The technical delay to a flight is measured in our optimization model by subtracting the scheduled flight time on the timetable from the time arranged for the flight to take-off/land. This sort of delay depends on the original scheduled time, but not on the time a flight is ready to take-off/land. Although flights aim to be on time, in reality they are
TABLE VII Total delay for different weights (unit: min) Delay Note:The numbers in parentheses represent average delay per flight.
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unable to follow precisely the time scheduled on the timetable. Times for flights scheduled at a specific time ready to take-off/land are ran-domly distributed over some period of time. The assumption that all flights will follow precisely the scheduled time may result in over-estimating flight technical delay. In order to clarify this inconsistency and the possible discrepancy between our optimization model and the real world, this paper goes a step further by conducting simulation and regression analyses.
6.1. Testing of the Optimization Model
Quite clearly, actual flight technical delays should be based on real flight operations. Thus we have simulated take-off/landing times of flights so as to sort their sequence in order for delay analysis. Flight times were randomly distributed over the allocated time interval.
For instance, at 09:00, five flights are shown on the timetable and the allocated time interval for these flights to operate is 5 min. The simulated flight time can thus be randomly generated as follows:
09:03:16 (AW), 09:01:03 (DE), 09:04:28 (AE), 09:04:05 (DW), and 09:03:32 (DW). The sequence of these flights to take-off/land depends, however, on the ordering rule used in the simulation study. Two rules were considered in this simulation study: the ‘‘first come first served’’
(FCFS) rule and the ‘‘arrival priority’’ rule (which means that when there is competition for the time slot between arrival and departure, the arrival flight always has priority). Under the FCFS rule, the sequence of these five flights will be 09:01:03 (DE), 09:03:16 (AW), 09:03:32 (DW), 09:04:05 (DW), and 09:04:28 (AE). Under the ‘‘arrival priority’’ rule, the sequence becomes 09:01:03 (DE), 09:03:16 (AW), 09:03:32 (DW), 09:04:28 (AE), and 09:04:05 (DW). By using these sorts of sequence data, the actual technical delay associated with each service rule can then be calculated and compared to those from the optimization model.
Four samples with 42 hourly operations were selected from the time-tables during the period from March 1995 to March 1997. For each sample, we tested 30 simulation runs and the statistics were analysed.
The results are shown in Table VIII.
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The total delay under the FCFS rule is smaller than that suggested by the optimization model. This is due to the assumption made in the theoretical delay optimization model, in which flights except those influenced by the scheduled timetable delay were assumed to be on time. If a flight is not on time, it will be assumed to be a technical delay resulting from ATC procedures. The difference in total delay between the optimization model and the FCFS rule is about 30 – 46 min for the 42 flights, and the difference in the average delay is about 0.71 – 1.1 min per flight.
The total delay under the ‘‘arrival priority’’ rule may be either smal-ler or larger than that of the optimization model, but the amount is marginal. The difference in the total delay between the optimization and the arrival priority rule is about 5–10 min, and the difference in the average delay is about 0.11–0.24 min per flight. Going one step further, we examine the delay distribution of the simulation results for the four samples. It suggests that while the arrival/departure flights fluctuate over the study period (with a larger standard deviation of flight operations per 5 min), no matter which rule is used, the total flight delay will generally increase. Among the four samples, the standard deviation of sample 1 is the smallest; its total delay appears to be the smallest too. Meanwhile, samples 3 and 4 have larger deviations, and their delays are also higher. All these results meet our expectations.
Meanwhile, from the simulation runs, we could observe clearly that under a given flight timetable, flight delay is not a constant. Instead, it is a random variable and is influenced by actual flight operations,
TABLE VIII Results of the simulation study (unit: min)
Sample fcfs(1) Arrival
priority(2)
Optimization (3)
(1)–(3) (2)–(3)
1 137.97(34.28) 164.68(37.95) 168.25 30.28 3.57
2 150.97(42.05) 200.65(53.15) 197.00 46.03 3.65
3 206.01(34.09) 231.39(42.61) 236.55 30.54 5.16
4 204.15(41.32) 256.34(48.89) 246.17 42.02 10.17
Average 174.78 213.27 211.99 37.21 1.28
SD 35.402 39.596 36.099 0.697 3.497
Note:The numbers in parentheses are the standard deviations of 30 simulation runs.
