168.653

Design type* = (D1-and-D2) dummy variable (i.e. D1 = 0 and D2 = 1).

positive sign, which indicates that as AADT increases, the frequency of HTP-related crashes increases.

This finding could be attributed to the fact that the AADT is considered as the exposure factor; more traffic at the HTP would lead to higher chances of crash occurrence. This is expected, since higher AADT results in higher exposure of vehicles to weaving maneuvers (change lanes) before and after the toll plaza, which in turn would result in higher crash frequencies.

The design type was found to be significant; the effect of design 2 (D2) of the HTP was compared to the design 1 (D1) (the base case). The parameter estimates given in Table 1 can be used to estimate the Incident Rate Ratios (IRR) by exponentiation of the regression coefficients Exp[β]. IRR value shows that the risk of crashes at D2 was approximately 19 percent higher than at the D1, given that all other variables are constant.

The increased crash risk at the D2 may be explained by the fact that more than 81 percent of the vehicles in Florida are equipped with prepaid toll transponders (FTE, 2017). Thus, the use of D2 will cause more than 81 percent of the traffic to diverge and merge before and after the toll plaza and that could be a very confusing to the drivers; while in D1 only 19 percent or less of the traffic (vehicles without transponders) will need to diverge and merge before and after the toll plaza.

The good news is that Florida Turnpike has scheduled all of the HTPs that have D2 to be converted to All-Electronic Toll Collection. However, D2 could be a good temporary design in the places that have low prepaid transponders users. In the other words, it is dependent upon the percentage of the automatic tolling users. So, as this percentage increases, more traffic will need to diverge and merge; thus, this design becomes riskier.

4.2. Part II: Comparison between diverge-and-merge areas

Similar to part I, data from 60 Hybrid Toll Plazas was used in this approach. Crash data from a seven-year period was investigated. Table 2 shows the parameter estimates of the final model resulting from 120 observations. Sixty Hybrid Toll Plazas, each one has two locations, one before (Diverge) and one after (Merge) the Toll plaza (60 ∗ 2 = 120 observations).

It should be noted that the data used in this part included only the mainline crashes, i.e. crashes that occurred at the toll booths were excluded. Fig. 2 shows the diverge-and-merge areas that were investigated in this part of the analysis.

The log Annual Average Daily Traffic (AADT) and the location came out to be significant with the expected signs in the final SPF model. The coefficient of AADT has a positive sign, which indicates that as AADT increases, the frequency of diverge-and-merge related crashes increases. This is expected, since higher AADT results in higher exposure of vehicles to weaving maneuvers (change lanes) before and after the toll plaza, which in turn would result in higher crash frequencies.

The location (diverge-and-merge) dummy variable (i.e. diverge = 1 and merge = 0) was found to be significant. Since the lengths are

Table 2 Estimates of Coefficients of diverge and merge areas of the HTP.

Negative binomial
Analysis of maximum likelihood parameter estimates
Crash type Injury level Parameter Estimates Pr > ChiSq AIC
All All Intercept
Log AADT
Location*
Dispersion		 −20.6811
2.2327
0.2103
2.2667		 < 0.0001
< 0.0001
0.0317		 365.607

Location* = (diverge-and-merge) dummy variable (i.e. diverge = 1 and merge = 0).

Fig. 2. Diverge-and-merge areas before and after the HTP (). Source: MUTCD, 2017

different between the (diverge-and-merge) areas, the frequency of crashes were controlled by the segments' lengths. The effect of diverge was compared to the merge (the base case), and the coefficient of the location was positive indicating that diverge section is associated with more crashes than the merge section. The Incident Rate Ratios (IRR) value shows that the risk of crashes at diverge area before the HTP was approximately 23 percent higher than at the merge area after the plaza, given that all other variables are constant.

The increased crash risk at diverge area may be explained by the fact that diverge section of the Hybrid Toll Plaza is associated with potential sudden lane change. Moreover, drivers may be distracted when they prepare to pay, search for cash or cards, and selecting either the cash or coin lane. While in the merge area, drivers just accelerate and focus on merging with traffic, especially if the acceleration lane has a good design and signage.

However, choosing a good toll plaza location and finding ways to increase the percentage of prepaid transponder users are potential means of reducing lane changes at toll plazas. Adequate warning of no sudden lane change and good signage should be given on the approach to the diverge area. Offering toll discounts for prepaid transponder users and educating drivers can incentivize drivers to enroll in this system.

