United States Air and Radiation EPA420-R-01-013 Environmental Protection April 2001 Agency M6.FLT.005 vvEPA Trip Length Activity Factors for Running Loss and Exhaust Running Emissions > Printed on Recycled Paper ------- EPA420-R-01-013 April 2001 Trip for Edward L. Glover David J. Brzezinski Assessment and Standards Division Office of Transportation and Air Quality U.S. Environmental Protection Agency NOTICE This technical report does not necessarily represent final EPA decisions or positions. It is intended to present technical analysis of issues using data which are currently available. The purpose in the release of such reports is to facilitate the exchange of technical information and. to inform the public of technical developments which may form the basis for a final EPA decision, position, or regulatory action. ------- 1.0 INTRODUCTION The original analysis of trip length distribution factors for running emissions was based on a detailed analysis of the EPA instrumented vehicle database. In this analysis individual distributions based on the EPA data were created for individual hours. Unfortunately, this ultimately created a problem in the MOBILE6 model because the corresponding running loss emission factors were never updated from MOBILES, and these older factors were not on an hourly basis. As a result, the new MOBILE6 trip length activity estimates were discarded and the original MOBILES running loss trip distribution was inserted into MOBILE6 so that consistency could be maintained between the activity information and the emission information. This document is structured so that it includes the new running loss trip length analysis description and the results as well as the original MOBILES results which will be used in MOBILE6. This inclusion is made so as to preserve a record of the analysis for possible future use should the emission estimates get updated. 2.0 DATA SOURCES USED The original analysis of running loss emissions soak distributions were based on the EPA instrumented vehicle study conducted in Baltimore and Spokane. This data set is described briefly in M6FLT003, M6FLT004 and M6FLT006. The revised analysis and running loss emission soak time distributions are based on the same datasets used to develop the daily numbers for MOBILES. 3.0 METHODOLOGY FOR RUNNING LOSS EMISSION ACTIVITY This section describes the basic methodology to develop the trip length activity estimates used to calculate running loss emissions. The process consisted of several steps. These are discussed below. 1.1 Definitions 1.1.1 Running Loss Emissions Running loss emissions are evaporative emissions which have escaped from a vehicle while the engine is operating. These emissions may appear from numerous locations on a vehicle such as the evaporative canister, the fuel inlet, the top of the gas tank, and other spots where the integrity of the evaporative system has broken down or the purge system has become inoperative. Running loss emissions may be an artifact of a particular evaporative system design or the result of poor maintenance. In severe cases the emissions can become quite high as the result of large thermal gradients around a vehicle's fuel and evaporative system. In addition, because of greater heating of the fuel and evaporative system on longer trips, running loss emissions are not constant throughout ------- a trip. Instead, the rate is assumed to continually increase as a function of trip length until it reaches a plateau at a trip length of about 50 to 60 minutes. 1.1.2 Running Loss Trip For the purpose of activity estimates for running loss emissions, a trip is defined as the duration of time or distance between a vehicle key on and key off (excluding engine stalls, which were removed from the database). Throughout this document the time duration of a trip will be referred to as the "trip time length". The duration of a trip in miles will be referred to as the "trip distance length". 1.2 Hourly Intervals and Weekday versus Weekend The running loss emission calculation result will be reported on an hourly and weekday versus weekend basis in MOBILE6. The results will vary by hour and weekday / weekend status because of a different number of trips per day for weekday and weekend (See Sections 1.3 and 1.4). 