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

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24 Overview The cumulative distribution function of the travel time index (TTI-CDF) curve was introduced in Chapter 1 as the funda- mental diagram from which reliability statistics can be com- puted. Chapter 1 presents methods to predict values along the TTI-CDF of a freeway segment based on fundamental traffic flow and physical and environmental characteristics. Chapter 1 further demonstrates how predicted TTI-CDFs for treated and untreated conditions can be used to calculate the operational benefits of a given design treatment. Figure 4.1 illustrates the process developed in Project L07 to calculate these benefits and indicates which sections in Chapter 4 cover different aspects of the process. prediction of Cumulative ttI Curve Background Research for SHRP 2 Project L03 (1) developed predictive relationships for several percentiles on the cumulative TTI curve for a given time-slice as a function of key parameters: • A general measure of highway congestion (ratio of demand to capacity) • A measure of temporal–spatial impacts of incidents and work zones (lane hours lost) • A measure of precipitation amount over a specified period (rain) The Project L03 models were developed for several time- slices (peak hour, peak period, midday, and weekday). The Project L07 research team was most interested in single-hour time-slices, which allow development of predictions for each of the 24 h of the day. This approach allows the consideration of all incidents or events that may potentially result in non- recurrent congestion (not just those that occur during already congested periods) and the aggregation of hourly operational measures into meaningful daily and annual statistics that can be used in economic analysis. Only the peak hour models in Project L03 are based on a single-hour time-slice. The Project L07 research team revised and extended these models to apply to nonpeak (uncongested) hours, as well. The Project L07 research team also extended the Project L03 models to include a snow variable, in addition to the rain variable already considered. Model Variables The models that were used and enhanced to predict cumula- tive TTI percentiles are based on four primary variables: • d/c—Demand-to-capacity ratio • LHL—Lane hours lost due to incidents and work zones • R0.05″—Hours of rainfall exceeding 0.05 in. • S0.01″—Hours of snowfall exceeding 0.01 in. Each variable is described in detail below. Demand-to-Capacity Ratio The d/c variable, which indicates the level of day-to-day congestion on the highway facility, is defined as the ratio of demand (d) to capacity (c) for a given highway segment over a given time-slice. calculaTing deMand Demand is defined as weekday nonholiday demand during the 30th-highest hour of the year during a given time-slice. Demand differs from volume in that demand represents all motorists who would travel on a section given unconstrained capacity during a given period (everyone who wanted to travel on the freeway section), and volume is equal to the observed or counted vehicles during the same period (everyone who C h a p t e r 4 Traffic Operational Assessment

25 actually traveled on the freeway section). Therefore, when demand is less than capacity, volume equals demand. Three methods of computing demand are described below: 1. If observed volume data for each nonholiday weekday hour for the entire year (roughly 250 counts for each of the 24 h) are available, then the analyst can directly select the 30th-highest volume (v30) for each of the 24 h. For all uncongested periods, demand equals volume (v30). For periods when demand may exceed capacity, volumes can be converted to demand by using one of the following two methods: a. If volume and speed data are available in 5-min incre- ments, the analyst can use the method developed in SHRP 2 Project L03 to compute demand (1). The pro- cedure identifies consecutive 5-min periods during which the mean speed drops below a congested level (typically the 35- to 45-mph range). Demand is esti- mated by extrapolating the flow rate just before the onset of congestion, resulting in an assumed queue, and then further assuming that the queue begins to dissipate midway through the congested period. Adjustments may be needed at the end of the congested period to ensure a smooth cumulative demand curve. b. If volume and speed data are not available in 5-min increments, and the analyst has only the hourly volumes to work with, it is recommended that the analyst make field observations of the times when congestion begins and ends on the facility and then estimate or measure the evolution of the queue during that congested period. The total number of vehicles queued upstream of the segment during the hour (q) can be assumed to be equal to the residual demand; thus, an approximation for the demand is given by Equation 4.1: 4.130d v q ( )= + 2. If, as is often the case, the analyst has a single-day or multi- day count, the following procedure can be used to com- pute the volume for the 30th-highest hour. Most state departments of transportation (DOTs) tabulate factors that allow conversion of average daily traffic (ADT) to annual ADT (AADT) as a function of the month of the year and day of the week on which the volumes were col- lected (seasonal and daily factors). The typical calculation is shown by Equation 4.2: AADT ADT 4.2month, day,f fm d ( )= × × where fmonth,m and fday,d are the factors to convert month m to the average month and day d to the average week- day, respectively. These factors can be used to convert the observed volume (vobs) to approximate the 30th-highest- hour volume (v30) for a given hour by using Equation 4.3: v v f f f fm d 30 =  obs month,MAX day,AVG month, day,   ( )4 3. where fmonth,MAX represents the factor for the maximum month of the year, and fday,AVG represents the average of the factors for all five weekdays. Thus, Equation 4.3 essentially sets v30 equal to the average day in the peak month (for the given hour). Allowing for some peak holiday and weekend travel, this is a good approximation for the 30th-highest hour. Figure 4.1. Calculation of operational effectiveness. Model Variables Calculating Operational Effectiveness: Overview Mapping Treatment Effects to Model Variables Prediction Models Basic Roadway Characteristics Treatment Characteristics Effect on: Untreated Model Inputs TT I P re di ct io n M od el s Geometry Demand Precipitation Incidents Work Zones Events Untreated TTI Curves Treated TTI Curves Change in Reliability Indicators Operational Benefits Demand Capacity Incidents Frequency Duration Lane Blockage d/c ILHL WZLHL R0.05* S0.01* Treated Model Inputs d/c* ILHL* WZLHL*

