Study on Tram Travel-Time Reliability Characteristics for Optimal Traffic Signal Control

Abstract

This paper quantitatively investigates the effects of the number of intersections between adjacent stations $(N)$ and different periods on tram travel-time reliability to provide a decision basis for adopting optimal signal-control methods. Station spacing data, intersection information on the line, 10 day planned operation schedules, and actual operation data of Zhangjiang tram line 1 were collected. The tram travel-time distributions were analyzed under seven typical scenarios (i.e., N = 0, 1, 2, 3, off-peak hours, morning peak hours, and evening peak hours). The results showed that the lognormal distribution described the tram travel time better than did the normal and gamma distributions. It was demonstrated that scenarios $N = 0$ , $N = 1$ , and off-peak hours were of high reliability; morning peak hours and evening peak hours were of medium reliability; and scenarios $N = 2$ and $N = 3$ were of low reliability. The unreliability of travel time increased along with the increase of the mean and the fluctuation of travel time. An optimized signal-control strategy based on travel-time reliability was put forward and VISSIM simulation of an interval was conducted, verifying the effectiveness of the proposed strategy. The findings will help tram-management agencies to adopt suitable and flexible signal-control strategies according to the actual varying condition.

Keywords

ram travel time reliability signal control lognormal model VISSIM

Travel-time reliability is an important indicator of traffic conditions and service, one which is influenced by many factors such as weather, tram rights-of-way (exclusive, non-exclusive, and semi-exclusive), traffic composition, road grades, line laying types, peak and off-peak hours ( 1 , 2 ). Many studies have been carried out on the distribution fitting of travel-time data to describe the characteristics of travel time. Common travel-time fitting models include normal, lognormal, gamma, beta, and Weibull distributions. Zou et al. ( 2 ) studied the effect of adverse weather on travel-time reliability, and the analysis showed that the lognormal distribution was the most capable of characterizing travel-time data. Herman and Lam ( 3 ) suggested using the gamma or lognormal distribution to characterize the travel-time distribution. Li et al. ( 4 ) studied the travel-time distribution of expressways and found that the beta distribution was the preferred fit for describing the distribution of routes with an obvious crest during peak hours. Emam and Al-Deek ( 5 ) suggested the Weibull distribution for fitting.

Modern trams are characterized by energy saving, environmental friendliness, and relative flexibility in line laying ( 6 ). However, trams face greater challenges to travel-time reliability and punctuality compared with other rail transportation because they usually share the road with other vehicles at the intersections ( 7 ). Therefore, it is necessary for modern trams to take priority at signalized intersections. Previous studies have proposed some signal-priority strategies from the perspective of improving transit punctuality, using different research methods. Ma et al. investigated and validated a new public-transport signal-control approach, CCBP (coordinated and conditional bus priority). The CCBP provided optimal priority strategies for late or early buses, based on predicted arrival time, to improve their arrival punctuality ( 8 ). Zhou et al. ( 9 ) developed an integrated optimization model for tram scheduling and signal priority to balance tram priority and social vehicles’ access by optimizing tram arrival time, departure time, and the location of the stop line. Zhang et al. ( 10 ) suggested an improved MULTIBAND trunk coordinated control scheme on tram lines and proposed a method for calculating the recommended speed to ensure the implementation of a green-wave band on the line. Considering travel-time variability when designing signal-control strategies is of great importance. Yin ( 11 ) proposed an analytical method to lower the standard deviation of delay and consequently improve the resilience of signal plans to changes in demand, which can be used at an isolated intersection. Based on Yin’s research, Zhang et al. ( 12 ) took several intersections along an arterial into consideration.

In conclusion, few studies have directly analyzed the effects of the number of intersections between adjacent stations, peak hours, and off-peak hours on the travel time of trams. There is also a lack of tram signal-priority strategies from the perspective of travel-time variation characteristics. Based on the existing studies on relative priority, absolute priority, and coordinated arterial control, the proposed signal-control strategy in this paper solves the problem of how to choose an optimal signal-control method at each intersection on the tram line under certain scenarios.

