Safety Performance Functions for Partial Cloverleaf On-Ramp Loops for Michigan

Transcription

1 Safety Performance Functions for Partial Cloverleaf On-Ramp Loops for Michigan Elisha Jackson Wankogere Department of Civil and Construction Engineering Western Michigan University 10 W. Michigan Ave Kalamazoo, MI 00-1 Tel: elishajackson.wankogere@wmich.edu Valerian Kwigizile, Ph. D., P.E.* Department of Civil and Construction Engineering Western Michigan University Kalamazoo, Michigan 00-1 Phone: valerian.kwigizile@wmich.edu and Jun-Seok Oh, Ph. D., PTOE. Western Michigan University Department of Civil and Construction Engineering Kalamazoo, Michigan 00-1 Phone: jun.oh@wmich.edu *Corresponding Author Paper Submitted for Presentation at the TRB rd Annual Meeting November 01 Number of words = 1 + ( Tables & Figure) x 0 words =1 words 1 Paper revised from original submittal 1 TRB 01 Annual Meeting

2 ABSTRACT Safety performance functions (SPFs) have become an essential part of analyses and evaluation processes to ensure safety of roadway users at optimal costs. Many states have calibrated the SPFs provided in the Highway Safety Manual (HSM) or developed their jurisdiction specific SPFs. Most of these SPFs have been for intersections and roadway segments. A limited number of states have developed SPFs for interchanges and especially on-ramps and their related sections such as ramp segments and point of freeway entry. This research paper is a documentation of the effort to develop SPFs for urban partial cloverleaf (parclo) on-ramp loops at freeway entry in Michigan. A number of factors associated with crash frequency on these facilities were examined, and the SPFs developed for partial cloverleaf loops, are presented TRB 01 Annual Meeting

3 1 1 INTRODUCTION Safety Performance Functions (SPFs) are equations/models developed to help in the prediction/estimation of expected number of crashes by relating the number of crashes to other highway related variables such as AADT, length of roadway segments, shoulder width, number of lanes and other roadway and surrounding environmental characteristics. SPFs can be used both at project design stage where the safety impact of various elements of design alternatives can be checked, and screening of existing sites for potential of safety improvement (PSI). Both uses of SPFs assist the transportation agencies to efficiently use the limited funding and resources to carry out the right projects and evaluation of the effectiveness of engineering treatments performed at sites to reduce crashes. SPFs form an essential part of the Empirical Bayes (EB) method - a method advocated by the Highway Safety Manual (1) and which has been mostly utilized to identify locations with potential for safety improvement (PSI). This is due to its several advantages such as curbing the effect of regression to the mean () Currently, a number of states have taken efforts to develop their own SPFs or calibrated those proposed by the Highway Safety Manual 0 (HSM) to fit their local scenarios which are much influenced by local conditions such as crash reporting practices, geographical conditions, weather and the like. The development of jurisdiction-specific SPFs helps in providing better predictions of crashes because jurisdiction-specific models are likely more accurate compared to those provided by the Highway Safety Manual. However, it is difficult to develop jurisdictionspecific SPFs partly because of lack of sufficient data for specific types of roadway facilities, for example freeway ramps. Most of the states that have developed SPFs have focused on intersections and segments, for which data needed is relatively easier to obtain. Some states have attempted to develop SPFs for ramps, especially ramp terminals. These few efforts include Torbic, et al in the development of the Interchange Safety Analysis Tools (ISAT) (), Persaud, et al in a an effort to assess safety performance of freeway interchanges, ramps and ramp terminals (), Persaud et al while developing SPFs for ramp terminals at diamond interchanges () and Wang, et al as they developed SPFs for signalized diamond interchange ramp terminals (). The studies mentioned above have looked into different aspects of ramp terminals including control type, geometry, leg numbers, ramp and crossroad volumes, and signal timings. Wang, et TRB 01 Annual Meeting

