Data-driven exploration of traffic speed patterns to identify potential road links for variable speed limit sign implementation

Figures & data

Table 1. Recent research on speed variation using a data-driven approach.

Authors	Focus	Data and methodology	Key conclusions
He (2016)	To investigate if higher FFS will lead to a less congested freeway; estimate the impact of varying FFS on the performance of a freeway system	Data: Numerical examples based on observation of the reality Method: Mathematical modeling/approach based on a numerical approximation model called Cell Transmission Model	With the increasing FFS, the average delay of vehicles decreases at the beginning and then increases; the actual bottleneck capacity increases at the beginning and then decreases with the continuous increase of FFS
Silvano et al. (2020)	To estimate the FFS and the impact of speed limit changes and road characteristics on FFS distribution	Data: Dataset of speed observations from urban roads with different characteristics Method: Parametric probabilistic latent approach	Land use, on-street parking, and the presence of sidewalks influence FFS; changes in posted speed limit impact the distribution of the free-flow vehicles and the speed distribution of the constrained vehicles
Yasanthi and Mehran (2020)	To investigate driver behavior in terms of variations in the desired driving speeds under adverse road-weather conditions	Data: Road-weather data and traffic data including traffic speeds from weigh-in-motion traffic counter Method: Linear and non-linear regression models	Slight, moderate, and heavy snow will respectively reduce the FFS of light vehicles traveling in the shoulder lane by 0.2%, 3.4%, and 0.8%, and by 0.3%, 0.4%, and 1.5% when traveling in the median lane
Duvvuri et al. (2020)	To examine the influence of historical speed patterns on the degree of speed variations during peak hours	Data: Traffic speeds using probe data and road characteristics Method: K-means clustering and forest-based classification	Traffic volumes and average speeds of upstream and downstream road links influence the average speed of the corresponding road link

Figure 1. Study area.

Table 2. Data summary.

Variable	Attribute	#	%
Road category
Functional class	1: Interstate and freeway/expressway	335	41.26
	2: Other principal arterial	409	50.37
	3: Minor arterial, collector, and local	68	8.37
Road geometry
Length	1: ≤ 0.5 mile	397	48.89
	2: > 0.5 mile & ≤ 1 mile	229	28.20
	3: > 1 mile & ≤ 1.5 miles	112	13.79
	4: > 1.5 miles	84	9.12
# of through lanes	1	47	5.79
	2	429	52.83
	3	195	24.01
	>4	141	17.37
Traffic-related
AADT	1: ≤ 17500	332	40.89
	2: > 17500 & ≤ 35000	187	23.03
	3: > 35000 & ≤ 52500	121	14.90
	4: > 52500 & ≤ 70000	101	12.44
	5: > 70000	71	8.74
Speed-related
Speed limit	1: 25 mph or 30 mph	78	9.61
	2: 35 mph or 40 mph	372	45.81
	3: 45 mph or 50 mph	154	18.97
	4: 55 mph or 60 mph	112	13.79
	5: 65 mph or 70 mph	96	11.82
Reference speed limit	1: ≤ 40 mph	29	3.95
	2: >40 mph & ≤50 mph	213	26.23
	3: >50 mph & ≤60 mph	194	23.89
	4: >60 mph & ≤70 mph	204	25.12
	5: >70 mph	169	20.81

Figure 2. Variation of the mean speed interval across months and times of the day.

Table 3. Summary statistics of traffic speeds (mph).

Timespan	Mean	SD	Min	Max	15%ile	85%ile
Weekday
12 AM − 3 AM	63.2	8.6	30	90	55	71
3 AM − 6 AM	63.6	9.6	31	88	53	73
6 AM − 9 AM	48.0	17.9	13	93	26	69
9 AM − 12 PM	48.1	18.0	12	85	26	69
12 PM − 3 PM	44.7	19.1	9	90	22	68
3 PM − 6 PM	39.6	19.4	3	99	18	65
6 PM − 9 PM	48.0	18.2	12	89	26	69
9 PM − 12 AM	57.8	14.2	19	85	40	71
Weekend
12 AM − 3 AM	61.4	11.8	24	99	48	72
3 AM − 6 AM	64.4	9.1	33	88	55	73
6 AM − 9 AM	60.9	14.1	23	84	43	74
9 AM − 12 PM	52.3	18.4	14	87	29	72
12 PM − 3 PM	47.3	19.7	9	93	24	71
3 PM − 6 PM	48.1	19.4	10	93	25	71
6 PM − 9 PM	52.0	17.9	14	86	30	71
9 PM − 12 AM	58.2	14.7	17	86	39	72

Table 4. Summary statistics of traffic speeds (mph) for 25 mph or 30 mph posted speed limit road links.

