A method to estimate urban work zone intersection capacity under multiple influencing factors

. Work zones generate significant congestion in urban centers, yet the influence of various capacity factors in urban arterials and intersections are poorly understood. This paper analyzes the influence of the following factors on urban arterial and intersection work zone capacity from 22 intersections: heavy vehicle flow, heavy vehicle percentage, work zone length, maximum speed limit, entrance lane width, left turn volumes, entrance and exit lane width reductions, and intersection length and width. An urban work zone was modeled using VISSIM simulation software, and regression models were developed based on the reduction coefficients with MATLAB software for fitting analysis. The results show that the proposed model estimated work zone capacity with high accuracy. Urban work zones were found to reduce capacity by 64% in the selected arterial and by 35% in the selected intersection, with corresponding increases in delay and queue length. The model also estimates the capacity improvement that can be expected given various mitigation factors. Transportation agencies may find work zone capacity estimates useful when planning construction in critical urban centers.


Introduction
With rising urban populations, traffic congestion in city centers has become a serious challenge for transportation agencies [1].Underground rail transit provides one solution to alleviate congestion [2], but subway construction can be quite disruptive to surface transportation with construction that is extensive in both duration and geographic area.At the same time, personal vehicle travel is increasing.According to the Statistical Bulletin of National Economic and Social Development of Wuhan issued by Hubei Provincial Bureau of Statistics, 3,123,000 cars are owned in Wuhan as of 2018 [3].The increase in car ownership has resulted in a corresponding increase in traffic congestion, especially at urban intersections [4].Without accurate estimates of the impact of work zones on urban intersection capacity, transportation agencies are unable to plan for effective mitigation strategies, leaving them vulnerable to severe congestion and higher crash rates [5][6].
In recent years, researchers have investigated the factors affecting the road capacity near work zones.In 2003, Jiang et al [7] analyzed 17 factors influencing highway capacity through work zones.Yang Qingxiang [8] developed a capacity model of urban work zones by identifying and calibrating the main factors affecting throughput.Weng et al [9] established two speed-flow models for traffic congestion, and calibrated the model against highway work zone capacities.The new model took into account the number of work zones, the length of work zones, as well as other factors.Zhang et al [10] used in VISSIM to simulate capacity along different travel paths through work zones and the surrounding network, and used the optimal nonlinear fitting theory to construct the capacity function of different paths under various conditions.The results showed that capacity is significantly affected by truck traffic volume and vehicle speed limits.Under the same truck percentages, when the traffic volume is less than the critical traffic volume, the linear increase of congestion is gradual; when the traffic volume is greater than the critical traffic volume, congestion increases irregularly and rapidly.Under the same traffic load, work zone congestion increases with an increase in truck speed.When the traffic volume is less than the critical traffic volume, the difference is not significant.When traffic volume is greater than critical volume, the congestion gradually increases with truck speed.
While past research has investigated the factors influencing work zone capacity, there is little analysis in the literature on urban work zones, and even less on urban arterial intersections in work zones.In order to better study the influence of work zones on urban road capacity, this paper models a typical 8-lane intersection of urban arterial in a large commercial district with a subway construction work zone reducing a four-lane directional segment to three lanes.Based on VISSIM simulation analysis, the regression models of the capacity of road sections and intersections in the construction area are established, the capacity reduction ratio of the work zone is analyzed quantitatively, and corresponding mitigation strategies are proposed.

Change of traffic volume in a work zone
During the subway construction period, the work zone is often divided into four areas: warning area, upstream transition area, active work zone area, and downstream transition area.The traffic flow changes as vehicles traverse the four areas.When upstream vehicles enter the warning area, the vehicles slow down upon approaching the upstream transition area.Here, vehicles are diverted and merged, and the traffic capacity is further reduced.When the vehicles arrive at the active work zone, a lane is dropped at capacity is reduced further.Vehicle speeds increase when entering the downstream transition area, alleviating congestion.The traffic volume is presented in Fig. 1.

Analysis of traffic characteristics in an urban work zone 3.1 Traffic characteristics of the work zone
The modeled network is based on the ongoing Metro Line 8 phase II subway construction of a station at an intersection of a commercial district.The station is located close to the southern end of the intersection consisting of an 8-lane North-South arterial and with 3.5m wide lanes and a 3.1m wide entrance lane.The intersection is shown in Fig. 2.

