Solution Chapter 9 - 1 Traffic Engineering 4th Edition...

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Unformatted text preview: 1 Traffic Engineering, 4th Edition Roess, R.P., Prassas, E.S., and McShane, W.R. Solutions to Problems in Chapter 9 Problem 9‐1 The problem calls for estimating a total 12‐hour volume for the study data shown. There is one control‐count station (Station A, Figure 9.19) and 9 coverage‐count stations (Stations 1‐9, Figure 9.19). There are several issues that must be addressed in the estimation process: • Data was taken in three four‐hour periods: 8 AM to 12 Noon, 12 Noon to 4 PM, and 4 PM to 8PM. To allow for movement of data crews, however, actual counts were taken for 3.75 hours out of each 4‐hour period. All counts, therefore, must be multiplied by 4.00/3.75 = 1.067 to estimate the actual 4‐hr counts. • Counts were taken using road tubes, and thus represent axle‐counts, not vehicle‐counts. Sample data on traffic composition (Table 9.16) must be used to estimate the average number of axles per vehicle, which can than be used to convert axle‐counts to vehicle‐counts. • Counts taken during one 4‐hour period must be expanded to estimate counts for the 12‐hour target period. • Counts were taken across three days. All counts must, therefore, be adjusted to reflect the average day of the count. These conversions can be done in almost any order, and are best done using a spreadsheet. As all results must be rounded to the nearest vehicle, the order of computations and the rounding mechanism used may cause small discrepancies in final answers. In this solution, rounding is done only in the final step, although most of the spreadsheet tables will appear to be rounded at each step. Table 1, which follows, computes the average number of axles per vehicle from the sample data of Table 9.16. The total number of axles observed is divided by the total number of vehicles observed to determine the conversion factor. 2 Table 1: Computing the Average Number of Axles Per Vehicle Vehicle Class 2-axle 3-axle 4-axle 5-axle Total Vehicles Observed 1,100 130 40 6 1,276 Axles Observed 2,200 390 160 30 2,780 Average Axles/Vehicle = 2,780/1,276 = 2.18 The data from the Control Count Station A must now be manipulated to produce conversion values for coverage counts. Two conversions must be conducted: a) from 4‐hr counts to 12‐hr counts, and b) from 12‐hr counts on a particular day to 12‐hr counts representing the average of the three days of the study. The first is accomplished by calibrating the percentage of 12‐hour volume that occurs in each 4‐hour period. For each day of the study, the percentage is computed as (V4/V12)*100. There will be different values for each day of the study. These can be applied separately to coverage counts on the same day, or the average percentages can be applied to all three days. The second conversion is accomplished by calibrating “daily variation factors” for each of the three days of the study. These factors are defined as VAVE/VDAY. The calibration of these values can be based directly on the 3.75‐hr axle‐counts of Table 9.15. These values could be converted to 4‐hr vehicle‐counts and used, but the conversions would affect every number equally, and none of the conversion values would be changed. Table 2 illustrates the computation of these conversion values in spreadsheet form. In terms of expanding counts from 4 hours to 12 hours, the percentages do not vary greatly for each day of the study. Therefore, percentages based upon the average data will be used. Coverage counts are now