4.3. Part III: Log-Linear models

Data including all types of toll plazas in Florida were used in this approach. A hundred mainline toll plazas, each one has two locations, one before and one after the toll plaza (100 ∗ 2 = 200 segments). Several Log-linear models with different variables in each model were developed, and only the significant variables and best fit model was presented. The effects of AADT and crash related factors were examined, and interactions among them were considered. Crash data from a seven-year period was used, and only crashes that occurred within the influence areas of the toll plazas were investigated. The final model was developed to investigate the association between toll plaza types and both driver-age and the AADT. The three main effects and all three possible two-way interactions were included in this model. Fig. 3 shows different types of mainline toll plazas.

It should be noted that in order for the model to fit the data in a proper way, the variables should be categorized. Thus, toll plaza types categorized to three categories, driver-age categorized to two categories, and the AADT categorized to two categories. These categories were as follows:

(1) " X = Toll Plaza Types: They were categorized into three levels and coded as follows:

i = level:

"1" = Hybrid Toll Plaza (HTP)

"2" = All-Electronic Toll Collection (AETC)

"0" = Traditional Toll Plaza (TTP) - (the base case).

(2) Y = driver-age: It was categorized into two levels and coded as follows:

j = level:

"1" = Young (15–30 years old)

"0" = Not young (Older than 30 years old) - (the base case).

The 30 years old was selected as the cutoff point for age based on the literature (FDOT, 2017) (Kim et al., 1995), and criteria similar to those used by car insurance companies for when drivers start to drive more carefully due changes in life style and their life cycle (FDOT, 2017).

(3) Z = Annual Average Daily Traffic (AADT): It was categorized into two levels based on the 50th percentile and coded as follows:

k = level:

"1" = Low

"0" = High (the base case).

Traditional Toll Plaza (TTP) (Source: FTE, 2017)

Hybrid Toll Plaza (HTP) (Source: CFX, 2017)

All-Electronic Toll Collection (AETC) (Source: FTE, 2017)

Fig. 3. Different types of the Mainline Toll Plazas.

This is a three-variable model with variables x = (toll plaza types), y = (driver-age), and z = (AADT).

Normally, the G2 goodness-of-fit statistic and p-value are used to determine the rejection or acceptance of the model. The larger value of G2, the more evidence there is against the null hypothesis (Ho), where Ho = model fits the relationship and Ha = model does not fit the relationship. Hence, the smaller G2 is better, but it depends on the degrees of freedom. The larger p-value (> 0.05) indicates that the estimated model fits the relationship. The model contains all three main effects and all three possible two-way interactions. Table 3 shows the parameter estimates and odds ratios.

The results showed that the values of the G2 = 1.27, Pvalue = 0.5311, and the DF = 2 indicated that the model significantly fits the data. So, it can describe the associations between the variables by computing the odds ratios. With the logit model, the parameters provide a measure of the magnitude and direction of effects of the independent variables on the response variable (Kim et al., 1995). The parameter estimates for individual and interaction terms and their odds ratios are presented in Table 3. Conceding the total number of crashes, the odds ratio is as follows:

The odds ratio of Hybrid Toll Plaza (level 1) is 0.553 (Safety Effectiveness = 100–55.3 = 44.7 percent) from the base case Traditional Toll Plaza (level 0). Also, the odds ratio of the level 2 = allelectronic toll collection is 0.274 (Safety Effectiveness = 100–27.4 = 72.6 percent) from the base case Traditional Toll Plaza, given that all other variables are constant. These results proved that the HTP and the AETC are much safer than the Traditional Toll Plaza, and this is consistent with the previous finding even with different statistical models (Abuzwidah et al., 2014; Yang et al., 2014; Abuzwidah, 2011; Zhang et al., 2009).

The estimate of driver-age is negative, so it gives odds of less than one. The decrease of the crash risk of this age group for total crashes at all types of toll plazas may be explained by the fact that the proportion of the young drivers is less than the middle age and older (age > 30). This is same for the interaction of (AETC (level 2) ∗ young age).

The odds of (HTP ∗ young age) is 3.2 percent higher than the base cases. This may be explained by the literature that very young and young drivers probably have less driving experience, and with low AADT they tend to speed and commit driving violations (Kim et al., 1995); especially with the risk of diverge-and-merge before and after the Hybrid Toll Plaza. This fact was clear for the total crashes at all types of toll plazas, the odds ratio of the interaction (young age ∗ Low AADT) is 9.5 percent more than the base case (older than 30∗ high AADT), so this might explain their involvement in crashes.