1.3 Trips per Car-Day The first necessary parameter in the model is the estimate for trips/car-day. Four different estimates were developed. There is one estimate for each combination of car or truck and weekday or weekend. These are average values obtained from the instrumented vehicle database. The values are shown in Table 2a. Table 2a Trips per Car per Day Cars Weekday 7.28 Weekend 5.41 Trucks Weekday 8.06 Weekend 5.68 ------- 1.4 Daily Trip Distribution by Hourly Group Table 2b contains distributions of vehicle trips by hourly group. One of the distributions is based on vehicle miles travelled (VMT) of the trips, and the other is based on the distribution of trip counts. Distance estimates and count-based estimates are provided for each of the fourteen groups, and separate estimates are provided for weekends and weekdays. The trip count distribution is shown for comparison purposes, since it is expected that the MOBILE6 model activity distribution for running losses will be based on trip distances in miles. The distance-based distribution will be used because it is directly proportional to the VMT accumulated during the hourly group. This is important because in the MOBILE6 model running loss emissions are a function of miles, and are presented in units of grams / mile. Table A2b Daily Distribution of Weekday Trips by Hourly Group (in percent) Hour 6 7 8 9 10 11 12 13 14 15 16 17 18 24 VMT Based 3.67 7.29 8.18 4.75 4.59 5.40 6.10 7.05 7.97 8.14 8.94 8.19 6.28 13.45 Trip Count Based 1.983 5.461 5.872 4.744 5.217 6.757 8.237 7.352 8.069 9.015 8.603 7.779 6.025 14.887 ------- Significant differences in the VMT based and the trip count based distribution can occur. For example, Table A2b shows that approximately 4.155 percent of the weekday daily trip VMT occured during the period from 6:00 AM to 6:59:59 AM; however, this VMT represented 1.983 percent of the total daily trips. The data which underlie Table 2b were obtained from the instrumented vehicle database. Each column sums to 100 percent. Table 2c Daily Distribution of Weekend Trips bv Hourly Group (in percent) Hour 6 7 8 9 10 11 12 13 14 15 16 17 18 24 VMT Based 0.90 1.70 2.84 4.57 6.20 7.62 8.79 9.98 7.64 9.19 9.04 6.88 6.57 18.07 Trip Count Based 0.905 1.962 3.068 6.590 6.992 7.998 10.312 7.294 8.803 7.294 7.998 7.042 6.087 17.656 ------- 1.4 Running Loss Trip Distance Length Distribution Within An Hourly Group The distribution of trip lengths used in computing running loss emissions in the MOBILE6 model are shown in Table 2d. These are the percentage of VMT that each type of trip represents in overall national driving over all times of the day. The skewing of the distribution towards the higher time lengths (i.e., 51+ minutes) reflect the fact that the longer duration trips contain the most VMT weighting. For example, Table 2d states that 16.775 percent of all trips (on a VMT basis) last 21 - 30 minutes. These results were taken from MOBILES, and will be applied in MOBILE6 for all individual hourly results. The original MOBILE6 analysis discussed in Appendix A included the development of separate distributions by hourly group. For example, the morning rush hour trip distribution was different than the late evening distribution. This revised trip distribution could not be used in MOBILE6 because the basic running loss emission factors (not updated from MOBILES) were not compatible with it. The overall set of MOBILES running loss activity estimates are shown in Table 2d (the percentages shown in Table 2d add up to 100%). For additional details regarding the MOBILES activity parameters for running losses see the EPA report EPA-AA-AQ-AB-94-01 May 94 entitled "User Guide to MOBILES." TABLE 2d MOBILES Running Loss Activities Trip Duration Range (min) Percentage 0- 10 minutes 6.744 11-20 minutes 18.507 21 -30 minutes 16.775 31 -40 minutes 13.108 41 -50 minutes 8.335 51+ minutes 36.531 ------- 1.5 Using the Hourly Running Loss Activities in MOBILE6 1.5.1 Hourly Running Loss Calculation The average hourly running loss emissions are calculated from four parameters. These are: (1) the six running loss emission values (one value for each trip duration category). These values will not be updated for MOBILE6, and can be found in EPA document AP-42 for MOBILES. (2) the six trip duration by hourly group running loss activity values shown in Table 2d. (3) the number of trips per day per vehicle values shown in Table 2a, and (4) the daily distribution of trips by hourly group (shown in Tables 2b and 2c). MOBILE6 will multiply each of the six running loss emission values with each of the corresponding six running loss activity values. The six products (emissions x activities) are then summed to produce an estimate of running losses on a per trip basis. The calculation is done only once for each of the 28 groups, and produces the same running loss emission value for each of the 28 groups. The second calculation takes the 28 hourly running loss emission values in per trip units, and converts them into average hourly running loss emission values. This is done by multiplying the 28 hourly per trip running loss values by the number of trips per day (shown in Table 2a) and by the appropriate value from the daily distribution of trips by hourly group table (shown in Table 2b or 2c). The daily distribution of trips by hourly group apportions the overall trips per day value into hourly group values. 