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727 APPENDIX F: ALGORITHM DESCRIPTION TABLE OF CONTENTS List of Figures ........................................................................................................................... 728 List of Tables ............................................................................................................................. 728 Algorithm Description for Freeway segments ........................................................................... 729 Input Data .............................................................................................................................. 729 Predictive Models .................................................................................................................. 731 Predictive Method .................................................................................................................. 733 Output .................................................................................................................................... 733 Algorithm Description for Freeway speed-Change Lanes ........................................................ 734 Input Data .............................................................................................................................. 734 Predictive Models .................................................................................................................. 736 Predictive Method .................................................................................................................. 738 Output .................................................................................................................................... 738 Algorithm Description for Ramp segments ............................................................................... 738 Input Data .............................................................................................................................. 738 Predictive Models .................................................................................................................. 740 Predictive Method .................................................................................................................. 742 Output .................................................................................................................................... 742 Algorithm Description for Crossroad Ramp Terminals .............................................................. 742 Input Data .............................................................................................................................. 742 Predictive Models .................................................................................................................. 745 Predictive Method .................................................................................................................. 746 Output .................................................................................................................................... 747 Software Documentation ........................................................................................................... 747 Flowcharts ............................................................................................................................. 747 Linkage Lists ......................................................................................................................... 751
728 LIST OF FIGURES Figure 1. Main Subroutine ......................................................................................................... 747 Figure 2. Performance Measures Subroutine ........................................................................... 748 Figure 3. Evaluation based on Predictive Model Only .............................................................. 748 Figure 4. Evaluation based on the Site-Specific EB Method .................................................... 750 Figure 5. Evaluation based on the Project-Level EB Method ................................................... 751 LIST OF TABLES Table 1. Linkage List for Key Subroutines ................................................................................ 752 Table 2. Subroutines Implementing the Predictive Method ...................................................... 753
729 ALGORITHM DESCRIPTION This document provides a description of the algorithms used in the predictive methods for evaluating freeways and ramps. These methods have been implemented in software in the Enhanced Interchange Safety Analysis Tool (ISATe). They are documented in the proposed HSM Freeways chapter (Appendix C), proposed HSM Ramps chapter (Appendix D), and proposed HSM Appendix B for Part C (Appendix E). The objective of this document is to identify the information needed to implement the predictive methods in software products other than ISATe, such as the Interactive Highway Safety Design Model (IHSDM). This objective is achieved by identifying the input data needed, and predictive models used, when implementing the predictive methods. Extensive reference is made to the content of the proposed documents identified in the previous paragraph, as opposed to repeating that material in this document. This document consists of five parts. Each part provides the information needed to implement the predictive method for one of the following freeway facility site types. ⢠Freeway segments. ⢠Freeway speed-change lanes. ⢠Ramp or C-D road segments. ⢠Crossroad ramp terminals. The fifth part of this document provides a series of flow charts that describe the logic flow used in the ISATe software implementation. ALGORITHM DESCRIPTION FOR FREEWAY SEGMENTS This part of the appendix provides information needed to implement the predictive method for freeway segments in software. This method is described in the proposed HSM Freeways chapter. The remainder of this part consists of four sections. The first section identifies the input data needed by the predictive method. The second section presents the crash prediction models. The third section describes the sequence of steps that comprise the predictive method. The last section describes the output data that are available from an application of the predictive method. Input Data This section describes the input data for the predictive method. These data are identified using the following categories. ⢠Evaluation period. ⢠Evaluation type. ⢠Crash data. ⢠Geometric design, traffic control, and traffic volume data.
730 Evaluation Period The evaluation period is the set of years in the combined study period and crash period. Every calendar year in the evaluation period is separately evaluated using the methodology. Specific details about this input are provided in Section 18.4.1, Step 2 of the proposed HSM Freeways chapter. Evaluation Type The predictive method can be used to evaluate one site, or a contiguous group of sites. The evaluation is described as one of several types, as determined by the analyst. When one site is being evaluated, the evaluation types are: A. Evaluation based on using the predictive model only. B. Evaluation based on using the predictive model and crash data. When a group of sites are being evaluated, the evaluation types are: A. Evaluation based on using the predictive model only for each site. B. Evaluation based on using the predictive model and crash data for each site. C. Evaluation based on using the predictive model for each site and crash data for the group of sites. When crash data are used, the empirical Bayes (EB) Method is used to combine the crash data with the predictive model estimate to obtain a more reliable estimate of the expected crash frequency. The three evaluation types are referred to herein as types A, B, and C. In the HSM, type B evaluation is referred to as the âsite-specificâ EB Method and type C is referred to as âproject-levelâ EB Method. There are several factors to be considered when determining whether the EB Method is appropriate for a given project. These criteria are described in Sections B.2.1 and B.2.2 of the proposed HSM Appendix B for Part C. Crash Counts If evaluation type B is input by the analyst, then the crash data for each site are necessary input data. The criteria for assigning crashes to individual freeway segment sites are described in Section B.2.3 of the proposed HSM Appendix B for Part C. If evaluation type C is input, then the crash data for the group of sites is needed. The crash counts must correspond to the crash period. The crash period can be site-specific; however, for coding convenience, the crash period should be the same for all sites. If the crash period includes multiple years, then the crash data do not have to be separately tabulated for each year at each site. Rather, it is sufficient for the analyst to input the total number of crashes for the crash period. Geometric Design, Traffic Control, and Traffic Volume Data The input data describing the geometric design and traffic volume data for freeway segments are identified in the following list. General ⢠Area type (urban or rural).