Traffic data collection method
A field survey method was used to collect data from the intersection work zone such as the signal phasing, vehicle volumes, and bus schedules were extracted through video recording.The statistical manual method was used to develop the signal plan.The traffic volume of the work zone is shown in the Table 1.

Total vehicle flows at the entrance of intersection
The simulation model of the work zone was developed using VISSIM software, The following steps were taken to model and measure capacity of an urban work zone intersection.First, a CAD base map of the intersection in the work zone was drawn and saved as a JPEG which could then be imported into VISSIM.A road network was then developed in VISSIM based on the JPEG.according to Code for Design of Urban Road Engineering (CJJ 37-2012) [11] The design speed of the urban arterial is normally distributed between 40-60 km/h.The width of lane is 3.5m, the length of work zone is 202m, and truck percentage is 0% as large vehicles are not allowed to travel in the work zone during the day.The ratio of passenger cars to motorcycles is 7:3.The model's data collection point was set on the downstream lane of the work zone so that measurements obtained from this collection point could be used to estimate total capacity of the work zone.See Table 2 and Fig. 3 for details.According to Table 2, when the upstream traffic volume is greater than 1460 veh•h-1, the work zone reaches maximum capacity with no change with increased inflow.Therefore, the simulation output value 1421veh•h-1 can be regarded as the capacity of the intersection work zone for vehicles approaching from the south.

Influence of large vehicle volumes on work zone capacity
Compared with passenger vehicles, large vehicles such as trucks and buses have the characteristics of longer body, wider chassis, and slower speeds.Due to the tight geometrics in the work zone, larger vehicles are forced to maneuver more slowly than passenger vehicles, increasing congestion.Therefore, it is of great practical significance to evaluate the impact of heavy vehicle percentages on work zone capacity.The network was simulated under the following conditions: one-way four lane, closed inner three lanes within the work zone, work zone length of 202m, design speed of 50 km/h, large vehicle percentages of 0%, 5.8%, 10.8%, 15.8%, 20.8%, 25.8%, 30.8% respectively.See Table 3 for details.It can be seen from Table 3 that when the work zone volumes nears capacity, the maximum capacity of the intersection decreases with higher truck percentages.By using MATLAB software to fit and analyze the capacity reduction ratio and large vehicle rate, the relationship between capacity reduction ratio y and large vehicle ratio x can be obtained.A linear regression was conducted and the resulting relationship can be expressed as follows:  According to equation (1) and Fig. 4, the coefficient of determination is 0.9484, suggesting a good fit.

Influence of speed limits on work zone capacity
In a subway construction area, road workers and drivers both face risks from vehicle crashes.Therefore, it is of major practical significance to limit the speed of vehicles to reduce crashes.To assess the impact of speed limit reductions on capacity, the network was simulated across several speed limits.The simulation test conditions are as follows: the length of the work zone is 202m, the truck percentage is 0%, and the speed limit is set as described in the Table 4.The details are shown in the table below.It can be seen from Table 4 that when the speed limit is 10 km/h, the capacity of the construction section will be reduced by about 50%, so the speed limit in the work zone should balance safety with capacity.Therefore, the limited speed in the construction area can be raised appropriately, to avoid reducing the traffic capacity of the work zone significantly.Similarly, the fitting curve of the speed limit and capacity reduction percentage in the occupied area is shown in Fig. 5.The coefficient of determination of equation ( 2) is 0.8969.When R2 > 0.8, it is generally considered to have a strong correlation.From the fitting curve of speed and capacity reduction ratio in Fig. 5, the scattered points of simulation samples are roughly on the fitting curve, which suggests a good fit.The expression and fitting curve is as following:

Influence of work zone length on traffic capacity
Research and analysis show that the shorter the work zone is, the greater the capacity.To establish a precise relationship between urban work zone length and capacity, various work zone lengths were simulated.The simulation parameter settings were the same as in previous examples, with differences indicated in Table 5 and Fig. 6.From Table 5, the work zone capacity decreases with the increase of the length of the work zone, but the capacity decrease is gradual.Capacity was reduced by approximately 0.51 percentage points for every 100m increase in the construction length of the road occupied area.Similarly, the fitting curve of the length of the work zone and the percentage of capacity reduction is illustrated in Fig. 6.The coefficient of determination of equation ( 3) is 0.9899.Because R2=0.9899>0.8, and samples generally fit the curve in a visual inspection, the equation is found to be a good fit to describe the relationship between work zone length and capacity.

