Result analyzing

We performed these tests on two different buses and in the period of lower speed when the traffic is congested. If the error value is positive, then it means that we over-estimate the arrival time. Otherwise, it means that we under-estimate. The results of the errors computed are as illustrated in Table 4-9 and Table 4-10(Figure 4.3 and Figure 4.4).

From these results, we can find that the errors of the estimated arrival time are roughly about 30 seconds, and the maximum one is 33 seconds. We may say that in this case, it performs well in arrival time estimation.

χ²

= Σ ^4.6 _е

i

( Oi – е

)

k

i = 1

Table 4-9 Error of arrival time (bus 1) Bus stop From 19:48:50 To 19:57:43; Wednesday

(Error of this estimation arrival time: second)

stop1 70 70 86 0 0 0 0 0 0 0

stop1 stop2 stop3 stop4 stop5 stop6 stop7 stop8

Figure 4.3 Error of arrival time (bus 1)

Table 4-10 Error of arrival time (bus 2) Bus

stop

From 18:59:25 To 19:11:20

(Error of this estimation arrival time: second)

Stop1 -1 -3

stop1 stop2 stop3 stop4 stop5 stop6 stop7 stop8

Figure 4.4 Error of arrival time (bus 2)

We performed these tests on two different buses and in the period of higher

speed when the traffic is not congested. If the error value is positive, then it means that we over-estimate the arrival time. Otherwise, it means that we under-estimate.

The results of the errors computed are as illustrated in Table 4-11 and Table 4-12(Figure 4.5 and Figure 4.5).

From these results, we can find that the errors of the estimated arrival time are roughly about 30 seconds, and the maximum one is 34 seconds. We may say that in this case, it performs well in arrival time estimation.

Table 4-11 Error of arrival time (bus 3)

Bus stop

From 14:20:15 To 14:29:41

(Error of this estimation arrival time: second)

Stop1 -34 11 11 1 1

Stop2 -78 -13 -13 -27 -27 -28 -4 Stop3 -61 43 43 28 28 27 51 30

Stop4 -107 15 15 -3 -3 -4 20 -1 -31 -31 Stop5 -134 25 25 5 5 4 8 7 -23 -23

Stop6 -93 80 80 60 60 59 63 66 32 32 25 25 Stop7 -107 96 96 69 69 64 68 67 33 33 26 26

Stop8 -106 99 99 70 70 65 69 68 64 64 57 57 31 31

-150 -100 -50 0 50 100 150

stop1 stop2 stop3 stop4 stop5 stop6 stop7 stop8

Figure 4.5 Error of arrival time (bus 3)

Table 4-12 Error of arrival time (bus 4) Bus stop From 15:59:01 To 16:06:05

(error of this estimation arrival time: second) Stop1 -56

Stop2 -37 19 18 18 12

Stop3 -44 12 9 9 1 12 12 Stop4 -4 52 45 45 38 25 25 Stop5 -3 53 45 45 36 23 23 2 Stop6 16 72 64 64 55 42 42 17

Stop7 18 77 64 64 51 38 38 13 4 4

Stop8 9 68 55 55 42 29 29 4 5 5 9 9 5

-80

stop1 stop2 stop3 stop4 stop5 stop6 stop7 stop8

Figure 4.6 Error of arrival time (bus 4)

2. Average error of the estimation waiting time

In order to analyze the error of the estimated waiting time, we perform the test on four different buses to compute the average error of the estimation waiting time. If the error value is positive, then it means that we over-estimate the arrival time.

Otherwise, it means that we under-estimate. The results of the errors computed are as illustrated in Table 4-13.

From these results, we can find that the errors of the estimated arrival time are roughly about 20 seconds, and the maximum one is 36 seconds. We may say that in this case, it performs well in arrival time estimation.

We analyze the results and find that, the error under lower speed situation is greater, and can even be as large as 36 seconds. There are two reasons to be so. First, the estimation model is constructed in higher speed situation, therefore if the police

manually adjust the phase planning table, a larger error will therewith occur.

Moreover, since the error enlarges as the previous error, intersections in the end of the route will be affected more.

Table 4-13 Average error of the estimation waiting time

Bus stop Bus 1 (second) Bus 2 (second) Bus 3 (second) Bus 4 (second)

stop1 51.000 36.000 43.000 98.000

3. Percentage of average absolute error of estimation travel time

In order to analyze the error of the estimated travel time, we perform the test on four different buses to compute the average absolute error of estimated travel time and average absolute error percentage. The results of the errors computed are as illustrated in Table 4-14.

From these results, we can find that the average absolute errors of the estimated travel time are all within 15 seconds, and the maximum one is 14 seconds. The average absolute error percentage is roughly less than 30%, and the maximum one is 93% We may say that in this case, it performs well in travel time estimation.

According to the results, we analyze and find that although we have only 12 seconds in average absolute error, but the average error percentage is as high as 93%.

This is mainly because that the travel time in that route is as short as 15 seconds, so that the percentage is also higher.

Table 4-14 Average absolute error of estimation travel time Number of Sub-link Average modulus error Percentage of average

modulus error (%)

We perform the goodness-of -fit-test to test if the error of estimated travel time and actual travel time falls in acceptable range or not. We take four buses to take to test, and the results are shown in table 4-15.

According to the results, after the test, all the estimated travel time in eight routes all fall in an acceptable range.

Table 4-15 Goodness-of -fit-test

4.3 Summary

According to the results of the model testing in section 4.2, we draw some conclusions as follows:

1. Whether in periods of higher speed or lower speed, the error of estimation travel time is about 30 seconds, and that falls in an acceptable range.

2. Whether in periods of higher speed or lower speed, the error of estimation waiting time is about 15 seconds, and that falls in an acceptable range.

3. The model may over-estimate or under-estimate the waiting time and sometimes a large error may occur. The reason is that the police manually adjusts the phase planning table, thus makes the error occur.

4. When the travel time in the route is shorter, we may obtain higher error percentage in estimation of travel time in that route.