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BTS Home > Publications > Journal of Transportation and Statistics > Volume 7 Number 2/3 > Paper 5
Printable Version

Figure 6 - Illustration of Covariance Function and Correlation for a Less-Congested Two-Link Example: Day 20

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6A: LINK 1

Time,
t (seconds)		 ln (travel time)
lnY g
20 4.55 4.55
31 4.66 4.55
35 4.58 4.55
42 4.61 4.55
57 4.60 4.55
66 4.62 4.55
80 4.61 4.55
155 4.49 4.55
161 4.48 4.55
186 4.44 4.55
194 4.61 4.55
200 4.63 4.55
220 4.51 4.55
230 4.50 4.55
236 4.48 4.55
296 4.60 4.55
312 4.57 4.55
320 4.55 4.55
330 4.51 4.55
347 4.61 4.55
353 4.66 4.55
390 4.71 4.55
415 4.72 4.55
423 4.69 4.56
450 4.68 4.55
468 4.60 4.56
471 4.57 4.55
474 4.55 4.55
490 4.54 4.55
502 4.62 4.55
518 4.48 4.56
520 4.62 4.56
525 4.62 4.56
573 4.58 4.56
594 4.56 4.55
640 4.50 4.56
647 4.62 4.56
654 4.54 4.56
656 4.52 4.56
661 4.56 4.56
695 4.50 4.55
711 4.54 4.56
755 4.55 4.56
766 4.50 4.56
768 4.50 4.55
769 4.49 4.56
837 4.50 4.55
859 4.56 4.55
871 4.65 4.55
874 4.65 4.56
914 4.56 4.56
952 4.60 4.55
960 4.61 4.55
963 4.62 4.55
998 4.54 4.55
1,030 4.52 4.55
1,079 4.44 4.55
1,093 4.37 4.55
1,094 4.52 4.55
1,101 4.52 4.55
1,102 4.53 4.55
1,155 4.61 4.55
1,158 4.63 4.55
1,171 4.60 4.55
1,178 4.63 4.55
1,193 4.57 4.55
1,239 4.52 4.55
1,282 4.54 4.55
1,325 4.55 4.55
1,357 4.52 4.55
1,407 4.57 4.54
1,423 4.52 4.54
1,427 4.56 4.55
1,446 4.54 4.54
1,448 4.51 4.54
1,469 4.49 4.54
1,493 4.73 4.54
1,550 4.51 4.54
1,598 4.57 4.54
1,632 4.47 4.54
1,639 4.53 4.54
1,652 4.62 4.54
1,654 4.63 4.54
1,667 4.60 4.53
1,671 4.58 4.54
1,717 4.51 4.54
1,736 4.56 4.54
1,753 4.62 4.54
1,761 4.61 4.53
1,829 4.54 4.53
1,859 4.54 4.53
1,860 4.52 4.53
1,869 4.49 4.53
1,875 4.47 4.53
1,906 4.60 4.53
1,912 4.58 4.53
1,917 4.51 4.53
1,926 4.64 4.53
1,932 4.41 4.53
1,939 4.41 4.53
1,964 4.47 4.53
1,969 4.38 4.53
1,981 4.61 4.53
2,004 4.43 4.53
2,012 4.44 4.53
2,027 4.60 4.53
2,028 4.50 4.53
2,061 4.55 4.53
2,070 4.58 4.53
2,075 4.51 4.53
2,097 4.45 4.52
2,172 4.44 4.52
2,174 4.49 4.52
2,261 4.51 4.52
2,348 4.62 4.52
2,408 4.61 4.51
2,457 4.39 4.51