26 In some cases, the analyst may be aware that, due to extreme volume fluctuations or the presence of major traffic generators, the 30th-highest hour is higher than Equation 4.3 would suggest. One way to illustrate this issue is to consider special events. If the volume is known to be heavier than the calculated v30 on more than 30 days (due to special events), v30 can be set equal to the volume of the 30th highest of these event days. The above method for including events is recommended as an initial proce- dure. To convert v30 to demand for use in the d/c equation, Procedure 1.b above using field observations (d = v30 + q) is recommended for any periods that experience congestion. Because the frequency of events and demand surges var- ies from facility to facility and from city to city, incorporat- ing event-related demand surges into reliability calculations is a complex endeavor that has not been fully addressed in previous research. 3. If the analysis is based on future volumes, a travel-demand forecasting model can be used to predict demand. How- ever, as the forecasted demand may be the mean and not the 30th-highest hour, the monthly and daily factors described above may also need to be applied. All demand volumes should be converted to passenger car equivalents by using heavy-vehicle percentages and passenger car–equivalent factors from the Highway Capacity Manual (HCM), Chapter 11 (2). calculaTing caPaciTy To calculate capacity, procedures from Chapter 11 of the HCM 2010 are used to derive the free-flow speed for the free- way section by using geometric information about the sec- tion. The free-flow speed is converted into a lane capacity and multiplied by the number of lanes to give total segment capacity in vehicles per hour. Capacity may vary throughout the day. For example, a reversible lane may be available only at certain times of day, or a shoulder may be used as a lane only during peak periods. In dividing the day into 24 separate 1-h periods, the analyst must ensure that the capacity values for each hour account for these effects if present. effecTS of long-TerM work ZoneS This research distinguishes between short- and long-term work zones. Short-term work zones (lasting 7 days or less) are con- sidered nonrecurrent congestion, and as such are evaluated as part of the work-zone lane hours lost (WZLHL) variable dis- cussed later in this section. Long-term work zones (longer than 30 days) do not comfortably fit into the nonrecurrent conges- tion category, and therefore a different analysis approach must be used. A long-term work zone essentially establishes a “new normal” base capacity that should be used to test against any potential improvements affecting nonrecurrent congestion in the work zone (such as emergency pulloffs). Medium-term work zones, lasting between 8 and 29 days, currently fall into an analytical gray area. They typically provide WZLHL values that fall outside the TTI prediction models discussed in Chap- ter 3; the analyst is cautioned to carefully weigh analysis results for work zones of these durations. calculaTing d/c The adjusted hourly volumes (d*) are divided by the capacity (c) for each hour to calculate an individual d/c value for each of the 24 h of the day. (The asterisk [*] indicates the variable as affected by the treatment.) Lane Hours Lost Due to Incidents and Work Zones This variable is a quantitative measure of the extent, duration, and frequency of incidents and work zones—items that tem- porarily reduce freeway capacity. LHL is defined as the sum of incident lane hours lost (ILHL) and work-zone lane hours lost (WZLHL) for a time-slice. Conceptually, LHL represents the effective number of lanes blocked due to all incidents and work zones during the time-slice, multiplied by the average block- age time for each incident and work zone. It correlates to the nonrecurrent capacity decreases attributable to these causes. The two components of LHL, ILHL and WZLHL, are defined and described below. lane HourS loST due To incidenTS ILHL is defined as the effective number of lanes blocked due to all incidents occurring during a time-slice, multiplied by the average blockage time for each incident type. ILHL is cal- culated as shown by Equation 4.4: N N Ti i iiILHL 1 60 4.4incidents, blocked, incidents,∑ ( ) ( )= where Nincidents,i = number of incidents of type i during the time-slice; Nblocked,i = average number of lanes blocked per incident of type i; and Tincidents,i = average duration of incident of type i (min). Each element of the ILHL equation is discussed below. Incident Type. Project L07 considers six incident types. The first three are crashes categorized by the standard crash sever- ity scale, and the last three are noncrash incidents. • Crash—property-damage-only (PDO) • Crash—minor injury • Crash—major injury or fatal

27 the relative proportions of noncrash incidents are based on Project L07 discussions with highway agencies. Diurnal Distribution of Nincidents. As Nincidents,i must be cal- culated for each hour of the day, the analyst must distribute annual incidents over 24 h. If crash data are not available by hour of day, or data are being forecasted, the following procedures can be used: • Diurnal distribution of crashes. Project L07 developed a relationship between crash rates and traffic density, the level of service measure for freeways (see Chapter 5). This relationship can be used to distribute crashes between hours of the day over the 24-h period. By using methods discussed in HCM, Chapter 11 (see HCM Exhibit 11-3) (2), the average operating speed (S) for each hour is calculated on the basis of the hourly vehicular volume (or demand) (V) and free-flow speed. The density D for each hour i can then be determined by using Equation 4.5: 4.5D V S i i i ( )= Using this density, the analyst can then use the L07 crash– density relationship presented in Table 4.2 to predict a crash rate (per million vehicle miles traveled) for that hour of the day for each crash type. Although these relationships could be used to predict an hourly number of crashes, it is assumed that the analyst already knows the observed site-specific crash totals, so the individual hourly predictions are used only to prorate the known annual crash total. Thus, for each of the three crash types, Nincidents is calculated for each hour of the day (i) as shown by Equation 4.6: 4.6incidents, , ,1 24N C C Ci H i H jj D∑ ( ) ( )= ∗ ∗ = • Disabled vehicle—non-lane-blocking (shoulder) • Disabled vehicle—lane-blocking • Other noncrash incidents Many items can potentially be included in the “other non- crash incidents” category, such as roadway obstructions and message-board gawking. The Project L07 research team included gawking (rubbernecking) as an opposite-direction incident in this category. In other words, a slowdown caused by gawking at an incident in the opposite direction is itself considered an incident. The literature is inconclusive on whether gawking is included in the typical definition of an incident, but the L07 research team has found this categori- zation necessary to ensure that the analysis methodology is applicable for evaluating treatments that mitigate this type of gawking. Calculating Nincidents. Calculating the number of incidents of each type i during the time-slice is generally straightforward for crashes, but typically less so for noncrash incidents. Often, an agency will have detailed information on crashes, but very little data on noncrash incidents. If such data are unavailable, the values in Table 4.1 are suggested as defaults. The first two values in the table are based on Project L03 research (1), and Table 4.1. Suggested (Default) Proportions for Noncrash Incidents Percentage of incidents that are crashes 22% → Inferred ratio of noncrash incidents to crash incidents 3.545 Proportion of noncrash incidents by type Disabled—non-lane-blocking 71% Disabled—lane-blocking 18% Other noncrash incidents 11% Table 4.2. Predicted Crash Rate as a Function of Traffic Density (Project L07) Crash Severity Crash Rate As Function of Density (Di) If Di < 20 If 20 <– Di <– 78 If Di > 78 C  a1D3i  a2D2i  a3Di  a4 a1 a2 a3 a4 Fatal or major injury (Cfatal or Cmajor) 0.25 -1.795 × 10-5 0.00264 -0.0842 1.022 2.02 Minor injury (Cminor) 0.25 -1.795 × 10-5 0.00264 -0.0842 1.022 2.02 Property-damage only (CPDO) 0.55 -3.01 × 10-5 0.00444 -0.1301 1.614 4.20 Total crashes (Ctot) 0.80 -4.80 × 10-5 0.00708 -0.2143 2.636 6.22 Note: The development of this relationship is discussed in Chapter 5.

