analytical methods for deriving work zone capacities from field data

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ANALYTICAL METHODS FOR DERIVING WORK ZONE CAPACITIES 1 FROM FIELD DATA 2 3 Jalil Kianfar 4 Ph.D. Student, 5 E1511 Lafferre Hall 6 University of Missouri-Columbia 7 Columbia, Missouri 65201 8 [email protected] 9 Fax: 573-882-4784 10 11 Praveen Edara*, Ph.D. 12 Assistant Professor 13 E3502 Lafferre Hall 14 University of Missouri-Columbia 15 Columbia, Missouri 65201 16 [email protected] 17 Tel: 573-882-1900 18 Fax: 573-882-4784 19 20 Carlos Sun, Ph.D., P.E. 21 Associate Professor 22 E2509 Lafferre Hall 23 University of Missouri-Columbia 24 Columbia, Missouri 65201 25 [email protected] 26 Tel: 573-884-6330 27 Fax: 573-882-4784 28 29 Submission Date: July 31, 2010 30 Word Count: 7750 (5750 text plus 2000 (4 figures and 4 tables)) 31 32 33 * Corresponding author 34 35 36

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Analytical Methods for Deriving Work Zone Capacities From Field Data

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Page 1: Analytical Methods for Deriving Work Zone Capacities From Field Data

ANALYTICAL METHODS FOR DERIVING WORK ZONE CAPACITIES 1

FROM FIELD DATA 2 3

Jalil Kianfar 4 Ph.D. Student, 5

E1511 Lafferre Hall 6 University of Missouri-Columbia 7

Columbia, Missouri 65201 8 [email protected] 9 Fax: 573-882-4784 10

11 Praveen Edara*, Ph.D. 12

Assistant Professor 13 E3502 Lafferre Hall 14

University of Missouri-Columbia 15 Columbia, Missouri 65201 16

[email protected] 17 Tel: 573-882-1900 18 Fax: 573-882-4784 19

20 Carlos Sun, Ph.D., P.E. 21

Associate Professor 22 E2509 Lafferre Hall 23

University of Missouri-Columbia 24 Columbia, Missouri 65201 25

[email protected] 26 Tel: 573-884-6330 27 Fax: 573-882-4784 28

29 Submission Date: July 31, 2010 30

Word Count: 7750 (5750 text plus 2000 (4 figures and 4 tables)) 31 32 33

* Corresponding author 34 35

36

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ABSTRACT 1

This paper compares work zone capacity values determined from field data using different capacity 2 definitions. Three different methods were used: 1) maximum sustained flow method, 2) re-scaled 3 cumulative flow curves method, and 3) 85th percentile method. To our knowledge, this is the first 4 application of the re-scaled cumulative curves method to work zones. Field data was collected at four 5 short-term work zones on two lane sections of I-70 in Missouri. 6

The study findings showed that the maximum sustained flows decreased as the aggregation 7 interval increased from 5 to 15 minutes. The queue discharge flow (QDF) values were the most 8 conservative estimates of capacity. The 85th percentile flows were lower than the 15-min sustained flow 9 values in all but one location where the 85th percentile flow was slightly higher by 4 vphpl. The pre-queue 10 flow (PQF) values, indicative of near-constant flow prior to breakdown, did not occur in any of the four 11 work zones. This finding has implications on the design of traffic control methods to alleviate work zone 12 congestion. The existence of PQF and its corresponding probability of breakdown have been exploited in 13 the design of ramp metering on freeways. The success of such methods in short-term work zones is 14 questionable due to the absence of PQF. 15

The average capacities obtained by averaging values from all four sites were 1301, 1149, 1267 16 vphpl, for 15-min sustained flow, QDF, and 85th percentile flow, respectively, which were close to the 17 capacity value of 1240 vphpl currently used by Missouri DOT. 18

19

20

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INTRODUCTION 1

A considerable amount of research has been conducted in the area of work zone capacity estimation. 2 Analytical (1), regression (2), neural network (3), and other models have been developed using observed 3 values of capacities at work zones. Different definitions of capacity were used to determine capacity 4 values from field studies. In this paper, capacity values obtained using different definitions of capacity are 5 compared. Re-scaled cumulative flow curves (4), a popular technique for analyzing freeway bottlenecks, 6 is used to evaluating work zone bottlenecks. Field data was collected at four work zones on two lane 7 sections of I-70 in Missouri. The main objective of this paper is to present different methods based on 8 different definitions of capacity to compute capacity from field data. The study goal was not to develop 9 capacity estimation models (e.g., regression) but to compare different methods of extracting capacity 10 information from the field data which will serve as the training (or estimating) data for capacity 11 estimation models. 12