4 al reports the major deficiency of the ISAT ramp terminal SPFs to be their link to SafetyAnalyst which was developed for conventional intersections and did not consider signal timing as well as terminal spacing, hence their development of SPF for signalized diamond ramp terminals taking these factors into consideration On-ramp can be challenging in terms of grouping and treating them as compared to off ramps. A very limited number of agencies have focused on developing SPFs for on-ramps (). When examining on-ramps, areas of interest include point of entry to the ramp from urban street, along the ramp segment, and the point of entry to the freeway. Examination of Michigan crashes indicated concentration of crashes at the point of entry to the freeway for parclo on-ramp loops. The complex interaction between vehicles at these locations as drivers try to merge into the mainline flow from a loop as opposed to other freeway entrances in which vehicles enter freeway from relatively straight on-ramps, such as diamond interchange on-ramp, may have impact on the number of crashes. Most studies looking at freeway merging crashes have not specifically considered the type of on-ramp. Also, the merging area has been generalized to include the length of 0 ft stated in the Highway Capacity Manual (HCM 0) as the critical merging area influencing safety. As shown in Figure1, this length could be examined incrementally, especially when considering the type of on-ramp. This study focused on 0 ft on both sides of the geometric confluence point: 0 ft downstream of this point and 0 ft beyond the point. The study concentrates on urban parclo on-ramps. 1 TRB 01 Annual Meeting

5 Figure 1. Crashes concentration within 0 ft buffer LITERATURE REVIEW The HSM as well as the SafetyAnalyst - one of the analytical tools developed by FHWA to implement the HSM procedures, contain SPFs that need to be calibrated to local conditions and characteristics. The calibration is required since the general level of crash frequencies may vary substantially from one jurisdiction to another for a variety of reasons including crash reporting thresholds and crash reporting system procedures (1). The HSM s SPFs were developed with data from four states only: California, Minnesota, Ohio and Washington. Although the calibration of SPFs to local conditions might give crash frequencies that reflect the crash pattern for the specific area, it has several limitations. Crash reporting systems vary by different states. This difference might affect the calibration between states with very contrasting reporting systems. Dixon et al. () indicated that the calibration factor for the state of Oregon four-lane divided facility on state highway is very low (0.) and suggested that it might be due to it being characterized as self-reporting state. Other limitation associated with calibration of SPFs is that TRB 01 Annual Meeting

6 variables such as weather, terrain and animal populations are not considered into the calibration exercise. Saito et al. () determined that the HSM model for rural two-way roadway segment underpredict the number of accidents for the state of Utah by 1 percent. Even when the model is calibrated to the local conditions, Harwood et al. () recommend that, when using the model, the sample for new jurisdictions is such that the distribution of traffic volumes is similar to that in the data used for the original calibration. 1 1 Due to limitations associated with calibration of HSM SPFs to local conditions as depicted above, the importance of developing of SPFs from local data is apparent. These SPFs can easily consider local factors contributing to crash occurrence and their relationship besides the traffic volume (AADT). Since the main constraint for the development of SPFs is the availability of data, when enough data is available, the HSM recommends states to create jurisdiction-specific models Safety Analyst tool, which is used for screening roadway network and prioritization of sites that have potential for safety improvements, selection of possible countermeasures for a specific site to mitigate a safety concern, performing economic appraisal to rank sites, and estimating the safety effect of countermeasures implemented at specific sites, uses SPFs with AADT as the only independent (predictor) variable for intersections and AADT and segment length for segments. Safety Analyst incorporates state-of-the-art safety management approaches into computerized analytical tools for supporting the decision-making process to identify safety improvement needs and develop a system wide program of site-specific improvement projects (). It is recommended that SPFs be developed for total crashes (TOT) in which the SPF predicts the number of all crashes at all severity levels combined and for fatal and injury crashes (FI) which predicts crashes that either resulted to an injury or was fatal (1), (). The rest of the combinations can be obtained by the used of respective crash type multiplicative proportions or subtraction such as the difference between TOT and FI frequencies to give PDO crash frequencies. TRB 01 Annual Meeting