28 Calculating Nblocked. To calculate Nblocked,i (the average number of lanes blocked per incident for each incident type i), the recommended procedure is to use the ratio of the blocked and unblocked capacities to calculate an effective equivalent number of blocked lanes, as shown by Equation 4.8: 1 4.8blocked, cap,N N Ri L i( ) ( )= − where Nblocked,i = average number of lanes blocked per incident of type i; NL = number of lanes on the facility (one direction); and Rcap,i = capacity for incident of type i. To calculate Rcap,i, the recommended procedure is to adapt ratios from HCM, Exhibit 22-6 (2), which provides freeway capacity reduction proportions for various types of incidents. The HCM exhibit is based on a combination of incident types and lane blockages; therefore, Project L07 developed a procedure to convert the percentage of freeway capacity available (from the HCM exhibit) to the capac- ity reduction ratio for the six incident types used in this research. Table 4.3 includes recommended values for Rcap,i and the assumptions used to develop them from the HCM. Calculating Tincidents. To determine Tincidents,i (the average dura- tion for an incident of type i), the analyst can use local data. where C *H,i = predicted total crash frequency for hourly time- slice i from Project L07 crash–density relationship for given crash severity (see Table 4.2); and CD = observed total crash frequency for all hours of the day over the entire year for given crash severity (based on crash history data). Other crash prediction methods are becoming available that also incorporate the influence of roadway geometric features. For example, NCHRP Project 17-45 includes crash prediction guidance for geometric design elements such as shoulder width, lateral clearance, and presence and type of outside barriers. As these methods become more widely adopted, analysts can use them, coupled with procedures from the AASHTO Highway Safety Manual (5), to enhance the methodology presented above. • Diurnal distribution of noncrash incidents. A reasonable assumption is to distribute noncrash incidents through- out the day in proportion to the hourly volumes, as shown by Equation 4.7: 4.7incidents, , ,1 24N V V Ii H i H jj D∑ ( ) ( )= = where VH,i is the traffic volume for hour i, and ID is the daily incident total for a given incident type (see default percent- ages in Table 4.1). Table 4.3. Rcap,i Values Used to Calculate Nblocked,i for ILHL No. of Freeway Lanes (One Direction) Crash Type Noncrash Incident Type (Disabled Vehicle) PDO Minor Injury Major Injury and Fatal Non-Lane- Blocking Lane-Blocking Other 2 0.67 0.58 0.16 0.95 0.34 0.83 3 0.73 0.64 0.29 0.99 0.48 0.87 4 0.77 0.69 0.38 0.99 0.57 0.89 5 0.80 0.74 0.48 0.99 0.64 0.90 6 0.84 0.78 0.56 0.99 0.70 0.92 7 0.86 0.81 0.62 0.99 0.74 0.93 8 0.89 0.84 0.66 0.99 0.77 0.94 Values above are adapted from HCM, Exhibit 10-17, based on assumed conversions below from blockage type to incident type Shoulder disablement 0% 0% 0% 100% 0% 50% Shoulder crash 72% 59% 5% 0% 0% 39% 1 Lane blocked 26% 28% 35% 0% 96% 10% 2 Lanes blocked 2% 10% 45% 0% 3% 1% 3 Lanes blocked 0% 3% 15% 0% 1% 0%

29 result in longer queues and therefore queue discharge times (all else being equal). The time required for queue discharge is not included in the incident duration as defined for this project. Lane Hours Lost Due to Work Zones WZLHL is a measure of the effective number of lanes blocked due to all short-term work zones occurring during a time- slice, multiplied by the effective amount of time they will be active during the time-slice. WZLHL is calculated as shown by Equation 4.9: ( )= − WZLHL 1 4.9WZ lanes,WZlanes days c N cN N where cWZ = per lane capacity of the work zone (passenger cars per hour per lane [pcphpl]; HCM 2010, Chap- ter 10 suggests a default capacity of 1,600 pcphpl, with adjustments due to lane width and ramp presence); Nlanes,WZ = number of open lanes through the work zone; c = per lane capacity of the freeway section before establishment of the work zone (this should be the same value used in the d/ccrit calculation); Nlanes = number of lanes on the segment before estab- lishment of the work zone; and Ndays = number of days the work zone is active during the time-slice. For the purposes of Project L07, long-term work zones were not considered as nonrecurrent congestion. If a work zone will be in place for a relatively long period of time (e.g., more than 30 days), rather than being considered as part of the WZLHL calculation, it should be factored into base capacity assumptions for the highway segment of interest (see the previous d/c discussion). If local data are unavailable, the default values in Table 4.4 are suggested by the Project L07 research team, based on interviews and focus groups with highway agencies. How- ever, incident duration is heavily dependent on emergency response and clearance times and certain highway agency policies, so these values should be adjusted based on local agency practices and actual experience wherever possible. Treatments or actions that shorten the incident time- line should, by definition, reduce incident duration. Typi- cal incident timelines are illustrated in Figure 4.2 for two cases: (1) when an incident is left in place (blocking traffic lanes) until cleared, and (2) when an incident is moved to the shoulder for further responder work before clearing the incident—converting to a rubbernecking incident until it is completely cleared. In both cases, what is referred to through- out this document as “incident duration” is measured from the point marked “incident occurrence” to the point marked “incident cleared.” As the figure suggests, the timing of sev- eral events—including responder notification (e.g., via 911), initial response time (time to arrive on scene), and others not specified (such as response protocols once on scene)—can heavily influence incident duration. The incident duration further influences overall delay, because longer incidents Table 4.4. Incident Duration Default Values, Tincident Incident Type Incident Duration (min) Noncrash Lane-blocking 20 Non-lane-blocking 26 Other noncrash incidents 28 Crash PDO 28 Minor injury 40 Major injury and fatal 45 Figure 4.2. Typical incident timelines.