731 Geometric Design ⢠Number of through lanes. ⢠Segment length. ⢠Length and radius of horizontal curve. ⢠Lane width. ⢠Inside and outside shoulder width. ⢠Median width. ⢠Length of rumble strips on inside and outside shoulders. ⢠Length of (and offset to) median barrier. ⢠Length of (and offset to) outside barrier. ⢠Clear zone width. ⢠Presence and length of Type B weaving section. Traffic Characteristics ⢠AADT volume of (and distance to) nearest upstream and downstream entrance ramp. ⢠AADT volume of (and distance to) nearest upstream and downstream exit ramp. ⢠AADT volume of freeway segment. ⢠Proportion of AADT that occurs during hours where the lane volume exceeds 1,000 veh/h/ln. Specific details about these input data are provided in Section 18.4.2 of the proposed HSM Freeways chapter. These details include the method of measurement and the value limits for each variable. The AADT volume ranges for the predictive models are listed in Table 18-4 of the proposed HSM Freeways chapter. The units of measurement for all input data are U.S. customary. If input data are provided in metric units, then they should undergo soft conversion to U.S. customary units before their use in the predictive method. Predictive Models The general structure of the predictive model is described by Equation 18-1 of the proposed HSM Freeways chapter. A more specific structure is described by Equation 18-2. Safety Performance Functions Separate safety performance functions (SPFs) are provided for the following conditions: ⢠Area type (rural or urban). ⢠Through lanes (4, 6, 8, 10 in urban areas). ⢠Crash type (multiple-vehicle, single-vehicle). ⢠Crash severity (fatal-and-injury, property-damage-only).
732 All total, there are 28 SPFs represented by unique combinations of the four conditions identified in the preceding list. Specific details about the SPF regression coefficients are provided in Section 18.6.1 of the proposed HSM Freeways chapter. Section 18.6.1 of the proposed HSM Freeways chapter describes a procedure for extending the SPFs to segments with an odd number of lanes. Section B.2.7 of the proposed HSM Appendix B for Part C describes a procedure for applying the EB Method to segments with an odd number of lanes. The overdispersion parameter is computed as a function of segment length. The equation for this calculation is provided in Section 18.6.1 of the proposed HSM Freeways chapter. A procedure for calibrating the predictive models is described in Section B.1.1 of the proposed HSM Appendix B for Part C. Crash Modification Factors Eleven crash modification factors (CMFs) are provided in the predictive method. The geometric design features and traffic conditions that they address are identified in the following list. ⢠Horizontal curvature. ⢠Lane width. ⢠Inside shoulder width. ⢠Median width. ⢠Median barrier. ⢠High-volume (congested) conditions. ⢠Lane change activity related to ramp entrances and ramp exits. ⢠Outside shoulder width. ⢠Shoulder rumble strip presence. ⢠Outside clearance. ⢠Outside barrier. Specific details about the CMF formulation and regression coefficients are provided in Section 18.7.1 of the proposed HSM Freeways chapter. This section also identifies conditions where a CMF is not applicable. Supplemental calculations for using the barrier-related CMFs are described in Section 18.7.3 of the proposed HSM Freeways chapter. Crash Type Distribution The predicted crash frequency from a predictive model can be disaggregated into estimates of crash frequency by crash type. The crash type categories for multiple-vehicle crashes include head-on, right- angle, rear-end, and sideswipe. The crash type categories for multiple-vehicle crashes include animal, fixed object, other object, and parked vehicle.
733 Distribution percentages for these crash types are provided in Section 18.6.1 of the proposed HSM Freeways chapter. Application of these percentages is described in Sample Problem 1 in Section 18.13.1 of the proposed HSM Freeways chapter. Crash Severity Distribution The predicted crash frequency from a predictive model can be disaggregated into estimates of crash severity. Specifically, the predicted fatal-and-injury crash frequency can be disaggregated into estimates of fatal (K), incapacitating injury (A), non-incapacitating injury (B), and possible injury (C) crash frequency. A severity distribution function is used for this purpose. The function is an equation that includes some of the same variables used in the predictive model. The equations that comprise the severity distribution function are described in Section 18.8 of the proposed HSM Freeways chapter. Application of these equations is described in Sample Problem 1 in Section 18.13.1 of the proposed HSM Freeways chapter. A procedure for calibrating the severity distribution functions is described in Section B.1.4 of the proposed HSM Appendix B for Part C. Predictive Method The predictive method for freeway segments is described as a flow chart in Figure 18-1 of the proposed HSM Freeways chapter. The flow chart indicates that the method includes 18 steps that are completed in sequence when evaluating one or more sites. The method is described in sufficient generality that it can be applied to one or more sites, for one or more years, with or without the use of crash data. The steps that comprise the predictive method are described in detail in Section 18.4.1 of the proposed HSM Freeways chapter. If the EB Method is used in the method, the related calculations are described in Section B.2 of the proposed HSM Appendix B for Part C. A key step of the predictive method is to divide the facility being evaluated into individual sites (i.e., segments and speed-change lanes). The procedure for dividing the freeway into individual sites is described in Section 18.5 of the proposed HSM Freeways chapter. Application of the predictive method is described in the sample problems in Section 18.13 of the proposed HSM Freeways chapter. Limitations of the predictive method are identified in Section 18.10 of the of the proposed HSM Freeways chapter. Output The output data computed using the predictive method consists primarily of the expected crash frequency for each site and year in the evaluation period. Only the output data computed for the study period should be summarized given that it is most relevant to the analyst. Data for the crash period (available when the EB Method is used) may be of nominal interest, but its primary purpose to support the calculation of the expected average crash frequency for the study period. The estimated crash frequency for a site can be reported in terms of the following performance measures: ⢠Total estimated number of crashes for the study period. ⢠Estimated crash frequency for each year during the study period
734 Either of these two measures can be further disaggregated in terms of crash severity or crash type. For example, the âtotal estimated number of crashes for the study periodâ can be disaggregated into the following measures. ⢠Total estimated number of crashes for each severity level ⢠Total estimated number of crashes for each crash type (e.g., head on, fixed object, etc.) Other combinations of study year, severity level, and crash type can be devised, if desired. If there are multiple sites, then the aforementioned measures should be computed for all sites combined. This type of project-wide aggregation will provide meaningful summary measures that facilitate the comparison of competing projects or alternatives for a given project. Detailed output data can also be made available on a site-by-site basis. Of particular note are the crash modification factors. The value of a factor can be used as an indicator of relative crash risk. Collectively, these factors provide insight into geometric design and traffic control features that have potential for safety improvement. If the input AADT volume data were incomplete (i.e., some years missing) and values were estimated (within the software) for the missing years, then the AADT volume history should be reported so that the analyst can review and confirm the suitability of the estimated volumes. Step 3 in Section 18.4.1 of the proposed HSM Freeways chapter provides some rules for estimating missing AADT volumes. These rules are implemented in ISATe. ALGORITHM DESCRIPTION FOR FREEWAY SPEED-CHANGE LANES This part of the appendix provides information needed to implement the predictive method for freeway speed-change lanes in software. This method is described in the proposed HSM Freeways chapter. The remainder of this part consists of four sections. The first section identifies the input data needed by the predictive method. The second section presents the crash prediction models. The third section describes the sequence of steps that comprise the predictive method. The last section describes the output data that are available from an application of the predictive method. Input Data This section describes the input data for the predictive method. These data are identified using the following categories. ⢠Evaluation period. ⢠Evaluation type. ⢠Crash data. ⢠Geometric design, traffic control, and traffic volume data. Evaluation Period The evaluation period is the set of years in the combined study period and crash period. Every calendar year in the evaluation period is separately evaluated using the methodology. Specific details about this input are provided in Section 18.4.1, Step 2 of the proposed HSM Freeways chapter.
