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Day, Sturdevant, and Bullock

10-0008

Outcome Oriented Performance Measures for
Signalized Arterial Capacity Management
by
Christopher M. Day
Purdue University
James R. Sturdevant
Indiana Department of Transportation
Corresponding author:
Darcy M. Bullock
Purdue University
550 Stadium Mall Dr
West Lafayette, IN 47906
Phone (765) 496-2226
Fax (765) 496-7996
darcy@purdue.edu

November 13, 2009
TRB Paper 10-0008
Word Count: 4148 words + 13 x 250 words/Figure-Table = 4148 + 3250 = 7398

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10-0008

ABSTRACT
Traffic signal timing plans are typically designed from manual turning movement counts
collected during peak periods. Once systems are constructed and settings are implemented, they
receive maintenance on fixed schedules that can extend to several years. Public feedback (e.g.,
phone calls) is in many cases the primary channel by which information about the system is
obtained by the agency. System assessment is often conducted by collecting a new small data
sample and repeating the design process. One common and frustrating result is that the same
settings are frequently recommended by the design software, even when problems are known to
exist.
This paper illustrates how fundamental traffic engineering concepts can be integrated with traffic
signal system detection and controller status information to provide outcome based arterial
system performance measures. These outcome based performance measures characterize the
operation of a signal system and provide a data set that can be used to identify and prioritize
opportunities for operational improvements in the system. This paper focuses on performance
measures oriented analysis of capacity utilization.
A consistent set of performance measures used across a signal network would impact traffic
signal operations at two distinct levels. At the regional or district level, it would provide a
continuously updated list of problem areas with greater accuracy than telephone reports. At the
agency jurisdiction level, it would provide quantitative data for prioritizing resources across
multiple districts, and by time of day.

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INTRODUCTION
Signalized arterials represent a substantial component of the highway transportation network in
the United States. The task of maintaining appropriate signal timing plans is a major challenge
due to a scarcity of engineering resources needed to monitor and update those plans (1, 2). Figure
1 shows a diagram of the current signal timing design and maintenance process. Based on agency
objectives (i.e., policies), data is collected for specific times of day. A variety of software
packages are used to design cycle length, offsets, and splits for intersections based on
performance measures. After the timing plans are documented, they are deployed in the field; the
next step in the process is maintenance.
The signal timing process has significant quantitative feedback in the modeling/design stages
(Figure 1, FB1), but little quantitative feedback in the deployment stages (Figure 1, FB2). There
are certain inherent weaknesses that can lead to operational deficiencies:


Data collected for the timing process typically does not include off-peak and weekend
conditions.



Timing plans are static, while the network they control is dynamic and changes over time.
Signal timing plans are often reevaluated on rather long time periods (sometimes on the
order of years), or in response to user complaints. Information received from system
users rarely describe a problem with a high degree of precision.



When new data is collected as scheduled or in response to user feedback, performance
measures to evaluate the system are often estimated from the same tools used to design
signal timings. It is not uncommon for the software to return the same settings that are
known to have deficiencies.

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I.
Define
Objectives,
Assess and
Prioritize
Activities

II.
Assemble
relevant data
to support
timing and
documentation
objectives

10-0008

III.
Software
Modeling

IV.
Timing Design
and
Documentation

FB1

V.
Deployment

VI.
Evaluation

FB2

Figure 1. Procedural steps and feedback (FB) loops in signal timing design and maintenance.
We propose a data-rich strategy for evaluating signal systems that leverages real data to
accomplish performance measurement rather than estimation by software or modeling. Data is
continuously collected throughout the signal network, and performance measures are tabulated
and archived in a central database. The performance of the system is frequently reviewed.
Subject to agency objectives and constraints, the decision is made whether to intervene and make
adjustments to the system. In making that determination, the following questions are asked:
1. Which intersections have the most capacity and progression deficiencies?
2. Are these deficiencies recurring or non-recurring?
3. At intersections with capacity deficiencies, is there sufficient unused capacity at certain
time periods of the day to mitigate deficiencies by reallocating green times and/or cycle
lengths?
4. At intersections with progression deficiencies, are there opportunities to mitigate
deficiencies by adjusting offsets and/or cycle lengths?
5. At what periods of the day do opportunities for mitigation occur?
6. What phases should be allocated additional capacity and what phases could perform
acceptably with a reduced capacity allocation?
7. What changes should be made to offsets and/or cycle length?