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which in essence is random. In the case of sample 2, details of the 30 simulation runs are listed in Tables IX and X. These data suggest that when the standard deviation of air delay or ground delay increases, the corresponding total delay also increases. When the total separation of flights and their standard deviations are small, the associated total delays tend to be small. Under the FCFS rule, because of the regulation on flight separation, following flights must wait for service until the completion of service of the previous flight. Therefore, when the
TABLE IX The 30 simulation runs of sample 2 under FCFS rule (unit: min)
Number Air
delay
Ground delay
Total delay
Total separation time 1 61.468(2.023) 74.389(2.315) 135.857(2.035) 54.900(0.284) 2 66.965(2.170) 77.023(2.343) 143.988(2.051) 54.500(0.297) 3 103.310(3.427) 118.324(3.581) 221.634(3.220) 57.100(0.387) 4 87.645(3.089) 108.478(3.457) 196.124(3.232) 55.983(0.393) 5 60.368(1.881) 85.376(2.512) 145.744(1.965) 54.883(0.173) 6 57.900(2.095) 74.240(2.515) 132.139(2.393) 53.583(0.281) 7 84.466(2.801) 89.767(2.787) 174.233(2.609) 54.883(0.300) 8 70.189(2.325) 88.814(2.663) 159.002(2.293) 54.433(0.276) 9 59.997(2.260) 68.026(2.444) 128.023(2.518) 53.450(0.297) 10 80.193(3.136) 88.212(2.885) 168.404(3.152) 56.767(0.396) 11 69.563(1.995) 74.424(2.220) 143.987(1.702) 54.550(0.316) 12 51.248(1.704) 53.694(1.610) 104.941(1.516) 54.483(0.298) 13 87.170(3.310) 106.285(3.343) 193.455(3.372) 56.250(0.396) 14 79.256(2.683) 93.731(2.572) 172.987(2.278) 54.950(0.294) 15 124.586(4.075) 150.648(4.280) 275.235(3.623) 57.050(0.399) 16 40.823(1.432) 45.578(1.428) 86.401(1.389) 53.867(0.291) 17 65.156(1.968) 50.841(1.677) 115.997(1.684) 54.850(0.301) 18 90.883(2.960) 118.249(3.336) 209.132(2.723) 56.483(0.405) 19 71.974(2.607) 84.486(2.419) 156.460(2.363) 54.850(0.291) 20 85.919(2.887) 100.494(2.958) 186.414(2.657) 54.683(0.289) 21 62.939(2.327) 91.195(2.716) 154.133(2.474) 56.333(0.390) 22 87.819(2.985) 94.955(2.855) 182.774(2.716) 57.483(0.470) 23 68.423(2.209) 76.861(2.229) 145.284(1.933) 53.800(0.300) 24 53.585(1.861) 67.978(2.022) 121.562(1.822) 53.900(0.293) 25 49.716(1.516) 62.608(1.870) 112.324(1.476) 53.717(0.294) 26 51.746(1.775) 44.505(1.570) 96.250(1.715) 54.067(0.292) 27 57.986(1.965) 68.013(2.089) 125.999(1.909) 54.533(0.286) 28 48.338(1.536) 41.586(1.518) 89.924(1.307) 54.033(0.279) 29 62.482(2.082) 70.986(2.124) 133.468(1.334) 55.233(0.314) 30 51.629(1.592) 65.616(1.959) 117.245(1.428) 54.467(0.285)
Average 69.791 81.179 150.971 55.002
SD 18.407 24.375 42.054 1.144
Note: The numbers in parentheses are the standard deviations of flight delay or separation.
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distribution of flights tends to fluctuate and is concentrated on some time points, the flight inter-arrival/departure times will frequently be less than the required separation times. This will cause flight delays to spread and increase. In these situations, the flight delay under FCFS is possibly larger than that of the optimization model. In Table IX, numbers 3, 15, 18, 20 and 22 of the simulation runs show this phenomenon. The associated air and ground delays are not only larger, but their standard deviations are also higher. On the other hand, if the inter-operation times are more uniformly distributed, the flight delay and the associated standard deviation will be smaller.