1.5.2 Daily Running Loss Calculation An overall daily running loss average is computed by weighting together the average running loss values of the 28 groups. The weighting factors are the daily distribution of trips by hourly group values shown in Tables 2b and 2c. The number of trips per day per vehicle from Table 2a is used to calculate the final daily running loss emissions. ------- Appendix A New Methodology for Running Loss Emission Activity Some of this material is duplicative of the material in the Main Section of the document. It was retained so that this section would appear to the reader as cohesive and complete. Al.O METHODOLOGY FOR RUNNING LOSS EMISSION ACTIVITY This section describes the basic methodology to develop the trip length activity estimates used to calculate running loss emissions. The process consisted of several steps. These are discussed below. Al.l Definitions Al.1.1 Running Loss Emissions Running loss emissions are evaporative emissions which have escaped from a vehicle while the engine is operating. These emissions may appear from numerous locations on a vehicle such as the evaporative canister, the fuel inlet, the top of the gas tank, and other spots where the integrity of the evaporative system has broken down or the purge system has become inoperative. Running loss emissions may be an artifact of a particular evaporative system design or the result of poor maintenance. In severe cases the emissions can become quite high as the result of large thermal gradients around a vehicle's fuel and evaporative system. In addition, because of greater heating of the fuel and evaporative system on longer trips, running loss emissions are not constant throughout a trip. Instead, the rate is assumed to continually increase as a function of trip length until it reaches a plateau at a trip length of about 50 to 60 minutes. Al.l.2 Running Loss Trip For the purpose of activity estimates for running loss emissions, a trip is defined as the duration of time or distance between a vehicle key on and key off (excluding engine stalls, which were removed from the database). Throughout this document the time duration of a trip will be referred to as the "trip time length". The duration of a trip in miles will be referred to as the "trip distance length". A1.2 Hourly Intervals The 24 hour day was divided into 14 different hourly groups. Thirteen of these groups have a duration of one hour. These start at 6:OOAM and run through 7:59:59PM. The fourteenth group contains the remaining nighttime hours as one interval. Collapsing these hours into one group was done for three reasons: (1) the emissions contributed during the night have a relatively smaller ------- impact on daily ozone or CO formation than those contributed during the morning or day, (2) there were relatively little data for these time periods, and (3) what data were available produced results which showed very little hour to hour variance. The hourly intervals are shown in Table Al. In addition to their use for the running loss activity estimates presented here, the same hourly group intervals are used in the calculation of activity estimates for start emissions, running emissions, hot soak emissions, resting loss emissions, and diurnal emissions. Table Al Hourly Ranges Group Name 6 7 8 9 10 11 12 13 14 15 16 17 18 24 Hourly Range 6-7 7-8 8-9 9- 10 10- 11 11 - 12 12- 13 13- 14 14- 15 15- 16 16- 17 17- 18 18- 19 19 -24 and 24 -5 Time 6 am to 7 am 7 am to 8 am 8 am to 9 am 9 am to 10 am 10 am to 11 am 1 1 am to noon noon to 1 pm 1 pm to 2 pm 2 pm to 3 pm 3 pm to 4 pm 4 pm to 5 pm 5 pm to 6 pm 6 pm to 7 pm 7 pm to 6 am A1.3 Weekday Versus Weekend For a number of the activity parameters a significant difference existed between the value for the weekday and the value for the weekend. Conceptually this make sense since most motorists have different usage patterns for their vehicles on weekdays than on weekends. Differences may also exist for the various days of the week; however, the database was too small to reliably discern these differences. ------- The MOBILE6 model will distinguish between weekend and weekday in terms of activity and emissions, and a user input will be required to tell the