Speed limit cluster	Timespan	Mean	SD	Min	Max	15%ile	85%ile
25/30 mph	Weekday
	12 AM − 3 AM	51.7	9.6	30	66	40	62
	3 AM − 6 AM	50.8	9.3	31	64	39	61
	6 AM − 9 AM	36.0	11.9	14	57	23	51
	9 AM − 12 PM	36.4	13.0	13	59	22	53
	12 PM − 3 PM	32.8	13.0	10	57	19	50
	3 PM − 6 PM	29.6	11.7	9	53	17	44
	6 PM − 9 PM	35.8	12.1	14	58	22	51
	9 PM − 12 AM	42.8	12.2	19	62	28	57
	Weekend
	12 AM − 3 AM	47.1	11.5	24	64.5	33	60
	3 AM − 6 AM	52.2	8.6	33	65	42	62
	6 AM − 9 AM	46.6	12.3	23	66	32	61
	9 AM − 12 PM	39.2	13.3	15	62	24	57
	12 PM − 3 PM	35.1	13.0	12	59	21	52
	3 PM − 6 PM	35.3	12.9	12	59	21	52
	6 PM − 9 PM	38.0	12.8	14	60	24	54
	9 PM − 12 AM	42.7	13.0	17	63	27	58

Table 5. Summary statistics of traffic speeds (mph) for 35 mph or 40 mph posted speed limit road links.

Speed limit cluster	Timespan	Mean	SD	Min	Max	15%ile	85%ile
35/40 mph	Weekday
	12 AM − 3 AM	60.4	7.4	43	71	51	68
	3 AM − 6 AM	59.9	9.3	39	73	48	70
	6 AM − 9 AM	39.4	14.2	14	64	23	57
	9 AM − 12 PM	39.0	14.9	12	65	22	58
	12 PM − 3 PM	35.2	14.8	9	63	19	55
	3 PM − 6 PM	30.2	13.1	7	57	16	46
	6 PM − 9 PM	39.3	15.2	12	66	22	59
	9 PM − 12 AM	51.5	13.8	24	71	34	67
	Weekend
	12 AM − 3 AM	57.3	11.5	32	73	42	70
	3 AM − 6 AM	61.2	8.5	42	73	51	70
	6 AM − 9 AM	54.7	13.9	27	74	37	70
	9 AM − 12 PM	43.1	16.1	14	70	25	63
	12 PM − 3 PM	37.1	15.7	9	66	20	58
	3 PM − 6 PM	38.3	15.7	10	67	21	58
	6 PM − 9 PM	43.1	15.5	15	69	25	62
	9 PM − 12 AM	51.9	14.4	23	72	34	68

Table 6. Summary statistics of traffic speeds (mph) for 45 mph or 50 mph posted speed limit road links.

Speed limit cluster	Timespan	Mean	SD	Min	Max	15%ile	85%ile
45/50 mph	Weekday
	12 AM − 3 AM	61.2	9.6	39	75	48	71
	3 AM − 6 AM	61.0	10.3	39	75	47	72
	6 AM − 9 AM	44.8	18.0	13	74	25	69
	9 AM − 12 PM	45.3	17.9	13	74	26	69
	12 PM − 3 PM	42.0	18.9	9	74	22	68
	3 PM − 6 PM	35.7	17.7	5	70	18	61
	6 PM − 9 PM	42.8	16.6	14	71	25	65
	9 PM − 12 AM	55.9	15.0	26	77	37	72
	Weekend
	12 AM − 3 AM	59.4	12.6	33	77	43	72
	3 AM − 6 AM	62.2	10.0	40	76	49	73
	6 AM − 9 AM	58.8	15.6	27	80	39	75
	9 AM − 12 PM	50.8	19.2	15	80	29	74
	12 PM − 3 PM	46.0	20.2	10	78	24	73
	3 PM − 6 PM	46.8	19.8	11	78	25	73
	6 PM − 9 PM	50.3	18.8	15	79	29	73
	9 PM − 12 AM	56.4	15.7	25	78	37	73

Table 7. Summary statistics of traffic speeds (mph) for 55 mph or 60 mph posted speed limit road links.