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By asking these questions, the problem areas of the system are defined and prioritized, and by
answering them, potential solutions are identified. The current paper focuses on the questions
oriented toward capacity management through green time allocation (3, 4, 6). Progression quality
is also important to monitor; we will briefly discuss the progression aspect in this paper, but
would also point to parallel work for further discussion (5).

REAL-TIME SIGNAL PERFORMANCE MONITORING
The concept of monitoring traffic detector and signal states in real time has been used
extensively in traffic control systems. A number of minicomputer-controlled, centralized systems
were developed in the 1960s and 1970s (7, 8, 9, 10). From the 1980s to the present day, a
number of adaptive (11, 12, 13, 14, 15) systems became commercially available, which made
extensive use of detector information to adjust signal parameters. These systems can provide
some information to the operator about the network state.
Today, the vast majority of traffic signals belong to the class of systems referred to as “closedloop” because they are linked to a system infrastructure that allows remote management of field
devices. This architecture has provided a mechanism for synchronizing time clocks, managing
databases, and collecting diagnostic data. However, little operational information is provided by
field devices to the system. Historically, bandwidth has been a limiting factor. Perhaps the most
functionality is extracted from legacy communication infrastructure by ACS-Lite (15), which
uses current closed-loop signal architecture to adaptively control signal timing plans. In ACSLite, information is streamed to the control system in 1-minute bins.
Recent research studies have applied real time data collection concepts to closed-loop systems.
Alternative tools for obtaining data include industrial I/O devices (17, 21), the input monitoring
capabilities of video systems (16,18,19,20), and other external systems (22). For this paper, a
data collection software module running on a traffic signal controller logged events in real time.
Compressed 1-hour log files were collected over FTP using an IP connection.

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10-0008

DEVELOPMENT OF AN ARTERIAL TESTBED
Figure 2 shows the instrumented section of the SR 37 corridor deployed as of July 2009
(Intersections 1001, 1002, 1003, and 1004). Each of these intersections has the capability of
logging high-resolution controller data (phase and detector status changes) at a resolution of 0.1
seconds. Ethernet communication is available at each intersection. Signal event data is retrieved
by scheduled automatic FTP downloads over a virtual private network (VPN) connection.
SR 37 is an actuated coordinated corridor. Each intersection features stop bar detectors on minor
movements (all left turns and side street through phases), and advance detectors on the
coordinated arterial through movements. Advance detectors are set back 405 ft from the stop bar
at each intersection. The signal controllers use the advance detector data to determine whether
coordinated phases should terminate early, in the absence of demand, which allows up to 10% of
the cycle length to be redistributed according to coordinated phase capacity utilization. This
mode of operation provides modest operational improvement, and is discussed in detail
elsewhere (19).
There are no pedestrian phases on SR 37. However, we acknowledge that monitoring of
pedestrian phases is critical in any signal network topology. It has been demonstrated that signal
event data can be leveraged to evaluate pedestrian service (23).

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10-0008

191st St.

6+5046

Instrumented Corridor Section

7450 ft

1001 (SR 32)

5+2880
2300 ft

1002 (Pleasant St.)

5+0580

2500 ft

1003 (Town and Country Blvd.)

4+3350

3660 ft

3+4970

1004 (Greenfield Ave.)

8352 ft

2+1900

146th St.

N

2670 ft
1+4520

141st St.
5320 ft

0+4470

131st St.
2650 ft

0+1820

126th St.
1820 ft

I-69

0+0000
(mi+ft)

Figure 2. Indiana State Road 37 is a signalized arterial system with a segment of four adjacent
intersections serving as an instrumented corridor.