30 in the travel time reliability models to predict various TTI percentiles, or points along the cumulative TTI curve. These models are designed to be applied for single-hour time- slices. The development of these models is described in Appendix A. The reliability models used in Project L07 to estimate the effectiveness of design treatments at reducing nonrecurrent congestion and, thus, improving travel time reliability are expressed as shown in Equation 4.10: TTI TTI for 0.8 TTI 1 2 TTI 1 2 TTI for 0.8 4.10 NP, NP, days NP FF 05 FF NP, 01 FF NP, 05 01e d c N N V R c V c S d V d d c n n c R d S n n n n n n n n n ( ) = × ≤ × + + + +             >      ( )+ ′′ ′′ ′′ ′′ where TTIn = predicted nth percentile TTI; TTINP,n = nonprecipitation portion of TTIn = e(an d/c + bnLHL); LHL = LHL due to incidents and work zones; d/c = demand-to-capacity ratio; R05″ = number of hours in time-slice with rain exceed- ing 0.05 in.; S01″ = number of hours in time-slice with snow exceed- ing 0.01 in.; Ndays = number of hours in time-slice (365); NNP = number of hours in time-slice with no precipita- tion (i.e., Ndays - R05″ - S01″); VFF = free-flow travel time on segment (mph); an, bn = nth percentile coefficients for nonprecipitation components (d/c and LHL); cn, dn = nth percentile coefficients for rain and snow components, respectively (d/c < 0.8); c1n, c2n = nth percentile coefficients for rain component (d/c > 0.8); and d1n, d2n = nth percentile coefficients for snow component (d/c > 0.8). The four primary variables (LHL, d/c, R05″, and S01″) are discussed above under Model Variables. Table 4.5 shows the TTI prediction model coefficients for d/c ≤ 0.8 and d/c > 0.8. For the d/c ≤ 0.8 models, the four coefficients (an, bn, cn, dn) were developed as continuous functions of the TTI per- centile (n), allowing prediction of any percentile value (the entire cumulative TTI curve), not just the five percentiles shown in Table 4.5. These coefficient functions are built with subcoefficients, as shown in Equation 4.11. Table 4.6 shows If more than one short-term work zone is expected to occur on a highway segment during the time-slice, individual WZLHL values are computed for each work zone and then summed. Hours of Rainfall Exceeding 0.05 in. R0.05″ is the measure, for a particular time-slice, of the total num- ber of hours in which 0.05 in. or more of rainfall is observed. Because data on hourly rainfall over long periods of time are not readily available to transportation analysts, the research team has assembled default data that can be applied by users of the Project L07 methods. The research team developed these data on the basis of 10 years (2001 through 2010) of hourly precipitation data at 387 weather stations across the United States (see Figure 4.3). The spreadsheet tool described in Chapter 2 under Products of the Research incorporates the rainfall database to automatically determine a value for R0.05″ when any city in the United States is selected. Hours of Snowfall Exceeding 0.01 in. S0.01″ is the measure, for a particular time-slice, of the total number of hours in which snowfall exceeding trace amounts (0.01 in.) is observed. The original Project L03 models, which did not contain snowfall data, were enhanced by the Project L07 research team to account for snow. The snowfall data were obtained from the same weather stations as were the rainfall data for R0.05″. Appen- dix A describes the development of the snow model extension. Prediction Models The four variables described in the previous section (d/c, LHL, R0.05″, and S0.01″) are the independent variables used Source: © Microsoft Streets and Trips. Figure 4.3. U.S. weather stations used to determine R0.05″ and S0.01″.

31 Table 4.5. TTI Prediction Model Coefficients N (percentile) d/c < 0.8 d/c > 0.8 an bn cn dn an bn c1n c2n d1n d2n 10 0.01400 0.00099 0.00015 0.00037 0.07643 0.00405 1.364 -28.34 0.178 15.55 50 0.07000 0.00495 0.00075 0.00184 0.29097 0.01380 0.966 -6.74 0.345 3.27 80 0.11214 0.00793 0.00120 0.00310 0.52013 0.01544 0.630 6.89 0.233 5.24 95 0.19763 0.01557 0.00197 0.01056 0.63071 0.01219 0.639 5.04 0.286 1.67 99 0.47282 0.04170 0.00300 0.02293 1.13062 0.01242 0.607 5.27 0.341 -0.55 Note: Coefficients for d/c ≤ 0.8 are continuous functions of n. See text for more description. Table 4.6. Subcoefficient Values for TTI Prediction Model (d/c < 0.8) coeffn Subcoefficient w x y z an 0.14 0.504 96 9 bn 0.0099 0.0481 96 9 cn 0.00149 0.0197 68 6 dn 0.00367 0.0248 36 7 the subcoefficient values for the TTI prediction model with d/c < 0.8. ( )= + ( )−coeff 4.111wn xyn z n where coeffn = one of the four coefficients in the TTIn formula (an, bn, cn, dn); n = percentile (scaled between 0 and 1.0); and w, x, y, z = subcoefficients. Quantifying Design Treatment Effects on Reliability by Using the Cumulative TTI Curve The preceding section included a detailed explanation of methods to construct a predictive cumulative TTI curve using four primary variables (d/c, LHL, R0.05″, and S0.01″). Chapter 1 of this report describes how various reliability and delay mea- sures can be extracted from this curve. This section describes how the impacts of highway design treatments can be mapped to the four variables, and how the cumulative TTI curve can be used to evaluate the effectiveness of a design treat- ment at improving reliability, by comparing TTI curves for the untreated and treated conditions. For various reasons, not all treatments studied in Project L07 are discussed in this section: • Some treatments do not affect reliability, or reliability vari- ables, in a way that can be meaningfully predicted by the models. For example, ramp closures, such as gates used dur- ing flooding events, make a freeway reliable in the sense that it has no congestion—by virtue of its carrying no traffic. • Some treatments are beyond the scope of the reliability models. For example, improvements to diversion routes may need to be modeled using travel-demand models. Mapping Treatment Effects to Model Variables To enable calculation of the reliability effects of highway design treatments, it is necessary to determine how each treatment affects the independent variables in the TTI prediction models. This principle can be represented as shown by Equations 4.12 and 4.13: f Td c R S Untreated: TTI , ILHL, WZLHL, , 4.120.05 0.01{ } ( )= ′′ ′′ f d c R S Treated: TTI , ILHL , WZLHL , , 4.130.05 0.01{ } ( )∗ = ∗ ∗ ∗ ∗ ∗′′ ′′ where f is a mathematical function (as described under Cal- culating Demand, starting on page 24), and an asterisk (*) indicates the variable as affected by the treatment (recall that ILHL + WZLHL = LHL). In this section, treatments are classified by which of these five variables they affect. Most treatments only affect one of the five, although some affect more than one. Class I: Demand-to-Capacity Ratio Many design treatments aimed at recurrent congestion can also affect nonrecurrent congestion and reliability, and this effect is captured in the model variable d/c.

