Bureau of Transportation Statistics (BTS)
BTS Home > Publications > Journal of Transportation and Statistics > Volume 7 Number 2/3 > Paper 5
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Figure 4 - Illustration of Covariance Function and Correlation for a Moderately Congested Two-Link Example: Day 10

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4A: LINK 1

Time,
t (seconds)		 In (travel time)
lnY g
10 4.62 4.63
12 4.67 4.63
24 4.72 4.63
94 4.62 4.62
97 4.62 4.62
103 4.54 4.61
123 4.66 4.61
136 4.65 4.61
138 4.66 4.61
194 4.58 4.60
195 4.60 4.59
208 4.61 4.59
226 4.51 4.59
228 4.51 4.59
239 4.56 4.59
281 4.51 4.58
290 4.51 4.58
296 4.50 4.58
322 4.49 4.58
323 4.49 4.57
346 4.44 4.57
383 4.58 4.56
395 4.51 4.56
418 4.48 4.56
438 4.56 4.56
478 4.54 4.55
479 4.47 4.55
495 4.62 4.54
503 4.60 4.54
509 4.58 4.54
512 4.64 4.54
520 4.63 4.54
543 4.65 4.54
546 4.62 4.54
551 4.63 4.54
564 4.58 4.54
645 4.57 4.54
647 4.60 4.54
661 4.60 4.54
682 4.47 4.54
697 4.49 4.54
706 4.48 4.54
720 4.55 4.54
760 4.48 4.54
797 4.62 4.55
809 4.55 4.55
814 4.56 4.55
835 4.61 4.56
862 4.44 4.56
877 4.57 4.57
905 4.62 4.57
918 4.55 4.58
942 4.61 4.60
943 4.50 4.60
958 4.54 4.61
1,017 4.48 4.65
1,054 4.56 4.68
1,079 4.66 4.69
1,098 4.70 4.70
1,114 4.80 4.72
1,121 4.84 4.72
1,162 4.95 4.75
1,169 4.89 4.75
1,183 4.98 4.76
1,302 4.80 4.83
1,316 4.70 4.84
1,336 4.79 4.85
1,359 4.69 4.86
1,362 4.73 4.86
1,392 4.82 4.88
1,396 4.78 4.88
1,410 4.78 4.88
1,425 4.80 4.89
1,445 4.75 4.90
1,459 4.96 4.91
1,486 5.00 4.92
1,492 5.00 4.92
1,527 5.02 4.93
1,548 4.98 4.94
1,556 4.96 4.94
1,577 5.02 4.95
1,598 4.96 4.95
1,600 5.04 4.95
1,606 4.83 4.95
1,609 5.00 4.95
1,618 4.99 4.96
1,622 4.98 4.95
1,623 4.86 4.95
1,626 4.99 4.95
1,638 5.02 4.96
1,649 5.01 4.95
1,667 4.96 4.95
1,686 5.11 4.95
1,710 4.98 4.95
1,712 4.93 4.95
1,758 5.02 4.94
1,759 4.96 4.94
1,792 4.86 4.93
1,805 4.88 4.93
1,829 4.90 4.92
1,832 4.90 4.92
1,844 4.89 4.91
1,856 4.85 4.91
1,912 4.84 4.89
1,954 4.92 4.88
1,958 4.83 4.87
1,960 4.90 4.87
1,980 4.86 4.87
1,994 5.11 4.86
2,004 4.80 4.86
2,032 4.84 4.85
2,036 5.09 4.85
2,045 4.84 4.84
2,069 4.77 4.84
2,079 4.88 4.83
2,159 4.71 4.79
2,307 4.79 4.75
2,317 4.74 4.75
2,325 4.75 4.75
2,370 4.74 4.73
2,418 4.60 4.73
2,431 4.69 4.72
2,463 4.57 4.72
2,504 4.56 4.72
2,515 4.62 4.72
2,568 4.60 4.72
2,571 4.50 4.73
2,603 4.62 4.74
2,608 4.73 4.74
2,609 4.65 4.74
2,662 4.73 4.77
2,669 4.81 4.77
2,692 4.79 4.79
2,695 4.80 4.79
2,751 4.68 4.81
2,757 4.70 4.81
2,765 4.74 4.81
2,767 4.74 4.81
2,774 4.84 4.81
2,779 4.78 4.81
2,788 4.87 4.82
2,808 5.05 4.82
2,810 4.88 4.82
2,841 4.88 4.83
2,846 4.91 4.82
2,866 4.91 4.83
2,879 4.88 4.82
2,896 4.87 4.82
2,945 4.84 4.82
2,948 4.80 4.82
2,974 4.74 4.82
2,979 4.88 4.82