735 Evaluation Type The predictive method can be used to evaluate one site, or a contiguous group of sites. The evaluation is described as one of several types, as determined by the analyst. When one site is being evaluated, the evaluation types are: A. Evaluation based on using the predictive model only. B. Evaluation based on using the predictive model and crash data. When a group of sites are being evaluated, the evaluation types are: A. Evaluation based on using the predictive model only for each site. B. Evaluation based on using the predictive model and crash data for each site. C. Evaluation based on using the predictive model for each site and crash data for the group of sites. When crash data are used, the empirical Bayes (EB) Method is used to combine the crash data with the predictive model estimate to obtain a more reliable estimate of the expected crash frequency. The three evaluation types are referred to herein as types A, B, and C. In the HSM, type B evaluation is referred to as the âsite-specificâ EB Method and type C is referred to as âproject-levelâ EB Method. There are several factors to be considered when determining whether the EB Method is appropriate for a given project. These criteria are described in Sections B.2.1 and B.2.2 of the proposed HSM Appendix B for Part C. Crash Counts If evaluation type B is input by the analyst, then the crash data for each site are necessary input data. The criteria for assigning crashes to individual freeway speed-change lane sites are described in Section B.2.3 of the proposed HSM Appendix B for Part C. If evaluation type C is input, then the crash data for the group of sites is needed. The crash counts must correspond to the crash period. The crash period can be site-specific; however, for coding convenience, the crash period should be the same for all sites. If the crash period includes multiple years, then the crash data do not have to be separately tabulated for each year at each site. Rather, it is sufficient for the analyst to input the total number of crashes for the crash period. Geometric Design, Traffic Control, and Traffic Volume Data The input data describing the geometric design and traffic volume data for freeway speed-change lanes are identified in the following list. General ⢠Area type (urban or rural). Geometric Design ⢠Number of through lanes. ⢠Segment length. ⢠Length and radius of horizontal curve.
736 ⢠Lane width. ⢠Inside shoulder width. ⢠Median width. ⢠Length of rumble strips on inside shoulders. ⢠Length of (and offset to) median barrier. ⢠Presence and length of Type B weaving section. Traffic Characteristics ⢠AADT volume of ramp associated with speed-change lane. ⢠AADT volume of freeway segment. ⢠Proportion of AADT that occurs during hours where the lane volume exceeds 1,000 veh/h/ln. Specific details about these input data are provided in Section 18.4.2 of the proposed HSM Freeways chapter. These details include the method of measurement and the value limits for each variable. The AADT volume ranges for the predictive models are listed in Table 18-4 of the proposed HSM Freeways chapter. The units of measurement for all input data are U.S. customary. If input data are provided in metric units, then they should undergo soft conversion to U.S. customary units before their use in the predictive method. Predictive Models The general structure of the predictive model is described by Equation 18-1 of the proposed HSM Freeways chapter. A more specific structure is described by Equation 18-7 and Equation 18-10. Safety Performance Functions Separate safety performance functions (SPFs) are provided for the following conditions: ⢠Area type (rural or urban). ⢠Through lanes (4, 6, 8, 10 in urban areas). ⢠Crash type (multiple-vehicle, single-vehicle). ⢠Crash severity (fatal-and-injury, property-damage-only). All total, there are 28 SPFs represented by unique combinations of the four conditions identified in the preceding list. Specific details about the SPF regression coefficients are provided in Section 18.6.2 of the proposed HSM Freeways chapter. Section 18.6.1 of the proposed HSM Freeways chapter describes a procedure for extending the SPFs to freeways with an odd number of lanes. Section B.2.7 of the proposed HSM Appendix B for Part C describes a procedure for applying the EB Method to freeways with an odd number of lanes. The overdispersion parameter for ramp entrance speed-change lanes is computed as a function of speed- change lane length. The equation for this calculation is provided in Section 18.6.2 of the proposed HSM
737 Freeways chapter. The factor for ramp exit speed-change lanes is a constant (i.e., it is not a function of speed-change lane length). A procedure for calibrating the predictive models is described in Section B.1.1 of the proposed HSM Appendix B for Part C. Crash Modification Factors Eight crash modification factors (CMFs) are provided in the predictive method. The geometric design features and traffic conditions that they address are identified in the following list. ⢠Horizontal curvature. ⢠Lane width. ⢠Inside shoulder width. ⢠Median width. ⢠Median barrier. ⢠High-volume (congested) conditions. ⢠Ramp entrance length and side of freeway. ⢠Ramp exit length and side of freeway. Specific details about the CMF formulation and regression coefficients are provided in Section 18.7.2 of the proposed HSM Freeways chapter. This section also identifies conditions where a CMF is not applicable. Supplemental calculations for using the barrier-related CMFs are described in Section 18.7.3 of the proposed HSM Freeways chapter. Crash Type Distribution The predicted crash frequency from a predictive model can be disaggregated into estimates of crash frequency by crash type. The crash type categories for multiple-vehicle crashes include head-on, right- angle, rear-end, and sideswipe. The crash type categories for multiple-vehicle crashes include animal, fixed object, other object, and parked vehicle. Distribution percentages for these crash types are provided in Section 18.6.2 of the proposed HSM Freeways chapter. Application of these percentages is described in Sample Problem 3 in Section 18.13.3 of the proposed HSM Freeways chapter. Crash Severity Distribution The predicted crash frequency from a predictive model can be disaggregated into estimates of crash severity. Specifically, the predicted fatal-and-injury crash frequency can be disaggregated into estimates of fatal (K), incapacitating injury (A), non-incapacitating injury (B), and possible injury (C) crash frequency. A severity distribution function is used for this purpose. The function is an equation that includes some of the same variables used in the predictive model. The equations that comprise the severity distribution function are described in Section 18.8 of the proposed HSM Freeways chapter. Application of these equations is described in Sample Problem 3 in Section 18.13.3 of the proposed HSM Freeways chapter.