The remainder of this paper is structured as follows. The next section gives the definition of travel-time reliability of trams and analyzes the factors affecting tram travel-time reliability. Then, the relevant data, covering more than a week, are declared, and statistical analysis applied to quantitatively investigate the statistical effects of peak hours and the intersections in between adjacent stations on tram travel time, using three travel-time stochastic models, including normal, lognormal, and gamma distributions. After that, a tram signal-control strategy is proposed, based on the fitting results, and the VISSIM simulation models are established to compare the performance of the proposed signal-control strategy with the existing signal-control strategy at the intersections. The paper concludes with a summary of the findings and future work.

Methodology

Travel-time reliability can be used to describe the probability of arriving on time. Asakura and Kashiwadani ( 13 ) defined travel-time reliability as the probability of completing a trip within a specified time for a given origin–destination pair (OD) when the roadway capacity varies randomly. Researchers have summarized several travel-time reliability measures for quantitative analysis, which can be generally categorized into three types: the statistical index, the buffer time index, and the probabilistic index ( 14 ).

In this paper, we combine statistical analysis and probabilistic index to count and fit the Zhangjiang tram travel-time data under different scenarios. Then, from the perspective of the definition of travel-time reliability, we measure the probability of on-time arrival according to the timetable. Travel-time reliability is defined in Figure 1a and Equation 1. For example, the probability density functions of the distribution of travel times for scenarios A, B, and C are shown in Figure 1b. It can be concluded that the probability of on-time arrival and the travel-time reliability under scenario A is higher than that under scenarios B and C.

R_{(t)} = P_{(t \leq scheduledtime)}

(1)

where $R_{(t)}$ is the travel-time reliability when travel time of the tram is $t$ and $P_{(t \leq scheduledtime)}$ is the probability that the tram travel time is less than the scheduled time.

Figure 1.

Diagram of: (a) definition of tram travel-time reliability and (b) tram travel-time reliability under scenarios A, B, and C.

Modern tram travel-time reliability is influenced by various factors, divided into two major categories: static factors and dynamic factors. Static factors include rights-of-way, line laying, the distance between adjacent stations, vehicle characteristics, and so forth; dynamic factors include passenger demand, traffic-flow characteristics, signal-control methods, and so forth. Once a modern tram is built and operating, the static factors are basically unchanged, and the passenger-flow demand and signal-control method are assumed to be basically unchanged in the short term. So, the scenarios studied in this paper based on the collected data mainly consider the impact of changes in traffic-flow characteristics and the different number of intersections between adjacent stations on travel-time reliability. The studied seven scenarios are divided into two groups. Group 1 contains four scenarios: $N = 0$ , $N = 1$ , $N = 2$ , and $N = 3$ ( $N$ is the number of intersections between adjacent stations). Group 2 contains three scenarios: off-peak hours, morning peak hours, and evening peak hours.

Case Study

Testbed

Zhangjiang tram line 1 is the first modern tram line in Shanghai. The first and last stations of the upstream line are Zhangjiang subway station and Zhangdong Road Jinqiu Road respectively. The total length of the line is 9.2 km, with a total of 15 stations, and the line profile is shown in Figure 2.

Figure 2.

Map of Zhangjiang tram line 1 in Shanghai, China.

We collected the location information, station spacing data of 15 stations, and the intersection information of each interval. The planned schedule and actual operational data, including the arrival and departure times of trams in the upward direction from July 2, 2018 to July 11, 2018, were also obtained. Since the interval distances are different, it is difficult to carry out the analysis by directly comparing the travel times. So we choose to use travel time per kilometer unit, which can be obtained by calculating the ratio of travel time to distance between different ODs. The scheduled time between different ODs can be calculated according to the timetable and the station spacing data. The unit of travel time and scheduled time is minutes per kilometer (min/km).

Travel Time Statistical Analysis

Data Descriptive Statistics

Descriptive statistics of travel-time data under different scenarios are summarized in Table 1. The table indicates that when the number of intersections between adjacent stations increases, or from off-peak to peak hours, the average travel time and travel-time variability will increase. It should be emphasized that when analyzing tram travel time when $N$ varies in Group 1, the sample is the travel-time data of the interval (the line between two adjacent stations); when analyzing travel times during peak and off-peak hours in Group 2, the sample is the travel-time data of the whole line (from the first station to the last station). Travel-time data in Group 2 are calculated by the difference between the arrival time at the last station and the departure time from the first station of Zhangjiang tram line 1, including the stopping time at the intermediate stations, while travel-time data in Group 1 are calculated by the difference between the arrival time at station $i + 1$ and the departure time from station $i$ , not including the stopping time at the station. Therefore, travel times in Group 2 are generally greater than travel times in Group 1.

