J. Cent. South Univ. (2017) 24: 1513-1521

DOI: 10.1007/s11771-017-3555-0

Evaluation of mobility impact on urban work zones using statistical models

LIU Pei(刘培)¹, ZHANG Jian(张健)¹, QU Jun-rong(曲俊蓉)¹, LU Jia-jian(陆加健)¹,CHENG Yang(程阳)², TAN Hua-chun(谭华春)³

1. Jiangsu Key Laboratory of Urban ITS, Southeast University; Jiangsu Province Collaborative Innovation

Center of Modern Urban Traffic Technologies; Jiangsu Province Collaborative Innovation Center for

Technology and Application of Internet of Things, Southeast University, Nanjing 210096, China;

2. Traffic Operations and Safety (TOPS) Laboratory, Department of Civil and Environment Engineering,University of Wisconsin-Madison, Madison 53706, USA;

3. Department of Transportation Engineering, Beijing Institute of Technology, Beijing 100081, China

Central South University Press and Springer-Verlag Berlin Heidelberg 2017

Abstract: This work correlated the detailed work zone location and time data from the WisLCS system with the five-min inductive loop detector data. One-sample percentile value test and two-sample Kolmogorov-Smirnov (K-S) test were applied to compare the speed and flow characteristics between work zone and non-work zone conditions. Furthermore, we analyzed the mobility characteristics of freeway work zones within the urban area of Milwaukee, WI, USA. More than 50% of investigated work zones have experienced speed reduction and 15%-30% is necessary reduced volumes. Speed reduction was more significant within and at the downstream of work zones than at the upstream.

Key words: ITS data; mobility impact; work zone; statistical model

1 Introduction

A freeway work zone is “a segment of highway in which maintenance and construction operations impinge in the number of lanes available to traffic or affect the operational characteristics of traffic flowing through the segment [1]”. Work zone activities on freeways may cause both the mobility issues such as capacity drop, traffic breakdown, and safety issues e.g. rear-end and sideswiping crashes. In the U.S., work zones constitute 10% of the urban congestion, which translates into an annual fuel loss over $700 million [2]. In Germany, nonrecurring highway congestion as a result of work zone accounts for 30% of the nation’s traffic congestion [3]. Work zones account for nearly 24% of the nonrecurring delay in the U.S. The work zone safety issues also pose serious concerns. The U.S. had 87606 crashes in work zones in 2010, approximately 1.6% of the total number of roadway crashes [4]. Among those work zone related crashes, 0.6% were fatal crashes, 30% were injury crashes, and 69% were property damage only crashes, or one work zone injury every 14 min and one work zone fatality every 15 h.

This work focused on exploring the mobility impact of work zones. Readers can refer to Ref. [5] for a similar study on the work zone safety characteristics. Existing studies on the work zones mobility have focused on three main characteristics: speed reduction, queue length, and capacity. The speed reduction is usually studied through regression methods. BENEKOHAL et al [6] developed a model to determine speed reduction due to work intensity, narrow lanes and shoulders by using video data from 11 interstate highway work-zone sites in Illinois. ROUPHAIL and TIWARI [7] established a similar model and found that the observed mean speed at lane closure was 4.83 km/h (3 mph) lower than the predicted mean speed using non-work-zone data on average. The modeling of queue length at work zones includes two main methods, the deterministic queuing diagram method and the artificial intelligence method. Work zone capacity is also a critical mobility characteristic of interest. The Highway Capacity Manual (HCM) includes the short-term work zone capacity model originally developed by KRAMES and LOPEZ [8] who used data collected from 33 work zone sites in Texas between 1987 and 1991. Work zone capacity can be found within a 10% range of base value. According to the Iowa work zone data collected, MAZE et al [9] showed the volume was stable before and after queuing, whereas the average speed dropped. AL-KAISY et al [10] examined queue discharge flow as a measurement for long term work zone capacity with the data from Toronto, Canada. The observed capacity values were from 1800 pc/h/ln to 2050 pc/h/ln with a large variation. Linear regression [11] and decision tree models [12] can also be found in the literature as work zone modeling techniques.

In the existing studies, the data is a key limitation. Many traffic flow data were collected on-site by using video cameras and automatic counting system [6, 9, 11]; while others used manual process to correlate work zone data with the corresponding loop detector data [10, 12]. Meanwhile, many DOTs and statewide traffic data centers have improved or are in the process of improving the GIS functionality of their systems by geocoding the traffic detectors and operational data [13, 14]. The geo-referenced data sources create new opportunities to analyze work zone mobility characteristics on a large scale (e.g. the freeway system within an urban area) and conduct continuous monitoring and routine evaluation of work zone operations. The Traffic Operations and Safety (TOPS) lab [15] at the University of Wisconsin-Madison currently hosts an ITS data hub for the Wisconsin DOT(Department of Transportation). Using the data hub, we correlated the detailed work zone data with the 5-min loop detector data through a statewide linear referencing system to provide a comprehensive analysis of the mobility characteristics of work zones within the urban area of Milwaukee, WI, USA. we also used the one-sample and two-sample method to evaluate the work zone impact based on the distribution of speed and volumes.