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10-0008

DEGREE OF INTERSECTION SATURATION
The degree of intersection saturation (XC) (24, 25) describes the overall utilization of the
intersection. The formula is:

XC 

V   C 


ci  C  L  ,

  s 
i

Equation 1

where:
C = cycle length (s),
L = lost time (s), and
∑(v/s)ci =the summation over critical phases ci of the ratio of served volume (V) to
saturation flow rate (s).
For a typical dual-ring eight phase controller, this equation simplifies to:

 v   v  
 v   v    C 
X C  max  ,     max  ,    
,
 s 12  s 56 
 s 34  s  78   C  L 


Equation 2

Where, for example, (v/s)12 = v1/s1 + v2/s2. Calculation of this performance measure on a cycleby-cycle basis at a local intersection was described in extensive detail in a previous paper (3).
Twenty-four hour plots of XC are shown for four arterial intersections in Figure 3. This figure
shows similar peaking trends among all four instrumented intersections, with the AM peak
occurring at around 0800, and the PM peak occurring at around 1700. Intersections 1001, 1002,
and 1004 have a rather high capacity utilization for much of the day, while intersection 1003
exhibits a considerable amount of slack, even during the peak periods.

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10-0008

1004

1003

1002

1001

1.25

1

1001

1002

Xc

0.75

0.5

1004

1003

0.25

0
0:00

2:00

4:00

6:00

8:00

10:00

12:00

14:00

16:00

18:00

20:00

22:00

0:00

Time of Day

Figure 3. Degree of Intersection Saturation over 24 hours. The lines show 20-point moving
averages.
This plot indicates times of day when spare capacity is available within the existing cycle length.
During those times, there are opportunities to reallocate green time from underutilized phases to
those with capacity deficiencies. As XC approaches 1, the amount of green time available for
reallocation becomes increasingly smaller. Not surprisingly, this occurs during the peak periods,
evident from the proximity of the XC traces to the 1.0 line in Figure 3. These plots also indicate
that some intersections have spare capacity that could potentially be rebalanced to address phase
capacity problems. For an arterial network with a large number of intersections, such trends
might not be reflected in anecdotal knowledge of the system.
While Figure 3 illustrates the relationship between time of day and capacity utilization, the high
density of information on the graph makes it difficult to envision expansion to more than four
intersections. Figure 4 provides a simplified view of the same data, where the cycle-by-cycle
values of XC have been sorted from greatest to least. Each value of XC plotted in Figure 4a

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10-0008

corresponds to a point in Figure 3. This plot shows the overall utilization of each intersection
throughout the day. The top 20% of cycles are magnified in Figure 4b. Intersection 1001 reports
over 100 cycles where XC exceeds the cutoff value, indicating that split adjustments alone might
not be an appropriate strategy for addressing operational issues at this intersection, at least during
a substantial portion of the day. In this case, it may be necessary to adjust the cycle length (3). In
contrast, intersection 1003 does not ever enter this region, indicating that capacity problems
would likely be handled by split rebalancing. The figure provides an illustrative example of the
concept; creating similar data views for only one particular time of day would allow a more
detailed analysis.

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Day, Sturdevant, and Bullock

10-0008

1004

1003

1002

1001

1.5

Top 20%
1.25

1

Xc

1001
1002

0.75

0.5

1004
0.25

1003

0
0

100

200

300

400

500

600

700

800

900

1000

175

200

225

250

Rank Order

(a) All cycles.
1004

1003

1002

1001

1.5

1.25

1001

1002

1004

Xc

1

0.75

1003
0.5

0.25

0
0

25

50

75

100

125

150

Rank Order

(b) Top 20% of cycles.
Figure 4. Sorted Degree of Intersection Saturation, 24 hours.

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10-0008

VOLUME-TO-CAPACITY RATIO
Quantifying Phase Utilization
While XC provides a picture of overall intersection saturation, it conceals the degree to which
each individual phase is used. For this purpose, the volume-to-capacity (V/C) ratio is calculated
(24):
v
Xi    
 c i

Vi
g
s i  i
 Ci







Vi C
si g i

Equation 3
,

Where:
Xi = the v/c ratio for phase i,
Vi = the flow rate for phase i (veh/h),
si = the saturation flow rate for phase i (veh/h),
gi = the effective green time for phase i (s), and
C = cycle length (s).
This measure can be used to estimate when a split failure has taken place. A split failure can be
defined as an occurrence when there is not enough green time to serve the demand. As Xi
increases, it becomes more likely that a split failure occurs. For the sake of expediency, we select
Xi = 1 as a convenient threshold for determining when a split failure takes place (26). Saturation
flow rate is an important characteristic that strongly affects the calculation of Xi, and should
accurately reflect the driver behavior at the intersection. In this paper, we have assumed a fixed
value of si, which is a conventional approximation in existing signal analysis methods. In reality,
si varies, and there is an opportunity to improve the accuracy of Xi by calibrating si in real time.
Figure 5 shows an example of cycle-by-cycle calculations of Xi for Intersections 1001 (Figure
5a) and 1003 (Figure 5b). In these plots, a line is drawn at Xi = 1.0. The number of points plotted
above this line correspond to probable occurrences of split failures. 20-point moving average
lines are drawn to show the trends in phase utilization. In these plots, the following individual
phases stand out as having deficiencies (i.e., many points above the 1.0 line):
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10-0008



