Identification and Evaluation of the Cost-Effectiveness of Highway Design Features to Reduce Nonrecurrent Congestion (2014)

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77 The reliability models developed in SHRP 2 Project L03 served as a starting point in Project L07 for evaluating the effectiveness of design treatments in reducing nonrecurrent congestion and improving travel time reliability. However, although these models included a variable (R0.05″) to account for rainfall, they did not account for snow conditions. Fur- thermore, the Project L03 models were more applicable to congested conditions and were not developed for the full range of demand-to-capacity (d/c) ratios. To address these and other issues, SHRP 2 approved an extension of Project L07 to further develop and refine the analytical framework and the spreadsheet-based Analysis Tool that were developed in the research. This appendix describes in detail the work conducted to (1) further develop the models to address the effects of snow and ice on the traffic operational effectiveness of design treat- ments and (2) develop reliability models for time periods with d/c < 0.8. Further Develop Models to address effects of Snow and Ice The objective of this effort was to develop a method for incor- porating consideration of snow and ice into the reliability models used to assess design treatments. The research team used existing traffic operational data from the Minneapolis– St. Paul, Minnesota, metropolitan area to quantify the rela- tive effects of snow and rain on travel time reliability and incorporate an explicit snow-and-ice term into the reliability models. Lookup tables for the annual number of hours with snowfall above a threshold, analogous to those already devel- oped for rainfall in Project L07, were developed for all U.S. weather stations that experience snowfall. Project L03 accounted for the effect of rainfall on travel time reliability by incorporating a rainfall term (R0.05″) into the reliability models. R0.05″ is defined as the number of times (during a given time-slice, e.g., 8:00 to 9:00 a.m.) during a year that hourly rainfall is greater than or equal to 0.05 in. The threshold of 0.05 in. was determined, in Project L03, to be the amount of rainfall that begins to have a noticeable effect on vehicle speeds. One of the first steps in this effort was to determine a similar threshold for snowfall. That is, what is the minimum amount of snowfall that begins to noticeably affect vehicle speeds? To determine this threshold, a database was assem- bled using weather data from the National Weather Ser- vice. Four pairs of freeway segments were identified in the Minneapolis–St. Paul area, with each pair corresponding to one of four weather stations. Figure A.1 shows the eight free- way segments and the corresponding four weather stations. Speed and volume data for these freeway segments were already available from other analyses in Project L07. Each 5-min record included an average per lane speed and a per lane volume. To determine the minimum snowfall rate that has an effect on travel speeds, the data were filtered in several ways. First, hours with traffic volumes greater than 1,200 vehicles/h were excluded, because in these cases, congestion may contrib- ute to a decrease in speed. Hours between sunset and sunrise were also excluded, because darkness may also contribute to speed reductions. A mean speed value was plotted for each hour according to the recorded snowfall amount that occurred during the hour. As shown in Figure A.2, the majority of hours had no snow- fall (0.00 in.). The mean speed of all “no precipitation” hours in the database was 67.0 mph. As the figure shows, there was a noticeable decrease in speed for snowfall amounts of as little as 0.01 in.; the mean speed of all hours with 0.01 in. of snow- fall was 60.2 mph. The magnitude of the speed reduction effect appears to increase with increasing rates of snowfall until approximately 0.05 in. of snowfall per hour, at which point the snowfall effect remains fairly constant. On the basis of this analysis, the research team concluded that the appropriate snow term to be used in the reliability a p p e N D I x a Background Information for Model Development

78 Figure A.1. Freeway stations used in Task IV-1 analysis. Source: © Microsoft Streets and Trips. Figure A.2. Mean hourly speeds by hourly snowfall amount.