Speed limit cluster	Timespan	Mean	SD	Min	Max	15%ile	85%ile
55/60 mph	Weekday
	12 AM − 3 AM	63.9	6.4	46	81	58	70
	3 AM − 6 AM	64.4	5.9	49	79	58	71
	6 AM − 9 AM	55.1	13.5	18	93	39	67
	9 AM − 12 PM	58.8	9.4	31	85	49	67
	12 PM − 3 PM	55.3	12.8	20	90	40	67
	3 PM − 6 PM	47.8	17.6	3	99	26	65
	6 PM − 9 PM	58.5	11.1	27	89	46	68
	9 PM − 12 AM	63.1	7.0	43	81	56	70
	Weekend
	12 AM − 3 AM	64.3	7.0	45	83	58	71
	3 AM − 6 AM	65.2	7.0	46	84	58	72
	6 AM − 9 AM	65.8	7.0	46	84	59	73
	9 AM − 12 PM	62.7	8.8	36	87	54	71
	12 PM − 3 PM	58.1	12.4	23	93	44	69
	3 PM − 6 PM	58.1	12.4	23	93	44	69
	6 PM − 9 PM	61.5	9.1	35	86	52	70
	9 PM − 12 AM	63.6	6.9	44	82	57	70

Table 8. Summary statistics of traffic speeds (mph) for 65 mph or 70 mph posted speed limit road links.

Speed limit cluster	Timespan	Mean	SD	Min	Max	15%ile	85%ile
65/70 mph	Weekday
	12 AM − 3 AM	69.2	7.0	47	90	63	76
	3 AM − 6 AM	71.2	6.2	53	88	64	77
	6 AM − 9 AM	70.2	5.5	52	87	65	75
	9 AM − 12 PM	70.1	4.9	54	84	65	75
	12 PM − 3 PM	70.0	4.9	54	84	65	75
	3 PM − 6 PM	68.0	7.0	43	89	62	74
	6 PM − 9 PM	70.6	5.7	52	87	65	76
	9 PM − 12 AM	70.8	5.6	55	85	65	76
	Weekend
	12 AM − 3 AM	69.8	8.6	31	99	63	77
	3 AM − 6 AM	71.1	6.3	53	88	64	77
	6 AM − 9 AM	73.5	4.5	62	84	69	78
	9 AM − 12 PM	72.7	4.6	58	85	68	77
	12 PM − 3 PM	72.0	4.7	56	86	67	76
	3 PM − 6 PM	72.3	4.6	58	85	68	77
	6 PM − 9 PM	72.0	5.1	56	86	67	77
	9 PM − 12 AM	71.6	5.3	56	86	66	77

Figure 3. Correlations of traffic speed measures for weekdays.

Note: *, **, and *** indicate that the corresponding coefficients are significant at the 95%, 99%, and 99.9% confidence levels, respectively.

Table 9. Correlations between traffic speed measures for weekdays (12 PM to 3 PM).