Table 1.

Summary Statistics of Tram Travel Time for Seven Scenarios

Scenario	Number of observations	Mean travel time (min/km)	Standard deviation of travel time (min/km)
(a) Group 1
N = 0	63	1.30	0.18
N = 1	53	1.52	0.26
N = 2	42	2.24	0.42
N = 3	59	2.34	0.51
(b) Group 2
Off-peak hours	30	3.70	0.23
Morning peak hours^a	31	3.88	0.24
Evening peak hours^b	31	3.86	0.28

Morning peak hours: 07:00 to 09:00.

Evening peak hours: 17:00 to 19:00.

Model Fitting

The histograms of frequency distributions were plotted as shown in Figures 3, a to d , and 4, a to c . The normal, lognormal, and gamma distributions were determined to fit the travel-time distribution according to the shape of the histograms. Figure 3, a to d , depicts the fitting situation of the interval travel time when $N$ is 0, 1, 2, and 3, respectively. Figure 4, a to c , depicts the fitting situation of the whole line travel time during the morning peak hours, evening peak hours, and off-peak hours.

Figure 3.

Distributions of travel times under scenarios: (a) N = 0, (b) N = 1, (c) N = 2, and (d) N = 3.

Figure 4.

Distributions of travel times during: (a) off-peak, (b) morning peak, and (c) evening peak hours.

The figures indicate that the tram travel-time data in different cases show skewed and long-tailed characteristics. The peak points of the fitted curve shift to the right and the distribution becomes more dispersed when the number of intersections between adjacent stations increases, or from off-peak hours to peak hours. This indicates that inter-station intersections and peak hours all have an impact on the tram travel time.

Statistical Tests

To determine the goodness of fit, the Kolmogorov–Smirnov modified test (K-S modified test) and Anderson–Darling test (A-D test) are applied in the analysis at the 5% significance level. The test results are given in Table 2. They show that the lognormal distribution fits the travel time better than the others do as, except for the cases of $N = 2$ , all instances pass both the modified K-S and A-D lognormal tests and have relatively large p-values. The test pass rates for the two groups of normal distributions are 65% and 83.3%, respectively; the test pass rates for the two groups of lognormal distribution are 87.5% and 100%, respectively; and the test pass rates for the two groups of gamma distributions are 65% and 100%, respectively. It can be concluded that the lognormal distribution is the preferred fit for travel-time data.

Table 2.

Results of K-S Modified Test and A-D Test at the 5% Significance Level

Type	Distribution	Goodness-of-fit tests	P-value	Decision at level (5%)
(a) Group 1
N = 0	Normal	K-S test (modified)	≤ 0.01	RE^a
		A-D test	0.1	AC^b
	Lognormal	K-S test (modified)	0.060	AC
		A-D test	0.41	AC
	Gamma	K-S test (modified)	0.049	RE
		A-D test	≥ 0.25	AC
N = 1	Normal	K-S test (modified)	> 0.15	AC
		A-D test	0.12	AC
	Lognormal	K-S test (modified)	> 0.15	AC
		A-D test	0.72	AC
	Gamma	K-S test (modified)	> 0.25	AC
		A-D test	≥ 0.25	AC
N = 2	Normal	K-S test (modified)	≤ 0.01	RE
		A-D test	2.59e-04	RE
	Lognormal	K-S test (modified)	0.061	AC
		A-D test	0.017	RE
	Gamma	K-S test (modified)	0.044	RE
		A-D test	0.0059	RE
N = 3	Normal	K-S test (modified)	> 0.15	AC
		A-D test	0.056	AC
	Lognormal	K-S test (modified)	> 0.15	AC
		A-D test	0.79	AC
	Gamma	K-S test (modified)	> 0.25	AC
		A-D test	≥ 0.25	AC
(b) Group 2
Off-peak hours	Normal	K-S test (modified)	> 0.15	AC
		A-D test	0.18	AC
	Lognormal	K-S test (modified)	> 0.15	AC
		A-D test	0.34	AC
	Gamma	K-S test (modified)	> 0.25	AC
		A-D test	≥ 0.25	AC
Morning peak hours	Normal	K-S test (modified)	0.044	RE
		A-D test	0.12	AC
	Lognormal	K-S test (modified)	0.08	AC
		A-D test	0.22	AC
	Gamma	K-S test (modified)	0.11	AC
		A-D test	0.21	AC
Evening peak hours	Normal	K-S test (modified)	> 0.15	AC
		A-D test	0.31	AC
	Lognormal	K-S test (modified)	> 0.15	AC
		A-D test	0.59	AC
	Gamma	K-S test (modified)	> 0.25	AC
		A-D test	≥ 0.25	AC

Note: K-S = Kolmogorov–Smirnov; A-D = Anderson–Darling.