TABLE X The 30 simulation runs of sample 2 under arrival priority rule (unit: min)
Number Air
delay
Ground delay
Total delay
Total separation time 1 24.835(0.820) 129.172(4.506) 154.007(4.153) 55.517(0.299) 2 22.120(0.913) 185.539(6.434) 207.659(6.121) 54.783(0.298) 3 21.455(0.917) 273.727(8.849) 295.182(8.505) 57.617(0.384) 4 17.852(0.868) 207.599(7.098) 225.451(6.844) 53.767(0.298) 5 23.340(0.924) 130.831(4.223) 154.171(3.892) 54.267(0.304) 6 17.059(0.728) 229.020(7.446) 246.079(7.172) 55.717(0.283) 7 24.184(0.954) 195.684(6.305) 219.868(5.931) 56.433(0.404) 8 19.913(0.951) 179.257(6.108) 199.170(5.837) 55.317(0.288) 9 18.585(0.881) 158.728(5.809) 177.313(5.576) 54.617(0.285) 10 13.281(0.645) 208.578(7.469) 221.859(7.279) 57.517(0.404) 11 18.274(0.797) 142.270(4.337) 160.544(4.062) 54.383(0.279) 12 7.460(0.369) 286.781(9.273) 294.241(9.146) 55.667(0.301) 13 14.928(0.675) 193.806(6.838) 208.733(6.622) 54.567(0.294) 14 18.893(1.002) 248.156(7.979) 267.049(7.696) 56.233(0.300) 15 31.108(1.297) 281.793(8.698) 312.9(8.195) 57.550(0.391) 16 14.354(0.527) 118.279(4.161) 132.633(3.952) 55.750(0.311) 17 25.599(1.113) 121.818(4.493) 147.417(4.219) 55.483(0.299) 18 22.999(1.041) 267.251(7.709) 290.250(7.306) 54.783(0.298) 19 20.718(0.889) 203.324(6.502) 224.042(6.178) 56.033(0.305) 20 20.526(0.924) 210.457(6.677) 230.983(6.358) 55.100(0.279) 21 18.449(0.797) 137.247(4.337) 155.696(4.062) 54.900(0.279) 22 15.400(0.669) 163.323(5.396) 178.723(5.162) 54.300(0.291) 23 18.460(0.757) 177.553(5.413) 196.013(5.106) 56.150(0.399) 24 9.401(0.482) 213.398(6.913) 222.803(6.760) 55.267(0.289) 25 20.127(0.727) 129.461(4.412) 149.587(4.120) 55.017(0.302) 26 21.63(0.911) 109.794(4.160) 131.425(3.921) 54.700(0.279) 27 13.855(0.561) 140.225(4.359) 154.080(4.130) 55.433(0.286) 28 15.992(0.596) 125.849(4.230) 141.841(3.989) 55.017(0.305) 29 17.134(0.681) 162.328(4.927) 179.461(4.637) 54.583(0.304) 30 25.864(0.940) 114.338(3.679) 140.202(3.314) 54.867(0.289)
Average 19.127 181.52 200.646 55.378
SD 4.973 53.362 53.145 0.972
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The 16 and 26 simulation runs shown in Table IX reveal this delay pattern.
Under the ‘‘arrival priority’’ rule, total delay is influenced less by the inter-operation times, but is more influenced by the flight arrival/
departure sequence. This is especially true when there is heavy compe-tition for slots for take-off/landing between arrivals and departures.
Because arrivals have priority over departures, when consecutive arri-vals occur frequently with small gaps, it causes not only delays to the following consecutive arrivals, but also to the departure flights. For instance, although a departure is expected to be earlier than the arrival, when the separation time is not good for the operation, the oncoming arrival still gets priority to use the runway and the take-off flight has to wait. Therefore, total delay under the ‘‘arrival priority’’ rule is generally higher than that of the optimization model. In Table X, simulation runs 3, 12, 14 and 15 show high ground and total delays. The total delay and the standard deviations illustrated in Table X reveal that flight delay under ‘‘arrival priority’’ is more serious than that of the FCFS rule in Table IX.