7 While developing SPFs for intersections, Tegge et. al noted that there are two types of SPFs according to the variables considered into the function. Level I SPFs are models based on traffic volumes should be considered (). The functional form of a Level I SPF for intersections is as follows: ( ) ( ) (i) where μ i represents the predicted crash frequency per year at a given intersection and α 0, α 1 and α are the regression parameters. The AADT of the major road has a larger coefficient in the SPF model due to its volume has the highest incidence (1). The weakness of SPFs using only traffic volumes is their inability to help in trying to identify the reason for a crash (). Level II SPFs include variables other than just traffic volumes (e.g. weather conditions, roadway geometries, traffic data, and human factors) to calculate the crash frequencies. A Level II SPF for the case of intersections usually takes on the following functional form: 1 1 (ii) where μ i is the predicted crash frequency per year at a given intersection, α, α,, α q are additional regression parameters, and X i, X i,., X qi are the variables of interest (). 1 Level II SPFs provide information for making future improvements to a given roadway, because they consider and determine the relationship between the variables and crash occurrence. By recognizing the impacts of changing a given geometry to safety allows engineers to have better safety judgment. Also, the additional variables allow for benefits such as education and enforcement (). Besides the advantages of accuracy of SPFs type II, there is a major limitation TRB 01 Annual Meeting

8 with this kind of models: the impossibility to be run in Safety Analyst (analytical tool developed by FHWA), since Safety Analyst only considers the traffic volume (SPFs type I) METHODOLOGY In the past the common form of models used to develop SPFs were linear regression models (1). These models used an incorrect assumption that the distribution defining the crash rates is a normal distribution, an assumption which many studies have found to be incorrect. In contrast with the fact that count data is never negative, these linear regression models sometimes resulted or predicted negative crashes. For this reason the most common methods used in the development of SPFs are Poisson regression modelling or Negative Binomial regression modelling (1), (1), (), (). These methods are best suited for count data to which crashes belong ()Harwood, et al. () suggests the use of Poisson Regression models or Negative binomial models for the development of SPFs. Poisson Regression models are used when the mean is equal to the variance (that is, assuming the crash data to follow a Poisson distribution, and hence the Poisson regression analysis can be performed). Overdispersion is said to occur when variance of the crash frequency observations is greater than the mean, In such cases, the Negative Binomial regression models become appropriate. (1), (). By generalizing the Poisson model by the addition of a gamma distributed error term EXP( with mean 1 and variance α, a Negative binomial model is obtained (). The modified equation of the Poisson model becomes: 0 1 (iii) where i is the expected number of crashes in a given time period for an urban parclo on-ramp- freeway entry i; is a vector of parameters to be estimated, the introduced error term, and is the vector of explanatory variables i. The negative binomial model follows a distribution of the form shown in Equation (iv). TRB 01 Annual Meeting

9 i i i (iv) where P y i is the probability urban parclo on-ramp terminal i having y i crashes in a given time period. (x) is a value of the gamma function, y i is the number of crashes for urban parclo on- ramp-freeway entry i, i is as previously defined and is an overdispersion parameter. The goodness-of fit (GOF) of the developed models can be assessed by comparing the Bayesian (Schwarz) Information Criterion (BIC).The BIC is computed as: (v) where ω is the number of parameters in the model, L is the final log-likelihood for the model estimated, and N 1 is the number of observations. The model with the lowest BIC value is selected as the best fitted DATA COLLECTION As mentioned earlier common variables used for development of SPFs are mainly AADT for the case of intersections, AADT and Segment length and Crash data. To well capture the influence of other variables such as roadway characteristics other variables may also incorporated as suggested by the Highway Safety Manual. This is done taking into consideration that highly correlated variables are avoided. The preferable amount of crash data to be used is a five years data set and a maximum of years. Sometimes a minimum of three years data can be used in case of crash data shortage (1). To explore the possibility of having both type I and type II SPFs several variables other than Loop ADTs and Mainline AADTs, were collected. TRB 01 Annual Meeting