expanded to full 12‐hour vehicle counts in Table 3, using the following equation: 1.067 V3.75i * DF j V12i = pk 3 Where: V12i V3.75i 1.067 DFj pk = = = = = 12‐hour vehicle count for Station i, vehs 3.75‐hour axle count for Station i, axles expansion factor, 3.75 hrs to 4 hrs daily adjustment factor for day j percentage of volume occurring during time period k, expressed as a decimal Table 2: Calibration of Conversion Values from Control‐Count Data Day 8:00-11:45 Monday Tuesday Wednesday Total Monday Tuesday Wednesday Total 3,000 3,300 4,000 10,300 30.30% 30.84% 31.75% 31.02% Time Period 12:00-3:45 4:00-7:45 Axle Counts 2,800 4,100 3,000 4,400 3,600 5,000 9,400 13,500 Percent of 12-Hour Total 28.28% 41.41% 28.04% 41.12% 28.57% 39.68% 28.31% 40.66% Total 9,900 10,700 12,600 33,200 100.00% 100.00% 100.00% 100.00% Daily Adj Factor 1.118 1.034 0.878 11,067 NA NA NA NA Table 3: Expansion and Adjustment of Coverage Counts to 12‐Hour Vehicle‐ Counts Station 1 2 3 4 5 6 7 8 9 Day Monday Monday Monday Tuesday Tuesday Tuesday Wednesday Wednesday Wednesday Time 8:00-11:45 12:00-3:45 4:00-7:45 8:00-11:45 12:00-3:45 4:00-7:45 8:00-11:45 12:00-3:45 4:00-7:45 Axle Count 1,900 2,600 1,500 3,000 3,600 4,800 3,500 3,200 4,400 Exp to 4 Hr 1.067 1.067 1.067 1.067 1.067 1.067 1.067 1.067 1.067 Exp to 12-Hr 0.3102 0.2831 0.4066 0.3102 0.2831 0.4066 0.3102 0.2831 0.4066 Daily Adj 1.118 1.118 1.118 1.034 1.034 1.034 0.878 0.878 0.978 12-Hr Vehs 7,307 10,956 4,401 10,670 14,030 13,024 10,570 10,589 11,292 Problem 9‐2 Daily variation factors may be computed as: V DF = AVE VDAY Where: VAVE = average daily count for all days of the week, vehs average daily count for each day of the week, vehs VDAY = These computations are carried out in Table 4. 4 Table 3: Calibration of Daily Adjustment Factors Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday TOTAL AVERAGE Ave Vol 3,500 4,400 4,200 4,300 3,900 4,900 3,100 28,300 4,043 Daily Factor 1.155 0.919 0.963 0.940 1.037 0.825 1.304 Problem 9‐3 a) 5 minutes or 15 minutes. Count 4 of 5 or 13 of 15. The counting period and the actual count time must be multiples of 1 minute. b) 6 minutes or 18 minutes. Count 4.5 of 6 or 15 of 18. The counting period and the actual count time must be multiples of 90 seconds or 1.5 minutes. c) 6 minutes or 18 minutes. Count 4 of 6 or 16 of 18. The counting period and the actual count time must be multiples of 2 minutes. Problem 9‐4 Daily adjustment factors are based upon the data in Table 9.18. The factors, which use the same equation noted in Problem 9‐2, are based upon the average of the 4 weeks of data provided. Monthly adjustment factors are based upon the data in Table 9.19, and are computed using the following equation: AADT MFi = ADTi Where: MFi AADT ADTi = = = monthly adjustment factor month i average annual daily traffic , vehs/day (estimated as the average of 12 monthly ADTs) average daily traffic for month I, vehs/day 5 Daily adjustment factors are calibrated in Table 4. Monthly adjustment factors are calibrated in Table 5. Monthly variation factors must be themselves “adjusted” to reflect the middle of each month. This is done graphically in Figure 1. Table 4: Daily Adjustment Factors Calibrated First Week In: January April July October TOTAL AVERAGE DF Monday 2,000 1,900 1,700 2,100 7,700 1,925 0.900 Tuesday 2,200 2,080 1,850 2,270 8,400 2,100 0.825 Wednesday 2,250 2,110 1,900 2,300 8,560 2,140 0.809 Day of the Week Thursday Friday 2,000 1,800 1,890 1,750 1,710 1,580 2,050 1,800 7,650 6,930 1,913 1,733 0.906 1.000 Saturday 1,500 1,400 1,150 1,550 5,600 1,400 1.237 Sunday 