“RE” means the distribution fit model is rejected.

“AC” means the distribution fit model is accepted.

Results Analysis

According to the definition of travel-time reliability (Equation 1), the values of travel-time reliability under seven scenarios are $R_{(N = 0)} = 0.99$ , $R_{(N = 1)} = 0.94$ , $R_{(N = 2)} = 0.24$ , $R_{(N = 3)} = 0.15$ , $R_{(off - peak hours)} = 0.91$ , $R_{(morning peak hours)} = 0.73$ , $R_{(evening peak hours)} = 0.73$ . The scenarios can be categorized into three types:

High reliability ( $0.8 < R \leq 1$ ): Scenario $N = 0$ , $N = 1$ , and off-peak hours;

Medium reliability ( $0.5 < R \leq 0.8$ ): Morning peak hours and evening peak hours;

Low reliability ( $0 < R \leq 0.5$ ): Scenario $N = 2$ and $N = 3$ .

Table 3 shows the fitting parameters of the lognormal distribution. The probability density function of the optimal distribution lognormal distribution is shown in Equation 2. According to Equation 2, $μ_{t}$ and $σ_{t}$ can be calculated by Equations 3 and 4 respectively. Table 4 summarizes the calculation results. Let $μ_{t}$ measure the average level of travel time during tram operation, and $σ_{t}$ measure the fluctuation of tram operation.

f (t) = \frac{1}{at \sqrt{2 π}} e^{- \frac{{(\ln t - b)}^{2}}{2 a^{2}}}

(2)

where $t$ is the tram travel time, $a$ is the standard deviation of $\ln t$ , and $b$ is the expected value of $\ln t$ .

μ_{t} = e^{(b + \frac{a^{2}}{2})}

(3)

σ_{t} = \sqrt{\exp (2 b + a^{2}) (\exp (a^{2}) - 1)}

(4)

where $μ_{t}$ and $σ_{t}$ are the expected value and standard deviation of tram travel time under the lognormal distribution.

As shown in Table 4, a decrease in travel-time reliability is accompanied by an increase in average travel time and fluctuation of the travel time.

Analysis of the mean travel time: When $N$ varies from 0 to 3, the increase rates of mean travel time are 17% ( $N = 0$ to $N = 1$ ), 47% ( $N = 1$ to $N = 2$ ), and 4% ( $N = 2$ to $N = 3$ ). The increase rates of mean travel time of another group are 5% (off-peak to morning peak) and 4% (off-peak to evening peak).

Analysis of the fluctuation of the travel time: When $N$ varies from 0 to 3, the increase rates of standard deviations are 21% ( $N = 0$ to $N = 1$ ), 58% ( $N = 1$ to $N = 2$ ), and 29% ( $N = 2$ to $N = 3$ ). The increase rates of standard deviations between groups are 9% (off-peak to morning peak) and 18% (off-peak to evening peak).

According to the above analysis, the conclusions and relevant improvement strategies are as follows:

Both $N$ values and peak hours have a large impact on travel-time reliability. The case of $N \geq 2$ needs to be focused on particularly. Compared with the off-peak travel-time reliability, the morning and evening peak travel-time reliability decreases by 20%. But compared with the case of $N = 1$ , the travel-time reliability of the case of $N = 2$ decreases by 74%.