2,992 4.75 4.81
3,005 4.87 4.81
3,018 4.82 4.81
3,055 4.72 4.80
3,081 4.67 4.79
3,087 4.80 4.79
3,111 4.75 4.78
3,115 4.71 4.78
3,117 4.71 4.78
3,126 4.79 4.78
3,147 4.72 4.77
3,153 4.74 4.77
3,187 4.88 4.75
3,188 4.89 4.75
3,198 4.82 4.74
3,210 4.79 4.74
3,221 4.81 4.73
3,232 4.80 4.72
3,235 4.81 4.72
3,257 4.74 4.70
3,293 4.63 4.68
3,300 4.74 4.67
3,348 4.52 4.63
3,357 4.55 4.63
3,396 4.44 4.60
3,414 4.49 4.59
3,425 4.45 4.58
3,458 4.44 4.56
3,521 4.50 4.52
3,531 4.52 4.51
3,547 4.95 4.50
3,568 4.61 4.49
3,582 4.39 4.49
3,594 4.57 4.48
3,601 4.45 4.48
3,608 4.54 4.48
3,611 4.38 4.48
3,618 4.42 4.47
3,621 4.41 4.47
3,650 4.45 4.47
3,669 4.36 4.46
3,676 4.37 4.47
3,679 4.33 4.46
3,752 4.44 4.45
3,787 4.39 4.45
3,799 4.34 4.45
3,800 4.37 4.45
3,816 4.45 4.45
3,856 4.51 4.45
3,871 4.45 4.45
3,882 4.42 4.46
3,890 4.51 4.46
3,940 4.36 4.46
3,950 4.38 4.46
3,985 4.38 4.47
3,995 4.47 4.47
4,027 4.52 4.47
4,038 4.36 4.47
4,048 4.55 4.47
4,051 4.65 4.47
4,084 4.41 4.47
4,127 4.48 4.47
4,133 4.63 4.47
4,189 4.49 4.47
4,195 4.38 4.47
4,208 4.42 4.47
4,210 4.43 4.47
4,222 4.42 4.47
4,240 4.42 4.47
4,265 4.47 4.48
4,279 4.30 4.48
4,305 4.50 4.49
4,332 4.44 4.49
4,335 4.49 4.49
4,356 4.44 4.50
4,383 4.53 4.50
4,392 4.58 4.50
4,400 4.43 4.51
4,433 4.44 4.51
4,438 4.45 4.51
4,490 4.51 4.52
4,539 4.43 4.52
4,566 4.51 4.52
4,584 4.43 4.51
4,612 4.55 4.51
4,614 4.44 4.51
4,633 4.55 4.51
4,652 4.58 4.51
4,654 4.58 4.51
4,704 4.52 4.51
4,706 4.42 4.51
4,738 4.47 4.51
4,744 4.60 4.51
4,748 4.58 4.51
4,774 4.53 4.51
4,787 4.48 4.51
4,790 4.53 4.52
4,794 4.54 4.52
4,813 4.43 4.52
4,861 4.50 4.52
4,892 4.51 4.51
4,895 4.41 4.51
4,911 4.38 4.51
4,928 4.41 4.51
4,961 4.43 4.50
5,008 4.41 4.49
5,009 4.74 4.49
5,011 4.43 4.5
5,023 4.43 4.49
5,040 4.50 4.49
5,093 4.41 4.49
5,111 4.37 4.48
5,170 4.39 4.48
5,171 4.53 4.48
5,177 4.37 4.48
5,213 4.47 4.47
5,242 4.50 4.47
5,245 4.47 4.47
5,249 4.45 4.47
5,251 4.48 4.47
5,282 4.47 4.46
5,284 4.39 4.46
5,292 4.38 4.46
5,302 4.44 4.46
5,304 4.44 4.46
5,310 4.42 4.46
5,321 4.43 4.46
5,364 4.38 4.45
5,381 4.50 4.44
5,426 4.51 4.43
5,434 4.38 4.43
5,472 4.34 4.42
5,526 4.43 4.42
5,555 4.49 4.41
5,573 4.43 4.41
5,577 4.49 4.41
5,651 4.39 4.40
5,676 4.47 4.40
5,679 4.38 4.40
5,695 4.42 4.40
5,707 4.37 4.40
5,708 4.37 4.40
5,722 4.47 4.40
5,731 4.41 4.40
5,820 4.42 4.41
5,869 4.44 4.41
5,881 4.50 4.41
5,884 4.48 4.41
5,887 4.50 4.41
5,888 4.43 4.41
5,911 4.41 4.41
5,920 4.45 4.41
5,924 4.44 4.41
5,932 4.42 4.41
5,941 4.38 4.41
5,958 4.54 4.41
5,992 4.42 4.41
6,033 4.42 4.42
6,044 4.48 4.42
6,107 4.42 4.42
6,221 4.43 4.44
6,313 4.51 4.45
6,316 4.42 4.44
6,323 4.43 4.44
6,372 4.42 4.44
6,405 4.48 4.44
6,413 4.39 4.44
6,445 4.55 4.44
6,458 4.44 4.44
6,484 4.41 4.43
6,494 4.41 4.43
6,543 4.54 4.43