950 890 800 1,010 3,650 913 1.898 TOTAL 12,700 12,020 10,690 13,080 12,123 1,732 Table 5: Monthly Adjustment Factors Calibrated Third Week In January February March April May June July August September October November December TOTAL AVERAGE Ave 24-Hr Count 2,250 2,200 2,000 2,100 1,950 1,850 1,800 1,700 2,000 2,100 2,150 2,300 24,400 2,033 Monthly Factor 0.904 0.924 1.017 0.968 1.043 1.099 1.130 1.196 1.017 0.968 0.946 0.884 6 Figure 1: Monthly Adjustment Factors “Adjusted” 1.300 1.200 Daily Factor DF 1.100 1.000 0.900 0.800 0 1 2 3 4 5 6 7 8 9 10 11 12 Third Week in Month No. In Figure 1, Monthly Factors are plotted at the end of the 3rd week of each month, when the counts were taken. Ideally, factors should represent the “middle” of the month, which is usually at the end of the 2nd week. The graph approximates four weeks per month (except for Feb, there are actually 4 + a fraction). The end of the 2nd week can, therefore, be approximated as one week earlier than the actual count. The factors for the “middle” of the month are read from the graph, and are entered in Table 6. Table 6: Monthly Factors Adjusted for the Middle of the Month Month Adjusted Monthly Factor MF January 0.900 February 0.920 March 1.005 April 0.975 May 1.020 June 1.090 July 1.120 August 1.200 September 1.060 October 0.975 November 0.955 December 0.900 7 Problem 9‐5 The four control count stations of text Table 9.20 are proposed to form a single “group” for the purpose of calibrating Daily Adjustment Factors DF. To be an appropriate grouping, the “average” factor for each day of the week cannot differ from the factors at each station by more than ± 0.10. The grouping is evaluated in Table 7. Table 7: Average Daily Factors for Group and Assessment Station 1 2 3 4 Total Average OK Range Monday 1.04 1.12 0.97 1.01 4.14 1.035 0.935-1.135 Tuesday 1.00 1.07 0.99 1.00 4.06 1.015 0.915-1.115 Wednesday 0.96 0.97 0.89 1.01 3.83 0.9575 0.8575-1.0575 Thursday 1.08 1.06 1.01 1.09 4.24 1.06 0.96-1.16 Friday Saturday 1.17 0.90 1.02 0.87 0.86 1.01 1.10 0.85 4.15 3.63 1.0375 0.9075 0.9375-1.1375 0.8075-1.0075 Sunday 0.80 0.82 1.06 0.86 3.54 0.885 0.785-0.985 Obviously, three of the factors lie outside the acceptable range. It appears that Station 3 should be eliminated. Assuming that they are still spatially contiguous, Stations 1, 2, and 4 may be grouped, and must again be tested, as shown in Table 8. Table 8: Re‐Grouped Stations Tested Station 1 2 4 Total Average OK Range Monday 1.04 1.12 1.01 3.17 1.057 0.957-1.157 Tuesday 1.00 1.07 1.00 3.07 1.023 0.923-1.123 Wednesday 0.96 0.97 1.01 2.94 0.980 0.880-1.080 Thursday 1.08 1.06 1.09 3.23 1.077 0.977-1.177 Friday 1.17 1.02 1.10 3.29 1.097 0.997-1.197 Saturday 0.90 0.87 0.85 2.62 0.873 0.773-0.973 Sunday 0.80 0.82 0.86 2.48 0.827 0.727-0.927 The re‐grouping meets the acceptability criteria, and would be used. Problem 9‐6 Data from coverage counts within the control area depicted in text Table 9.11 are given. We are asked to estimate the annual VMT for each section counted. To do this, the AADT at each location must be estimated. The following equations are used: AADT = Counti , j * DFi * MF j Annual VMT = AADT * L 8 Where: AADT = average annual daily traffic, vehs/day Counti.j = count taken on day i in month j, vehs/day DFi = daily factor for day i MFj = daily factor for month j L = length of the study segment, mi These computations are illustrated in Table 9. Table 9: Estimated AADT and VMT for Stations in Text Table 9.21 Station 1 2 3 4 5 6 Length (mi) 3.0 2.7 2.5 4.6 1.8 1.6 Day Wed Tue Fri Sun Thu Fri Month March September