TABLE XI Results of the optimization model (unit: min) Sample Total
separation time
Air delay
Ground delay
Total delay
Air scheduled timetable delay
Ground scheduled timetable delay
Total scheduled timetable delay
Air technical
delay Ground technical
delay ATC technical
delay
1 52.42 91.63 76.62 168.25 28.45 26.98 55.43 63.18 49.63 112.82 2 52.22 113.95 83.05 197.00 31.05 37.10 68.15 82.90 45.95 128.85 3 52.12 134.85 101.70 236.55 40.70 53.93 94.63 94.15 47.77 141.92 4 52.47 140.40 105.77 246.17 46.23 63.07 109.3 94.17 42.70 136.87 5 50.92 82.82 55.53 138.35 10.55 7.95 18.50 72.27 47.58 119.85
6 49.10 63.52 46.97 110.48 8.70 4.45 13.15 54.82 42.52 97.33
7 49.20 65.65 48.80 114.45 13.88 8.25 22.13 51.77 40.55 92.32 8 49.78 78.28 52.93 131.22 10.55 7.95 18.50 67.73 44.98 112.72 9 49.68 77.02 53.75 130.77 10.92 7.88 18.80 66.10 45.87 111.97 10 47.92 58.52 55.25 113.77 11.02 9.98 21.00 47.50 45.27 92.77
11 48.92 56.08 43.70 99.78 17.87 6.73 24.60 38.22 36.97 75.18
12 48.88 56.85 48.70 105.55 21.07 6.25 27.32 35.78 42.45 78.23 13 48.82 63.15 45.07 108.22 19.45 7.92 27.37 43.70 37.15 80.85 14 48.92 64.17 46.63 110.80 23.40 8.20 31.60 40.77 38.43 79.20 15 50.95 97.12 83.58 180.70 29.08 34.37 63.45 68.03 49.22 117.25 16 48.33 95.92 65.78 161.70 47.92 18.47 66.38 48.00 47.32 95.32 17 46.08 72.05 53.43 125.48 24.85 15.25 40.10 47.20 38.18 85.38 18 46.08 93.85 69.32 163.17 44.05 28.62 72.67 49.80 40.70 90.50 19 46.78 86.30 83.63 169.93 45.05 22.17 67.22 41.25 61.47 102.72 20 46.35 87.53 97.15 184.68 43.55 24.72 68.27 43.98 72.43 116.42
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6.2. Correlation Analysis of Delays from Optimization and Simulation Models
A correlation between delays obtained from the optimization model and the simulation runs can be observed from the previous analyses.
In order to make the optimization model more realistic, we tried a further 20 simulations and observations. The results from the optimi-zation model and the simulations are shown in Tables XI–XIII, respectively. The estimated delays varied within some reasonable ranges. In Tables XII and XIII, the 95% confidence intervals clearly suggest that under a given flight timetable, the technical delay is not constant. The technical delay will vary with some uncontrollable factors; and the magnitude of the variation will increase with the number of hourly flights. This suggests that the more the delay grows, the more effective good air traffic management will be. On the other hand, it also implies that if the delay is large, forecasting flight delay exactly becomes more difficult.
The sample data and the associated results clearly show a high correlation between the estimated delays from the optimization model and the simulations. In addition, a high correlation is evident between total delay and the standard deviations of arrivals and departures per 5 min. Therefore, after a variety of correla-tion analyses, three variables – total delay from the optimizacorrela-tion model, the standard deviation of arrivals, and the standard deviation of departures – were selected for the regression analysis in an attempt to predict actual flight delays.
However, among these selected variables, the correlation coefficient between the standard deviation of arrivals and the standard deviation of departures is found to be very low (0.0153) and almost indepen-dent. But the correlation coefficient is high between the total delay of the optimization model and the standard deviation of arrivals/depar-tures. In order to avoid the co-linearity occurring in the regression analyses, only the variable of delay from the optimization model is selected. The regression equation is estimated as follows:
(1) The regression of flight delays for the FCFS rule:
Delay^
DelayFCFS¼ 20:3231 þ 0:920155 DelayOptimal t ¼(2.317) (16.328), R2¼0.937, F ¼ 266.588, N ¼ 20
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(2) The regression of flight delays for the ‘‘arrival priority’’ rule:
Delay^
DelayPRIORITY¼0:972079 DelayOptimal t ¼(35.513), R2¼0.867, F ¼ 124.222, N ¼ 20
The coefficients of both regressions clearly demonstrate that the total delays derived from the optimization model are larger than those of both the FCFS and ‘‘arrival priority’’ rules, as seems reasonable.