2 Data source

The work zone and traffic data used in this work were collected from two sources: the Wisconsin Lane Closure System (WisLCS) [16] and VSPOC (volume, speed and occupancy) [17] data system. Both data sources are accessible through the WisTransPortal system developed and maintained by the TOPS laboratory at the University of Wisconsin-Madison. The Wisconsin State Trunk Network (STN) Linear Referencing System is a tool system, which includes centerline files, shape files, and tables for state and federal highways in Wisconsin.

The WisLCS provides a centralized management system for highway lane closures statewide since April 2008. The detailed information of each lane closure in Wisconsin includes work zone operation time, GIS information, work zone types, traffic impact etc. In this work, we retrieved all the work zones on the state highway system in Milwaukee areas in year 2010. The WisLCS returned 2297 work zones in Wisconsin during 2010 (See Fig. 1). 40% were freeway work zones, and 307 of which were located within the Milwaukee urban area. Among the 307 freeway work zones, 130 work zones were on the mainline, which were the main focus of this work.

TOPS lab has maintained a statewide, traffic detector data archiving and retrieving system for the Wisconsin Department of Transportation (WisDOT) Advanced Traffic Management System (ATMS) since 1997. The archived data contain five-minute volume, speed, and occupancy data obtained from WisDOT ATMS freeway detectors. The entire database is updated daily with data from the previous day. The V-SPOC (volume, speed, and occupancy) is a web-based interface for data query, data visualization, data exporting, quality reporting, and corridor analysis. Traffic data archived in this system include five main regions including North central, Northwest, Northeast, Southwest, and Southeast region. Milwaukee area is within the Southeast region which has 959 freeway count locations. It should be noted that in the Milwaukee area loop detectors on the freeway are all “traps” (dual loop detectors) which can provide an accurate reading of spot speed at the detector location.

Fig. 1 Wisconsin work zone locations

STN is a GIS database of centerline files, shape files, and tables for state and federal highways in Wisconsin. STN also includes an STN-Link and STN-Chain linear referencing representation that enables corridor based analysis. STN-Link is a straight line bi-directional representation of state highways with the accurate link length; while STN-chain is a curvature representation that matches the geometry of state highways.

3 Methodology

All loop detectors in the Milwaukee area have GIS coordinates including longitude and latitude, state plane, and the linear referencing coordinates in STN-Link and STN-Chain. Using the route and route offset information in the STN-Link system, each work zone can be spatially matched with detector locations that are within, at upstream, and at downstream of the work zone. A work zone can be located between two RPs, RP1 (r₁, o₁) and RP2 (r₂, o₂), where r₁ and r₂ are route IDs, o₁ and o₂ are the corresponding offsets on their routes, respectively. Assume the work zone duration is specified by a date range (d₁, d₂), and a time of day range (t₁, t₂), where d₁ and d₂ are the start and end date, t₁ and t₂ are the start and end time, respectively. Then, database views can be created to obtain the corresponding traffic data at time t on day d at location (r, o), where r and o are route ID and offset of the detector. The spatial matching scenarios are listed as follows.

Within,

r₁=r₂=r, and o₁≤o≤o₂                          (1)

Upstream,

r₁=r₂=r, and o₁-d≤o≤o₁                                      (2)

Downstream,

r₁=r₂=r, and o₂≤o≤o₂+d                        (3)

where d is the predefine buffer distance towards the upstream and downstream of a work zone. In this wrok, d=0.805 km (0.5 mile). Since the duration of a work zone is specified by a date range and a time range within a day, there are two temporal matching scenarios depending on the time order of t₁ and t₂.

Within midday:

d₁≤d≤d₂, and t₁≤t≤t₂                                          (4)

Passing midnight:

d₁≤d≤d₂, and t₂≤t, and t≤t₁                                  (5)

Field speed and volume readings may not always follow a specific type of distribution. Therefore, in this work, we selected statistical comparison methods that 1) do not assume specific underlying distributions, e.g. normal or student-T distribution; 2) do not require the calibration of specific types of distribution. Furthermore, two types of statistical tests were used to comprehensively evaluate the traffic impact of work zones for both the time-of-day differences and the collective traffic flow impact during work zone duration.

3.1 One-sample test based on percentile values

Denote the random variable of speed (or volume) at a 5-minute time interval i of the day as X⁽ⁱ⁾ within samples (x_n, n=1, …, N, where N is the total number of five-minute readings during the investigation time periods). In the one-sample test, evaluate if any measurement x_n⁽ⁱ⁾ during the period of a work zone is significantly different from the mean using the one-tailed or two-tailed tests. One-tailed tests evaluate whether significant impact on speed (or volume) occurs. Two-tailed tests identify significant speed (or volume) drop or increase.