The paper is organized as follows. First, a review of the state of the practice in work zone 13 capacity studies is conducted. This involves a literature review and a state department of transportation 14 (DOT) survey that was administered to 50 states using a web service. Second, field studies are described 15 along with details of data collection and processing. Third, three methods of capacity computation are 16 applied using the collected field data. The first method is the maximum sustained flow method, the 17 second is the new (to work zones) re-scaled cumulative flow curves method, and the third method is the 18 85th percentile method which is also recently proposed in the literature. Conclusions are drawn in the final 19 section. 20

REVIEW OF STATE OF THE PRACTICE 21

A review of state of the practice in work zone capacity was conducted. First, the literature on work zone 22 capacity estimation was reviewed focusing on empirical studies and methods used to estimate capacity. 23 Then, a questionnaire survey was prepared and sent to 50 state DOTs to obtain knowledge of their current 24 practices in work zone capacity estimation. 25

Literature Review 26

Roadway capacities at work zones are lower than the capacities under normal operating conditions as 27 reported by Dudek and Richards (5) from the findings of capacity studies at 37 sites in Texas. The ranges 28 of observed work zone capacities for six lane closure were reported. These data were used to develop a 29 chart showing the cumulative distribution of the work zone capacities. The Highway Capacity Manual 30 (HCM) 1994 (6) (and 1985, 1987, 1993, 1998 editions) incorporated this chart as a procedure to 31 determine the capacity at work zones. 32

Krammes and Lopez (7) conducted research on work zones in major urban areas in Texas 33 (Austin, Dallas, Houston, and San Antonio) where extensive frontage roads running parallel with the 34 freeway function as an alternative to bypass the congested freeway conditions. Data were collected at 33 35 sites between 1987 and 1991 to update the capacity values for short-term freeway work zone lane 36 closures. The researchers found that the new capacity values of short-term freeway work zone lane 37 closures of 2 to 1 and 3 to 2 were significantly higher than the values reported in HCM 1994. HCM 2000 38 incorporated these findings. Unlike the capacity charts used in HCM 1994, a base capacity value of 1,600 39 pcphpl is used for capacity computations in HCM 2000. This base value is adjusted through the 40 application of adjustment factors. Using professional judgment and simple empirical equations, the 41 adjustment factors account for intensity of work activity, effect of heavy vehicles, and presence of ramps 42 in close proximity to the work zone. 43

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Dixon and Hummer (8) conducted capacity studies at North Carolina work zones as they believed 1 that the capacity values reported in HCM 1994 were applicable only to Texas. They collected capacity 2 data at 24 short-term freeway work zones during 1994 and 1995. They found that North Carolina work 3 zone capacities were higher than the HCM capacities by at least 10 percent. 4

Karim and Adeli (3) developed a neural network-based tool for the estimation of capacity and 5 delay at work zones. The model considers 11 parameters in the estimation of capacity including number 6 of lanes, number of open lanes, layout, percent trucks, grade, and intensity of work. The justification for 7 using neural networks for this problem is that the functional form of the relationship between capacity and 8 the identified independent variables is not known. This model is incorporated into a decision support 9 system, IntelliZone (9), which is easy to use and quick to estimate results. After estimating the capacity, 10 IntelliZone uses a deterministic queuing model to predict the queue length and delay. 11

Al-Kaisy and Hall (10) studied freeway capacities at six long-term work zone sites in Ontario, 12 Canada. They found that all six sites had base capacity values lower than the HCM base capacity value. A 13 generic capacity model having a multiplicative form was proposed for capacity estimation at long-term 14 work zones, as it produced better estimates for the effect of heavy vehicles when compared to the 15 estimates of the additive form model. 16

Sarasua et al. (11) conducted a study to determine the base capacity of short-term freeway work 17 zones in South Carolina and eventually to determine the work zone capacity using equations derived from 18 HCM 2000. Traffic volume, speed, and queue length data were collected at 22 sites on four interstates 19 over a 1-year period. A straight line was fitted between speed and density based on linear regression. 20 Using this equation along with the speed-flow-density relationship, the maximum value of flow, i.e., base 21 capacity, was obtained. This base capacity value (1,460 pcphpl) was much higher than the threshold lane 22 volume (1,230 pcphpl) currently used by the South Carolina DOT for deciding lane closure times. 23