Table 3 The estimate of log-linear model.

| Response | | TPT × Driver-age × AADT | | | | |-------------------|----|-------------------------|------------|--|--| | Source | DF | Chi-Square | Pr > ChiSq | | | | TPT* | 2 | 6.36 | 0.0257 | | | | Driver-age | 1 | 2.23 | 0.1124 | | | | TPT × driver-age | 2 | 4.69 | 0.0581 | | | | AADT | 1 | 1.22 | 0.3153 | | | | TPT × AADT | 2 | 0.33 | 0.8368 | | | | Driver-age × AADT | 1 | 1.77 | 0.1664 | | | | Likelihood Ratio | 2 | 1.27 | 0.5311 | | |

Parameter Estimate& (Odds ratio) Standard Error Chi-Square Pr > ChiSq
TPT* 1 −0.5922 0.1335 5.79 0.0192
(0.553)
2 −1.2935 0.2112 0.22 0.5442
(0.274)
Driver-age Young −0.07543 0.1324 2.23 0.1245
(0.927)
TPT × Driver-age 1 Young 0.0321 0.1415 0.06 0.6523
(1.032)
2 Young −0.3822 0.2505 4.12 0.0352
(0.682)
AADT Low 0.0223 0.1107 1.22 0.2532
(1.022)
TPT × AADT 1 Low −0.5229 0.1532 0.00 0.8851
(0.593)
2 Low −0.9795 0.1907 0.28 0.4211
(0.375)
Driver-age × AADT Young Low 0.0915 0.1292 1.77 0.1237
(1.095)

TPT* = Toll Plaza Types (i.e. TTP (0), HTP (1), and AETC (2)).

The low AADT has odds 2.2 percent higher than the high AADT. This is because at low AADT, the speed is usually high. So, drivers are more likely to make a sideswipe, hit the tollbooths and/or lost control.

5. Conclusions

Expressways (toll roads) are considered as an important part of any successful transportation system, because they are carrying a significant number of the daily trips and offering a high level of service. however, traditional toll plazas still experience many crashes, many of which are severe and the literature showed a very limited studies that addressed toll plaza safety, and non of them were evaluated the safety impacts of using different design of Hybrid Toll Plazas (HTP). Therefore, this study examines for the first time the traffic safety impact of using different designs of HTP. And to the best of our knowledge, there is an urgent need for this evaluation since many agencies want to adopt Design 2 of the HTP (Fig. 1) because it just requires adding separate ORT lanes to the side without touching the existing main-line toll plazas. Also, this study helps understand the relationship between the crash frequency and several important crash-related factors and circumstances such as toll plaza types, traffic volume, and driver-age. Crash data from a sevenyear period was investigated, and a hundred mainline toll plazas were evaluated using multiple analytical techniques. The current data has indicated that certain designs and locations at toll plazas are more likely to experience traffic crashes than regular segments of the expressways.

The Incident Rate Ratios (IRR) value shows that the risk of crashes at design 2 (D2) of the Hybrid Toll Plaza was approximately 19 percent higher than at the design 1 (D1), given that all other variables are constant. The increased crash risk at D2 may be explained by the fact that more than 81 percent of the vehicles in Florida are equipped with prepaid toll transponders. Thus, the use of D2 will cause more than 81 percent of the traffic to diverge and merge before and after the toll plaza. While in D1, only 19 percent or less of the traffic (vehicles without transponders) will need to diverge and merge before and after the toll plaza. However, D2 could be a good temporary design in the places that have low prepaid transponder users. In other words, it is dependent upon the percentage of the ETC users; as this percentage increases, more traffic will need to diverge and merge; thus, this design becomes riskier.

Another finding is there is an indication that the majority of crashes occurred at diverge and merge areas before and after the HTP. The IRR value shows that the risk of crashes at diverge areas were approximately 23 percent higher than at the merge areas, given that all other variables are constant. The increased crash risk at diverge areas may be explained by the fact that diverge sections before the Hybrid Toll Plazas are associated with potential sudden lane change. Moreover, drivers may be distracted when they prepare to pay, search for cash or cards, and selecting either the cash or coin lane, while in the merge area they just accelerate and focus on merging with traffic, especially if the acceleration lane has a good design and signage.

The results also indicated significant relationships between the crash frequency and toll plaza types, annual average daily traffic, and driver-age. This means all of these three variables significantly affect the frequency of toll plazas-related crashes. Moreover, it was found that the HTP and the All-Electronic Toll Collection (AETC) were associated with less number of crashes than at the Traditional Toll Plaza by 44.7 and 72.6 percent, respectively. Therefore, HTPs and AETCs are much safer than the Traditional Toll Plazas. For those agencies that cannot adopt the AETC systems, improving traffic safety at HTP and traditional toll plazas should take a priority.

Acknowledgements

The authors would like to thank SAFER-SIM for partially funding this research. SAFER-SIM is funded by a University Transportation Center lead by the University of Iowa.

References