738 A procedure for calibrating the severity distribution functions is described in Section B.1.4 of the proposed HSM Appendix B for Part C. Predictive Method The predictive method for freeway speed-change lanes is described as a flow chart in Figure 18-1 of the proposed HSM Freeways chapter. The flow chart indicates that the method includes 18 steps that are completed in sequence when evaluating one or more sites. The method is described in sufficient generality that it can be applied to one or more sites, for one or more years, with or without the use of crash data. The steps that comprise the predictive method are described in detail in Section 18.4.1 of the proposed HSM Freeways chapter. If the EB Method is used in the method, the related calculations are described in Section B.2 of the proposed HSM Appendix A for Part C. A key step of the predictive method is to divide the facility being evaluated into individual sites (i.e., segments and speed-change lanes). The procedure for dividing the freeway into individual sites is described in Section 18.5 of the proposed HSM Freeways chapter. Application of the predictive method is described in the sample problems in Section 18.13 of the proposed HSM Freeways chapter. Limitations of the predictive method are identified in Section 18.10 of the of the proposed HSM Freeways chapter. Output The output data computed using the predictive method consists primarily of the expected crash frequency for each site and year in the evaluation period. Useful performance measures and techniques for presenting this output are presented in the Output section in the previous part of this document. ALGORITHM DESCRIPTION FOR RAMP SEGMENTS This part of the appendix provides information needed to implement the predictive method for ramp segments in software. This method is described in the proposed HSM Ramps chapter. The remainder of this part consists of four sections. The first section identifies the input data needed by the predictive method. The second section presents the crash prediction models. The third section describes the sequence of steps that comprise the predictive method. The last section describes the output data that are available from an application of the predictive method. Input Data This section describes the input data for the predictive method. These data are identified using the following categories. ⢠Evaluation period. ⢠Evaluation type. ⢠Crash data. ⢠Geometric design, traffic control, and traffic volume data.
739 Evaluation Period The evaluation period is the set of years in the combined study period and crash period. Every calendar year in the evaluation period is separately evaluated using the methodology. Specific details about this input are provided in Section 19.4.1, Step 2 of the proposed HSM Ramps chapter. Evaluation Type The predictive method can be used to evaluate one site, or a contiguous group of sites. The evaluation is described as one of several types, as determined by the analyst. When one site is being evaluated, the evaluation types are: A. Evaluation based on using the predictive model only. B. Evaluation based on using the predictive model and crash data. When a group of sites are being evaluated, the evaluation types are: A. Evaluation based on using the predictive model only for each site. B. Evaluation based on using the predictive model and crash data for each site. C. Evaluation based on using the predictive model for each site and crash data for the group of sites. When crash data are used, the empirical Bayes (EB) Method is used to combine the crash data with the predictive model estimate to obtain a more reliable estimate of the expected crash frequency. The three evaluation types are referred to herein as types A, B, and C. In the HSM, type B evaluation is referred to as the âsite-specificâ EB Method and type C is referred to as âproject-levelâ EB Method. There are several factors to be considered when determining whether the EB Method is appropriate for a given project. These criteria are described in Sections B.2.1 and B.2.2 of the proposed HSM Appendix B for Part C. Crash Counts If evaluation type B is input by the analyst, then the crash data for each site are necessary input data. The criteria for assigning crashes to individual ramp segment sites are described in Section B.2.3 of the proposed HSM Appendix B for Part C. If evaluation type C is input, then the crash data for the group of sites is needed. The crash counts must correspond to the crash period. The crash period can be site-specific; however, for coding convenience, the crash period should be the same for all sites. If the crash period includes multiple years, then the crash data do not have to be separately tabulated for each year at each site. Rather, it is sufficient for the analyst to input the total number of crashes for the crash period. Geometric Design, Traffic Control, and Traffic Volume Data The input data describing the geometric design and traffic volume data for ramp segments are identified in the following list. General ⢠Area type (urban or rural).
740 Geometric Design ⢠Number of through lanes. ⢠Segment length. ⢠Length and radius of horizontal curve. ⢠Lane width. ⢠Left and right shoulder width. ⢠Length of (and offset to) right side barrier. ⢠Length of (and offset to) left side barrier. ⢠Presence of lane add or drop. ⢠Presence of speed-change lane (associated with a ramp-to-ramp merge or diverge). ⢠Presence and length of weaving section (only applicable to C-D roads). Traffic Characteristics ⢠AADT volume of ramp segment. Specific details about these input data are provided in Section 19.4.2 of the proposed HSM Ramps chapter. These details include the method of measurement and the value limits for each variable. The AADT volume ranges for the predictive models are listed in Table 19-4 of the proposed HSM Ramps chapter. The units of measurement for all input data are U.S. customary. If input data are provided in metric units, then they should undergo soft conversion to U.S. customary units before their use in the predictive method. Predictive Models The general structure of the predictive model is described by Equation 19-1 of the proposed HSM Ramps chapter. A more specific structure is described by Equation 19-2 and Equation 19-7. Safety Performance Functions Separate safety performance functions (SPFs) are provided for the following conditions: ⢠Area type (rural or urban). ⢠Ramp type (entrance ramp, exit ramp, C-D road) ⢠Through lanes (1, 2 in urban areas). ⢠Crash type (multiple-vehicle, single-vehicle). ⢠Crash severity (fatal-and-injury, property-damage-only). All total, there are 36 SPFs represented by unique combinations of the five conditions identified in the preceding list. Specific details about the SPF regression coefficients are provided in Section 19.6.1 of the proposed HSM Ramps chapter.