Schnell et al. (12) evaluated traffic flow analysis tools applied to work zones. Highway Capacity 24 Software (HCS), Synchro, CORSIM, NetSim, QUEWZ 92, and the Ohio DOT spreadsheet were used to 25 estimate the capacity and queue length at four work zones on multilane freeways in Ohio. The results 26 were compared with the field data. The simulation models could not be calibrated for oversaturated 27 conditions that existed at the work zones, and even after calibration for other conditions, these models 28 consistently underpredicted the queue lengths. They found that QUEWZ 92 was the most accurate in 29 estimating the work zone capacity. When this capacity estimate was used in the Ohio DOT spreadsheet, 30 it produced the most realistic estimates of queue lengths as compared to the estimates from other tools. 31

Chitturi and Benekohal (13) compared the performance of QUEWZ 92, FRESIM, and QuickZone 32 with field data at 11 freeway work zone locations in Illinois. Some of these work zones did not have 33 queues. The results of the study showed that none of these models gave an accurate representation of real 34 field conditions. QUEWZ 92 overestimated the capacity and underestimated the queue lengths, mainly 35 because of its use of an outdated speed-flow relationship. FRESIM consistently overestimated the speeds 36 under queuing conditions, overestimated the queue lengths for half of the cases, and underestimated the 37 queue lengths for the other half of the cases. QuickZone consistently underpredicted the queue length and 38 delay as compared to the field data. 39

Kim et al. (2) developed a multiple regression model to estimate the capacity at work zones as a 40 function of several key independent variables such as number of closed lanes, percentage of heavy 41 vehicles, grade, and work intensity. To develop this model they collected data at 12 work zone sites in 42 Maryland. They found that their regression model produced better estimates as compared to the HCM 43 model. 44

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Sarasua et al. (14) proposed two methods to estimate capacities at short-term work zones in South 1 Carolina. The first method used curve fitting to establish speed-density-flow relationship in work zones 2 and derived capacity as the maximum flow from the speed-flow curve. They reported that the parabolic 3 curve of speed-flow overestimated the capacity compared to observed capacities. To address this issue, 4 they proposed an alternative method that uses the 85th percentile volume as capacity. 5

Xing et al. (15) analyzed the work zone capacities of expressways in Japan. They used two 6 definitions of capacity: 1) breakdown flow which is the 15-minute flow rate immediately before the 5-7 minute space-mean speed decreases below 25 mph at a point immediately upstream of a bottleneck and 2) 8 queue discharge flow which is the average flow rate discharged during the congested conditions at 9 bottleneck. 10

Nikolic et al. (16) estimated the work zone capacities on single lane expressways outside Toronto. 11 They used three methods: 1) direct estimation of capacity by identifying the maximum five-minute flows 12 while queuing conditions were present, 2) estimation using time headways for different vehicle type 13 combinations and their proportions and 3) estimation from the VISSIM microscopic simulation model, 14

In summary, several studies involved extensive field data collection at work zones and extraction 15 of capacity information from the collected data. The primary focus of most of these studies was to 16 develop a capacity estimation model, from the field data, that could be used for estimating capacity at 17 other similar work zones without observing the actual traffic flows. These studies assumed a certain 18 definition of capacity (e.g., 15 minute sustained flow) in estimating the models. The contribution of this 19 paper is to illustrate the differences in capacity values obtained from different capacity definitions. This is 20 important in two ways. First, when comparing capacity values of different work zones, the amount of 21 variation that can be attributed to the difference in capacity definition will be known. Second, the 22 differences in the predicted values obtained from capacity estimation models that are estimated using 23 different capacity definitions will also be known. 24

25

State-of-the-practice survey of state departments of transportation 26

A survey questionnaire was prepared and administered via a web service. The survey participation request 27 was sent to 50 DOTs in the U.S. via email. Overall, 24 DOTs responded to the survey. The survey 28 consisted of two sections. The first section (questions 1 to 5) identified the organization (question 1) and 29 inquired about the definition of work zone capacity and the location where it is measured in the work 30 zone. The second section (questions 6 to 9) was about factors affecting work zone capacity, tools used by 31 DOTs to estimate capacity, and capacity values for different lane configurations. The list of questions 32 included in the survey is shown next. 33