The impact of $N$ values on travel-time reliability is reflected in the increase of the mean value and fluctuation of the travel time, and the impact of peak hours on travel-time reliability is mainly reflected in the increase of the fluctuation of the travel time. Although theoretically, the whole line has significantly more intersections than in any one interval, the fitting results show that $σ_{t}$ of the interval with three intersections is more than 0.5 min/km, which is higher than that in the whole line during peak hours and off-peak hours. In China, the actual situation is that trams are usually driven visually by tram drivers. The drivers are mainly responsible for controlling the speed and ensuring the safety of the tram. So, if the tram arrives late at station $i$ , the driver will speed up appropriately during interval $i$ (station $i$ to station $i + 1$ ). If the tram arrives at station $i$ earlier, the driver will slow down appropriately during interval $i$ (station $i$ to station $i + 1$ ) or stay at station $i$ for a short period of time. Since the $σ_{t}$ of the whole journey depends on the time at which the tram arrives at the last station, the various factors mentioned above lead to the easing of the travel-time standard deviation throughout the journey.

It is recommended to adopt signal-priority measures during peak hours and consider ensuring the traffic efficiency of social vehicles as much as possible. Especially in intervals with more than two intersections, it is necessary to increase the signal-priority level of trams and adjust the timetable accordingly to make trams operate more in line with the schedule, improving the travel-time reliability.

Table 3.

Fitting Parameters and Standard Error of the Lognormal Distribution

Type	Parameter	Standard Error
(a) Group 1
N = 0	$a = 0.139$	0.013
	$b = 0.256$	0.018
N = 1	$a = 0.165$	0.016
	$b = 0.406$	0.023
N = 2	$a = 0.176$	0.020
	$b = 0.791$	0.027
N = 3	$a = 0.209$	0.020
	$b = 0.827$	0.027
(b) Group 2
Off-peak hours	$a = 0.062$	0.008
	$b = 1.307$	0.011
Morning peak hours	$a = 0.061$	0.008
	$b = 1.355$	0.008
Evening peak hours	$a = 0.070$	0.009
		0.013

Table 4.

Expected Value and Standard Deviation of Tram Travel Time under the Lognormal Distribution

Type	Parameter
(a) Group 1
N = 0	$μ_{t} = 1.304$
N = 0	$σ_{t} = 0.208$
N = 1	$μ_{t} = 1.521$
N = 1	$σ_{t} = 0.252$
N = 2	$μ_{t} = 2.240$
N = 2	$σ_{t} = 0.398$
N = 3	$μ_{t} = 2.339$
N = 3	$σ_{t} = 0.512$
(b) Group 2
Off-peak hours	$μ_{t} = 3.702$
Off-peak hours	$σ_{t} = 0.231$
Morning peak hours	$μ_{t} = 3.882$
Morning peak hours	$σ_{t} = 0.236$
Evening peak hours	$μ_{t} = 3.865$
Evening peak hours	$σ_{t} = 0.273$

Analysis of Intersection Signal-Control Strategies

Intersection signal control of public transport can be divided in three ways according to priority design: no priority, relative priority, and absolute priority. As a type of public transport, trams usually run on relatively high-grade roads ( 15 ). In most cases, the types of intersections to which each of the three modes applies are as follows ( 15 – 17 ):

Absolute priority: Absolute priority is preferred at the intersection of an arterial and a branch road, especially when the traffic volume of the road on which the trams run is significantly higher than the traffic volume of the intersecting road. When the tram arrives at the intersection, the green light will be opened unconditionally and will be restored to the original control after the tram passes completely. Absolute priority can greatly improve the efficiency of modern trams at intersections.

Relative priority: Relative priority is preferred at the intersection of an arterial and a secondary road, especially when the traffic volume of the road on which the trams run is slightly higher than the traffic volume of the intersecting road. Relative priority has certain conditions attached to the signal changeover process compared with absolute priority. Moreover, relative priority also considers the operating situation of social vehicles and pays more attention to the overall effect of the intersection.

No priority: No priority is preferred at the intersection of an arterial with another arterial road, especially when the traffic volumes of the road on which the trams run and the intersecting road are both large. Based on the shortest green time needed to ensure the tram passes the intersection at the required speed, it has no priority and is controlled by the original signal.

In the analysis of travel-time fitting, it is concluded that travel-time volatility is influenced by two aspects. From the time perspective, morning and evening peak hours need to be focused on. From the spatial perspective, the intervals containing a high number of intersections need to be focused on. It is necessary to set up suitable signal-control strategies considering the two factors. Combining the fitting results with the analysis above, signal-control strategies are set for the different types of intersections during peak hours:

Type 1: When $N$ is relatively small $(N = 1)$ and the tram road grade is higher than the crossing road grade, absolute priority is given to the arterial–branch intersection, and relative priority is given to the arterial–secondary and the secondary–branch intersection.