2,473 4.47 4.51
2,579 4.49 4.50
2,602 4.44 4.51
2,604 4.45 4.51
2,660 4.42 4.50
2,670 4.45 4.50
2,698 4.48 4.50
2,738 4.43 4.50
2,757 4.47 4.50
2,759 4.45 4.50
2,767 4.51 4.50
2,774 4.45 4.50
2,778 4.44 4.50
2,788 4.45 4.50
2,807 4.41 4.50
2,833 4.55 4.50
2,834 4.50 4.50
2,839 4.48 4.50
2,866 4.48 4.50
2,894 4.51 4.50
2,905 4.57 4.50
2,910 4.54 4.49
2,944 4.44 4.50
2,962 4.48 4.49
2,964 4.50 4.49
2,966 4.49 4.49
2,967 4.50 4.49
2,973 4.53 4.50
3,006 4.44 4.49
3,038 4.54 4.49
3,043 4.45 4.49
3,049 4.44 4.49
3,052 4.44 4.49
3,099 4.52 4.49
3,165 4.41 4.49
3,232 4.36 4.49
3,242 4.41 4.49
3,244 4.43 4.49
3,246 4.39 4.49
3,255 4.51 4.49
3,259 4.41 4.48
3,271 4.51 4.49
3,283 4.47 4.48
3,309 4.34 4.48
3,316 4.38 4.48
3,338 4.54 4.48
3,364 4.61 4.48
3,367 4.58 4.48
3,402 4.42 4.48
3,403 4.42 4.48
3,407 4.51 4.48
3,410 4.44 4.48
3,496 4.50 4.48
3,507 4.54 4.48
3,521 4.52 4.48
3,523 4.55 4.48
3,532 4.50 4.48
3,600 4.53 4.47
3,602 4.60 4.47
3,622 4.58 4.47
3,656 4.42 4.47
3,660 4.43 4.47
3,672 4.44 4.47
3,680 4.44 4.47
3,733 4.47 4.47
3,802 4.47 4.47
3,806 4.50 4.47
3,841 4.43 4.47
3,873 4.39 4.46
3,879 4.41 4.47
3,890 4.42 4.46
3,897 4.45 4.47
3,901 4.47 4.47
3,936 4.36 4.46
3,937 4.57 4.46
3,956 4.47 4.46
3,965 4.43 4.46
3,980 4.74 4.46
4,006 4.52 4.46
4,014 4.49 4.46
4,021 4.57 4.46
4,030 4.42 4.46
4,051 4.50 4.46
4,076 4.45 4.46
4,078 4.43 4.46
4,081 4.42 4.46
4,151 4.32 4.46
4,157 4.34 4.46
4,173 4.33 4.46
4,179 4.64 4.46
4,197 4.52 4.46
4,231 4.56 4.46
4,260 4.56 4.46
4,264 4.42 4.46
4,286 4.49 4.46
4,301 4.48 4.45
4,315 4.37 4.45
4,330 4.39 4.45
4,371 4.39 4.45
4,389 4.54 4.45
4,411 4.42 4.45
4,427 4.34 4.45
4,458 4.43 4.45
4,465 4.41 4.45
4,473 4.39 4.45
4,503 4.41 4.45
4,513 4.49 4.45
4,525 4.57 4.45
4,550 4.49 4.44
4,557 4.36 4.45
4,589 4.42 4.44
4,602 4.39 4.44
4,639 4.54 4.44
4,670 4.49 4.44
4,689 4.39 4.44
4,693 4.34 4.44
4,697 4.45 4.44
4,759 4.41 4.44
4,760 4.37 4.44
4,772 4.52 4.44
4,825 4.51 4.44
4,856 4.39 4.43
4,863 4.42 4.43
4,869 4.51 4.43
4,886 4.56 4.43
4,894 4.45 4.44
4,899 4.45 4.43
4,934 4.61 4.43
4,955 4.57 4.43
4,995 4.29 4.43
5,006 4.43 4.43
5,036 4.37 4.43
5,059 4.38 4.43
5,069 4.43 4.43
5,086 4.44 4.43