34

Survey Questionnaire 35

2. Please choose your agency’s definition of work zone capacity? 36 • Based on maximum hourly flow rate before queue formation 37 • Based on maximum 15 minute flow rate 38 • Based on mean queue discharge flow 39 • Based on 95th percentile of mean queue discharge flow 40 41

3. Does your agency collect field data to measure work zone capacity? 42 • Yes 43

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• No 1 2

4. If you answered yes to the above question, please state the type of traffic data collected to 3 calculate capacity (please check all that apply) 4

• Speed of the vehicles in the work zone 5 • Volume of traffic 6 • Queue length 7 • Headways 8 • Other, please specify 9 10

5. At what location is the capacity value measured? 11 • Beginning of the taper area 12 • End of the taper area 13 • Well into lane closure 14 • Other, please specify 15 16

6. In addition to the field data collected, does your agency use any of the following methods to 17 estimate the work zone capacity values? (Please check all that apply) 18

• HCM procedure 19 • Work zone software (If yes, please specify below the name of the software) 20 • Simulation Tool (If yes, please specify below which ones) 21 • Regression Tool (If yes, please specify below which ones) 22 23

7. Which of the following factors are considered while estimating work zone capacities? Also, 24 please state what adjustment factors your agency uses for the selected factors. 25

• work zone configuration (number of total lanes before work zone to number of lanes 26 open during work zone) 27

• location of closed lane(left or middle or right) 28 • presence of ramps near the work zone 29 • length of work zone 30 • work zone grade 31 • driver familiarity 32 • intensity of the work zone 33 • proportion of heavy vehicles 34 • work duration factor 35 • lane width 36 • posted speed reduction 37 • partial lane closure versus crossover 38 • horizontal alignment 39 • day time versus night time 40 • short term versus long term 41 • type of lane delineation (whether cones or concrete barriers used to separate closed lanes 42

from open ones) 43 • if any other , please mention here 44 Please specify the adjustment factors here 45 46

8. What is the average value(s) of work zone capacity in your state for each of the following lane 47 configurations (i.e. actual number of lanes before work zone to the number of lane open during 48 work zone) 49

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For 2 to 1 lane (specify units) ………………………… 1 For 3 to 2 lane (specify units) ………………………… 2 For 3 to 1 lane (specify units) ………………………… 3 For 2 way 1 lane (specify units) ………………………… 4 For work zones with median crossover ………………….. (Head to head traffic control) 5 6

9. Does your agency have a policy on when lane closures can/cannot occur? 7 • Yes, Off-peak hours only 8 • Yes, Nighttime only 9 • No 10 • Others, Please specify 11

12 Survey responses 13

Work Zone Capacity Definition Majority of the respondent DOTs define work zone capacity as the 14 maximum observed hourly flow during pre-queue conditions. Only three state DOTs, Texas, Maine and 15 Washington plus Washington, D.C. consider mean queue discharge flow as the work zone capacity. Few 16 states such as Oregon and Colorado defin work zone capacity as the maximum observed 15 minute flow 17 rate irrespective of the existence of a queue. 18

Work Zone Capacity Measurement in Field Fifty-four percent of the respondents indicated that they 19 collect field data to estimate work zone capacity. Majority of these states collect volume, queue lengths 20 and speed of the vehicles in the work zone to estimate capacity. Few states such as Minnesota, 21 Washington DC, Montana and Oregon also measure average headways of the vehicles in the work zone. 22 Survey results suggested that majority of these states measure work zone capacity well into the work zone 23 area (i.e. near activity area). Few states such as Iowa, Oregon and Wisconsin measure capacity at the 24 beginning of the taper whereas Massachusetts measures it at the end of the taper area. Remaining DOTs 25 use pre-defined work zone capacity values from past experience and simulation studies rather than field 26 measurements. 27

Tools to Estimate Work Zone Capacity Majority of the respondents follow the HCM procedure to 28 estimate work zone capacity. Only a few states such as West Virginia, Texas and Washington use 29 analytical tools such as QUEWZ to estimate capacity values, while New York and Rhode Island use 30 micro-simulation tools such as VISSIM and CORSIM for estimating work zone capacities. Florida DOT 31 has developed their own work lane closure policy document based on some past empirical studies. 32