Type 2: When $N$ is relatively small $(N = 1)$ and the tram road is of the same grade as the crossing road, relative priority is adopted.

Type 3: When $N$ is relatively small $(N = 1)$ and the tram road grade is lower than the crossing road grade, no priority is given.

Type 4: When $N$ is relatively high $(N \geq 2)$ , absolute priority is adopted if the tram road grade is higher than or the same as the crossing road grade.

Type 5: When $N$ is relatively high $(N \geq 2)$ and the tram road grade is lower than the crossing road grade, no priority is given to the branch–arterial intersection, and relative priority is given to the secondary–arterial and the branch–secondary intersection.

Additionally, when $N$ is relatively high $(N \geq 2)$ , coordinated control can be adopted in the interval instead of adopting priority at each intersection if the line conditions allow. To ensure the feasibility of a green-wave band on the tram line, trams’ right-of-way should be exclusive in the interval, reducing the interference to tram operation.

The basic logic of the signal-control strategies is illustrated in Figure 5. Based on the above principle, the signal-control method of each intersection on the line is determined. Taking Zhangjiang tram line 1 as an example, Table 5 shows the result, which can be implemented during peak hours, reducing the waiting time for trams stopping at the intersection and increasing the travel-time reliability.

Figure 5.

Basic logic of the recommended signal-control strategies.

Table 5.

Intersection Signal-Control Methods for Zhangjiang Tram Line 1 (Upward Direction)

No.	Interval	Intersection	Type of intersection^a	Signal-control method^b
1	Zhangjiang Metro Station–Bibo Road Gaoke Road	Bibo Road / Chenhui Road	S/B	(2)
2	Bibo Road Gaoke Road–Huatuo Road Darwin Road	Bibo Road / Central Gaoke Road	B/S	(2)
		Darwin Road / Huatuo Road	S/S	(1)
3	Huatuo Road Darwin Road–Huatuo Road Keyuan Road	Huatuo Road / Keyuan Road	B/S	(3)
4	Huatuo Road Keyuan Road–Cailun Road Jinke Road	Huatuo Road / Cailun Road	B/B	(2)
5	Cailun Road Jinke Road–Cailun Road Halley Road	Cailun Road / Jinke Road	B/A	(3)
		Cailun Road / Libing Road	B/B	(1)
		Cailun Road / Halley Road	B/B	(1)
6	Cailun Road Halley Road–Copernicus Road Libing Road	Cailun Road / Edison Road	B/B	(1)
		Cailun Road / Copernicus Road	B/S	(2)
		Copernicus Road / Libing Road	S/B	(1)
7	Copernicus Road Libing Road–Ziwei Road Gauss Road	Copernicus Road / Central Gaoke Road	S/A	(2)
		Ziwei Road / Gauss Road	B/B	(1)
8	Ziwei Road Gauss Road–Gauss Road Zhangjiang Road	None	None	None
9	Gauss Road Zhangjiang Road–Zhangjiang Middle School	Gauss Road / Zhangjiang Road	S/S	(1)
		Guanglan Road / Ziwei Road	S/S	(1)
10	Zhangjiang Middle School–Guanglan Road Zuchongzhi Road	Guanglan Road / Zuchongzhi Road	S/S	(2)
11	Guanglan Road Zuchongzhi Road–Guanglan Road Dangui Road	Guanglan Road / Qingtong Road	S/B	(1)
		Guanglan Road / Dangui Road	S/B	(1)
12	Guanglan Road Dangui Road–Dangui Road Qingtong Road	Dangui Road / Qingtong Road	B/B	(2)
13	Dangui Road Qingtong Road–Dangui Road Zhangdong Road	Dangui Road / Shenjiang Road	B/A	(3)
		Dangui Road / Zhangdong Road	B/S	(2)
14	Dangui Road Zhangdong Road–Zhangdong Road Jinqiu Road	None	None	None

Note: No. = number.

“A” indicates an artery, “S” indicates a secondary road, and “B” indicates a branch road.

“(1)” indicates absolute priority or coordinated control, “(2)” indicates relative priority, and “(3)” indicates no priority.