In addition, the U-statistic values for estimations of the FCFS and the ‘‘arrival priority’’ rules (0.0066 and 0.0148), respectively are close to 0. This indicates that this estimator can reasonably be applied to estimate the flight delays under the rules of both FCFS and ‘‘arrival priority’’. Tables XIV and XV show that the 20 samples are all well predicted within 95% confidence intervals. The forecasting capability of the optimization model can therefore be regarded as rather good and reliable. Therefore, it could have potential as tool for measuring the performance of air traffic management; it could also be applied
TABLE XII The simulation results under FCFS rule (unit: min) Sample Air
delay Ground
delay Total delay
Standard deviation of air delay
Standard deviation of ground delay
Standard deviation of
total delay
Lower bound of95%
confidence interval
Upper bound of95%
confidence interval
1 67.28 70.70 137.97 17.36 19.29 34.28 94.43 217.73
2 69.79 81.18 150.97 18.41 24.37 42.05 89.92 221.63
3 99.30 106.71 206.01 18.05 18.49 34.09 156.25 269.59 4 90.13 114.02 204.15 20.19 31.69 41.32 147.49 268.12 5 73.36 91.73 165.08 18.68 18.59 35.14 111.12 216.99
6 42.76 48.55 91.31 15.03 17.81 31.97 60.17 163.26
7 33.53 41.68 75.21 7.69 11.05 17.21 50.67 111.83
8 35.66 43.32 78.98 9.31 9.96 17.12 56.31 112.65
9 37.24 43.76 81.00 12.28 13.80 24.53 53.25 148.16
10 39.70 46.28 85.98 10.28 16.92 26.03 54.08 148.85
11 40.53 43.73 84.26 7.95 8.71 15.70 60.35 110.72
12 46.33 32.68 79.01 8.95 7.83 15.57 57.94 113.07
13 50.79 36.01 86.80 8.60 6.23 12.35 66.47 107.97
14 52.25 37.74 89.99 8.64 7.84 14.56 70.59 117.06
15 54.04 35.20 89.24 10.98 6.79 10.91 72.01 107.66
16 80.19 46.62 126.81 12.77 7.43 18.75 105.28 169.39
17 55.68 49.54 105.22 9.18 9.04 15.30 83.14 130.34
18 74.04 64.82 138.86 14.16 10.18 22.91 107.35 168.63
19 63.49 66.29 129.78 8.05 7.03 12.52 112.60 150.68
20 66.16 78.58 144.74 9.53 9.58 14.81 126.07 173.19
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to evaluate the appropriateness of a flight timetable by calculating the associated scheduled timetable delay.
7. CONCLUSIONS
Flight delays at an airport affect not only passengers and airlines but also the performance of the airport and its air traffic management.
Thus, a convincing tool is needed to measure effectively technical delay. In this paper, a theoretical static delay optimization model with related constraints has been formulated, tested, and its perform-ance analysed. In addition, simulation and regression analyses were introduced to help clarify the validity of the model. The major findings from this study can be briefly stated as follows:
First, the origin of technical delay may come from either insufficient facility capacity or poor schedule planning. Therefore, technical delay due to air traffic control should be distinguished from scheduled
TABLE XIII The simulation results under the ‘‘arrival priority’’ rule (unit: min) Sample Air
delay Ground
delay Total delay
Standard deviation of air delay
Standard deviation of ground delay
Standard deviation of
total delay
Lower bound of95%
confidence interval
Upper bound of95%
confidence interval 1 21.63 143.05 164.68 6.25 38.65 37.95 121.55 245.23 2 19.13 181.52 200.65 4.97 53.36 53.15 132.63 295.18 3 27.45 203.94 231.39 8.19 41.06 42.61 164.25 318.26 4 25.36 230.98 256.34 6.08 47.32 48.89 172.77 329.76 5 17.53 184.55 202.08 6.46 42.00 41.64 136.72 276.55
6 15.65 94.32 109.98 5.56 30.44 31.93 67.06 169.32
7 13.96 72.43 86.39 3.39 16.07 17.16 59.46 124.09
8 12.55 81.80 94.34 3.66 19.15 20.23 65.81 131.53
9 13.32 77.70 91.02 4.14 26.28 25.27 61.75 144.75
10 17.15 80.65 97.80 4.54 29.99 29.30 60.68 167.28
11 15.57 83.39 98.96 4.64 16.32 17.92 75.53 129.65
12 24.94 71.81 96.75 6.87 30.20 29.96 69.41 174.95
13 22.14 85.54 107.69 4.57 22.18 20.93 80.03 150.28
14 23.62 83.80 107.43 6.21 20.55 18.46 80.11 143.01
15 27.06 79.66 106.71 6.41 17.00 16.11 85.78 139.98
16 21.00 133.25 154.25 4.61 22.31 19.95 123.9 190.89 17 16.21 117.92 134.14 5.48 21.93 20.18 98.02 159.24
18 15.20 186.75 201.95 6.49 35.30 35.14 154.26 264
19 12.97 146.56 159.54 3.78 18.03 17.76 136.47 192.08 20 13.62 157.72 171.33 4.84 16.77 16.85 144.23 199.31
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timetable delay so as to capture the essence of delay and propose appropriate countermeasures.