5,092 4.28 4.43
5,099 4.43 4.43
5,115 4.42 4.43
5,220 4.44 4.43
5,223 4.38 4.43
5,225 4.37 4.43
5,240 4.52 4.43
5,335 4.37 4.43
5,342 4.37 4.43
5,344 4.52 4.43
5,381 4.39 4.43
5,416 4.44 4.43
5,429 4.39 4.43
5,438 4.37 4.43
5,439 4.57 4.43
5,454 4.41 4.42
5,472 4.39 4.43
5,490 4.33 4.42
5,494 4.47 4.43
5,533 4.25 4.42
5,554 4.44 4.43
5,607 4.44 4.42
5,615 4.41 4.42
5,625 4.36 4.43
5,629 4.47 4.42
5,634 4.62 4.42
5,640 4.5 4.43
5,642 4.41 4.42
5,709 4.45 4.42
5,722 4.39 4.43
5,751 4.34 4.42
5,776 4.3 4.42
5,786 4.44 4.42
5,822 4.41 4.42
5,953 4.39 4.42
5,976 4.37 4.42
6,013 4.44 4.42
6,023 4.44 4.42
6,037 4.42 4.42
6,051 4.61 4.42
6,102 4.38 4.42
6,116 4.48 4.42
6,120 4.48 4.42
6,165 4.33 4.42
6,305 4.49 4.42
6,315 4.48 4.42
6,323 4.43 4.42
6,355 4.45 4.42
6,421 4.42 4.42
6,426 4.44 4.42
6,434 4.54 4.42
6,437 4.44 4.42
6,466 4.48 4.42
6,531 4.39 4.42
6,536 4.38 4.41
6,565 4.44 4.42
6,595 4.39 4.41
6,627 4.54 4.41
6,634 4.33 4.41
6,639 4.41 4.42
6,644 4.47 4.41
6,655 4.49 4.42
6,661 4.43 4.41
6,680 4.38 4.41
6,681 4.38 4.42
6,720 4.33 4.41
6,800 4.45 4.41
6,806 4.50 4.41
6,822 4.52 4.41
6,842 4.47 4.41
6,848 4.45 4.41
6,872 4.37 4.41
6,885 4.43 4.41
6,891 4.45 4.41
6,894 4.41 4.41
6,903 4.39 4.41
6,964 4.34 4.41

6B: LINK 2

Time,
t (seconds)		 ln (travel time)
lnY g
20 5.08 5.15
31 5.24 5.15
35 5.18 5.15
42 5.17 5.15
57 5.16 5.15
66 5.22 5.15
80 5.16 5.15
155 5.14 5.15
161 5.16 5.15
186 5.11 5.15
194 5.16 5.15
200 5.25 5.15
220 5.13 5.14
230 5.09 5.14
236 5.08 5.15
296 5.15 5.14
312 5.25 5.14
320 5.15 5.14
330 5.16 5.14
347 5.16 5.14
353 5.17 5.14
390 5.16 5.14
415 5.23 5.14
423 5.12 5.14
450 5.19 5.14
468 5.12 5.14
471 5.07 5.14
474 5.09 5.14
490 5.09 5.14
502 5.20 5.14
518 5.07 5.14
520 5.11 5.14
525 5.18 5.14
573 5.15 5.14
594 5.09 5.14
640 5.09 5.14
647 5.06 5.14
654 5.08 5.14
656 5.18 5.14
661 5.14 5.14
695 5.08 5.14
711 5.14 5.14
755 5.11 5.14
766 5.13 5.13
768 5.14 5.14
769 5.14 5.14
837 5.06 5.13
859 5.04 5.14
871 5.16 5.13
874 5.15 5.13
914 5.15 5.13
952 5.22 5.13
960 5.25 5.13
963 5.25 5.13
998 5.18 5.13
1,030 5.20 5.13
1,079 5.11 5.13
1,093 5.09 5.13
1,094 5.17 5.13
1,101 5.09 5.13
1,102 5.08 5.13
