Figure 5 Illustration of Covariance Function and Correlation for a Very Congested Two-Link Example: Day 7,,,,,,,,,
5A: LINK 1,,,,,,,,,
"Time,
t (seconds)",In (travel time),,,,,,,,
,lnY,g,,,,,,,
102,6.21,6.25,,,,,,,
109,6.12,6.25,,,,,,,
137,6.27,6.26,,,,,,,
204,6.36,6.26,,,,,,,
205,6.44,6.26,,,,,,,
214,6.27,6.26,,,,,,,
227,6.46,6.27,,,,,,,
233,6.27,6.27,,,,,,,
259,6.48,6.29,,,,,,,
271,6.46,6.30,,,,,,,
327,6.43,6.33,,,,,,,
362,6.42,6.37,,,,,,,
379,6.40,6.40
401,6.38,6.43
403,6.50,6.43
419,6.39,6.44
430,6.46,6.44
516,6.61,6.49
519,6.60,6.50
522,6.45,6.50
549,6.59,6.52
572,6.61,6.54
582,6.68,6.55
606,6.70,6.56
625,6.59,6.58
634,6.59,6.58
641,6.43,6.59
669,6.64,6.61
730,6.90,6.66
751,6.71,6.68
772,6.90,6.71
773,6.74,6.71
814,6.79,6.75
821,6.73,6.76
850,6.87,6.77
855,6.69,6.77
881,6.93,6.77
906,6.92,6.78
910,7.00,6.78
913,6.81,6.78
915,6.68,6.78
974,6.94,6.78
994,6.65,6.78
"1,012",7.01,6.79
"1,036",6.67,6.79
"1,038",6.67,6.79
"1,040",6.70,6.79
"1,042",6.70,6.79
"1,101",6.68,6.77
"1,166",6.65,6.74
"1,185",6.65,6.73
"1,198",6.77,6.72
"1,237",6.66,6.70
"1,332",6.61,6.59
"1,396",6.58,6.48
"1,978",5.51,6.28
"2,033",6.77,6.34
"2,058",6.55,6.36
"2,066",6.39,6.37
"2,286",6.48,6.50
"2,296",6.47,6.50
"2,335",6.47,6.49
"2,340",6.46,6.49
"2,346",6.46,6.49
"2,355",6.46,6.49
"2,552",6.31,6.31
"2,805",5.70,6.14
"3,122",6.69,6.31
"3,136",6.58,6.32
"3,212",5.56,6.34
"3,274",6.32,6.35
"3,326",6.73,6.36
"3,411",6.27,6.33
"3,520",6.17,6.27
"3,888",6.36,6.13
"3,959",5.46,6.11
"3,972",6.35,6.10
"4,028",6.18,6.07
"4,038",5.97,6.07
"4,081",5.95,6.07
"4,086",6.26,6.07
"4,185",6.02,6.03
"4,207",6.09,6.02
"4,243",5.95,6.01
"4,275",6.04,5.99
"4,281",6.04,5.99
"4,301",5.92,5.98
"4,309",6.12,5.97
"4,316",6.00,5.97
"4,318",5.43,5.97
"4,467",5.72,5.93
"4,486",5.97,5.94
"4,510",6.07,5.94
"4,517",6.08,5.94
"4,527",5.88,5.95
"4,557",5.89,5.96
"4,563",5.91,5.96
"4,566",6.10,5.96
"4,673",5.67,5.96
"4,897",5.94,5.95
"4,932",5.99,5.95
"4,938",6.03,5.96
"5,006",5.87,5.96
"5,243",6.03,5.97
"5,272",5.95,5.95
"5,403",5.83,5.86
"5,410",5.83,5.85
"5,642",4.92,5.40
"5,751",4.74,5.24
"5,833",5.38,5.23
"5,851",5.05,5.23
"5,924",4.94,5.20
"5,929",5.59,5.20
"5,950",5.64,5.19
"5,982",5.50,5.18
"5,984",5.57,5.18
"6,048",5.02,5.16
"6,074",5.38,5.16
"6,142",5.20,5.13
"6,174",5.16,5.10
"6,201",5.09,5.06
"6,202",4.95,5.06
"6,212",5.04,5.04
"6,214",5.10,5.04
"6,220",5.11,5.03
