Exploring Travel Time Distribution and Variability Patterns Using Probe Vehicle Data: Case Study in Beijing

Table 2

The goodness-of-fit test results of four road types during different periods.

Road types	Time periods		Distributions	Test methods			Average acceptance rates of			Best-fitted distribution
				Accepted by K-S (%)	Accepted by A-D (%)	Accepted by (%)	each distribution type (%)	each time period (%)	each road type (%)
Urban expressways	Weekdays	Peak hours 17:30–18:30	Normal	58.4	73.2	66.4	66.0	67.1	73.6	Lognormal
			Lognormal	60.4	75.2	69.6	68.4
			Gamma	58.4	73.6	69.6	67.2
			Weibull	56.8	70.4	73.2	66.8
		Off-peak hours 12:30–13:30	Normal	72.8	80.4	77.2	76.8	76.6		Lognormal
			Lognormal	77.6	84.0	79.6	80.4
			Gamma	73.6	82.0	76.0	77.2
			Weibull	65.2	75.6	74.8	71.9
	Weekends	Peak hours 15:00–16:00	Normal	70.0	83.0	76.0	76.3	76.9		Weibull
			Lognormal	72.0	84.0	75.0	77.0
			Gamma	70.0	83.0	76.0	76.3
			Weibull	75.0	80.0	79.0	78.0
		Off-peak hours 12:00–13:00	Normal	67.0	78.0	80.0	75.0	73.8		Lognormal
			Lognormal	70.0	78.0	80.0	76.0
			Gamma	70.0	78.0	79.0	75.7
			Weibull	61.0	72.0	73.0	68.7
Auxiliary roads of urban expressways	Weekdays	Peak hours 17:30–18:30	Normal	75.6	82.4	78.8	78.9	82.0	89.0	Lognormal
			Lognormal	83.2	88.8	87.2	86.4
			Gamma	78.8	88.4	85.6	84.3
			Weibull	73.6	80.8	80.8	78.4
		Off-peak hours 12:30–13:30	Normal	89.2	92.8	89.6	90.5	90.8		Lognormal
			Lognormal	90.8	95.2	90.8	92.3
			Gamma	91.2	93.6	90.0	91.6
			Weibull	88.0	91.2	86.8	88.7
	Weekends	Peak hours 10:00–11:00	Normal	90.0	92.0	88.0	90.0	90.4		Lognormal
			Lognormal	90.0	96.0	90.0	92.0
			Gamma	90.0	95.0	90.0	91.7
			Weibull	84.0	91.0	89.0	88.0
		Off-peak hours 13:30–14:30	Normal	94.0	95.0	89.0	92.7	92.7		Gamma
			Lognormal	93.0	96.0	90.0	93.0
			Gamma	94.0	96.0	91.0	93.7
			Weibull	93.0	93.0	88.0	91.3
Major roads	Weekdays	Peak hours 17:30–18:30	Normal	77.6	82.4	75.6	78.5	83.9	89.6	Lognormal
			Lognormal	87.6	92.0	86.4	88.7
			Gamma	85.2	88.0	84.4	85.9
			Weibull	82.8	85.2	79.2	82.4
		Off-peak hours 12:30–13:30	Normal	91.2	94.8	92.8	92.9	93.0		Lognormal
			Lognormal	94.8	96.8	93.6	95.1
			Gamma	92.8	95.6	92.0	93.5
			Weibull	87.6	91.2	93.2	90.7
	Weekends	Peak hours 15:30–16:30	Normal	87.0	89.0	85.0	87.0	88.8		Lognormal
			Lognormal	92.0	92.0	92.0	92.0
			Gamma	89.0	92.0	88.0	89.7
			Weibull	86.0	88.0	85.0	86.3
		Off-peak hours 12:30–13:30	Normal	94.0	97.0	89.0	93.3	92.8		Lognormal
			Lognormal	94.0	96.0	92.0	94.0
			Gamma	94.0	96.0	89.0	93.0
			Weibull	90.0	92.0	91.0	91.0
Secondary roads	Weekdays	Peak hours 17:00–18:00	Normal	52.4	63.2	64.4	60.0	66.7	70.4	Lognormal
			Lognormal	68.0	77.6	76.4	74.0
			Gamma	62.8	72.8	71.6	69.1
			Weibull	55.2	62.0	74.0	63.7
		Off-peak hours 12:30–13:30	Normal	62.4	70.8	70.0	67.7	71.6		Lognormal
			Lognormal	71.2	80.4	78.0	76.5
			Gamma	68.0	76.0	74.8	72.9
			Weibull	62.0	69.6	76.0	69.2
	Weekends	Peak hours 16:30–17:30	Normal	56.0	69.0	61.0	62.0	68.4		Lognormal
			Lognormal	68.0	78.0	75.0	73.7
			Gamma	66.0	75.0	74.0	71.7
			Weibull	59.0	67.0	73.0	66.3
		Off-peak hours 12:30–13:30	Normal	69.0	75.0	74.0	72.7	74.8		Lognormal
			Lognormal	79.0	84.0	78.0	80.3
			Gamma	76.0	81.0	72.0	76.3
			Weibull	63.0	75.0	72.0	70.0