1,155 5.11 5.13
1,158 5.23 5.13
1,171 5.09 5.13
1,178 5.18 5.12
1,193 5.12 5.12
1,239 5.16 5.12
1,282 5.19 5.12
1,325 5.09 5.12
1,357 5.12 5.12
1,407 5.17 5.12
1,423 5.11 5.12
1,427 5.15 5.12
1,446 5.07 5.12
1,448 5.08 5.12
1,469 5.13 5.12
1,493 5.24 5.12
1,550 5.09 5.12
1,598 5.20 5.12
1,632 5.09 5.11
1,639 5.10 5.11
1,652 5.19 5.11
1,654 5.19 5.11
1,667 5.18 5.11
1,671 5.18 5.11
1,717 5.08 5.11
1,736 5.16 5.11
1,753 5.18 5.11
1,761 5.20 5.11
1,829 5.06 5.11
1,859 5.11 5.11
1,860 5.13 5.11
1,869 5.13 5.11
1,875 5.12 5.11
1,906 5.18 5.11
1,912 5.16 5.11
1,917 5.18 5.11
1,926 5.20 5.11
1,932 5.02 5.11
1,939 5.08 5.11
1,964 5.14 5.11
1,969 5.06 5.11
1,981 5.20 5.11
2,004 4.98 5.11
2,012 5.04 5.11
2,027 5.12 5.11
2,028 5.07 5.11
2,061 5.09 5.11
2,070 5.16 5.10
2,075 5.02 5.11
2,097 5.12 5.11
2,172 5.08 5.10
2,174 5.06 5.10
2,261 5.06 5.10
2,348 5.25 5.10
2,408 5.19 5.10
2,457 4.98 5.10
2,473 5.03 5.10
2,579 5.06 5.09
2,602 5.11 5.09
2,604 5.12 5.09
2,660 5.12 5.09
2,670 5.11 5.09
2,698 5.17 5.09
2,738 5.11 5.09
2,757 5.19 5.09
2,759 5.11 5.09
2,767 5.06 5.09
2,774 5.08 5.09
2,778 5.04 5.09
2,788 5.06 5.09
2,807 5.11 5.09
2,833 5.16 5.09
2,834 5.09 5.09
2,839 5.08 5.09
2,866 5.02 5.09
2,894 5.11 5.09
2,905 5.25 5.08
2,910 5.12 5.09
2,944 5.06 5.08
2,962 5.13 5.08
2,964 5.12 5.08
2,966 5.13 5.08
2,967 5.10 5.08
2,973 5.16 5.08
3,006 5.06 5.08
3,038 5.14 5.08
3,043 5.00 5.08
3,049 5.04 5.08
3,052 5.04 5.08
3,099 5.13 5.08
3,165 5.04 5.08
3,232 5.00 5.08
3,242 4.97 5.08
3,244 5.02 5.08
3,246 4.96 5.08
3,255 5.08 5.08
3,259 5.01 5.08
3,271 5.10 5.08
3,283 5.06 5.08
3,309 5.04 5.08
3,316 5.05 5.08
3,338 5.05 5.08
3,364 5.24 5.08
3,367 5.11 5.08
3,402 5.00 5.07
3,403 5.00 5.08
3,407 5.00 5.08
3,410 5.01 5.08
3,496 5.04 5.07
3,507 5.14 5.07
3,521 5.08 5.07
3,523 5.15 5.07
3,532 5.03 5.07
3,600 5.02 5.07
3,602 5.01 5.07
3,622 5.20 5.07
3,656 5.08 5.07
3,660 5.06 5.07
3,672 5.04 5.07
3,680 5.09 5.07
3,733 5.04 5.07
3,802 5.00 5.07
3,806 5.10 5.07
3,841 4.98 5.07
3,873 5.02 5.07
3,879 5.04 5.07
3,890 5.05 5.07
3,897 5.04 5.07
3,901 5.03 5.06
3,936 5.00 5.07
3,937 5.06 5.07
3,956 5.04 5.07
3,965 5.02 5.07
3,980 5.00 5.07
4,006