32 Class II is further subdivided into six cases, as described in the following subsections. These cases are not necessarily exhaustive, but they cover the relevant nonrecurrent conges- tion design treatments studied and provide a guide that could be extrapolated to other types of ILHL-reducing treatments. In all the described cases, Nblocked,i = Rcap,iNlanes except where noted. See Table 4.3 for appropriate values of Rcap,i. caSe iia: incidenT eliMinaTion wiTH unSPecified average TreaTaBle incidenT duraTion For treatments that eliminate a fraction (pi) of incidents of type i, only the remaining incidents of that type (1 - pi) con- tribute to ILHL. For Case IIA, it is assumed that additional information is either unknown or unneeded regarding the duration of the type of incidents for which the treatment will be applied. In this case, only one variable is affected, as shown by Equation 4.17: N p Ni i i1 4.17incidents, incidents,( ) ( )∗ = − The (1 - pi) term is directly related to the concept of a crash modification factor (CMF). Formally introduced to practice through the AASHTO Highway Safety Manual (5), CMFs can be defined as the ratio of the expected average crash fre- quency in a treated condition to the expected crash frequency in the untreated condition. Because the frequency is defined as the number of incidents over a specified period, the follow- ing logic applies, as shown by Equation 4.18: CMF 1 1 CMF 4.18 incidents, incidents, incidents,N N p N p i i i i i ( ) ( ) ∗ = × = − ⇒ = − Thus, if the CMF is known for a particular treatment, pi can be easily calculated for that treatment. The other two variables remain the same as in the untreated condition (i.e., N*blocked,i = Nblocked,i and T*incidents,i = Tincidents,i). Treatments in this category include wildlife–vehicle collision reduction, anti-icing, snow fences, and blowing sand reduction. caSe iiB: incidenT eliMinaTion wiTH SPecified average TreaTaBle incidenT duraTion As with Case IIA, Case IIB covers treatments that elimi- nate a portion of incidents. However, in this instance it is assumed that the duration of incidents (of a given type) to which the treatment applies is longer than the overall average duration (for that type). In other words, the treat- ment is likely to be applied only to incidents that are much more severe than average. For these cases, since the average incident duration (Tincidents,i) in the base condition is already specified, the analyst must specify Ttreatable, the average inci- dent duration for those incidents to which the treatment caSe ia: BaSe caPaciTy iMProveMenTS Base capacity improvements could include adding a lane or lanes, increasing lane width, adding a shoulder, or increasing shoulder width. Although only the latter two are specifically addressed in the Project L07 research, all these treatments have the same general effect: they increase the c term in the denominator of d/c, as expressed in Equation 4.14: d c d c d rc 4.14( )∗ = ∗ = where c* = treated capacity; c = original capacity; r = ratio between c* and c (i.e., c*/c); d = demand (here assumed unchanged); and d/c* = resulting demand-to-capacity ratio. For lane additions, r = N*L/NL (the ratio of the number of lanes after treatment implementation to the original number of lanes). For increased lane width, r = f *LW/fLW (the ratio of the treated and untreated HCM lane width adjustment factors for the respective widths). Similarly, shoulder addition or widening is based on fLC, the HCM adjustment factor for lateral clearance. caSe iB: deMand reducTionS Demand-reduction strategies could include the construction of alternate routes, relief of bottlenecks on existing alternate routes, or introduction of high-occupancy vehicle lanes (which have more complex effects beyond pure demand reduction). Case IB strategies affect the numerator of d/c, as shown in Equation 4.15: d c d c rd c 4.15( )∗ = ∗ = where d* = demand after strategy implementation; d = original demand; r = ratio between d* and d (d*/d); c = capacity (here assumed unchanged); and d/c* = resulting demand-to-capacity ratio. Class II: Incident Lane Hours Lost Many of the design treatments studied fall into Class II; that is, they affect ILHL. ILHL can be calculated for various inci- dent types. For each type i, the treatment can affect any of three variables (previously defined in Model Variables), as shown by Equation 4.16: N N T i i i i ILHL 60 4.16 incidents, blocked, incidents, ( )∗ = ∗ ∗ ∗