10 ADT and AADT Data ADT data was processed from a Microsoft Excel file provided by the Michigan Department of Transportation (MDOT). The file contained traffic volume counts of all Michigan ramps. It also contained other details such as date and time of counts, ramp location, count location on the ramp recorded in x, y coordinates and the volume counts entered against the time they were obtained. Counts were either 1-minutes counts or hourly counts that both lasted for at least hours of continuous counting. Different ramps had different number of complete hour counts. The data was filtered to contain only on-ramp loops. x, y coordinates of the count locations on the loops were converted into a shapefile in ArcGIS. This enabled selection of urban parclo loop on-ramps from the Michigan road network shapefile as this loop type distinction information was not directly provided in the volume count file. After plotting, processing and random sampling was done; a sample of 1 urban parclo loop on-ramps was obtained. ADTs were processed for these 1 samples. The averages of hour counts were calculated for each of the ramps to obtain ADT (veh/day). For the remainder of the paper, this volume is referred to as loop ADT Mainline AADT data was obtained by using AADTs from shapefiles provided by MDOT. They contained 00 and 0 AADTs for the whole state road network. There was little difference between the two AADTs and so they were averaged and used as Mainline AADTs (veh/day). The distribution of ADTs and AADTs for the sampled ramps is as shown in Figure. Both the loop ADTs and Mainline AADTs were linked to the specific crashes that they were attributerelated or spatially related to through GIS processing. Logarithms of the loop ADT and Mainline AADT were calculated and recorded as Ln_Loop_ADT and Ln_Main_AADT respectively. These were later used for finding alternative models to explore the possibility of better fitting model by log transformation of traffic volumes. TRB 01 Annual Meeting

11 Frequency Loop ADT Distribution Frequency 1 0 Distribution of Mainline AADT LoopADT(veh/day) 1 Mainline AADT (Veh/day) Figure. Loop ADT and Mainline AADT Distribution Other Ramp and Roadway Variables As mentioned above, other mainline and ramp variables were also collected for the sampled ramps. Lane configuration in the vicinity of merging point such as weaving, merging or added lane, acceleration lane length and ramp speed limit were obtained though Google Earth TM. Mainline speed limit, average shoulder width and percentage of commercial vehicles was obtained though state road network shapefile provided. The variables were named as follows Acc_ln_lng for acceleration lane length, Merging_lane (a dummy variable of whether the lane at the ramp-freeway entry was a merging lane or not) Weaving_lane ( a dummy variable of whether the lane at the ramp-freeway entry was a weaving lane or not) Loop_speed_lt for loop speed limit, Mainline_No_Lanes for mainline number of lanes, PCT_COMM for percentage of commercial vehicles on the mainline and Average_SHDR_WID for average shoulder width. Table 1a and Table 1b below show the descriptive statistics of the variables and the correlation between the variables, respectively. It is important to note that it was assumed that there were no significant geometric changes to the configuration of the ramps as well as the mainlines in the study period. It was also difficult to obtain exact geometry of the ramp in 0 as well as its geometry in TRB 01 Annual Meeting

12 Ramp-Freeway Entry Crash Data As a proposed minimum number of years by the HSM (1) for SPF development, crash data for three years 00, 0, 0 was extracted from crash data file provided by the Office of Highway Safety Planning (OHSP) of the Michigan State Police (MSP). The file has an indicator of ramp related crashes, a close look of some of the crashes in GIS indicated that some of the crashes had occurred at the ramps or at the ramp-freeway merge point but were not recorded as ramp related. With the aim of obtaining quality data it was decided to completely base the selection and classification of data as ramp related using GIS processing starting by plotting the crashes using their recorded x,y coordinates. Crashes that were close to the sampled ramp were extracted using as 0ft circular buffer developed at the ramp-freeway entry points. The 0ft buffer was chosen since an observation of the crash patterns at the vicinity of the freeway entry indicated that of most crashes reported as ramp related happened within this range (see Figure 1). After cleaning the 0ft-buffer extracted crashes making sure the selected crashes were within the ramp-freeway merging point vicinity, a total of fatal and injury crashes (F+I) and total crashes, were extracted. These crashes were linked with their specific loop ADTs as well as mainline AADTs. Thus crashes within 0ft of the ramp-freeway confluence point vicinity were considered to be ramp-freeway entry point related crashes. As expected higher exposures (in this case ADT and AADT) were related to higher crashes as seen in Figure. The crash related variables developed were F+I_total for the total fatal and injury crashes for all the three years, and total_crashes for the total crashes in three years. 1 Table 1a. List of Variables statistic Count Mean Std. Error Median Mode Std. dev Sample Variance Min Max Sum F_I_Total Total_Crashes Merging_lane Weaving_lane Loop_speed_lt Main_No._LANES Main_SPD_LIMIT Average_SHDR_WID PCT_COMM Acc_ln_lng TRB 01 Annual Meeting