"6,244",5.04,5.00
"6,251",5.03,4.99
"6,255",5.20,4.99
"6,294",5.21,4.94
"6,317",4.84,4.92
"6,438",4.76,4.88
"6,482",4.89,4.85
"6,526",4.88,4.82
"6,558",4.82,4.79
"6,565",4.86,4.79
"6,566",4.93,4.79
"6,603",4.89,4.74
"6,626",4.88,4.72
"6,653",4.66,4.70
"6,664",4.76,4.70
"6,671",4.65,4.70
"6,726",4.80,4.70
"6,742",4.65,4.69
"6,795",4.66,4.71
"6,879",4.50,4.75
"6,916",4.50,4.72
"6,920",4.43,4.72

5B: LINK 2,,
"Time,
t (seconds)",In (travel time),
,lnY,g
102,6.71,6.69
109,6.72,6.68
137,6.68,6.68
204,6.61,6.67
205,6.59,6.67
214,6.61,6.67
227,6.57,6.67
233,6.66,6.67
259,6.62,6.66
271,6.60,6.66
327,6.62,6.66
362,6.63,6.66
379,6.62,6.66
401,6.62,6.67
403,6.84,6.67
419,6.62,6.67
430,6.59,6.68
516,6.61,6.68
519,6.73,6.68
522,6.61,6.68
549,6.59,6.67
572,6.73,6.67
582,6.78,6.66
606,6.74,6.65
625,6.62,6.64
634,6.63,6.64
641,6.66,6.64
669,6.62,6.63
730,6.62,6.61
751,6.54,6.60
772,6.63,6.60
773,6.51,6.60
814,6.57,6.59
821,6.52,6.59
850,6.53,6.58
855,6.52,6.58
881,6.55,6.58
906,7.01,6.57
910,6.65,6.57
913,6.62,6.57
915,6.59,6.57
974,6.59,6.56
994,6.56,6.55
"1,012",6.64,6.55
"1,036",6.52,6.55
"1,038",6.53,6.55
"1,040",6.50,6.55
"1,042",6.49,6.55
"1,101",6.50,6.55
"1,166",6.51,6.54
"1,185",6.50,6.54
"1,198",6.50,6.54
"1,237",6.48,6.54
"1,332",6.49,6.53
"1,396",6.48,6.53
"1,978",6.79,6.54
"2,033",6.38,6.54
"2,058",6.51,6.54
"2,066",6.53,6.53
"2,286",6.37,6.44
"2,296",6.38,6.44
"2,335",6.37,6.42
"2,340",6.38,6.42
"2,346",6.35,6.41
"2,355",6.35,6.41
"2,552",6.38,6.34
"2,805",6.42,6.28
"3,122",6.17,6.26
"3,136",6.15,6.25
"3,212",6.30,6.22
"3,274",6.08,6.19
"3,326",6.12,6.17
"3,411",6.17,6.14
"3,520",6.12,6.11
"3,888",6.06,6.07
"3,959",6.22,6.06
"3,972",6.07,6.06
"4,028",6.00,6.06
"4,038",6.04,6.06
"4,081",6.04,6.06
"4,086",6.06,6.06
"4,185",6.05,6.06
"4,207",5.95,6.06
"4,243",5.98,6.05
"4,275",6.08,6.04
"4,281",6.08,6.04
"4,301",6.06,6.03
"4,309",6.00,6.03
"4,316",6.06,6.03
"4,318",6.07,6.02
"4,467",6.01,5.95
"4,486",5.95,5.94
"4,510",5.86,5.93
"4,517",5.87,5.93
"4,527",5.94,5.92
"4,557",5.85,5.91
"4,563",5.87,5.91
"4,566",6.01,5.91
"4,673",5.91,5.88
"4,897",5.82,5.84
"4,932",5.83,5.83
"4,938",5.82,5.82
"5,006",5.78,5.79
"5,243",5.58,5.69
"5,272",5.50,5.67
"5,403",5.51,5.58
"5,410",5.53,5.58
"5,642",5.55,5.53
"5,751",5.56,5.53
"5,833",5.63,5.54
"5,851",5.77,5.55
"5,924",5.60,5.56
"5,929",5.51,5.56
"5,950",5.59,5.56
"5,982",5.49,5.55
"5,984",5.58,5.56