33 these cases, ILHL* is composed of three terms: one for inci- dents unaffected by the treatment; one for incidents affected by the treatment but before treatment implementation with a duration until conversion T*i ; and one for incidents affected by the treatment after treatment implementation (conversion to the new treatment type), to which the remaining treatment duration is applied. These three variations are expressed by Equations 4.24 through 4.26: Unaffected incidents: ILHL 1 – 60 4.241 incidents, blocked, incidents,p N N Ti i i i( ) ( )∗ = Affected incidents, preconversion: ILHL2 ∗ = pi N N Ti i iincidents blocked, , . ∗ ( )60 4 25 p N N T Ti i k i i Affected incidents, postconversion: ILHL – 60 4.263 incidents, blocked, incidents,( ) ( )∗ = ∗ Equation 4.27 gives the total treated ILHL, which is the sum of these three terms: ILHL ILHL ILHL ILHL 4.271 2 3 ( )∗ = ∗ + ∗ + ∗ This formulation assumes that the overall incident duration is the same as in the untreated condition; the latter portion of the duration consists of the second incident type (generally, a nonblocking shoulder incident). Treatments in this category include accessible shoulder, alternating shoulder, crash inves- tigation site, and emergency pulloff. caSe iie: incidenT TyPe converSion wiTH SPecified average TreaTaBle incidenT duraTion Like Case IID, Case IIE includes treatments that essentially transform a portion of incidents, midduration, from one type (i) into another type (k). However, for this treatment type, crashes are more severe, and it is assumed (as in Case IIB) that the duration of incidents (of a given type) to which the treatment applies is longer than the overall average duration (for that type). As in Case IIB, the analyst must specify Ttreatable, the average duration of incidents to which the treatment will be applied. As in Case IID, ILHL* is composed of three terms: one for incidents unaffected by the treatment, and two for incidents affected by the treatment (with a duration until conversion T*i ), as shown by Equations 4.28 to 4.30: p N N T T p i i i i p i i i Unaffected incidents : ILHL 1 – 60 1 – 4.28 1 incidents, blocked, incidents, treatable, [ ] ( ) ( ) ( ) ( ) ∗ = × − will be applied. Thus, the treated duration (applied only to the incidents that remain) is computed as shown by Equa- tions 4.19 and 4.20: T T p T p i i i i1 4.19incidents, incidents, treatable ( )∗ = − − with a notable boundary condition: ( )≤ 4.20treatable incidents,T T p i i N*incidents is calculated as in Case IIA (including the same relationship with CMFs), and N*blocked remains equal to the untreated condition (i.e., N*blocked = Nblocked). One example of a treatment falling in this category is the runaway truck ramp. caSe iic: reSPonSe TiMe reducTion Certain treatments reduce response time, allowing responders to reach (and therefore clear) certain types of incidents more quickly than in the untreated condition. Unlike incidents in Cases IIA and IIB, a Case IIC treated incident is not eliminated, but its duration is shortened. Therefore, ILHL* for a given incident type i is composed of two terms: one for incidents unaffected by the treatment, and one for incidents affected by the treatment (with a reduced duration T*i ), as shown by Equations 4.21 and 4.22, respectively: p N N Ti i i i Unaffected incidents : ILHL 1 – 60 4.211 incidents, blocked, incidents,( ) ( )∗ = Affected incidents: ILHL incidents b2 ∗ = p N Ni i, locked, .i iT ∗ ( )60 4 22 Equation 4.23 gives the total treated ILHL, which is the sum of these two terms: ILHL ILHL ILHL 4.231 2 ( )∗ = ∗ + ∗ One example of a treatment falling in this category is emer- gency access between interchanges. Some other treatments, such as median crossovers or contraflow lanes, could also be used for these purposes but are not studied in detail. caSe iid: incidenT TyPe converSion wiTH unSPecified average TreaTaBle incidenT duraTion Case IID includes treatments that essentially transform a por- tion of incidents, midduration, from one type (i) into another type (k), typically by providing an opportunity for incidents to be shifted from lane-blocking to shoulder-blocking. In

34 it is assumed that incidents for which this treatment would be deployed have a longer-than-average duration. Ttreatable is used in a different way with Case IIF than it is used in Cases IIB and IIE, as discussed below. For Case IIF, the reduction in LHL is treated as “lane hours gained,” as shown by Equations 4.32 and 4.33: ( )∆ =ILHL 4.32incidents, lanes div treatablep N N c T C i i ILHL ILHL ILHL 4.33( )∗ = + ∆ Therefore, unlike other cases, ILHL is not made up of three terms, although ∆ILHL is made up of three terms analogous to the typical ILHL calculation: • piNincidents,i represents the number of treated incidents. • Nlanescdiv/C (or [cdiv/C] × Nlanes) represents the equivalent number of lanes “unblocked” (cdiv is in units of vehicles per year, and C is in units of vehicles per lane hour). • Ttreatable represents duration. Although each time-slice covers 1 h of the day, default values of Ttreatable are often greater than 1 h. For Case IIF (not unlike Cases IIB and IIE), this duration accrues to a single time-slice, even when longer than 60 min. This simplification yields some lane hour savings accounted for during the “wrong hour,” but accumulates correctly when all 24 h of the day are considered. Treatments in this class include emergency crossovers, con- trolled or gated turnarounds, drivable shoulders, and movable cable median barriers. Table 4.7 summarizes the ILHL equation terms for each of the six cases and their subcases. claSS iii: work-Zone lane HourS loST For short-term work zones, three variables can affect the calculation of WZLHL in the treated condition: the per lane capacity of the work zone, the number of lanes avail- able through the work zone, or the number of days the work zone is active. Short-term WZLHL is calculated as shown by Equation 4.34: WZLHL 1 4.34 WZ lanes,WZ lanes days c N cN N ( )∗ = − ∗ ∗     ∗ Therefore, if a treatment affects one of these variables, this formula can be used in the TTI prediction models. claSS iv: r0.05″ Design treatments do not affect the variable R0.05″ because they cannot influence the amount of rain that falls. However, Affected incidents, preconversion: ILHL2 ∗ = pi N N Ti i iincidents blocked, , . ∗ ( )60 4 29 p N p N T Ti i r k i i Affected incidents, postconversion: ILHL 1 – – 60 4.303 incidents, blocked, treatable,( )( ) ( )∗= ∗ Equation 4.31 gives the total treated ILHL, which is the sum of these three terms: ILHL ILHL ILHL ILHL 4.311 2 3 ( )∗ = ∗ + ∗ + ∗ One example of a treatment in this category is the incident screen. caSe iif: incidenT diverSion Case IIF includes treatments that, when deployed during an incident, allow vehicles upstream of the input to detour via temporary new capacity (either by leaving the mainline or using a shoulder). None of the prediction model variables (as strictly defined) directly addresses the effects of this type of improvement. The two model variables with the greatest potential for addressing incident diversion, ILHL and d/c, have the following challenges: • ILHL is based on incident duration. Diverting vehicles does not shorten incident duration as defined in Case IIC; diversion theoretically has no effect on the time to clear an incident, although it can have a profound effect on the time until normal flow is recovered. • d/c is a measure characterizing the general level of satura- tion of a facility. It was not designed to emulate the effects of incidents. One might be tempted to use it as a proxy since demand is being diverted and additional capacity is being provided, but rare diversion events would not typi- cally affect annual demand or capacity enough to signifi- cantly affect the cumulative TTI curve. Even though neither of these measures is satisfying, based on tests and theoretical explorations, the Project L07 research team concluded that ILHL was better suited to account for the effects of diversion-related treatments. Two important parameters need to be defined in conjunc- tion with the analysis of diversion-related treatments: • The capacity, or throughput, of the diversion treatment itself is termed cdiv. For example, a gravel crossover may be able to process fewer vehicles per hour than a paved crossover. • The typical duration of an incident for which the crossover would be used is termed Ttreatable. As with Cases IIB and IIE,