741 The overdispersion parameter is computed as a function of segment length. The equation for this calculation is provided in Section 19.6.1 of the proposed HSM Ramps chapter. A procedure for calibrating the predictive models is described in Section B.1.1 of the proposed HSM Appendix B for Part C. Crash Modification Factors Nine crash modification factors (CMFs) are provided in the predictive method. The geometric design features and traffic conditions that they address are identified in the following list. ⢠Horizontal curvature. ⢠Lane width. ⢠Right shoulder width. ⢠Left shoulder width. ⢠Right side barrier. ⢠Left side barrier. ⢠Lane add or drop. ⢠Ramp speed-change lane. ⢠Weaving section. Specific details about the CMF formulation and regression coefficients are provided in Section 19.7.1 of the proposed HSM Ramps chapter. This section also identifies conditions where a CMF is not applicable. Supplemental calculations for using the barrier-related CMFs and the Horizontal Curve CMF are described in Section 19.7.3 of the proposed HSM Ramps chapter. Crash Type Distribution The predicted crash frequency from a predictive model can be disaggregated into estimates of crash frequency by crash type. The crash type categories for multiple-vehicle crashes include head-on, right- angle, rear-end, and sideswipe. The crash type categories for multiple-vehicle crashes include animal, fixed object, other object, and parked vehicle. Distribution percentages for these crash types are provided in Section 19.6.1 of the proposed HSM Ramps chapter. Application of these percentages is described in Sample Problem 1 in Section 19.14.1 of the proposed HSM Ramps chapter. Crash Severity Distribution The predicted crash frequency from a predictive model can be disaggregated into estimates of crash severity. Specifically, the predicted fatal-and-injury crash frequency can be disaggregated into estimates of fatal (K), incapacitating injury (A), non-incapacitating injury (B), and possible injury (C) crash frequency. A severity distribution function is used for this purpose. The function is an equation that includes some of the same variables used in the predictive model. The equations that comprise the severity distribution function for ramp segments are described in Section 19.8.1 of the proposed HSM Ramps chapter. Application of these equations is described in Sample Problem 1 in Section 19.14.1 of the proposed HSM Ramps chapter.
742 A procedure for calibrating the severity distribution functions is described in Section B.1.4 of the proposed HSM Appendix A for Part C. Predictive Method The predictive method for ramp segments is described as a flow chart in Figure 19-2 of the proposed HSM Ramps chapter. The flow chart indicates that the method includes 18 steps that are completed in sequence when evaluating one or more sites. The method is described in sufficient generality that it can be applied to one or more sites, for one or more years, with or without the use of crash data. The steps that comprise the predictive method are described in detail in Section 19.4.1 of the proposed HSM Ramps chapter. If the EB Method is used in the method, the related calculations are described in Section B.2 of the proposed HSM Appendix A for Part C. A key step of the predictive method is to divide the facility being evaluated into individual sites (i.e., ramp segments and crossroad ramp terminals). The procedure for dividing the ramps into individual sites is described in Section 19.5 of the proposed HSM Ramps chapter. Application of the predictive method is described in the sample problems in Section 19.14 of the proposed HSM Ramps chapter. Limitations of the predictive method are identified in Section 19.11 of the of the proposed HSM Ramps chapter. Output The output data computed using the predictive method consists primarily of the expected crash frequency for each site and year in the evaluation period. Useful performance measures and techniques for presenting this output are presented in the Output section in the part titled Algorithm Description for Freeway Segments. ALGORITHM DESCRIPTION FOR CROSSROAD RAMP TERMINALS This part of the appendix provides information needed to implement the predictive method for crossroad ramp terminals in software. This method is described in the proposed HSM Ramps chapter. The remainder of this part consists of four sections. The first section identifies the input data needed by the predictive method. The second section presents the crash prediction models. The third section describes the sequence of steps that comprise the predictive method. The last section describes the output data that are available from an application of the predictive method. Input Data This section describes the input data for the predictive method. These data are identified using the following categories. ⢠Evaluation period. ⢠Evaluation type. ⢠Crash data. ⢠Geometric design, traffic control, and traffic volume data.
743 Evaluation Period The evaluation period is the set of years in the combined study period and crash period. Every calendar year in the evaluation period is separately evaluated using the methodology. Specific details about this input are provided in Section 19.4.1, Step 2 of the proposed HSM Ramps chapter. Evaluation Type The predictive method can be used to evaluate one site, or a contiguous group of sites. The evaluation is described as one of several types, as determined by the analyst. When one site is being evaluated, the evaluation types are: A. Evaluation based on using the predictive model only. B. Evaluation based on using the predictive model and crash data. When a group of sites are being evaluated, the evaluation types are: A. Evaluation based on using the predictive model only for each site. B. Evaluation based on using the predictive model and crash data for each site. C. Evaluation based on using the predictive model for each site and crash data for the group of sites. When crash data are used, the empirical Bayes (EB) Method is used to combine the crash data with the predictive model estimate to obtain a more reliable estimate of the expected crash frequency. The three evaluation types are referred to herein as types A, B, and C. In the HSM, type B evaluation is referred to as the âsite-specificâ EB Method and type C is referred to as âproject-levelâ EB Method. There are several factors to be considered when determining whether the EB Method is appropriate for a given project. These criteria are described in Sections B.2.1 and B.2.2 of the proposed HSM Appendix A for Part C. Crash Counts If evaluation type B is input by the analyst, then the crash data for each site are necessary input data. The criteria for assigning crashes to individual crossroad ramp terminal sites are described in Section B.2.3 of the proposed HSM Appendix A for Part C. If evaluation type C is input, then the crash data for the group of sites is needed. The crash counts must correspond to the crash period. The crash period can be site-specific; however, for coding convenience, the crash period should be the same for all sites. If the crash period includes multiple years, then the crash data do not have to be separately tabulated for each year at each site. Rather, it is sufficient for the analyst to input the total number of crashes for the crash period. Geometric Design, Traffic Control, and Traffic Volume Data The input data describing the geometric design and traffic volume data for crossroad ramp terminals are identified in the following list. General ⢠Area type (urban or rural).