Factors Influencing Work Zone Capacity Majority of the states responding to the survey indicated that 33 they consider all factors documented in HCM 2000, i.e., proportion of heavy vehicles, presence of ramp, 34 work zone intensity and number of open lanes while estimating capacity. In addition, many DOTs also 35 consider length of a work zone, location of closed lane (s), posted speed limit, short term versus long term 36 and night time versus day time as factors affecting work zone capacity. All DOTs were asked to specify 37 the adjustment values that they used for the chosen factors. Only Wisconsin DOT provided these values, 38 which are as follows: 39

• Capacity values for urban work zones are typically more than rural areas by 200 pcphpl 40 • If the shoulder width is less than 6 ft the base capacity value should be reduced by a factor of 41

0.97 42 • Presence of ramp within 1500 ft of the work zone reduces the base capacity value by hourly 43

ramp volume or maximum of 600 vph 44 • One truck is equivalent to 2 passenger cars 45 • Long term work zones may have capacities as much as 150 pcphpl higher than short term 46

work zones 47

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• Lane width adjustments: Multiply base capacity by 0.97 if lane width is 11 ft, and by 0.95 if 1 lane width is 10.5 ft 2

• Work zone capacity with crossover may have 200 pcphpl less than without crossover, 3 especially in rural areas 4

5 Work Zone Capacity Values Adopted by State DOTs The capacity values adopted by the state DOTs 6 that responded to the survey are shown in Table 1. 7

TABLE 1 Work Zone Capacity Values Adopted by State DOTs 8

Florida 1800 vph 3600 vph 1400 vphWisconsin 1500 pcphpl 1500 pcphpl 1500 pcphpl 1400 pcphplNevada 1500-1600 pcphpl 1500-1600 pcphpl 1500-1600 pcphpl 1500-1600 pcphpl 1500-1600 pcphpl

Massachusetts 1500 vph 1500 vph 3000 vph 850-1100 vphHawaii 1600 pcphpl 1600 pcphpl 1600 pcphpl 600-800 pcphplIowa 1450 vphpl 1450 vphpl

New York 1800 pcphpl 1600 pcphpl 1700 pcphpl 1800 pcphplNew Jersey 1300-1400 vphpl 1200-1300 vphpl 3000-3200 vphpl 600-750 vphpl 1200-1500 vphpl

State 2 to 1 3 to 1 3 to 2Two way one lane

(TWOL)TWOL (with

median crossover)

9

Note: vph means vehicle per hour, vphpl means vehicles per hour per lane, pcphpl means passenger car 10 per hour per lane 11

Work Zone Lane Closure Policy Several DOTs indicated that they have a policy of closing lanes either 12 during night time or off-peak hours depending on the type of roadway (e.g., highway, secondary roadway, 13 etc) 14

DATA COLLECTION AND PROCESSING 15

Field measurements were taken from four short-term maintenance work zones on Interstate 70 (I-70). Due 16 to the heavy daytime traffic volumes on I-70 inside the urban area of Columbia, MoDOT did not close 17 lanes during the day (17). Accordingly, all work zones involved nighttime lane closures starting after 7:00 18 pm and continuing until midnight or later. Data was collected at the following work zones (see Figure 1 19 for locations on the map): 20 21

Case 1. On June 22, 2009 data was collected at mile marker 125.7 on I-70. Approximate times of 22 collection were between 7:00 PM and 9:30 PM. Westbound traffic was filmed. 23

Case 2. On June 23, 2009 data was collected at mile marker 125.7 on I-70. Approximate times of 24 collection were between 7:00 PM and 10:00 PM. Westbound traffic was filmed. 25

Case 3. On June 28, 2009 data was collected at mile marker 124.7 on I-70. Approximate times of 26 collection were between 7:00 PM and 10:00 PM. Westbound traffic was filmed. 27

Case 4. On June 29, 2009 data was collected at mile marker 124.7 on I-70. Approximate times of 28 collection were between 7:00 PM and 10:00 PM. Westbound traffic was filmed. 29

30

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1 FIGURE 1 Location of work zones field sites on I-70 (Google, 2010) 2

3 All work zones involved a right lane closure with the passing lane open (2 to 1 work zone). The 4

traffic was filmed using two cameras – one camera looking at vehicles approaching the taper, and the 5 second camera looking at vehicles receding from the taper. The details of the standard MUTCD-type 6 work zone setup can be found in the MoDOT policy on temporary traffic control (18). 7