Simulation

Study Interval

VISSIM is a simulation modeling tool based on microscopic and driving behaviors that can be used to simulate and analyze the operation of different types of vehicle operations under various traffic conditions. The interval simulated in VISSIM is Cailun Road Jinke Road–Cailun Road Halley Road of Zhangjiang tram line 1, which has a length of about 0.9 km, the line profile being shown in Figure 6. Each intersection normally has two or three phases. The signal timing schemes at the three intersections are predetermined in SCATS (Sydney Coordinated Adaptive Traffic System) based on the changes in social traffic flow, without giving priority to the trams at the intersections. The track line of Zhangjiang tram line 1 is arranged in the middle of the road, and the right-of-way is non-exclusive, sharing the same phase with vehicles traveling in the east–west direction.

Figure 6.

The simulated interval of Zhangjiang tram line 1 $(N = 3)$ .

To meet the simulation needs in VISSIM, the traffic flow, road conditions, and signal timing plan at the three intersections were investigated on October 24, 2022, during the peak hours and off-peak hours. Since SCATS was used at all three intersections and the timing scheme varied dynamically with the traffic flow, the data of signal phase time during the morning peak, evening peak and off-peak hours (07:55–08:55, 12:30–13:30, 17:20–18:20) were collected, and the cycle time and the green time of each phase were averaged separately as the existing signal-control strategy, as shown in Table 6. According to the proposed strategy in Table 5, the tram does not take priority at intersection 1, keeping the original fixed signal timing after averaging, and should have absolute priority at intersections 2 and 3. Absolute priority can be achieved by the VISVAP module attached to VISSIM, which has three forms: insertion phase, green-light extension, and red-light early interruption.

Table 6.

Current Signal Timing of Three Intersections

Type	Cycle time (s)	Stage 1 (s)	Stage 2 (s)	Stage 3 (s)
(a) Intersection 1: Cailun Road / Jinke Road
Off-peak hours	168	39	101	28
Morning peak hours	186	40	114	32
Evening peak hours	181	42	110	29
(b) Intersection 2: Cailun Road / Libing Road
Off-peak hours	100	59	41	na
Morning peak hours	114	72	42	na
Evening peak hours	119	72	47	na
(c) Intersection 3: Cailun Road / Halley Road
Off-peak hours	86	56	30	na
Morning peak hours	125	76	49	na
Evening peak hours	132	78	54	na

Note: na = not applicable.

Simulation Model

The Wiedemann model is integrated into VISSIM as its core model, in which Wiedemann-74 (W74) is for urban roads, and Wiedemann-99 (W99) is for highways ( 18 ). Since trams run on urban roads, Wiedemann-74 (W74) is selected as the car-following model in simulation, and the default lane-change behavior is accepted.

According to the above testbed, the simulation model is established. The main steps are as follows:

Delineate the simulated interval through the field surveys and map website, as shown in Figure 7.

Configure the basic parameters of trams, including the length, desired speed, desired acceleration, and deceleration.

Set traffic flow and traffic compositions during peak hours and off-peak hours respectively.

Configure vehicle routes.

Set signal controllers of each intersection and achieve absolute priority at intersections 2 and 3 by VISVAP.

Set detectors on the road to collect the data that need to be analyzed.

Test the simulation model (Figure 8) and correct errors.

Travel-time detectors were set at Cailun Road Jinke Road and Cailun Road Halley Road stations in the upward direction (from west to east), recording the travel times and delays of the trams between the stations. Travel-time detectors were also set at all three intersections in the north–south straight road section with a length of 100 m, and the data collected included travel times and delays of all vehicle types, which can be used to indicate the operation of the conflicting directions.

Figure 7.

Sketch of the interval in VISSIM simulation.

Figure 8.

Screenshot of the simulation at intersection 2.

Results.

The simulation was divided into six groups, simulating the performance of trams and other vehicles during the off-peak, morning peak, and evening peak periods under the existing and proposed strategies, respectively. All elements of the six models were the same except for the signal-control strategy, traffic flow, and the departure interval of trams. The travel-time and -delay data were obtained by running several simulations. The results are shown in Table 7 and visualized as shown in Figure 9, a and b .

As shown in Figure 9a, implementation of the priority strategy has significant efficiency superiority over the existing strategy, with the average interval travel times reduced by 24%, 26%, and 28%, and the standard deviations of travel times reduced by 16%, 39%, and 45% during the off-peak, morning peak, and evening peak periods respectively.