744 ⢠Ramp terminal configuration. Geometric Design Data for All Terminals ⢠Number of through lanes on each crossroad approach. ⢠Number of lanes on the exit ramp. ⢠Number of crossroad approaches with left-turn lanes. ⢠Number of crossroad approaches with right-turn lanes. ⢠Number of unsignalized public street approaches to the crossroad leg outside of the interchange. ⢠Distance to the next public street intersection ⢠Distance to the adjacent crossroad ramp terminal. ⢠Crossroad median width and left-turn lane width. Geometric Design Data for Signalized Terminals Only ⢠Number of unsignalized driveways on the crossroad leg outside of the interchange. ⢠Number of crossroad approaches with protected-only left-turn operation. ⢠Number of crossroad approaches with right-turn channelization. ⢠Presence of exit ramp right-turn channelization. ⢠Presence of a non-ramp public street leg at the terminal. Geometric Design Data for Unsignalized Terminals Only ⢠Skew angle. Traffic Control ⢠Type of traffic control (signal, one-way stop, all-way stop). ⢠Type of control for the exit ramp right-turn movement. Traffic Characteristics ⢠AADT volume for the inside and outside crossroad legs ⢠AADT volume for each ramp leg. Specific details about these input data are provided in Section 19.4.2 of the proposed HSM Ramps chapter. These details include the method of measurement and the value limits for each variable. The AADT volume ranges for the predictive models are listed in Table 19-11 of the proposed HSM Ramps chapter.
745 The units of measurement for all input data are U.S. customary. If input data are provided in metric units, then they should undergo soft conversion to U.S. customary units before their use in the predictive method. Predictive Models The general structure of the predictive model is described by Equation 19-1 of the proposed HSM Ramps chapter. A more specific structure is described by Equation 19-12 and Equation 19-15. Safety Performance Functions Separate safety performance functions (SPFs) are provided for the following conditions: ⢠Area type (rural or urban). ⢠Terminal configuration (D3ex, D3en, D4, A4, B4, A2, B2) ⢠Control mode (signal, one-way stop) ⢠Crossroad through lanes (2, 3, 4, 5 signalized in urban areas, 6 signalized in urban areas). ⢠Crash severity (fatal-and-injury, property-damage-only). All total, there are 196 SPFs represented by unique combinations of the five conditions identified in the preceding list. Specific details about the SPF regression coefficients are provided in Section 19.6.2 of the proposed HSM Ramps chapter. The overdispersion parameter is constant. It is provided in Section 19.6.2 of the proposed HSM Ramps chapter. A procedure for calibrating the predictive models is described in Section B.1.1 of the proposed HSM Appendix A for Part C. Crash Modification Factors Eleven crash modification factors (CMFs) are provided in the predictive method. The geometric design features, traffic control features, and traffic conditions that they address are identified in the following list. ⢠Exit ramp capacity. ⢠Crossroad left-turn lane. ⢠Crossroad right-turn lane. ⢠Access point frequency. ⢠Segment length. ⢠Median width. ⢠Protected left-turn operation (signalized terminals only). ⢠Channelized right turn on crossroad (signalized terminals only). ⢠Channelized right turn on exit ramp (signalized terminals only). ⢠Non-ramp public street leg (signalized terminals only). ⢠Skew angle (unsignalized terminals only).
746 Specific details about the CMF formulation and regression coefficients are provided in Section 19.7.2 of the proposed HSM Ramps chapter. This section also identifies conditions where a CMF is not applicable. A CMF for all-way stop control is also provided with the predictive model for one-way stop controlled terminals. A procedure for using it is described in Section 19.10 of the proposed HSM Ramps chapter. It is an interim procedure to be used to evaluate all-way stop controlled terminals until a better procedure can be developed through research. Crash Type Distribution The predicted crash frequency from a predictive model can be disaggregated into estimates of crash frequency by crash type. The crash type categories for multiple-vehicle crashes include head-on, right- angle, rear-end, and sideswipe. The crash type categories for multiple-vehicle crashes include animal, fixed object, other object, and parked vehicle. Distribution percentages for these crash types are provided in Section 19.6.2 of the proposed HSM Ramps chapter. Application of these percentages is described in Sample Problem 4 in Section 19.14.4 of the proposed HSM Ramps chapter. Crash Severity Distribution The predicted crash frequency from a predictive model can be disaggregated into estimates of crash severity. Specifically, the predicted fatal-and-injury crash frequency can be disaggregated into estimates of fatal (K), incapacitating injury (A), non-incapacitating injury (B), and possible injury (C) crash frequency. A severity distribution function is used for this purpose. The function is an equation that includes some of the same variables used in the predictive model. The equations that comprise the severity distribution function for crossroad ramp terminals are described in Section 19.8.2 of the proposed HSM Ramps chapter. Application of these equations is described in Sample Problem 4 in Section 19.14.4 of the proposed HSM Ramps chapter. A procedure for calibrating the severity distribution functions is described in Section B.1.4 of the proposed HSM Appendix A for Part C. Predictive Method The predictive method for crossroad ramp terminals is described as a flow chart in Figure 19-2 of the proposed HSM Ramps chapter. The flow chart indicates that the method includes 18 steps that are completed in sequence when evaluating one or more sites. The method is described in sufficient generality that it can be applied to one or more sites, for one or more years, with or without the use of crash data. The steps that comprise the predictive method are described in detail in Section 19.4.1 of the proposed HSM Ramps chapter. If the EB Method is used in the method, the related calculations are described in Section B.2 of the proposed HSM Appendix A for Part C. A key step of the predictive method is to divide the facility being evaluated into individual sites (i.e., ramp segments and crossroad ramp terminals). The procedure for dividing the ramps into individual sites is described in Section 19.5 of the proposed HSM Ramps chapter. Application of the predictive method is described in the sample problems in Section 19.14 of the proposed HSM Ramps chapter. Limitations of the predictive method are identified in Section 19.11 of the of the proposed HSM Ramps chapter.