Processing work zone capacity data involved counting vehicles approaching the work zone 8 upstream of the taper area. Image processing software was used to automate data extraction using virtual 9 count detectors. The filtering of erroneous data was achieved through scripts written in the Matlab 10 program. 11

COMPUTATION OF CAPACITY FROM FIELD DATA 12

Method 1: Sustained flow 13

Chapter 13 of the HCM (1) defines freeway capacity as “the maximum sustained 15-min flow rate, 14 expressed in passenger cars per hour per lane, that can be accommodated by a uniform freeway segment 15 under prevailing traffic and roadway conditions in one direction of flow.” In addition to the maximum 16 sustained 15-min flow rate, maximum sustained 10-min and 5-min flow rates were also computed in this 17 research. Moving time windows of 15-min, 10-min, and 5-min were obtained by grouping 1-min traffic 18 counts over the size of the respective time window. The maximum sustained flow rate was then obtained 19 by aggregating counts within a group (see Table 2). To be consistent with Missouri DOT’s units for work 20 zone capacities (19) the reported capacities are in vehicles per hour per lane (vphpl). The truck 21 percentages observed at each site was used in conjunction with passenger car equivalents (PCE) to 22 convert capacities to equivalent passenger cars per hour per lane. 23

6/28/09 and 6/29/09 MM 124.7

6/22/09 and 6/23/09 MM 125.7 WB

N

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TABLE 2 Capacity as maximum sustained flow rate 1 Maximum Sustained Flow (vphpl) Percentage of Trucks

15-min 10-min 5-min

Case 1 1256 1314 1440 15.9% Case 2 1408 1410 1524 22.2% Case 3 1192 1290 1380 12.8% Case 4 1348 1386 1404 14.8%

Method 2: Automated re-scaling of cumulative flow curves 2

The capacity definition from the previous section (i.e. maximum sustained flows) could have occurred 3 before or after the formation of queues. Past studies have demonstrated that there are two different types 4 of maximum flow observed at freeway bottlenecks: queue discharge flow (QDF) and pre-queue flow 5 (PQF) (by Banks (20, 21, 22), Hall and Agyemang-Duah, (23), Persaud et al.,(24)). The QDF is the traffic 6 flow discharged from an active bottleneck and PQF is the near-constant flow observed before the 7 breakdown of flow (21). Persaud and Hurdle (25), Ringert and Urbanik (26) have conducted freeway 8 bottleneck capacity studies using the mean discharge flow rate as a good proxy for the maximum 9 sustained flow rate. 10

This section applies the concept of QDF and PQF to work zones. Cassidy and Bertini (27) 11 proposed the use of re-scaled cumulative vehicle arrival curves (re-scaled N-curves) to study the traffic 12 features at two freeway bottlenecks in Toronto, Canada. First, an N-curve is built by piece-wise linear 13 approximation of vehicle arrivals in discrete time intervals. A background cumulative vehicle count is 14 then subtracted from the N-curve to form a rescaled N-curve. The re-scaling procedure assists in the 15 visual identification of changes in flow. Using this methodology, they identified the differences in QDF 16 and PQF, and flow patterns observed during queue discharge (stationary versus non-stationary patterns). 17 The re-scaling procedure has since been used in other bottleneck studies (28, 29). 18

In a recent study Banks presented an alternative to the visual identification of changes in flow. 19 Banks (4) explains, “The cumulative curves eliminate most of the noise in the data without obscuring 20 rapid changes in the average value of the time series; however, the identification of periods of nearly 21 constant flow requires visual identification of segments of the cumulative curve that are nearly straight. 22 There were no definite criteria (other than the analyst’s subjective impression) for deciding what 23 segments were “nearly” straight”. 24

In other words, the visual identification of periods of constant flow, straight lines in the curve, 25 depends on analyst judgment and could vary from one researcher to another. To alleviate this 26 inconsistency, Banks (4) suggested an automated method for freeway bottleneck analysis. The method 27 consists of programming routines to identify periods of breakdown and prequeue flow. He used this 28 method to identify PQF and QDF in 21 freeway bottleneck sites (none were due to work zones) in several 29 metropolitan areas in United States. In this paper, we apply this automated flow analysis method to 30 identify PQF and QDF in work zones. To our knowledge, this is the first application of this method to 31 work zones. Some of the routines such as identifying active bottlenecks and distinguishing spillbacks 32 from downstream are not described as they are not used in this application. For all work zone applications 33 studied in this research, the flow breakdown was a result of an active bottleneck being present at the work 34 zone location and not due to a downstream queue spillback. Readers interested in those topics are 35 referred to Banks (30). 36