Measure 1	Measure 2	Speed limit cluster (mph)
		25/30	35/40	45/50	55/60	65/70
Mean	SD	−0.24*	−0.11*	−0.64***	−0.40***	−0.13
Mean	15%ile	0.99***	0.98***	0.99***	0.97***	0.95***
Mean	85%ile	0.98***	0.98***	0.99***	0.98***	0.96***
Mean	RSP	0.69***	0.87***	0.83***	0.82***	0.78***
Mean	SPL	−0.06	−0.08	0.17*	0.21*	0.17
SD	15%ile	−0.37***	−0.27	−0.73***	−0.58***	−0.41***
SD	85%ile	−0.08	0.06	−0.54***	−0.20*	0.15
SD	RSP	−0.10	0.02	−0.50***	−0.07	−0.17
SD	SPL	0.16	−0.05	−0.11	−0.28***	0.05
15%ile	85%ile	0.95***	0.93***	0.97***	0.91***	0.83***
15%ile	RSP	0.68***	0.83***	0.82***	0.74***	0.75***
15%ile	SPL	−0.07	−0.07	0.16*	0.25**	0.14
85%ile	RSP	0.68***	0.86***	0.83***	0.86***	0.75***
85%ile	SPL	−0.07	−0.09	0.16*	0.17	0.19
RSP	SPL	−0.07	−0.03	0.17*	−0.03	0.28***
			≥0.5		>0 & <0.5
			≤ − 0.5		> −0.5 & <0

Note: *, **, and *** indicate that the corresponding coefficients are significant at the 95%, 99%, and 99.9% confidence levels, respectively. RSP is reference speed and SPL is posted speed limit.

Figure 4. Speed variations for weekdays between 9 AM and 12 PM.

Table 10. 65/70 mph posted speed limit road links of high-speed variations.

Time of the day	TMC code
Weekday
12 AM − 3 AM	N/A
3 AM − 6 AM	125N10200
6 AM − 9 AM	125N16944
9 AM − 12 PM	N/A
12 PM − 3 PM	N/A
3 PM − 6 PM	N/A
6 PM − 9 PM	N/A
9 PM − 12 AM	N/A
Weekend
12 AM − 3 AM	N/A
3 AM − 6 AM	N/A
6 AM − 9 AM	125N10200, 125N16944
9 AM − 12 PM	125P10200, 125N16944
12 PM − 3 PM	125N10200, 125P10200, 125N16944
3 PM − 6 PM	125N10200, 125P10200, 125N16944
6 PM − 9 PM	125N10200, 125N16944
9 PM − 12 AM	N/A

Note: N/A indicates the absence of any road link exhibiting high-speed variation.

Figure 5. Skewness-kurtosis plot for traffic speeds on the road link “125N10200” during the weekend time interval of 3 PM to 6 PM.

Figure 6. Goodness-of-fit plots of the candidate distributions fitted to the weekend time interval (3 PM to 6 PM) traffic speeds on the road link “125N10200”.

Table 11. Comparison of goodness-of-fit results for the weekend time interval (3 PM to 6 PM) traffic speeds on the road link ‘125N10200’.

Goodness-of-fit statistic	Gamma	Weibull	Log-normal	Log-logistic	Burr
Kolmogorov-Smirnov statistic	0.20	0.14	0.22	0.09	0.09
Cramer-von Mises statistic	40.86	17.09	55.17	5.81	5.20
Good-of-fit criteria (AIC)	22756.19	20477.35	23731.25	20176.99	19938.96
Good-of-fit criteria (BIC)	22768.62	20489.78	23743.68	20189.42	19957.61

He, S. X. (2016). Will a higher free-flow speed lead us to a less congested freeway? Transportation Research Part A: Policy and Practice, 85, 17–38. https://doi.org/10.1016/j.tra.2015.12.003

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Silvano, A. P., Koutsopoulos, H. N., & Farah, H. (2020). Free flow speed estimation: A probabilistic, latent approach. Impact of speed limit changes and road characteristics. Transportation Research Part A: Policy and Practice, 138, 283–298. https://doi.org/10.1016/j.tra.2020.05.024

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Yasanthi, R. G., & Mehran, B. (2020). Modeling free-flow speed variations under adverse road-weather conditions: Case of cold region highways. Case Studies on Transport Policy, 8(1), 22–30. https://doi.org/10.1016/j.cstp.2020.01.003

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Duvvuri, S. V., Mathew, S., Gouribhatla, R., & Pulugurtha, S. S. (2020). Identifying road links and variables influencing the applicability of variable speed limits using supervised machine learning and travel time data. Journal of Modern Mobility Systems, 1, 125–130. https://doi.org/10.13021/jmms.2020.2931

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