model which one is to be reported. The default will likely be the "weekday." Also, since the default MOBILE6 hourly activity estimates are based exclusively on 168 vehicles, and cannot possibility reflect all geographical areas, times, or other variables, the user will have the option of providing running loss activity data into the MOBILE6 model from an external file. A1.4 Trips per Car-Day The first necessary parameter in the model is the estimate for trips/car-day. Four different estimates were developed. There is one estimate for each combination of car or truck and weekday or weekend. These are average values obtained from the instrumented vehicle database. The values are shown in Table A2a. Table A2a Trips per Car per Day Cars Weekday 7.28 Weekend 5.41 Trucks Weekday 8.06 Weekend 5.68 These estimates are based on the instrumented car data, and are subject to revision pending completion of a thorough analysis of national trip data by an EPA contractor. The values could potentially vary considerably from those presented here. A1.5 Daily Trip Distribution by Hourly Group Table A2b contains distributions of vehicle trips by hourly group. One of the distributions is based on vehicle miles travelled (VMT) of the trips, and the other is based on the distribution of trip counts. Distance estimates and count-based estimates are provided for each of the fourteen groups, and separate estimates are provided for weekends and weekdays. The trip count distribution is shown for comparison purposes, since it is expected that the MOBILE6 model activity distribution for running losses will be based on trip distances in miles. The distance-based distribution will be used because it is directly proportional to the VMT accumulated during the hourly group. This is important because in the MOBILE6 model running loss emissions are a function of miles, and are presented in units of grams / mile. ------- Table A2b Daily Distribution of Weekday Trips by Hourly Group (in percent) Hour 6 7 8 9 10 11 12 13 14 15 16 17 18 24 VMT Based 3.67 7.29 8.18 4.75 4.59 5.40 6.10 7.05 7.97 8.14 8.94 8.19 6.28 13.45 Trip Count Based 1.983 5.461 5.872 4.744 5.217 6.757 8.237 7.352 8.069 9.015 8.603 7.779 6.025 14.887 Significant differences in the VMT based and the trip count based distribution can occur. For example, Table A2b shows that approximately 4.155 percent of the weekday daily trip VMT occured during the period from 6:00 AM to 6:59:59 AM; however, this VMT represented 1.983 percent of the total daily trips. The data which underlie Table A2b were obtained from the instrumented vehicle database. Each column sums to 100 percent. 10 ------- Table A2c Daily Distribution of Weekend Trips bv Hourly Group (in percent) Hour 6 7 8 9 10 11 12 13 14 15 16 17 18 24 VMT Based 0.90 1.70 2.84 4.57 6.20 7.62 8.79 9.98 7.64 9.19 9.04 6.88 6.57 18.07 Trip Count Based 0.905 1.962 3.068 6.590 6.992 7.998 10.312 7.294 8.803 7.294 7.998 7.042 6.087 17.656 A1.6 Running Loss Trip Distance Length Distribution by Hourly Group A distribution of running loss trip distance lengths was developed for each of the 28 hourly group / weekday-weekend groups. The methodology used to analyze the data, and the results of the analysis are presented below. This particular methodology for estimating running loss activity was chosen because it fits the running loss emission values that are available in MOBILES (these will not be updated in MOBILE6). The only enhancement for the new model is that these activity parameters will be available for each hourly group and for weekday/weekend categorization (28 groups) rather than just an overall average set which represents all hours and days of the week. The overall set of MOBILES running loss activity estimates are shown in Table A2d (the percentages shown in Table A2d add up to 100%). For additional details regarding the MOBILES activity parameters for running losses see the EPA report EPA-AA-AQ-AB-94-01 May 94 entitled "User 11 ------- Guide to MOBILES." TABLE A2d MOBILES Running Loss Activities Trip Duration Range (min) Percentage 0- 10 minutes 6.744 11-20 minutes 18.507 21 -30 minutes 16.775 31 -40 minutes 13.108 41 -50 minutes 8.335 51+ minutes 36.531 Al.6.1 Methodology The analysis consisted primarily of categorizing each of the 8,500 vehicle trips in the database into a particular hourly / weekday-weekend group. This was done by examining the day of the week of the trip, and the starting and ending time of each trip. A vehicle trip was classified as a weekday trip if it started on Monday through Friday. It was a weekend trip if it started on Saturday or Sunday. A vehicle trip was classified