747 Output The output data computed using the predictive method consists primarily of the expected crash frequency for each site and year in the evaluation period. Useful performance measures and techniques for presenting this output are presented in the Output section in the part titled Algorithm Description for Freeway Segments. SOFTWARE DOCUMENTATION This part of the document uses a series of flow charts and linkage lists to document the logic flow for the ISATe software. Flowcharts The calculation sequence is controlled by the subroutine titled Main_PerformanceCalculations. It calls other subroutines in the sequence needed to complete the calculations. This subroutine is shown in Figure 1. The subroutines called by this main subroutine are identified by name in parentheses in the flowchart boxes. When the main subroutine is invoked, it initially clears any data in the output worksheets that is left from a prior evaluation. It also sets all variable values to zero. Next, the main subroutine calls a subroutine that reads the regression coefficients and local calibration factors from the Calibration Factors worksheet. Then, it calls the performance measures subroutine. This subroutine implements the calculations associated with the predictive methods described in the proposed HSM chapters. When the calculations are complete, a subroutine is called to write the performance measures to the output worksheets. More information about these subroutines is provided in the section titled Linkage Lists. Clear old output and variables (ClearOutput, ClearVariables) Read SPF coefficients (ReadCalibData) Read input data (ReadInputData) Compute performance measures (ComputePerformance) Report safety performance measures (Sum_ReportData) Finish Start Figure 1. Main Subroutine The calculation sequence for the performance measures subroutine (i.e., ComputePerformance) is shown in Figure 2. Initially, it checks the input AADT volume data to determine if there are any missing data. If one or more volumes are missing, then a subroutine is called that implements the rules for estimating missing volume. These rules are described in Step 3 in Section 18.4.1 of the proposed HSM Freeways chapter.
748 Compute CMFs (ComputeCMFs) Apply predictive model (ComputeNpredicted) Set period = study period Set site = first freeway segment Site = last freeway segment? Compute severity levels (ComputeSeverityDistribution) Start Set site = next freeway segment Finish Yes No Compute CMFs (ComputeCMFs) Apply predictive model (ComputeNpredicted) Set period = study period Set site = first ramp segment Site = last ramp segment? Compute severity levels (ComputeSeverityDistribution) Start Set site = next ramp segment Finish Yes No Compute curve speed (ComputeSpeed) Start Compute missing AADT data (ComputeMissingAADT)Missing AADT data? Evaluation type? Predictive model only Site-specific EB Method Project-level EB Method Finish Yes No No crash data Crash data for each site Crash data for all sites combined Figure 2. Performance Measures Subroutine Once the AADT data are determined to be complete, the predictive method is initiated. This method has three variations, depending on whether crash data are available and, if available, whether it can be correctly associated with individual sites. One of three evaluation types is identified based on these three considerations. The choice of evaluation type dictates the subsequent sequence of calculations. Predictive Model Only If the evaluation is determined to be based on the predictive model only, then the calculation sequence is shown in Figure 3. Two variations are shown in the figure. One variation applies to freeway segments. The other variation applies to ramp segments. This latter variation includes a subroutine to calculate ramp curve speed. The chart shown in Figure 3b can be applied to crossroad ramp terminals if the subroutine for computing curve speed is removed and the references to âramp segmentâ are changed to âramp terminal.â a. Freeway Segments b. Ramp Segments Figure 3. Evaluation based on Predictive Model Only
749 The subroutine sequence in Figure 3 is shown to be repeated for each site. The first subroutine called in Figure 3a is used to calculate the CMFs for each year at the subject site. These CMFs are then used in the second subroutine to calculate the predicted average crash frequency using the predictive model. Finally, the third subroutine computes the crash severity distribution and combines it with the predicted average crash frequency from the previous subroutine to estimate the crash frequency by severity level. The sequence is repeated until all sites are evaluated. Site-Specific EB Method If the evaluation is determined to be based on the site-specific EB Method, then the calculation sequence is shown in Figure 4. Two variations are shown in the figure. One variation applies to freeway segments. It includes a subroutine to calculate an equivalent overdispersion parameter for odd-lane cross sections based on the parameters provided for even-lane SPFs. The other variation applies to ramp segments. This variation includes a subroutine to calculate ramp curve speed. The chart shown in Figure 4b can be applied to crossroad ramp terminals if the subroutine for computing curve speed is removed and the references to âramp segmentâ are changed to âramp terminal.â The subroutine sequence in Figure 4 is shown to have two looping sequences. In the first loop, the sequence is repeated for each site. Each site is evaluated once for the crash period and once for the study period. The first subroutine called in Figure 4a is used to calculate the CMFs for each year at the subject site. These CMFs are then used in the second subroutine to calculate the predicted average crash frequency using the predictive model. Finally, the third subroutine computes the equivalent overdispersion parameter, as described in the previous paragraph. The sequence is repeated until all sites are evaluated. In the second loop shown in Figure 4, the sequence is again repeated for each site but only for the study period. The first subroutine implements the EB Method to combine the predicted crash frequency with the crash data to obtain an estimate of the expected average crash frequency. The second subroutine computes the crash severity distribution and combines it with the expected average crash frequency from the previous subroutine to estimate the crash frequency by severity level.