"6,048",5.76,5.55
"6,074",5.47,5.55
"6,142",5.49,5.54
"6,174",5.51,5.53
"6,201",5.50,5.53
"6,202",5.57,5.53
"6,212",5.51,5.52
"6,214",5.50,5.52
"6,220",5.47,5.52
"6,244",5.48,5.52
"6,251",5.48,5.51
"6,255",5.61,5.51
"6,294",5.59,5.50
"6,317",5.48,5.50
"6,438",5.54,5.49
"6,482",5.52,5.48
"6,526",5.53,5.48
"6,558",5.49,5.48
"6,565",5.49,5.47
"6,566",5.51,5.48
"6,603",5.48,5.47
"6,626",5.48,5.47
"6,653",5.49,5.46
"6,664",5.51,5.46
"6,671",5.51,5.46
"6,726",5.46,5.44
"6,742",5.45,5.43
"6,795",5.38,5.41
"6,879",5.29,5.36
"6,916",5.26,5.34
"6,920",5.22,5.33

5C: LINKS 1 and 2,,
"Time,
t (seconds)","Covariance, untransformed scale",
,5th percentile,95th percentile
102,"-2,324.34","-1,014.81"
109,"-2,354.33","-1,011.67"
137,"-2,440.88","-1,009.05"
204,"-2,682.59","-1,018.79"
205,"-2,685.41","-1,020.02"
214,"-2,712.88","-1,023.91"
227,"-2,747.73","-1,035.53"
233,"-2,759.29","-1,039.30"
259,"-2,826.37","-1,058.60"
271,"-2,853.28","-1,065.96"
327,"-2,986.16","-1,111.99"
362,"-3,066.18","-1,141.66"
379,"-3,097.59","-1,150.47"
401,"-3,148.64","-1,173.57"
403,"-3,158.22","-1,173.88"
419,"-3,201.78","-1,188.86"
430,"-3,229.12","-1,195.75"
516,"-3,465.64","-1,269.29"
519,"-3,479.25","-1,271.86"
522,"-3,491.86","-1,275.82"
549,"-3,581.20","-1,302.93"
572,"-3,646.20","-1,326.05"
582,"-3,670.02","-1,337.35"
606,"-3,731.31","-1,361.35"
625,"-3,759.18","-1,376.50"
634,"-3,782.78","-1,386.89"
641,"-3,790.97","-1,393.76"
669,"-3,859.30","-1,425.78"
730,"-3,992.19","-1,470.35"
751,"-4,029.73","-1,488.37"
772,"-4,078.59","-1,506.39"
773,"-4,087.30","-1,507.45"
814,"-4,140.83","-1,515.79"
821,"-4,139.59","-1,518.21"
850,"-4,158.80","-1,516.91"
855,"-4,158.16","-1,516.40"
881,"-4,170.82","-1,515.84"
906,"-4,158.27","-1,504.73"
910,"-4,154.19","-1,505.62"
913,"-4,151.60","-1,505.77"
915,"-4,151.23","-1,504.60"
974,"-4,037.40","-1,468.04"
994,"-3,993.51","-1,454.06"
"1,012","-3,950.28","-1,439.94"
"1,036","-3,886.02","-1,423.37"
"1,038","-3,882.83","-1,422.65"
"1,040","-3,880.78","-1,422.27"
"1,042","-3,871.31","-1,420.58"
"1,101","-3,677.82","-1,374.15"
"1,166","-3,442.04","-1,322.07"
"1,185","-3,374.32","-1,313.50"
"1,198","-3,339.00","-1,308.59"
"1,237","-3,231.50","-1,288.74"
"1,332","-2,923.14","-1,244.79"
"1,396","-2,719.45","-1,229.89"
"1,978","-2,253.95","-1,005.90"
"2,033","-2,298.06",-981.64
"2,058","-2,298.71",-971.74
"2,066","-2,301.48",-970.13