into a particular hourly group if any part of the trip duration was in a given hourly group. A given vehicle trip could potentially be classified into one, two, or even three different hourly groups depending on the duration of the trip, and how many group interval boundaries it crossed. This classification could fit two general cases which are best illustrated with an example. (1) If a vehicle trip was from 8:20 AM to 8:40 AM it was classified as a twenty minute trip in Hourly Group 8. (2) If the trip was from 7:51 to 8:15, its contribution had to be split between two hourly groups (7 and 8 hour). Thus, a nine minute trip was assigned to the Hour 7 group, and a nine to twenty-five minute trip was assigned to the Hour 8 group. The nine to twenty-five minute label was assigned to the hour 8 group rather than a fifteen minute label, because the vehicle had been operating for nine minutes prior to the 8th hour, and would nominally have higher running losses than a vehicle which was just starting its trip. This is reflected in the MOBILE6 model because running losses are a function of the duration of the trip. After labeling each of the trips in the database using the method above, each trip was classified into one of six trip duration categories based on trip duration in minutes (see Table 3). For example, the trip which lasted from 8:20 to 8:40 AM would fall into category #2 and hour 8. The trip which lasted from 7:51 to 8:15 AM would be treated as two trips. The first phase (nine minutes) would fall into the category #1 and hour 7. The second phase would fall into category #3 and hour 8. Category #3 is used because the upper duration of the trip is 25 minutes, and the maximum length of the trip is used to determine category number. Running loss emissions from trips are also measured in 10 minute intervals, and are keyed to the upper duration of the trip. 12 ------- Table A3 Trip Duration Categories Category Number 1 2 3 4 5 6 Trip 0 - 11 - 21 - 31 - 41 - 51+ Duration Range (in Minutes) 10 minutes 20 minutes 30 minutes 40 minutes 50 minutes minutes After classifying the trips and phases of trips by hourly / weekday-weekend group, and by category number, the duration in miles of each trip and trip phase was found. In cases where the trip contained only one phase the trip distance in miles was readily available. In cases where two phases were present, the mileage was split according to the length of the trip in time. This assumes that the average speeds in both phases were equal. After obtaining the mileage for each trip and trip phase, the mileages were summed for each hourly / weekday-weekend group and for each category within a hourly /weekday-weekend group. From the sums, percentages contributions were calculated for each category within a group. Tables A4a and A4b show these percentages for weekdays and weekends. 13 ------- TABLE A4a and A4b Mileage (VMT) Distribution by Trip Length (in time) Weekday Weekday Weekday Weekday Weekday Weekday Weekday Weekday Weekday Weekday Weekday Weekday Weekday Weekday Weekend Weekend Weekend Weekend Weekend Weekend Weekend Weekend Weekend Weekend Weekend Weekend Weekend Weekend Hour 6 7 8 9 10 11 12 13 14 15 16 17 18 24 Hour 6 7 8 9 10 11 12 13 14 15 16 17 18 24 0-10 Min 14.89% 16.06% 14.56% 27.40% 28.47% 32.94% 33.41% 28.89% 27.08% 26.79% 24.91% 21 .09% 26.80% 20.95% 0-10 Min 18.98% 26.89% 20.60% 29.83% 25.57% 27.61% 25.85% 18.37% 23.71% 21.16% 25.66% 24.31% 18.01% 15.69% TABLE 4a 11 -20 Min 22.70% 31 .05% 33.48% 32.71 % 42.99% 32.78% 39.64% 46.80% 39.31 % 41 .84% 40.78% 34.84% 32.23% 37.26% 21-30 Min 29.44% 40.00% 18.37% 22.20% 17.06% 14.96% 15.19% 13.93% 18.29% 24.28% 18.79% 29.41 % 25.10% 24.51 % TABLE 4b 11 -20 Min 60.63% 42.40% 41 .68% 38.26% 42.08% 36.42% 35.51 % 19.41% 39.19% 25.39% 25.90% 37.71 % 38.43% 27.42% 21-30 Min 20.39% 30.71% 18.82% 23.09% 16.58% 13.25% 28.61 % 22.48% 12.26% 25.46% 12.34% 27.30% 18.27% 15.74% 31 -40 Min 20.76% 9.13% 18.49% 4.75% 7.92% 7.53% 1 1 .76% 9.27% 3.18% 3.90% 10.87% 9.23% 1 1 .98% 7.52% 31 -40 Min 0.00% 0.00% 0.00% 8.82% 15.77% 10.31% 3.54% 9.86% 14.93% 4.07% 6.60% 3.91% 20.83% 9.57% 41-50 Min 12.22% 3.75% 3.01 % 0.00% 3.56% 5.34% 0.00% 1.10% 1 .38% 2.20% 1 .76% 5.42% 3.05% 6.37% 41-50 Min 0.00% 0.00% 18.90% 0.00% 0.00% 3.38% 6.49% 4.32% 9.91% 0.00% 15.03% 0.00% 4.46% 2.58% 51+ Min 0.00% 0.00% 12.10% 12.94% 0.00% 6.47% 0.00% 0.00% 10.76% 0.99% 2.89% 0.00% 0.84% 3.38% 51+ Min 0.00% 0.00% 0.00% 0.00% 0.00% 9.03% 0.00% 25.56% 0.00% 23.92% 14.48% 6.76% 0.00% 28.99% Al.6.2 Results Tables A4a and A4b show the running loss activity estimates for all 28 groups and 6 categories. Each of the cells in Tables A4a and A4b show the percentage of vehicle miles travelled (VMT) for a given hourly / weekday-weekend group which falls in a given trip duration category. For example, 14.89 percent of the VMT in the 6 AM to 7 AM time interval on a weekday occurs in trips which are 0 to 10 minutes in duration. Also, each of the rows in the tables sums to 100 percent. 