The method starts with a piecewise linear approximation of the cumulative vehicle arrivals. The 37 points of greatest change in the average flow rate are then identified. This is done by locating points that 38

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maximize the absolute value of the difference between the cumulative curve and a straight line 1 representing its average value. Identification of these points is an iterative procedure and continues until a 2 desired level of linear approximation is achieved. These points divide the time series into periods or 3 segments that are further analyzed. The procedure is as follows (30): 4

Let’s assume ( )v t is the value of traffic flow time series during the time period 0t to nt ; cumulative flow 5

( )C t at time t is defined as: 6

( ) ( )0

t

tC t v t= ∑ 7

The mean value of cumulative flow between 0t and nt is defined as: 8

( ) ( ) ( )00

0

, nn

n

C t C tx t t

t t−

=−

9

The difference between cumulative flow at time t and a straight line representing the mean value of 10 cumulative flow between 0t to nt : 11 ( ) ( ) ( )0 , nt C t tx t t∆ = − 12

The point of greatest change in the mean cumulative flow, t′ , is selected such that 13 ( ) ( )( ) 0max , for nt t t t t′∆ = ∆ ≤ ≤ 14

The change in mean cumulative flow at time t′ is considered significant if 15 ( )( ) ( )0 , ,

C

n x

t

x t t x t t

′∆ ≥ ∆

′ ′− ≥ ∆ 16

Where, C∆ represents the minimum difference between cumulative flow and the mean of cumulative flow 17 that is considered significant and x∆ represents the minimum change in the mean of the cumulative flow 18 that is considered significant. 19

Periods (i.e. segments) of congestion are identified by their average speed; if the average speed of 20 a period is below a threshold value, critu , and the period lasts five minutes or longer, the period is 21 considered to be congested. Periods before congestion are examined to identify PQF by fitting a 22 regression line to flow time series before breakdown. The slope of regression line shows increasing, 23 decreasing, or constant flow. By definition, PQF is a period of nearly constant flow. Nearly constant flow 24 is verified based on three conditions: (i) slope of the regression line should be less than 100 vehicles per 25 hour per lane per hour (vphplph), (ii) a t-test at 85% confidence should verify that the slope is statistically 26 significant, and (iii) an additional test to verify that a small slope is not a result of fluctuations in flow 27 (described in detail later.) 28

The routine to find PQF is as follows: Let’s assume qt is the breakdown time. Consider the 29 period of piecewise linear approximation of cumulative flow between 1qt − and qt . A linear regression line 30 is fitted to flow time series between 1qt − and qt : 31

0q̂ bt q= + 32

where, q̂ represents the linear estimate of flow q at time t , b indicates the change of flow rate and 0q is 33 the flow at beginning of the period 1qt − . This process is repeated for periods starting at 2 3,q qt t− − until the 34 beginning of analysis period or another congestion period. The result is a set of regression slopes 35 { }1 2, , , , ,i nb b b bL L , where ib represents the slope of regression line for the segment q it − to qt . The starting 36 time pt of PQF is then obtained as: 37

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( )min :p i q n q i qb b i t t t− −= ∀ < < provided the following three conditions are satisfied: 1

100pb vphplph≤ (Condition 1) 2

0.85pα ≥ , where pα is the significance level of pb (Condition 2) 3

A nearly zero pb value could be a result of a period with highly fluctuating flow, where 4 decreasing and increasing flows could cancel out each other. To eliminate such a possibility in PQF 5 computation, a period is only considered if 6

( ) ( ) ( )

1

32 ,

200

q pj j p j p j q

q p

p q

C t C tq t t vpl t t t t

t t

q q vphpl−

− − − ≤ ∀ < < −

− < (Condition 3)

7

where, ( )C t represents the cumulative flow at time t and pq and 1qq − are average flow between ,p qt t and 8

1,q qt t − , respectively. 9

Banks (30) method was applied for the four work zones to identify PQF and QDF values. The 10 average speed threshold critu was assumed to be 30 mph, C∆ to be 10 vpl, and x∆ to be 2vpl. The 11 segmented cumulative vehicle arrival plot and the regression lines fitted to the corresponding segments of 12 the flow time series plot are shown in Figure 2 for case 1 data. 13