6,551 4.38 4.42
6,558 4.41 4.42
6,572 4.49 4.42
6,639 4.49 4.41
6,696 4.42 4.40
6,708 4.32 4.40
6,725 4.34 4.40
6,743 4.49 4.40
6,752 4.43 4.40
6,756 4.41 4.40
6,762 4.42 4.40
6,800 4.29 4.40
6,838 4.37 4.39
6,861 4.38 4.38
6,874 4.43 4.38
6,902 4.44 4.38
6,936 4.33 4.37
6,941 4.44 4.37
6,943 4.51 4.37
6,951 4.43 4.37
6,972 4.32 4.36

4B: LINK 2

Time,
t (seconds)		 In (travel time)
lnY g
10 5.58 5.48
12 5.53 5.48
24 5.52 5.49
94 5.47 5.50
97 5.47 5.49
103 5.48 5.49
123 5.44 5.50
136 5.43 5.50
138 5.44 5.50
194 5.48 5.50
195 5.48 5.50
208 5.58 5.51
226 5.46 5.51
228 5.46 5.51
239 5.51 5.51
281 5.51 5.53
290 5.51 5.53
296 5.51 5.53
322 5.53 5.53
323 5.50 5.53
346 5.47 5.54
383 5.56 5.55
395 5.53 5.55
418 5.51 5.56
438 5.61 5.56
478 5.64 5.57
479 5.43 5.57
495 5.59 5.57
503 5.60 5.57
509 5.60 5.57
512 5.62 5.57
520 5.66 5.57
543 5.67 5.57
546 5.61 5.57
551 5.67 5.58
564 5.66 5.58
645 5.58 5.60
647 5.59 5.59
661 5.63 5.60
682 5.64 5.60
697 5.59 5.61
706 5.59 5.61
720 5.58 5.61
760 5.53 5.63
797 5.58 5.64
809 5.51 5.64
814 5.58 5.64
835 5.51 5.65
862 5.52 5.66
877 5.51 5.66
905 5.70 5.67
918 5.75 5.67
942 5.75 5.68
943 5.70 5.68
958 5.79 5.68
1,017 5.76 5.70
1,054 5.78 5.72
1,079 5.74 5.73
1,098 5.72 5.74
1,114 5.74 5.74
1,121 5.74 5.74
1,162 5.70 5.76
1,169 5.72 5.76
1,183 5.71 5.76
1,302 5.84 5.78
1,316 5.84 5.78
1,336 5.81 5.78
1,359 5.80 5.78
1,362 5.80 5.78
1,392 5.82 5.78
1,396 5.81 5.78
1,410 5.84 5.77
1,425 5.78 5.77
1,445 5.79 5.77
1,459 5.75 5.76
1,486 5.72 5.75
1,492 5.76 5.75
1,527 5.75 5.74
1,548 5.72 5.73
1,556 5.74 5.73
1,577 5.74 5.72
1,598 5.74 5.71
1,600 5.73 5.71
1,606 5.73 5.70
1,609 5.71 5.70
1,618 5.72 5.70
1,622 5.77 5.69
1,623 5.71 5.69
1,626 5.73 5.69
1,638 5.73 5.69
1,649 5.76 5.68
1,667 5.72 5.67
1,686 5.72 5.66
1,710 5.62 5.64
1,712 5.68 5.64
1,758 5.60 5.62
1,759 5.60 5.61
1,792 5.64 5.59
1,805 5.62 5.59
1,829 5.59 5.57
1,832 5.58 5.57
1,844 5.58 5.57
1,856 5.55 5.56
1,912 5.50 5.54
1,954 5.55 5.52
1,958 5.47 5.52
1,960 5.55 5.52
1,980 5.48 5.52
1,994 5.50 5.51
2,004 5.37 5.51
2,032 5.42 5.50
2,036 5.57 5.50
2,045 5.55 5.50
2,069 5.35 5.50
2,079 5.40 5.50
2,159 5.35 5.49
2,307 5.53 5.49
2,317 5.53 5.49
2,325 5.50 5.49
2,370 5.51 5.48
2,418 5.49 5.48
2,431 5.58 5.48
2,463 5.41 5.47
2,504 5.43 5.45
2,515 5.58 5.45
2,568 5.49 5.43
2,571 5.48 5.42
2,603 5.42 5.41
2,608 5.46 5.40
2,609 5.38 5.40
2,662 5.38 5.37
2,669 5.38 5.37
2,692 5.37 5.36
2,695 5.31 5.36
2,751 5.30 5.33
2,757 5.28 5.33
2,765 5.27 5.33
2,767 5.27 5.33
2,774 5.23 5.33
2,779 5.25 5.32
2,788 5.33 5.32
2,808 5.42 5.31
2,810 5.25 5.31
2,841 5.27 5.30
2,846 5.26 5.30
2,866 5.19 5.29
2,879 5.24 5.29
2,896 5.17 5.29
2,945 5.38 5.28
2,948 5.22 5.28
2,974 5.29 5.27
2,979 5.27 5.27
2,992 5.25 5.27
3,005 5.33 5.27