79 TTI for Hours with Rain >–0.05 in. For each of the five TTI percentiles, speed data from those hours with rain ≥0.05 in. (RTTIn) were compared with speed data from those hours with no precipitation, and the follow- ing regression equation (Equation A.3) was developed: = +RSpeed NPSpeed (A.3)m bn np where RSpeedn = average nth percentile speed for hours with rainfall ≥0.05 in.; NPSpeedn = average nth percentile speed for hours with no precipitation; and m, b = coefficients for nth percentile TTI. NPSpeedn is calculated using the relationship shown by Equation A.4: =NPSpeed FFS NPTTI (A.4)n n where FFS is free-flow speed. Table A.2 lists the coefficients that correspond to the five TTI percentiles (with rain) under consideration. The variable RSpeedn can be converted back into a TTI for rain (RTTI) by using Equation A.5: =RTTI FFS RSpeed (A.5)n n models was Snow01. This value is defined as the number of hours per year during a particular time-slice when snowfall exceeds 0.01 in. Having defined the snow variable to be used in the reliabil- ity models, the research team developed a speed distribution for each hour by using average per lane speeds and per lane volumes from the raw data. The speed distribution for each hour was then assigned to one of three categories: no pre- cipitation (NP), rain above 0.05 in. per hour, or snow above 0.01 in. per hour. The 5th percentile speed was calculated for each hour at each freeway section. (The 5th percentile speed corresponds to the 95th percentile travel time index [TTI].) An average of the 5th percentile speeds were calculated for the NP hours, the rain hours, and the snow hours. The three average values were then compared. As expected, the average 5th percentile speed for NP hours was greater than the average 5th percen- tile speed for rain hours, which was greater than the average 5th percentile speed for snow hours. The following discus- sion describes how the results of the observed data analysis were incorporated into the L03 equations. TTI for Hours with No Precipitation The peak hour reliability model from Project L03 can be rep- resented by Equation A.1: en j k l Rn n nTTI (A.1)% dc LHLcrit 0.05= ( )+ + ′′ where TTIn% = nth percentile TTI; dccrit = critical d/c ratio within the time-slice of interest (e.g., 7:00 to 8:00 a.m.); LHL = annual lane hours lost due to incidents and work zones that occur within the time-slice of interest (e.g., 7:00 to 8:00 a.m.); R0.05″ = hours in the year with rainfall ≥0.05 in. that occur within the time-slice of interest (e.g., 7:00 to 8:00 a.m.); and jn, kn, ln = coefficients that correspond to the nth percentile TTI. Table A.1 lists the coefficients that correspond to the NP TTI percentiles under consideration. The 95th percentile equation is the only percentile from the Project L03 peak hour model to have a nonzero coefficient for the rain variable. Therefore, the research team used the L03 peak hour model without the rain variable to develop a TTI for no precipitation (NPTTI), as shown by Equation A.2: en j kn nNPTTI (A.2)% dc LHLcrit= ( )+ where NPTTIn% is the nth percentile no precipitation TTI, and the other variables are as defined for Equation A.1. Table A.1. Coefficients Corresponding to nth Percentile TTI: No Precipitation TTI Percentile jn kn ln 10 0.07643 0.00405 0.00000 50 0.29097 0.01380 0.00000 80 0.52013 0.01544 0.00000 95 0.63071 0.01219 0.04744a 99 1.13062 0.01242 0.00000 a The 95th percentile equation is the only one with a rain variable. Table A.2. Coefficients Corresponding to nth Percentile TTI for Rain TTI Percentile m b 10 1.364 -28.34 50 0.966 -6.74 80 0.630 6.89 95 0.639 5.04 99 0.607 5.27

80 TTI for Hours with Snow >–0.01 in. For each of the five TTI percentiles, speed data from those hours with snow ≥0.01 in. (STTIn) were compared with speed data from those hours with no precipitation, and the follow- ing regression equation (Equation A.6) was developed: = +SSpeed NPSpeed (A.6)m bn np where SSpeedn = average nth percentile speed for hours with snow ≥0.01 in.; NPSpeedn = average nth percentile speed for hours with no precipitation; and m, b = coefficients for nth percentile TTI. NPSpeedn is calculated using the relationship shown by Equation A.7: =NPSpeed FFS NPTTI (A.7)n n Table A.3 lists the coefficients corresponding to the five TTI percentiles with snow. The variable SSpeedn can be converted back into a TTI for snow by using Equation A.8: =STTI FFS SSpeed (A.8)n n Final Reliability Model Incorporating Rain and Snow On the basis of the number of days of each type of precipita- tion, a weighted average TTI can be calculated, as shown by Equation A.9: n n n n p p p TTI NPdays NPTTI Raindays RTTI Snowdays STTI 365 (A.9)= + + where TTIn = nth percentile TTI for a 1-h time-slice over 1 year; NPdays = number of days (for a 1-h time-slice) with no precipitation; NPTTIn = nth percentile TTI for days with no precipitation; Raindays = number of days (for a 1-h time-slice) with rain ≥0.05 in.; RTTIn = nth percentile TTI for days with rain ≥0.05 in.; Snowdays = number of days (for a 1-h time-slice) with snow ≥0.01 in.; and STTIn = nth percentile TTI for days with snow ≥0.01 in. analyze existing Data to Improve applicability of reliability Models for time periods with d/c < 0.8 The objective of this effort was to improve the applicability of reliability models for periods with d/c ratios less than 0.8. The Project L03 reliability model that was of most use to Proj- ect L07 for evaluating design treatments was the peak hour model. Originally, the research team anticipated being able to use the L03 peak hour model without adjustment to calculate the TTI distribution for each hour of the day. However, apply- ing the peak hour model to an hour with a low d/c yielded unrealistic results. These results were likely because the sub- set of data used to create the peak hour model in Project L03 included only peak hour (i.e., congested) data, and freeway sections with peak hours of d/c < 0.8 are relatively rare. Because of this, the existing models show an effect on nonrecurrent congestion only during peak time periods when there is also substantial recurrent congestion. This limitation meant that the available reliability models were very applicable to peak periods on freeways in major metropolitan areas, but had limited applicability to off-peak periods on freeways in major metropolitan areas, peak and off-peak periods in medium and smaller metropolitan areas, and peak and off-peak conditions on rural freeways. The research team analyzed the data that were already avail- able from Project L03 for time periods with d/c < 0.8 to better quantify the contributions of incidents during those periods to travel time reliability. For every hour of the day (not just the peak hours), the research team calculated values for the model input variables (d/c, LHL) and compared the observed cumu- lative TTI curves with the predicted cumulative TTI curves (i.e., predicted with the L03 reliability models). In some cases, the observed and predicted curves were very similar; in other cases, they were markedly different. The Project L03 research team had developed the reliabil- ity models based on roadway sections, but the Project L07 Table A.3. Coefficients Corresponding to nth Percentile TTI: Snow TTI Percentile m b 10 0.178 15.55 50 0.345 3.27 80 0.233 5.24 95 0.286 1.67 99 0.341 -0.55