35 applied to any treatment or operational strategy that can be mapped to at least one of the four variables in the TTI pre- diction models. Figure 4.5, presented earlier as Figure 4.1, is re–presented here to illustrate the process that leads to the final calculation of operational benefits. Many operational measures were introduced in Chapter 1, and the changes in all of them can be computed based on the computed cumulative TTI curves. However, in prepara- tion for calculation of economic benefits (see Chapter 6), the two most important measures are the lateness index (LI) and the standard deviation. Calculation of changes in these measures is discussed in the following two sections. Calcula- tion of other measures, such as the semivariance and various indices, are discussed under Background at the beginning of Chapter 1. The TTI prediction models have a feature that is important to note in reliability calculations: there is no smooth transi- tion between the d/c ≤ 0.8 and d/c > 0.8 models. This could cause an overestimation of operational benefits if a treat- ment causes a d/c above 0.8 to decrease below 0.8. Therefore, in all cases, it is recommended that the model used for the untreated condition (with respect to d/c) should be used for the treated conditions, even if the treatment causes d/c to cross the 0.8 boundary. Change in Lateness Index As described in Chapter 1, the unitless area between the cumulative TTI curve and the vertical line at TTI = 1.0 R0.05″ is an important variable in the model because it helps describe the base conditions. Class V: s0.01″ Just as design treatments do not affect the variable R0.05″, they do not affect the variable S0.01″ because they cannot influence snowfall. However, S0.01″ is an important variable in the model because it helps describe the base conditions. Although the amount of snow that falls cannot be influenced by design treatments, treatments like snow fences may reduce snow accumulation on the roadway and improve visibility, thereby reducing the number of snow-related crashes and, therefore, ILHL. Table 4.8 provides suggested default coefficient values for treatment mapping to TTI predictions models. Calculating Operational Effectiveness: Overview As described in the previous section, each treatment changes reliability by modifying the value of either LHL or d/c. For each hour of the day, untreated and treated TTI curves can be generated for a particular freeway segment and placed on the same graph. Thus, the key step in quantifying the effect of design treatments on reliability is to estimate TTI dis- tribution curves, like those shown in Figure 4.4. The area between the untreated and treated TTI curves is proportional to the overall delay reduction resulting from the treatment. Although this report focuses on a specific set of treatments to address nonrecurrent congestion, this approach can be Table 4.7. Terms in Treated ILHL Equations: Six Class II Cases Case a N*incidents,i N*blocked,i T*incidents,i IIA: Incident elimination with unspecified average treatable incident duration (1 - pi) Ninc,i (1 - Rcap,i)Nlanes Tinc,i IIB: Incident elimination with specified average treatable incident duration (1 - pi) Ninc,i (1 - Rcap,i)Nlanes (Tinc,i - piTtreatable)/(1 - pi) IIC: Response time reduction unaffected: (1 - pi) Ninc,i (1 - Rcap,i)Nlanes Tinc,i affected: pi Nincidents,i (1 - Rcap,k)Nlanes T*i IID: Incident type conversion with unspecified average treatable incident duration, passive treatment unaffected: (1 - pi) Ninc,i (1 - Rcap,i)Nlanes Tinc,i affected, preconversion: pi Ninc,i (1 - Rcap,i)Nlanes T*i affected, postconversion: pi Ninc,i (1 - Rcap,k)Nlanes Tinc,i - T*i IIE: Incident type conversion with specified average treatable incident duration, active treatment unaffected: (1 - pi) Ninc,i (1 - Rcap,i)Nlanes - affected, preconversion: pi Ninc,i (1 - Rcap,i)Nlanes T*i affected, postconversion: pi Ninc,i (1 - Rcap,i)(1 - pr)Nlanes Ttreatable - T*i IIF: Incident diversion incidents, lanes div treatableILHL ILHL p N N c T C i i∗ = + a For Cases IIA through IIE, ILHL* = N*incidents,i × N*blocked,i × T*incidents,i. For Case IIF, ILHL* is as shown in the table.

36 a Italicized values are user-modifiable in the Analysis Tool. b There are many varieties of wildlife collisions, each with its own set of potential treatments and effects. Note: Min = minor injury; Maj/Fat = major injury or fatality; NLB = non-lane-blocking; LB = lane-blocking; na = not applicable. Deployment Timea (min) Incident screens IIE 0 0.05 0.10 20 Ratio of Applicable Duration to Average Incident Length Lost Capacity Restored (%), pr,i PDO Min Maj/Fat PDO Min Maj/Fat 2 2 2 10 10 10 Emergency crossovers IIF 0 0.01 0.05 na na na Controlled/gated turnarounds IIF 0 0.01 0.05 na na na Drivable shoulder IIF 0.05 0.15 0.25 na 0.05 0.05 Movable cable median barrier IIF 0 0.01 0.05 na na na Applicable Duration (h) v/c Threshold of Application PDO Min Maj/Fat PDO Min Maj/Fat 1.0 1.5 2.0 1.0 1.0 1.0 1.0 1.5 2.0 1.0 1.0 1.0 1.0 1.5 2.0 1.0 1.0 1.0 1.0 1.5 2.0 1.0 1.0 1.0 Incident Duration with Treatment, T* (min) Crashes Noncrashes PDO Min Maj/Fat NLB LB Other 5 5 5 na na na 25 35 45 na 20 20 25 35 45 15 20 20 25 35 45 15 20 20 25 35 45 15 20 20 Portion of Incidents Using or Affected by Treatment, pi Crashesa Noncrashesa PDO Min Maj/Fat NLB LB Other Emergency access between interchanges IIC 0.05 0.10 0.20 na na na Accessible shoulder IID 0.50 0.30 0.10 na 0.60 0.25 Alternating shoulder IID 0.35 0.25 0.05 na 0.50 0.20 Crash investigation site IID 0.40 0.20 0 0.20 0.40 0.10 Emergency pulloff IID 0.40 0.20 0 na 0.15 0.10 Table 4.8. Suggested Default Coefficients or Terms for Treatment Mapping to TTI Prediction Models for Class II (Incident Lane Hours Lost) Treatment Case Portion of Incidents Using or Affected by Treatment, pi Crashesa Noncrashesa PDO Min Maj/Fat NLB LB Other Anti-icing systems IIA 0.10 0.10 0.10 na na na Blowing sand IIA 0 0 0 na na na Extra-high median barrier IIA Apply to opposite-direction incidents Snow fence IIA 0.10 0.10 0.10 na na na Wildlife collision reduction IIA b b b na na b Runaway truck ramp IIB 0.001 0.001 0.001 na na na Ratio of Applicable Duration to Tincident PDO Min Maj/Fat 4 4 4