Let be a reordering of {x_n}, s.t. Then, the significant values for the one-tailed and two-tailed tests can be calculated using the pth percentile value in the reordering. The index of freeway detector location is denoted as d, and D is the total number of work zone related detectors.

Given these notations, the pth percentile speed (or volume) of detector location d at the ith 5-minute time interval of the day can be calculated as

                           (6)

such that

m=[N_p]+1                                (7)

where N is the total number of days, and [N_p] is the greatest integer smaller or equal to N_p. Then, we applied the following hypothesis test using the empirical percentile values as the following.

H₀: there is no significant difference between the selected work zone data and the rest of data within the same distribution.

The One-sample test method compares the work zone traffic measures at each time interval of the day during the work zone period with the historical traffic state pattern.

3.2 Two-sample kolmogorov-smirnov (K-S) test

The two sample Kolmogorov-Smirnov (K-S) [18] test is based on the maximum difference between two cumulative functions. The method can effectively test whether the two underlying one-dimensional probability distributions are significantly different without fitting the data into a specific distribution. The traffic data from the same month of work zones were split into two sets, the work-zone and non-work-zone data. Denote the two work zone data sets as follows:

X_w={x_wd (d, i)|d∈ non work zone operation days, i∈ work zone operation time}                      (8)

X_n={x_d (d, i)|d∈non work zone operation days, i∈ work zone operation time}                          (9)

In order to test whether the work zone data samplehas the same cumulative distribution as that of non-work-zone data, K-S test uses the following statistics

                    (10)

where S_n(x)is the cumulative distribution function of work zone data. When D_n exceeds the critical values for confidence level a, the K-S test rejects the null hypothesis and reports greater than (or less than) for one-tailed test. The two-sample K-S test function was implemented in MATLAB.

4 Data processing and evaluation scenarios

The data processing procedure began with 130 candidate mainline work zones in the Milwaukee urban area. All work zones were first inspected for their traffic data availability. A series of detector quality screening criteria were executed using database view. The screening test eliminated about 56 work zones whose detector data were invalid 40% of the time. None of the long term work zones passed the availability test since the detectors usually were shut down during long-term road work in Milwaukee. Table 1 shows the detector data validity statistics within, upstream and downstream of different types of short-term work zones.

As shown in Table 1, the average valid rate of detector data among the selected work zones is around 61%. Detector data valid rate within a work zone is lower than that of the upstream and downstream. After breaking down the availability rate by lanes affected and peak or nonpeak hours, the valid rates of different categories are quite similar. The valid rate is lower at night which may be caused by the lower traffic volume. The volume and speed measurements were used to analyze the work zone mobility impact. Since the VSPOC data are lane-specific, at each count location, traffic data from all lanes were aggregated to form the approach volume and speed. Assume the detector reading for time t across lane l=1, …, L, can be denoted by q_l (t) and v_l(t), the approach volume q(t) and speed v(t) can be calculated as follows:

                             (11)

                    (12)

In this work, the mobility characteristics within, at upstream, and at downstream of work zones were investigated. Furthermore, for traffic flow upstream of a work zone, speed drop, volume drop, and volume increase were evaluated. For detector data within work zone, the key focus is to evaluate the performance reduction; hence only when the speed drop and volume drop tests were conducted, traffic data downstream can provide insights regarding the traffic flow discharged from work zone. The speed increase was included to capture the possible acceleration of traffic flow passing through the work zone location.

Table 1 Data validity rates of filtered work zones

5 Result analysis

5.1 One-sample test result analysis

The one-sample test examines whether the work-zone detector data fall into the significant tails of the historical distribution of non-work-zone detector data for the same time interval of day. A total of 74 work zones, 181 detector locations, and 16531 observations were examined to identify the mobility impact on speed and volume due to work zones.

Figure 2 illustrates the histogram of the percentages of the total number of time intervals rejected by the null hypothesis for each testing scenario. Based on the histogram, significant speed drop can be observed both within and upstream of many work zones with more than 80% of the work zones 20%-100% of the time during work zone period. Speed drop was also observed at downstream although the number of detectors available was not as many as those within and at the upstream of work zones. The speed increase at the downstream can be observed in half of the work zones 10%-50% of the time intervals during work zones. Figure 3 displays the percentage histogram for all volume testing scenarios which can be observed at many work zones. The percentages of time intervals with significant volume drop are less than 20%. About half the studied work zones experienced volume increase 10%-40% of the time during work zone. This may indicate the demand increase upstream induced by work zones.