"2,286","-2,255.43",-913.97
"2,296","-2,250.53",-912.15
"2,335","-2,231.90",-900.98
"2,340","-2,220.98",-896.34
"2,346","-2,208.66",-893.58
"2,355","-2,194.53",-891.77
"2,552","-1,818.41",-823.61
"2,805","-1,506.82",-729.20
"3,122","-1,562.91",-677.77
"3,136","-1,555.28",-672.86
"3,212","-1,552.15",-657.18
"3,274","-1,534.31",-649.32
"3,326","-1,526.08",-644.71
"3,411","-1,456.70",-638.55
"3,520","-1,358.60",-637.29
"3,888","-1,173.04",-514.36
"3,959","-1,164.09",-478.00
"3,972","-1,160.15",-472.83
"4,028","-1,135.95",-450.03
"4,038","-1,133.57",-447.13
"4,081","-1,113.49",-432.35
"4,086","-1,112.52",-430.72
"4,185","-1,063.61",-406.24
"4,207","-1,048.22",-399.99
"4,243","-1,032.07",-390.45
"4,275","-1,013.64",-382.92
"4,281","-1,013.81",-381.79
"4,301",-998.51,-376.35
"4,309",-993.52,-374.90
"4,316",-988.14,-373.02
"4,318",-987.26,-372.23
"4,467",-904.44,-346.70
"4,486",-895.07,-344.67
"4,510",-889.39,-343.43
"4,517",-888.25,-342.42
"4,527",-885.91,-343.00
"4,557",-874.24,-342.94
"4,563",-869.20,-343.03
"4,566",-867.06,-342.92
"4,673",-812.94,-338.56
"4,897",-751.94,-317.65
"4,932",-737.80,-313.88
"4,938",-735.98,-313.06
"5,006",-703.41,-300.16
"5,243",-558.24,-242.17
"5,272",-539.01,-233.17
"5,403",-444.74,-194.25
"5,410",-439.94,-192.41
"5,642",-326.86,-144.29
"5,751",-314.00,-130.90
"5,833",-313.02,-125.48
"5,851",-312.28,-124.89
"5,924",-313.81,-121.73
"5,929",-313.94,-121.57
"5,950",-314.53,-120.79
"5,982",-313.24,-118.74
"5,984",-312.67,-118.55
"6,048",-302.36,-114.17
"6,074",-296.87,-112.03
"6,142",-281.77,-105.92
"6,174",-276.18,-102.61
"6,201",-268.80,-100.60
"6,202",-268.86,-100.58
"6,212",-266.46,-99.64
"6,214",-266.00,-99.53
"6,220",-264.90,-99.12
"6,244",-259.67,-97.04
"6,251",-258.19,-96.49
"6,255",-257.54,-96.15
"6,294",-248.52,-93.21
"6,317",-241.94,-91.54
"6,438",-216.46,-83.03
"6,482",-208.89,-79.90
"6,526",-200.45,-76.55
"6,558",-195.10,-73.66
"6,565",-193.28,-73.07
"6,566",-193.28,-73.00
"6,603",-184.06,-70.01
"6,626",-179.15,-68.14
"6,653",-173.41,-65.68
"6,664",-170.97,-64.69
"6,671",-169.10,-64.26
"6,726",-153.76,-59.65
"6,742",-149.29,-58.15
"6,795",-134.86,-54.22
"6,879",-110.27,-49.36
"6,916",-100.02,-47.59
"6,920",-98.94,-47.28
,,
"5D: CORRELATION, LINKS 1 and 2",,
?12,Count,
-1.0,0,
-0.5,0,
-0.5,1,
-0.4,4,
-0.4,23,
-0.3,47,
-0.3,122,
-0.2,112,
-0.2,113
-0.1,39
-0.1,31
-0.6,6
0.0,0
0.5,0
1.0,0