Second, results from the data samples for Taipei Airport show that both simulated flight delays under FCFS and ‘‘arrival priority’’ service rules are highly correlated with delays obtained from the optimization model. The flight delays predicted by using the regression model are also satisfactory. This shows that the optimization model is not only an analytical tool which is capable of measuring the performance of air traffic management schemes, but also useful for evaluating the appropriateness of a flight timetable and in planning a sound timetable.
Third, the arrangement of take-offs/landings has significant influ-ences on flight technical delay. When flights are more evenly distrib-uted, delay is lower; otherwise, technical delay will be higher. In addition, under a specified flight timetable, the flight technical delay is not constant, but varies. The magnitude of the variation increases with the scheduled hourly operations. These phenomena indicate that the greater the flight delays, the more improvements air traffic
TABLE XIV Delay forecasting for flights under the FCFS rule (unit: min)
Sample Lower
bound of 95% confidence
interval from the simulation
Average delay from the simulation
Upper bound of 95%
confidence interval from the simulation
Forecast average delay
1 94.43 137.97 217.73 134.49
2 89.92 150.97 221.63 160.95
3 156.25 206.01 269.59 197.34
4 147.49 204.15 268.12 206.19
5 111.12 165.08 216.99 145.95
6 60.17 91.31 163.26 106.98
7 50.67 75.21 111.83 81.34
8 56.31 78.98 112.65 84.99
9 53.25 81.00 148.16 100.42
10 54.08 85.98 148.85 100.01
11 60.35 84.26 110.72 84.36
12 57.94 79.01 113.07 71.49
13 66.47 86.80 107.97 76.80
14 70.59 89.99 117.06 79.26
15 72.01 89.24 107.66 81.63
16 105.28 126.81 169.39 128.47
17 83.14 105.22 130.34 95.14
18 107.35 138.86 168.63 129.82
19 112.60 129.67 150.68 136.04
20 126.07 144.74 173.19 149.61
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management could make. However, it also implies that forecasting flight delay precisely during busy periods is becoming more difficult.
Finally, the expected take-off/landing times of the scheduled flights in the simulation studies were randomly generated. Other possible dis-tributions have not yet been analysed. Further work on the expected take-off/landing distributions are needed to make the optimization model more convincing. The basic assumption of the optimization model is that flights must follow exactly the original scheduled depar-ture/arrival time. This does not agree with actual flight operations and causes the optimization model to over-estimate flight delays. In future, we suggest that research should relax this constraint so as to make the model more realistic and hence more reliable.
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TABLE XV Delay forecasting for flights under the arrival priority rule (unit: min) Sample Lower bound
of95% confidence interval from the simulation
Average delay from the simulation
Upper bound of95%
confidence interval from the simulation
Forecast average
delay
1 121.55 164.68 245.23 163.55
2 132.63 200.65 295.18 191.50
3 164.25 231.39 318.26 229.95
4 172.77 256.34 329.76 239.30
5 136.72 202.08 276.55 175.65
6 67.06 109.98 169.32 134.49
7 59.46 86.39 124.09 107.40
8 65.81 94.34 131.53 111.25
9 61.75 91.02 144.75 127.56
10 60.68 97.80 167.28 127.12
11 75.53 98.96 129.65 110.59
12 69.41 96.75 174.95 96.99
13 80.03 107.69 150.28 102.60
14 80.11 107.43 143.01 105.20
15 85.78 106.71 139.98 107.71
16 123.90 154.25 190.89 157.19
17 98.02 134.14 159.24 121.98
18 154.26 201.95 264.00 158.61
19 136.47 159.54 192.08 165.19
20 144.23 171.33 199.31 179.52
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