Capacity calculation of arterial work zone
Based on the analysis of the factors affecting urban work zone capacity, a model of the urban intersection work zone section capacity is proposed as follows: Where, C: actual capacity of the work zone, C0: basic capacity of operation area.fd: basic capacity of area without a work zone, fc: work zone length reduction factor, fs: speed limit reduction factor, fh: lane reduction factor, fk: lane width reduction factor, ff: non-motor vehicle percentage reduction factor.Using the modeled network, the work zone is 202m long, the vehicle speed is 50 km/h, and the proportion of large vehicles is 10.8%.The reduction ratios can be seen in Tables 3, 4 and 5. Taking the basic capacity of the road section into the above equation ( 4), the actual capacity of the road section with a work zone is 1323 veh/h, calculated as follows:

Capacity reduction
The measured capacity of this section before construction is 3712 veh/h, so the capacity reduction ratio is as follows: The capacity reduction ratio is about 64%, which indicates that the construction of a subway station occupying the intersection section will greatly reduce the capacity of the section.

Simulation analysis of factors affecting work zone intersection capacity 5.1 Intersection simulation modeling
The intersection simulation diagram is shown in Fig. 7. Intersections are critical nodes in urban networks, and their traffic capacities directly affect the capacity of connecting urban road segments [12].When a work zone is located close to the intersection, it will inevitably affect the capacity of the intersection.To establish the relationship between work zones and intersection capacity, 22 subway construction projects near signalized urban intersections were studied.Using these data, a mathematical model of the capacity of the intersection was established.Relationships between influencing factors and capacity were established using regression methods.By comparing the expected value from the regression model with the observed value, it was found that the two curve values are relatively close, which indicates that the model can accurately estimate the traffic capacity of work zone intersections.Finally, the simulation output was analyzed to evaluate queue length and intersection delay, and replacing the field survey data into the multivariate linear regression model to calculate the capacity reduction ratio of the intersection work zones.
Because the signal timing of each phase of intersection is different, the capacity cannot be directly calculated by standard formulas as the average saturation flow rate Sa of single lane assumes no signalized control.Therefore, the single lane saturation flow rate can be used for correlation analysis and modeling based on the Highway Capacity Manual's (HCM) [13]methodology for calculating signalized intersection capacity, which can then be adjusted to account for work zone impacts.Through the theory and method of correlation analysis, this paper studied the influence of the work zone on the capacity of the intersection, establishing the key factors affecting the capacity of the intersections with work zones [14].
The total capacity of an intersection is the sum of the capacities of each group of signalized lanes as follows: Where C i is the capacity of the i approach or lane group (vehicles/h); S i is the saturation flow rate (vehicle / Green hour); (g/t)i is the green signal ratio of the i approach or lane group, t is the total duration of one signal cycle of the i phase (s).Among them, saturation flow rate refers to the maximum allowable traffic flow (vehicle/h) under the assumption that the entrance road is green, which is independent of signal timing.

Correlation analysis
Past research has established that several factors impact capacities of work zones and intersections, such as entrance lane width, exit lane width, large vehicle percentages, the proportion of left turn vehicles, the proportion of right turn vehicles, non-motor vehicle volumes, lane drops and closures, and lane width reductions.In order to quantify the degree to which each factor affects capacity, simulations were run varying each factor to establish a mathematical relationship with capacity.Since the average saturation flow rate S a of a single lane is independent of signal timing, the correlation analysis and modeling of single lane saturation flow rate can be described as vector X=(x 1 ,x 2 ,.....x n ) T ,Y=(y 1 ,y 2 ,.....y n ) T with the correlation coefficient r calculated as follows:

Multiple linear regression model for work zone intersection capacity
According to the above correlation analysis, the stepwise regression method is used to select the independent variables of the saturated flow rate in the work zone.Uncorrelated factors are gradually screened out until the regression coefficients of each factor are statistically significant.The regression model results are shown in Table 7, and the multiple linear regression model is as follows: where S a is the average saturation flow rate of single lane, J k is the width of the entrance lane, Z c is the length of the intersection occupied by the work zone, Z k is the width of the intersection occupied by the work zone, D c is the proportion of large vehicles, Z z is the proportion of left turn vehicles, F j is the number of non-motor vehicles, J f is the isolation condition between motor vehicles and nonmotor vehicles, and J c is the reduction of the number of entrance and exit lanes.Constants a 0-8 are calibration parameters.According to Table 7, the critical value of the t statistic is t0.05(14)=1.7613.It can be seen from the table that the absolute values of t-test results for all variables are greater than 1.771, indicating that the regression coefficients corresponding to all variables are significant with 90% confidence.The independent variables selected in the model can accurately estimate the saturation flow rate of the intersection in the work zone.flow rate in the intersection work zone.Furthermore, the p-value is suggests that the findings are significant.The observed and estimated data are compared in Fig. 8.

Evaluation of intersection nodes
The work zone intersection node evaluation is conducted using the VISSIM simulation software, analyzing both queue length and delay.
It can be seen from Figure 9 that the average delay of vehicles at the intersection is about 55s, and the average queue length is about 80m.According to the service level classification standard of signalized intersections in China, this corresponds to a level of service grade of E. Prior to the beginning of construction, the intersection had a grade of C. The design capacity of the intersection before construction is 8506 veh/h, while the capacity of the intersection during construction is estimated to be 5523veh/h.Therefore, the capacity reduction ratio of the intersection is 35.1%.Capacity losses can be mitigated by restricting truck traffic, minimizing lane closures, maintaining lane widths, and reducing the length of the work zone.

Conclusion
This study evaluated the effect of various factors on the capacities of urban arterial segments and intersection during work zones.A model of an urban network with a work zone was simulated in VISSIM to test the impact of various geometric, design, and traffic factors.Regression models of the capacity of the intersection and segments in work zones were established.Mathematical relationships between factors and capacity were established allowing for the estimation of capacity for various work zone configurations.High-level findings were as follows: 1.When the input flow of the intersection reaches its capacity, the capacity of the work zone section decreases with an increase in large vehicle percentages.
2. The lower the speed limit of the work zone, the greater the reduction of the capacity of the work zone section.
3. The longer the work zone, the lower the capacity.4. According to the calibration results of multiple linear regression model parameters, the reduction of the number of lanes at the entrance and exit, the length and width of the intersection occupied by the work zone, the proportion of large vehicles, the number of nonmotor vehicles, and the proportion of left turn vehicles will greatly reduce the traffic capacity of the intersection.A reduction from four lanes to three lanes produces longer delays, long queue lengths, and a reduction in level of service (from C to E in the modeled network).Capacity of the modeled intersection was reduced by 35% with the introduction of the work zone.
I would like to thank my supervisor for his careful guidance and assistance in the implementation of my research project and thesis writing, as well as my classmates for their help in the experiment.Thanks to Education Department of Hebei Province and hope to continue cooperation in the future.

Fig. 1 .
Fig. 1.Change of accumulated traffic volume in work zone.

Fig. 3 .
Fig. 3. Simulation diagrams of lane reduction at the south entrance of intersection.

Fig. 4 .
Fig. 4. Linear relationship of large vehicle rate and capacity reduction ratio.

Fig. 6 .
Fig. 6.Fitting curves of work zone length capacity reduction ratio.

Table 1 .
Total flow at intersection entrance.

Table 2 .
Traffic simulation flows of work zone the road at the south entrance of intersection.

Table 3 .
Influence of vehicle occupancy rate on capacity of the south entrance road at intersection.

Table 4 .
Influence of speed limit on work zone capacity at the south entrance to the intersection.

Table 5 .
Influence of length of the work zone on capacity from the south entrance.

Table 6 .
Correlation matrix of influencing factors in road occupied construction area.

Table 7 .
Parameter calibrations of multivariate linear regression model.

Table 8 .
Statistical results of the regression model.

Table 8 ,
the goodness of fit of the adjusted regression model statistics is 0.920, which indicates that the above variables account for 92% of the change of saturation