37 Figure 4.4. Comparison of treated and untreated TTI curves. Figure 4.5. Calculation of operational effectiveness. Model Variables Prediction Models Calculating Operational Effectiveness: Overview Mapping Treatment Effects to Model Variables Figure 4.6. Change in lateness index.(i.e., the LI) is a measure similar to the mean of the TTI dis- tribution. The difference between untreated and treated LIs is equal to the area between the two curves (see Figure 4.6) and is proportional to the overall delay savings resulting from the treatment, because one can think of the reduced travel time at each TTI percentile as being applicable to the vehi- cles represented in that percentile. This unitless area can be multiplied by the vehicle volume for the time-slice and the free-flow travel time for the segment, resulting in a value that represents vehicle hours of delay reduced by implementing the treatment. To calculate delay, TTI is converted to an actual segment travel time. This can be accomplished with the following pro- cedure. The free-flow travel time (TTFF) is defined as the seg- ment length (L) divided by the free-flow travel speed (SFF), as shown by Equation 4.35: ( )=TT 4.35FF FF L S Percentiles of the TTI curve can be determined from the TTI prediction models described above under Prediction Models, as shown in Equation 4.36: TTI TTI for 0.8 TTI 1 2 TTI 1 2 TTI for 0.8 4.36 NP, NP, days NP FF 0.05 FF NP, 01 FF NP, 0.05 01e d c N N V R c V c S d V d d c n n c R d S n n n n n n n n n ( ) = × ≤ × + + + +             >      ( )+ ′′ ′′ ′′ ′′ The actual travel time (TT) corresponding to any given value of TTI is given by Equation 4.37: ( )= =  TT (TTI)(TT ) TTI 4.37FF FF L S

38 Therefore, the travel time savings (∆TTn)—and by implica- tion, delay reduction—at a given percentile n can be calculated as shown by Equation 4.38: L S n n n n nTT TT TT TTI TTI 4.38 FF ( ) ( )∆ = − ∗ = − ∗ where TTn = travel time (h) for percentile n of the cumulative travel time distribution (TT-CDF) in the untreated condition; TT*n = travel time (h) for percentile n of the TT-CDF in the treated condition; TTIn = TTI for percentile n of the cumulative TTI distri- bution (TTI-CDF) in the untreated condition; and TTI*n = TTI for percentile n of the TTI-CDF in the treated condition. If the treated and untreated TTI curves shown in Figure 4.6 were continuous functions (and note that the TTI prediction function for d/c ≤ 0.8 does predict continuous distributions), the total vehicle hours of delay (or change in LI) for the entire time-slice could be calculated as shown by Equation 4.39: N Nk d i ii d iiLI VLS TTI TTI di VLS TTI di 4.39 ff 0 100% ff 0 100%∫ ∫( ) ( ) ∆ = − ∗ = ∆ = = where ∆LIk = traffic operational delay reduction due to design treatment during time-slice k (change in LI); Nd = number of days in the time-slice (generally assumed as 250 nonholiday weekdays); and V = hourly vehicular volume during the time-slice. All other variables are as described previously. However, as the TTI prediction functions for d/c > 0.8 pre- dict five discrete percentiles of the cumulative TTI distribution, rather than a continuous curve, the area between the curves must be approximated by trapezoids, as illustrated in Fig- ure 4.7 (summing A1, A2, A3, and A4). Given that the area of a trapezoid is one-half the sum of the two parallel sides multi- plied by the distance between them, and simplifying terms, the area can be approximated as expressed by Equation 4.40: Nk dLI VLS 0.200 TTI 0.350 TTI 0.225 TTI 0.095 TTI 0.020 TTI 4.40 ff 10% 50% 80% 95% 99% ( ) ( ) ∆ ≈ ∆ + ∆ + ∆ + ∆ + ∆ This sum omits the area of the small tails at either end of the distribution that are considered negligible for the pur- poses of this analysis. Change in Variance Project L07 also focused on the reduction in the variance or standard deviation of travel time as a reliability measure, because that measure has an economic interpretation docu- mented in the literature. Therefore, the computation of the standard deviation of travel time is the focus of the following discussion. However, the state of knowledge about reliability and its economic value is rapidly evolving. If the entire distribution were known, the variance would be computed as indicated in Chapter 1 and expressed by Equation 4.41: TTI TTI di 4.41mean 2 0 100% i i ∫ ( ) ( )σ = − = Because the TTI prediction functions do not provide a con- tinuous distribution, the area under the five-point “curve” in Figure 4.8 is a reasonable approximation for the variance (s). Figure 4.7. Estimating delay by quantifying the area between treated and untreated TTI curves. Figure 4.8. Graphical presentation of procedure for approximating the variance of the TTI distribution.

39 However, the standard deviation is the measure suggested by the literature for calculating the economic value of reliability. Change in Other Reliability Measures The cumulative TTI curves for the treated and untreated conditions can also be used to derive any of the remaining reliability indicators presented in Chapter 1, most of which are indices. In general, the difference between the treated and untreated indices can be computed for each hour of the day, but no 24-h summary measures have yet been devel- oped for any of these indicators. It is illuminating to plot each of these indices as they vary by time of day, not only for treated and untreated conditions, but for the difference between the two. Because the x-axis is expressed in percentages, no normal- izing constant is needed. Using calculations for the trapezoi- dal Areas A1 through A4 and simplifying expressions yields Equation 4.42: S 0.300 0.350 0.225 0.095 0.020 4.42 FF 10% 50% 80% 95% 99% ( ) ( ) σ ≈ ∆ + ∆ + ∆ + ∆ + ∆ where ∆n equals (TTIn - TTImean)2. Similar approximations can be made in the case of semi- variance (sr), as shown by Equation 4.43: TTI 1 di 4.432 0 100% r i i ∫ ( ) ( )σ = − =