750 Compute CMFs (ComputeCMFs) Apply predictive model (ComputeNpredicted) Compute overdispersion factors (ComputeKfactors) Freeway has even number of lanes? Site = last freeway segment? Set period = crash period Period = study period? Set period = study period Set site = first freeway segment Set period = study period Set site = first freeway segment Site = last freeway segment? Compute severity levels (ComputeSeverityDistribution) Set site = next freeway segment Start Apply site-specific EB Method (ComputeNadjusted) Set site = next freeway segment Finish YesNo Yes No No Yes Yes No Compute CMFs (ComputeCMFs) Apply predictive model (ComputeNpredicted) Site = last ramp segment? Set period = crash period Period = study period? Set period = study period Set site = first ramp segment Set period = study period Set site = first ramp segment Site = last ramp segment? Compute severity levels (ComputeSeverityDistribution) Set site = next ramp segment Start Apply site-specific EB Method (ComputeNadjusted) Set site = next ramp segment Finish Yes No No Yes Yes No Compute curve speed (ComputeSpeed) a. Freeway Segments b. Ramp Segments Figure 4. Evaluation based on the Site-Specific EB Method Project-Level EB Method If the evaluation is determined to be based on the project-level EB Method, then the calculation sequence is shown in Figure 5. Two variations are shown in the figure. One variation applies to freeway segments. It includes a subroutine to calculate an equivalent overdispersion parameter for odd-lane cross sections based on the parameters provided for even-lane SPFs. The other variation applies to ramp segments. This variation includes a subroutine to calculate ramp curve speed. The chart shown in Figure 5b can be applied to crossroad ramp terminals if the subroutine for computing curve speed is removed and the references to âramp segmentâ are changed to âramp terminal.â The subroutine sequence in Figure 5 is shown to have two looping sequences. In the first loop, the sequence is repeated for each site. Each site is evaluated once for the crash period and once for the study period. This sequence of calculations is described in the discussion associated with Figure 4. When the loop is completed, the project-level EB Method calculations are completed for the collective set of sites to produce an estimate of the total expected average crash frequency. In the second loop shown in Figure 5, the sequence is again repeated for each site but only for the study period. The subroutine in this loop computes the crash severity distribution and combines it with the
751 Compute CMFs (ComputeCMFs) Apply predictive model (ComputeNpredicted) Compute overdispersion factors (ComputeKfactors) Freeway has even number of lanes? Site = last freeway segment? Set period = crash period Period = study period? Set period = study period Set site = first freeway segment Set period = study period Set site = first freeway segment Site = last freeway segment? Compute severity levels (ComputeSeverityDistribution) Set site = next freeway segment Start Set site = next freeway segment Finish YesNo Yes No No Yes Yes No Apply project-level EB Method (ComputeProjectNadjusted) Compute severity levels (ComputeProjectSeverity) Compute CMFs (ComputeCMFs) Apply predictive model (ComputeNpredicted) Site = last ramp segment? Set period = crash period Period = study period? Set period = study period Set site = first ramp segment Set period = study period Set site = first ramp segment Site = last ramp segment? Compute severity levels (ComputeSeverityDistribution) Set site = next ramp segment Start Set site = next ramp segment Finish Yes No No Yes Yes No Apply project-level EB Method (ComputeProjectNadjusted) Compute curve speed (ComputeSpeed) Compute severity levels (ComputeProjectSeverity) predicted average crash frequency from a previous subroutine to estimate the crash frequency by severity level for each site. After the loop is complete, the last subroutine uses the site estimates of predicted average crash frequency by severity level to compute a total by severity level for the project. The proportion of predicted crashes in each severity level is then multiplied by the total expected average crash frequency to compute the distribution of expected average crash frequency by severity level for the project. a. Freeway Segments b. Ramp Segments Figure 5. Evaluation based on the Project-Level EB Method Linkage Lists This section uses linkage lists to describe the main subroutines that comprise the ISATe software. Each list is provided in a table that identifies the main subroutine and the subroutines that it calls. A brief description is provided for each called subroutine. A linkage list is provided in Table 1 for the subroutines identified in Figure 1. The subroutine naming convention includes a prefix for many subroutines to denote their application to one of the three freeway facility components (i.e., freeway segments, ramp segments, and crossroad ramp terminals). In each case, the subroutine includes the same basic calculations but it is tailored to address some unique elements of
752 the associated facility component. The prefix is not shown in the table because the description offered is sufficiently general as to be applicable to all components. Table 1. Linkage List for Key Subroutines Main Subroutine a Called Subroutine a Called Subroutine Description Main_PerformCalculations CheckLaneCounts Check lanes entered for sites and report a warning message for any sites with a lane count that is not consistent with the limits of the predictive model for the input area type. ClearOutput Clear all cells in the output worksheets. Cells are blank (empty) after this subroutine is called. ClearVariables Set all variables and arrays to zero. ReadCalibData Read all regression coefficients, distribution values, and calibration factors in the Calibration Factors worksheet. ReadInputData Read input data from the input worksheets. ComputePerformance Compute performance measures for each year in the evaluation period for each site in the project. Sum_ReportData Combines the freeway, ramp, and ramp terminal performance measures and reports the results at the project level, as total crashes by severity and crash type. Reports results in the Output Summary worksheet. ReadInputData GetData Reads a cell with a blue background. If the background is not blue, then a zero or blank is returned. Sum_ReportData Report Combines site performance measures for a specified freeway component (i.e., freeway, ramp, or ramp terminal) as total crashes by severity and crash type. Report ClearMOCDistribution Clears the manner-of-collision-by-severity array. Sets all a values to zero. ComputeMOCDistribution Computes the manner-of-collision-by-severity array for all years and sites combined. Note: a. Underlined subroutine names actually represent three subroutines and have a prefix of âFrwy_,â âRamp_,â or âTerm_.â Each subroutine variation is minor variations to address one of the three freeway components: freeway, ramp, or crossroad ramp terminal. The linkage list provided in Table 2 is specific to the subroutines called by the performance measures subroutine. These subroutines are identified in Figure 2 to Figure 5.
753 Table 2. Subroutines Implementing the Predictive Method Main Subroutine a Called Subroutine a Called Subroutine Description ComputePerformance ComputeMissingAADT Scans the AADT input cells for each year at each site. If an AADT value for a given year is missing, then it is estimated using the rules described in Step 3 of the predictive method. ComputeCMFs Computes the value of each applicable CMF for each year at each site. ComputeNpredicted Combines the CMFs with the SPFs and the calibration factor to compute the predicted average crash frequency for each year at each site. Frwy_ComputeKfactors Used only in the Freeways module when the EB Method is applied. This subroutine computes an effective overdispersion parameter when the segment has an odd number of lanes. It is generalized such that it is called regardless of whether the lane count is even or odd. However, the computed overdispersion parameter is equal to the input factor value when the segment has an even number of lanes. ComputeNadjusted Used when the site-specific EB Method is applied. This subroutine combines the predictive model estimate with the crash count to determine the expected average crash frequency for each year at each site. ComputeSeverityDistribution Uses a severity distribution function to estimate the crash severity distribution. Combines this distribution with the estimated crash frequency to estimate the crash frequency by severity level for each site. ComputeProjectSeverity Uses the predicted crash frequency by severity level for each site from ComputeSeverityDistribution with the total expected number of crashes from ComputeProject- Nadusted to estimate the total crash frequency by severity level for the project. ComputeProjectNpredicted Used when the project-level EB Method is applied. This subroutine combines the predictive model estimates for each year at each site to produce a total estimated number of crashes for the project. ComputeProjectNadjusted Used when the project-level EB Method is applied. This subroutine combines the predictive model estimate with the crash count to determine the total expected number of crashes for the project. Ramp_ComputeSpeed Used only in the Ramps module. This subroutine computes the curve entry speed for each ramp curve. Note: a. Underlined subroutine names actually represent three subroutines and have a prefix of âFrwy_,â âRamp_,â or âTerm_.â Each subroutine variation is minor variations to address one of the three freeway components: freeway, ramp, or crossroad ramp terminal.