13 Table 1b. Correlation between the variables LooP_ ADT Main_ AADT Acc_ln _lng Merging_ lane Weaving_ lane Loop_speed_ lt Main_NUM _LANES Main_ SPD_ LIMIT Average_SHDR _WID PCT_COMM LooP_ADT Main_AADT Acc_ln_lng Merging_lane Weaving_lane Loop_speed_lt Main_NUM_LANES Main_SPD_LIMIT Average_SHDR_WID PCT_COMM Total Crashes Total_Crashes F_I Crashes Mainline AADT 1 TRB 01 Annual Meeting

14 Total Crashes Total_Crashes F_I Crashes Loop ADT 1 Figure. Crashes Against exposure (mainline and loop traffic volumes) RESULTS AND DISCUSSION The Negative binomial model was run several times using STATA statistical software using a combination of both backward and forward stepwise regression on each of the dependent variables F+I_total, and Total_Crashes against other independent variables listed previously. These variables were LooP_ADT for the loop ADT, Ln_Loop_ADT for the natural logarithm of the loop speed, Main_AADT for the mainline AADT, Ln_Main_AADT for the natural logarithm of the mainline AADT, Acc_ln_lng for acceleration lane length, Merging_lane ( a dummy variable of whether the lane at the ramp-freeway entry was a merging lane or not) Weaving_lane ( a dummy variable of whether the lane at the ramp-freeway entry was a weaving lane or not), Loop_speed_lt for loop speed limit and Main_No_Lanes for mainline number of lanes. A constant of three years hereby shown as Time_expos was used (since three years of crash data was considered) as a substitute of the exposure variable. This was to help convert the three years period prediction models to per year crash prediction by adjusting the intercept (constant). After running the models the final results of significant variables in different models that were chosen 1 TRB 01 Annual Meeting

15 as best models based on their BIC were as shown in the tables below. Two final models were chosen, one for each category of dependent variable (that is for the variables F+I_total and Total_Crashes ) as shown in the tables that follow. Table. Model 1: F+I total crashes F+I_Total Coef. Std. Err. z P> z Ln_Loop_ADT Ln_Main_AADT Mainline No. Lanes Constant ln(time_expos) 1 (exposure) alpha No. of obs = 1, Log likelihood = -1., LR chi() = 0.,Pseudo R = 0.00, Prob > chi = 0,Likelihood-ratio test of alpha=0: chibar(01) =. Prob>=chibar = 0.000, BIC=. For the F+I SPF, Table above shows the best model obtained for this dependent variable which had a BIC of. lower than the other tested models. The variables Ln_Loop_ADT and Ln_Main_AADT were all strongly significant significance as shown by the p-values of and 0.00 respectively. Mainline number of lanes is marginally significant (with p-value of 0.). This sums up to a type II SPF of the form shown in Equation (vi) below. 1 1 (vi) Where, is the number of expected F+I crashes now corrected for one year at a given urban parclo on-ramp freeway entry. Other variables are as previously defined. 1 1 TRB 01 Annual Meeting