14 ------- A1.7 Using the Hourly Running Loss Activities in MOBILE6 Al.7.1 Hourly Running Loss Calculation The average hourly running loss emissions are calculated from four parameters. These are: (1) the six running loss emission values (one value for each trip duration category). These values will not be updated for MOBILE6, and can be found in EPA document AP-42 for MOBILES. (2) the six trip duration by hourly group running loss activity values shown in Table 4a or 4b. (3) the number of trips per day per vehicle values shown in Table A2a, and (4) the daily distribution of trips by hourly group (shown in Tables 2b and 2c). MOBILE6 will multiply each of the six running loss emission values with each of the corresponding six running loss activity values. The six products (emissions x activities) are then summed to produce an estimate of running losses on a per trip basis. The calculation is done once for each of the 28 groups, to produce a value for each of the 28 groups. These 28 hourly running loss emission values are per trip estimates, and are the result of an intermediate calculation in the MOBILE6 model. The second calculation takes the 28 hourly running loss emission values in per trip units, and converts them into average hourly running loss emission values. This is done by multiplying the 28 hourly per trip running loss values by the number of trips per day (shown in Table A2a) and by the appropriate value from the daily distribution of trips by hourly group table (shown in Table A2b or A2c). The daily distribution of trips by hourly group apportions the overall trips per day value into hourly group values. Al.7.2 Daily Running Loss Calculation An overall daily running loss average is computed by weighting together the average running loss values of the 28 groups. The weighting factors are the daily distribution of trips by hourly group values shown in Tables A2b and A2c. The number of trips per day per vehicle from Table A2a is used to calculate the final daily running loss emissions. A2.0 METHODOLOGY FOR RUNNING EXHAUST EMISSION ACTIVITY This short section describes the basic methodology to develop the trip length activity estimates used to calculate running exhaust emissions. The process and the results are virtually identical to those shown in the running loss activity estimate sections, and are shown here for completeness. A2.1 Definition 15 ------- Exhaust running emissions are the emissions which exit a vehicle's tailpipe while the vehicle is operating in a warmed up condition. Excluded from the definition of exhaust running emissions are those emissions which occur during vehicle start (cranking the engine) and warm-up. Standardized test procedures such as the Federal Test Procedure (FTP), and test equipment have been extensively developed to measure exhaust emissions. The exhaust running emissions in the MOBILE6 model are based on such FTP data. Detailed information on the definition of start emissions, the methodology used to develop the start emission estimates, and the projected MOBILE6 light duty vehicle start emission factors are provided in the EPA reports M6.STE.003 entitled "Determination of Start Emissions as a Function of Mileage and Soak Time for 1981-1993 Model Year Light-Duty Vehicles", and M6.STE.002 entitled "The Determination of Hot Running Emissions from FTP Bag Emissions." Also, detailed information on the determination of running exhaust emission factors for MOBILE6 can be found in EPA report M6.EXH.001 entitled "Determination of Running Emissions as a Function of Mileage for 1981-1993 Model Year Light-Duty Vehicles." A2.2 Activity Estimates The activity estimates for exhaust running emissions required for the MOBILE6 model are minimal, since we assume exhaust running emissions are not a function of the trip length or the preceding soak period. Thus, the only activity estimates needed to calculate hourly running exhaust emissions in MOBILE6 are the trips per day per vehicle estimates and the daily trip distribution by hourly group. The trips per day per vehicle value is an estimate of overall daily vehicle usage. It is shown in Table A2a. The trip distribution by hourly group allocates the trips per vehicle over all 14 hourly groups. It is shown in Tables A2b and A2c. 16 ------- |