August May December January DF (Table 9.11) 1.108 1.121 1.015 0.789 1.098 1.015 MF (Table 9.11) 1.100 0.884 0.882 0.949 1.114 1.215 Daily Vol (vehs/day) 9,120 10,255 16,060 21,858 9,508 11,344 AADT (vehs/day) 11,115 10,162 14,377 16,366 11,630 13,990 Veh Miles 33,346 27,438 35,943 75,286 20,934 22,384 Problem 9‐7 Text table 9.22 gives the data from an origin and destination study. Only sample measurements are made, and an estimate of the actual O‐D counts for the period of the study is needed. The O‐D matches can be adjusted so that the row totals (origins) are correct, or so that the column totals (destinations) are correct. The accepted methodology is to average these two approaches until all row and column totals are within ±10% of the observed volumes at each origin and destination. This is an iterative process. Each row and each column has an adjustment factor that will resolve the row or column totals. The actual adjustment of the O‐D matches (cells of the table) are computed as follows: ⎛ F + Fdi ⎞ ODi +1 = ODi * ⎜ oi ⎟ 2 ⎝ ⎠ Where: ODi+1 = OD volume for the i+1 iteration, vehs ODi = OD volume for the ith iteration, vehs = adjustment factors based upon resolving origin totals, Foi ith iteration Fdi = adjustment factors based upon resolving destination totals, ith iteration 9 In each iteration, the adjustment factors are re‐computed as follows: Vo Foi = ∑iODij Vd Fdi = ∑ j ODij Where: Vo = total observed volume at origin “o” (vehs) Vd = total observed volume at destination “d” (vehs) ODij = OD matches for origin “i” and destination “j”, vehs These computations are shown in Table 10. Iterations are continued until all origin and destination totals are resolved to ±10%. Table 10: Origin and Destination Adjustments Destination Station 1 2 3 4 5 Origin Sum Origin Vol Fo Destination Station 1 2 3 4 5 Origin Sum Origin Vol Fo Destination Station 1 2 3 4 5 Origin Sum Origin Vol Fo 1 50 105 125 82 201 563 1,820 3.233 2 120 80 100 70 215 585 1,225 2.094 Origin Station 3 4 125 210 143 305 128 328 100 125 180 208 676 1,176 1,750 2,510 2.589 2.134 FIRST ITERATION Origin Station 3 4 291 441 384 750 289 666 232 262 472 498 1,668 2,617 1,750 2,510 1.049 0.959 SECOND ITERATION Origin Station 3 4 291 421 410 767 282 619 230 248 496 501 1,709 2,556 1,750 2,510 1.024 0.982 5 75 100 98 101 210 584 1,110 1.901 Destination Sum 580 733 779 478 1,014 3,584 Destination Vol 1,200 2,040 1,500 985 2,690 8,415 Fd 2.069 2.783 1.926 2.061 2.653 1 133 316 322 217 591 1,579 1,820 1.152 2 250 195 201 145 510 1,302 1,225 0.941 5 149 234 187 200 478 1,249 1,110 0.889 Destination Sum 1,264 1,879 1,666 1,057 2,550 8,415 Destination Vol 1,200 2,040 1,500 985 2,690 8,415 Fd 0.950 1.086 0.901 0.932 1.055 Note that in each iteration, any origin or destination adjustment factor that is less than 0.900 or more than 1.100 indicates that there is still a discrepancy greater than 10% in origin or destination totals. Iterations are continued until the 1 139 353 331 226 653 1,703 1,820 1.069 2 236 198 185 136 509 1,264 1,225 0.969 5 137 231 168 182 465 1,183 1,110 0.939 Destination Sum 1,224 1,959 1,584 1,023 2,625 8,415 Destination Vol 1,200 2,040 1,500 985 2,690 8,415 Fd 0.980 1.041 0.947 0.963 1.025 10 adjustment factors for both origins and destinations all lie within a range of 0.900 to 1.100. ...
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This note was uploaded on 01/18/2011 for the course PROJECT MA PM 587 taught by Professor Lee during the Spring '10 term at Keller Graduate School of Management.

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