5.2 Two-sample K-S test result

Among the 74 work zones, 18 work zones with the valid detector data at all three locations, upstream, within, and downstream were selected. The speed and volume at the three relative locations of 18 selected work zones were examined by K-S test at 0.05 confidence level. Table 2 lists the testing results for the speed in all 18 work zones. At the upstream location, four work zones experienced speed increase; while half of the work zones experienced speed decrease, indicating the effectiveness of temporal speed limit or the backward-propagated traffic congestion from the work zone location. Within work zones, 16 out of 18 work zones experienced significant speed drop when work zones were active. At the downstream location, travel speed in half of the work zones dropped significantly, indicating that vehicles exiting work zones did not resume their normal speed within 0.805 km (0.5 miles).

To further check the details of two-sample test results, the speed cumulative distribution function (CDF) plots of the K-S tests were evaluated. It can be observed that K-S tests are sensitive to the dominating relationship between the tested two CDF curves. As illustrated in Figs. 4(a, b, f), even though the decrease is only 3-5 km/h, K-S tests report significant test results. At the meantime, Figs. 4(c, d, e) exhibits significant differences in the speed CDF plot.

Fig. 2 Histogram of one-sample speed test:

Fig. 3 Histogram of one-sample volume test:

Table 2 Speed tests of two-sample test

Table 3 evaluates the volume test results at the three locations of a work zone. At the upstream location, traffic volume at 7 locations experienced decrease and remained unchanged for 8 and 9 work zone locations. At the downstream location, five work zones experienced volume drop; while the volume of the other work zones remained unchanged.

Figure 5 illustrates the CDF comparison results. Except for Fig. 5(d), significant difference between the distributions can be observed. In Fig. 5(d), even though the changes in volume are small, the dominance of the regular traffic volume over the work zone traffic volume can still be observed.

Table 4 compares the overall test results between one-sample and two-sample tests. The percentage within each cell was calculated by the number of work zones that were significant in a testing scenario over the total number of work zones. A work zone is only considered significant for the corresponding test scenarios if more than 30% of the time the null hypothesis is rejected. The results from both tests are consistent despite some minor discrepancies in describing the severity of speed drop and volume drop among the investigated work zones. The two-sample test may overestimate the speed or volume drops due to its sensitivity to the dominance relationship on CDF.

Fig. 4 Example of K-S speed test with work zone layout:

Table 3 Volume results of two-sample test

Fig. 5 Example of K-S volume test with work zone layout:

6 Conclusions

Two evaluation tools, one-sample percentile value test and the two-sample K-S test, were applied for work zone mobility monitoring and evaluation. Both tests can identify the work zone mobility impact by comparing work zone data and normal data without assuming specific types of statistical distribution. The spatial-temporal correlated WisLCS and VSPOC data from the WisTransPortal website were used as input to the evaluation tests. The mobility characteristics of freeway work zones in the Milwaukee area in 2010 were analyzed by using proposed tools. More than 50% of work zones experienced speed drop within and at the upstream of work zones. Such phenomenon may be caused by drivers’ compliance with the temporal work zone speed limit and possible congestion built up, or its propagation towards the upstream of the traffic flow.Speed increase can be observed in half of the work zones for 10%-50% of the time. The two-sample tests generated similar results, in spite of higher estimates on the number of work zones with volume drop. The overestimate may be caused by its high sensitivity to the domination of one CDF curve to another even with small overall differences.

Table 4 Percentage of work zones experiencing significant changes in speed or volume

Future work of this study may include the following directions. First, due to the strict screening criteria, many work zones with only partial valid data were eliminated. Since the employed methods are distribution based, exploring the work zone characteristics may still be possible for work zones with only partial detector data. Second parameters in the proposed tool such as the pth percentile, significant percentage threshold for one- sample test and the confidence level for two-sample test need to be calibrated and validated. Third, further improvement may be required to improve the K-S test methods to accommodate the situation when the CDF of one speed distribution is the same as the original one.

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(Edited by DENG Lü-xiang)

Cite this article as: LIU Pei, ZHANG Jian, QU Jun-rong, LU Jia-jian, CHENG Yang, TAN Hua-chun. Evaluation of mobility impact on urban work zones using statistical models [J]. Journal of Central South University, 2017, 24(6): 1513-1521. DOI: 10.1007/s11771-017-3555-0.

Foundation item: Project(61620106002) supported by the National Natural Science Foundation of China; Project(2016YFB0100906) supported by the National Key R&D Program in China; Project(2015364X16030) supported by the Information Technology Research Project of Ministry of Transport of China; Project(2242015K42132) supported by the Fundamental Sciences of Southeast University, China

Received date: 2016-12-15; Accepted date: 2017-04-01

Corresponding author: ZHANG Jian, PhD, Associate Professor; Tel: +86-25-83795356; E-mail: jianzhang@seu.edu.cn