81 observed values for each percentile with the predicted TTI values by using the L03 reliability models. The charts shown in Figure A.4 display an observed TTI distribution and a L03-predicted TTI distribution for several HYL combina- tions. In some cases, the observed and predicted curves are nearly identical; in others, they are significantly different. Figure A.5 shows the relative error (|observed - [predicted/ observed]|) of the 95th percentile prediction model for the 2006 Minneapolis–St. Paul data. Many of the points are above a relative error of 0.3, meaning that the prediction is off by over 30%. Figure A.5 also shows the largest TTI prediction error in the d/c range between 0.4 and 0.8. Similar graphs were created for the other four percentiles. Together, these graphs show that TTI distributions for HYL combinations with very low d/c values tend to vary widely. This variation is likely due to rare catastrophic incidents, because at such low d/c levels, it is unlikely that a bottleneck could be created by something other than an incident that blocks several lanes. The research team therefore concluded that the best range to model TTI per- centiles is between 0.4 and 0.8 d/c. This range of the observed data was extracted from the database and used by the statisti- cians on the research team to generate models appropriate to this range. Independent Variables To create a model to predict the five percentile values when d/c is less than 0.8, the independent variables for each HYL were identified and calculated. The first three independent variables were identified in Project L03: d/c, LHL, and R0.05″. The fourth independent variable (S0.01″) was developed and included in the model as part of Project L07. S0.01″ is defined as the number of hours per year during a particular time-slice when snowfall exceeds 0.01 in. Demand-to-Capacity Ratio The capacity for each link was obtained from a Project L03 database. Demand was not readily available and had to be determined from observed volumes and speeds and by calcu- lating median densities and 15th percentile speeds. Lane Hours Lost LHL represents the sum of the time when a lane (or shoul- der) is blocked by a crash-involved or disabled vehicle or by a work zone. The raw data from Minneapolis–St. Paul included records from a traffic management center that kept records of lane-blocking and shoulder-blocking events. The type of event for each record was determined and assigned the appropriate duration and lane-blocking space to each hour. research team conducted the analysis at the link level. (A link is defined as a continuous portion of freeway between an on- ramp and the next off-ramp; a section is a group of several consecutive links.) Because the input format for the Analysis Tool (one of the major deliverables of the L07 project) is at a link level, a model to predict cumulative TTI curves for a single link was deemed more applicable. Figure A.3 shows the distribution of link lengths for the Minneapolis–St. Paul data. Based on the development of the Project L03 models, the time period for predicting a TTI distribution should be 1 year. So, the models predict operations for a time-slice (e.g., 8:00 to 9:00 a.m.) over an entire year. To develop the d/c < 0.8 model, the raw data were transformed into this form. Each row of the database represented a single hour for the entire year at a given link. A single combination of hour–year–link (HYL) made up one data point in the database. Most of the raw data came in 5-min, by lane volumes and speeds, so a procedure was developed to filter and sum the data appropriately. For each HYL, the following values were determined on the basis of the observed data: • 99th percentile TTI • 95th percentile TTI • 80th percentile TTI • 50th percentile TTI • 10th percentile TTI These results were first used to verify that using the Proj- ect L03 models for periods with d/c < 0.8 did not produce sufficiently accurate results. The research team compared the Figure A.3. Histogram of link lengths for Minneapolis–St. Paul data.