14 FIGURE 2 (a) Segmented cumulative vehicle arrival plot, (b) Time series of flow showing 15

regression lines fitted to segments for case 1. 16

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In identifying the PQF, the first and second conditions of slope being less than 100 vphplph and 1 α being at least 0.85 were violated in all case studies. This meant that there was no period of PQF 2 preceding QDF period in any case study. Therefore, the PQF values did not exist; the QDF values and 3 their durations are reported in Table 3. 4

5 TABLE 3 Queue discharge flow (QDF) 6

QDF Flow (vphpl) Duration (min)

Case 1 1026 5 Case 2 1223 12 Case 3 1079 26 Case 4 1268 33

7 Method 3: 85th percentile traffic flow 8

As previously discussed, Sarasua et al. (14) proposed the use of 85th percentile traffic flow as capacity at 9 work zones. They explained that the 85th percentile value is extensively used as a threshold in 10 transportation and statistical areas and would be a suitable estimate of capacity. The 85th percentile traffic 11 flow values were computed for the four work zones using the five minute flow values. The cumulative 12 plots are shown in Figure 3 and the corresponding 85th percentile flows are shown in Table 4. 13

14 FIGURE 3 Cumulative flow plots for 85th percentile flows 15

16 17

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TABLE 4 85th percentile flows for all case studies 1

85th percentile flow (vphpl) Case 1 1260 Case 2 1356 Case 3 1110 Case 4 1343

2 The capacity values obtained using the three methods for all four cases are plotted in Figure 4. It 3

appears that the 15 minute sustained flow and the 85th percentile flow are closer in value than QDF. Since 4 85th percentile flow is based on the cumulative flow distribution it is heavily influenced by the demand. 5 A more frequently congested location will have a higher 85th percentile flow than a less frequently 6 congested location even though both locations could theoretically have the same 15 minute sustained 7 flows. The lower QDF values reflect hysteresis in traffic flow caused by the onset of congestion (31). 8

The average capacity value obtained by averaging all four cases were 1301, 1149, 1267 vphpl, for 9 15-min sustained flow, QDF, and 85th percentile flow, respectively. These values were close to the 10 capacity value of 1240 vphpl currently used by Missouri DOT for a 2 to 1 lane work zone (19). 11

12

13

FIGURE 4 Comparison of capacity values obtained from different definitions 14 15

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CONCLUSIONS 1

Based on the results the following conclusions were drawn: 2

1) As is intuitive, the maximum sustained flows decreased as the aggregation interval increased from 5 to 3 15 minutes. 4

2) The QDF values were the most conservative estimates of capacity in all four cases. The 85th percentile 5 flows were lower than the 15-min sustained flow values in all cases except case 1 where the 85th 6 percentile flow was slightly higher by 4 vphpl. One reason for this observation is that although the 85th 7 percentile flows only sustain for 5 minutes their values are computed using non-overlapping 5 minute 8 intervals unlike the 15-min sustained flows that are computed using a moving window. 9

3) The PQF values did not occur in any of the four work zones. This means that there was no period of 10 near-constant flow prior to the breakdown of flow. This study questions the existence of PQF conditions 11 at short-term maintenance work zones. This finding has implications on the design of traffic control 12 methods to alleviate work zone congestion. The existence of PQF and its correlation with probability of 13 flow breakdown provide guidance on delaying or eliminating flow breakdown using traffic control 14 methods such as ramp metering. The success of such methods in short-term work zones is questionable 15 due to the absence of near-constant flow conditions prior to flow breakdown. More research is needed to 16 verify the absence of PQF at short-term work zones. 17

In future research, the three methods should be compared using data obtained from long-term work zones. 18 A sensitivity analysis of the PQF and QDF values with respect to the threshold values used in the re-19 scaled method should also be conducted. 20

ACKNOWLEDGMENTS 21 This research project was funded by the Federal Highway Administration’s Smart Work Zone 22 Deployment Initiative Pooled Fund. The authors are thankful for the assistance provided by MoDOT 23 traffic engineers Ken Strube, Erik Menenga and Dan Smith for coordinating field data collection sites. 24 The authors wish to acknowledge the contributions of Amit Dhatrak, Jordan Freborg and Kyle Ervin, who 25 helped with data collection and analysis, and Indrajit Chatterjee, who assisted with the state of practice 26 survey. 27

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