Figure 9b illustrates that compared with the existing strategy, the implementation of the priority strategy results in an increase in the average delay of other vehicles on the crossing roads, but not significantly, about 0 to 5.2 s.

Table 7.

Data from VISSIM Output

		Tram travel time		Mean delay of intersecting roads (s)
Strategy	Type	Mean (s)	Standard deviation (s)	Intersection 1	Intersection 2	Intersection 3
Current strategy	Off-peak hours	145.12	25.29	13.13	20.75	19.05
	Morning peak hours	157.20	34.68	15.65	17.83	27.12
	Evening peak hours	157.54	36.55	16.13	16.32	23.59
Proposed strategy	Off-peak hours	110.74	21.25	18.19	21.06	20.93
	Morning peak hours	116.78	21.31	20.85	20.83	27.75
	Evening peak hours	113.08	20.03	21.28	17.19	26.93

Figure 9.

(a) Average delay of the intersecting roads and (b) mean and standard deviation of tram travel time in VISSIM simulation.

Overall, the proposed strategy effectively improves the tram operation efficiency, especially during peak periods. Although it causes more delays for social vehicles on the crossing roads, tram travel times are greatly reduced. In considering that trams are characterized by energy saving, environmental friendliness and large passenger capacity ( 6 ), the overall traffic benefit of the simulation interval is improved.

Summary and Discussions

This paper studied the effects of intervals with different numbers of intersections, and of peak and off-peak hours, on tram travel times, based on the operating data, timetable, and station information of Zhangjiang tram line 1.

Three models (normal, lognormal, and gamma distribution) were used to fit the distribution of travel times under seven scenarios. Comparing the results of the modified K-S test and A-D test, the lognormal distribution was the best fit.

Travel-time reliability under different scenarios was calculated under the lognormal distribution. Scenario $N = 0$ , $N = 1$ , and off-peak hours were of high reliability $(0.8 < R \leq 1)$ ; morning peak hours and evening peak hours were of medium reliability $(0.5 < R \leq 0.8)$ ; scenario $N = 2$ and $N = 3$ were of low reliability $(0 < R \leq 0.5)$ . Results indicated that both intervals having a relatively high number of intersections $(N \geq 2)$ and peak hours have a large impact on the travel-time reliability.

Based on the fitting parameters of the lognormal distribution, the mean and standard deviation of tram travel times were calculated and analyzed. The results indicated that the bigger $N$ values significantly increase the mean and the fluctuation of travel time per unit kilometer; during peak hours, the fluctuation of travel times per unit kilometer significantly increases compared with off-peak hours.

A signal-control scheme based on the tram travel-time analysis was set up, which can be used combined with timetable optimization to improve the travel-time reliability of trams.

There are two contributions in this paper. The first is finding a way to improve tram travel-time reliability and punctuality, which is helpful to improve the quality of service and provides a reference for tram-management agencies to set up signal-control methods. The second is proposing the preferable travel-time stochastic models for trams under different scenarios, which can provide a base for future research.

This work also points to a future research direction that we aim to pursue. Data with a longer period can be obtained to explore the effects of weather, season, epidemic, and other factors on tram travel-time reliability to further refine the signal-control strategy. In the simulation, the interference of pedestrians and non-motorized vehicles on tram operation is not considered, and field investigations can be combined to improve the model further.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: S. Lijuan, C. Yuntao, Z. Siqi, Z. Qirui; data collection: S. Lijuan, Z. Siqi, Z. Qirui, C. Yuntao; analysis and interpretation of results: Z. Siqi, S. Lijuan, C. Yuntao, Z. Qirui; draft manuscript preparation: Z. Siqi, S. Lijuan, C. Yuntao, Z. Qirui. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to acknowledge the support of the following research programs: Research and development of tram operation dispatching management system for the whole life cycle (No.19210730300), which is Scientific Research Project of Shanghai International Science and Technology Cooperation Fund Project funded by Shanghai Science and Technology Committee (STCSM). Research and Application Demonstration of key Technologies of Smart Freeway (No.2020C01057), Key Research and Development Plan of Zhejiang Province funded by Science and Technology Department of Zhejiang Province.

ORCID iDs

Lijuan Shi

Siqi Zhou

Yuntao Chang

Qirui Zhang

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