82 Figure A.4. Excerpt of figures comparing observed with L03-predicted TTI distributions.

83 Figure A.6 shows the resulting total LHL values (including WZLHL and LHL due to incidents) per hour with all links combined and averaged by mile. Each bar represents an hour in 2006 (Hour 0 is midnight, and Hour 23 is 11:00 p.m.). The bars are shaded by LHL cause to show the types of events that contributed most to the total LHL value. Total work-zone lane hours lost (WZLHL) for a given hour was determined by summing all incidents of the following categories from the incident database: scheduled construc- tion and unscheduled construction. However, before these LHLs could be assigned to links, an assumption had to be made about the length of a typical work zone. If work zones typically block only one link, they were distributed just as incidents were above, by link length alone. However, if work zones typically block all links within a section, the total WZLHL value was multiplied by the number of links in the section and then distributed by link length. The research team randomly selected 12 construction events and manu- ally matched each event to the right segment of freeway. The beginning and ending points of each link were also identified on the map to determine how many links were blocked by the construction event. The results of this analysis are shown in Table A.4. As shown in Table A.4, the percentage of a roadway section that was blocked by construction events varied from 14% to 100%. Ideally, one would analyze each work-zone event indi- vidually, and the WZLHL would be assigned only to those links actually affected by the work zone. However, because of the time-consuming nature of such an effort, a simplifying assumption was made. The total WZLHL for a section was multiplied by the number of links in that section and then multiplied by 50%. The total WZLHL was then distributed to each link based on the link length as a proportion of total section length. Figure A.5. Relative error of L03 95th percentile TTI models. Table A.4. Number of Links Blocked by Construction Events Construction Event No. of Links Blocked by Construction Event Total No. of Links in Section Section Blocked (%) 1 2 8 25 2 7 7 100 3 6 11 55 4 5 11 45 5 5 11 45 6 5 11 45 7 5 11 45 8 2 7 29 9 3 7 43 10 3 7 43 11 1 7 14 12 1 7 14

84 and S0.01″). These models retain the form used in L03 (expo- nential). The general form is as shown in Equation A.10: ei a d c b c R d Si i i i TTI (A.10) LHL 0.05 0.01 = ( ) ( ) ( ) ( )× + × + × + ×′′ ′′ where TTIi is the cumulative TTI at percentile i; ai, bi, ci, and di are coefficients at percentile i; and other variables are as defined previously. The coefficients a, b, c, and d are calculated for a given per- centile by using Equation A.11: ( )( )= × + × [ ]( )−coefficient (A.11)1w i x yi z i where i is a given percentile value (between 0 and 1), and w, x, y, and z are constants (see Table A.5). R0.05 and S0.01 R0.05″ is the number of times (during a given hour over the course of 1 year) that rainfall exceeds 0.05 in. S0.01″ is the num- ber of times snowfall exceeds 0.01 in. within the same time parameters. The values of R0.05″ and S0.01″ were determined using data from the National Weather Service. Four weather stations with complete data for the years of interest were identified in Minneapolis–St. Paul. Using Microsoft Streets and Trips soft- ware, the location of each weather station and each link was plotted on a map. The weather station nearest to each link was recorded, and data from that weather station were used to cal- culate the R0.05″ and S0.01″ values to be used for that link. R0.05″ values in the Minneapolis–St. Paul area ranged from two to 10, and S0.01″ values ranged from zero to six. Final Models The final database included 1,810 records. Each record repre- sented a single HYL and included values for d/c, LHL due to incidents, WZLHL, R0.05″, and S0.01″ for that HYL. The observed 10th, 50th, 80th, 95th, and 99th percentile TTIs for each HYL were calculated and displayed in the final database. This data- base was used to create the following models for predicting TTI values based on the four input variables (d/c, LHL, R0.05″, Figure A.6. Average LHL per mile by hour. Table A.5. Constants for Equation A.11 w x y z a 0.14 0.504 96 9 b 0.0099 0.0481 96 9 c 0.00149 0.0197 68 6 d 0.00367 0.0248 36 7