16 From the equation above it can be seen that both Loop ADT and mainline AADT (as expressed by the log of these variables) are associated with increasing the chances of fatal and injury crashes as they increase as shown by their positive coefficients 0.0 and 0. respectively. Mainline number of lanes is associated with decreasing the chances of fatal and injury crashes as they increase as shown by the negative coefficient (-0.1). That is the more number of lanes there are in the mainline, the lesser the chances of fatal and injury accidents. This may be attributed to the fact that drivers may be avoiding lanes close to the rampfreeway entries as they have more options on which lanes to drive on. The overdispersion parameter alpha is statistically different from zero (0.1) hence suggesting that the data is overdispersed and variance is not equal to the mean, thus the appropriateness of the negative binomial model Table presents a model for Total crashes. The model was selected as the best based on its lower BIC of. as compared to other models for total crashes for a three year period. The variables Ln_Loop_ADT and Ln_Main_AADT were all significant at % level of confidence as shown by the p-values of 0.01and 0.00 respectively. The effects of the Ln_Loop_ADT and Ln_Main_AADT variables on total crashes for three years are the same as those discussed in model 1 above as they have the same signs (positive), though this time with different coefficients and at % level of confidence. So is the same for the alpha value indicating overdispersion suitability of the negative binomial model (0.1). Table. Model :Total Crashes Total_Crashes Coef. Std. Err. z P> z Ln_Loop_ADT Ln_Main_AADT Constant ln(time_expos) 1 (exposure) alpha No.of obs = 1, Log likelihood = -., LR chi() = 1.,Pseudo R = 0.0; Prob > chi = 0,Likelihood-ratio test of alpha=0: chibar(01) =. Prob>=chibar = BIC=. 1 TRB 01 Annual Meeting

17 This results into a type I SPF shown in the Equation (vii) below. (vii) where, is the number of expected total crashes now corrected for one year at a given urban parclo on-ramp freeway entry. Other variables are as previously defined. As seen from above, the significant variables were only the natural logarithms of loop ADT, the natural logarithm of mainline AADT for all the two models and mainline number of lanes for the F+I total model. All other variables were found not to be significant through the modelling process. Some models with untransformed ADTs and AADTs had significant variables though they were not selected as best models due to higher BICs. Crashes are normally predicted in crashes per year for most practical purposes, and hence the time of exposure had to be introduced in the model to predict average crashes per year. Since the number of lanes in the mainline and the mainline AADT have a higher correlation (0.0) as show in the correlations in Table 1b, a model for the F+I crashes without this variable was also run and is presented in the Table below. 1 1 Table. Model : F+I total crashes F+I_Total Coef. Std. Err. z P> z Ln_Loop_ADT Ln_Main_AADT Constant ln(time_expos) 1 (exposure) alpha No. of obs = 1, Log likelihood = -1., LR chi() =.,Pseudo R = 0.0, Prob > chi = 0,Likelihood-ratio test of alpha=0: chibar(01) =.Prob>=chibar = 0.000, BIC=. 1 TRB 01 Annual Meeting

18 1 CONCLUSION SPFs for predicting both fatal and injury ( F+I ) crashes and total crashes for urban Parclo onramp freeway entry were successfully developed with log transformed loop ADTs and AADTs as predictor variables as well as number of mainline lanes for F+I total crashes.. As indicated by the results, the developed SPFs for urban Parclo on-ramp freeway entry can be modelled similar to the modelling of type I intersection SPFs proposed by the Highway Safety Manual since only log transformed traffic volumes can be used. Based on the current data at hand, only traffic volume data were found to be significant. In the future more efforts should be made to collect more samples of on-loops and related data to try to estimate type II SPFs as they may be more informative on the factors associated with the cause of accidents than just basic exposure variables or ADT and AADT. Efforts should also be made to consider other kinds of ramps whenever relevant data is available ACKNOWLEDGEMENT This study was funded by the Faculty Research and Creative Activities Award (FRACAA) from Western Michigan University (WMU). The authors wish to thank the WMU Office of the Vice President for Research for their support of the study. 1 TRB 01 Annual Meeting

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20 1. Washington, S., Karlaftis, M., & Mannering, F. (0). Statistical and Econometric Methods for Transportation Data Analysis, nd Edition. Boca Raton, FL: Chapman and Hall. 1. Hilbe, J. M. (0). Negative Binomial Regression. Cambridge University Press. 0 TRB 01 Annual Meeting