Phases 3, 4, and 5, at Intersection 1001.



Phases 3 and 7 at Intersection 1003.

These phases would be candidates for receiving additional green time, while the phases with
lower trends in Xi would be candidates for giving up some green time.

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1.5

10-0008

P1
SL

P2
N

P3
WL

P4
E

P5
NL

P6
S

P7
EL

P8
W

Volume-to-Capacity Ratio

1

0.5

0
1.5

1

0.5

0
0:00

12:00

24:00 0:00

12:00

24:00 0:00

12:00

24:00 0:00

12:00

24:00

12:00

24:00

Time of Day

(a) Intersection 1001.
1.5

P1
SL

P2
N

P3
WL

P4
E

P5
NL

P6
S

P7
EL

P8
W

Volume-to-Capacity Ratio

1

0.5

0
1.5

1

0.5

0
0:00

12:00

24:00 0:00

12:00

24:00 0:00

12:00

24:00 0:00

Time of Day

(b) Intersection 1003.
Figure 5. 24-hour cycle-by-cycle V/C ratio by TOD for all eight phases.

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10-0008

The possibility of downstream blockages should be taken into consideration when characterizing
phase utilization from Xi values. In a downstream blockage scenario, the affected phase is shown
the green indication, but queued vehicles are unable to depart from the approach because there is
no physical space to permit them to do so. In this case, the vehicle count would be low or even
zero, whereas occupancy would be high. Methods to detect this situation rely on investigating the
stop bar detector occupancy (26). When high occupancy during green coincides with low vehicle
counts, a downstream blockage would be suspected.

Estimating Split Failures
Split failures, estimated as phase instances where Xi > 1.0, can be summarized in a map view as
illustrated in Figure 6. Figure 6a shows the total number of split failures for each phase at each
intersection in the system, while in Figure 6b these numbers are represented as a percentage of
the total number of cycles in which the phases failed. The numbers in parentheses show the
number of phase instances that failed, which excludes cycles in which the phase was not
actuated. The zeros indicate phases that do not indicate problems in serving their demand. The
largest failure rate was for the northbound left turn at intersection 1002. This phase was
estimated to fail for 11.1% for all cycles in the day, or 15.4% for all cycles in which the phase
was actuated. Other phases with capacity deficiencies include the northbound left turn at
intersection 1001 and the eastbound through movements at intersections 1002 and 1004.

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10-0008

6
1

0.6
0.1 ((0.6)
0.3)

Day, Sturdevant, and Bullock

11
35

1.6 (1.6)
5.8 (7.6)

79
4

Int. 1001
8.5 (
0.4 (12.3)
0.4)

1.7 (4.4)
7.8 (8.5)

Int. 1001

16
72

6.3 (7.9)
1.5 (4.7)

42
10

Int. 1002

Int. 1002

11.1 (15.4)
0.1 (0.1)

7.5 (9.9)
4.3 (4.5)

0
5

0.0 (0.0)
0.6 (1.0)

74
1

50
29

0.6 (0.8)
4.3 (6.4)

5
35

5)
(5. .5)
2.3.4 (9
9

0
23

0.0
2.7 (0.0)
(3.9
)

3
0

3.2 (5.0)
0.0 (0.0)

0.4 (0.5)
0.0 (0.0)

Int. 1003

Int. 1003
25
0

0.0 (0.0)
6.3 (9.5)

0
58

201
8

Int. 1004

Int. 1004
)
.8
(0 3)
8 1.
0. .6 (
0

7

0
5

0.0
0.6 (0.0)
(0.6
)

5

(a) Count of split failures by phase.

(b) Percentage of cycles with split failures
(percent of actuated phases in parentheses).

Figure 6. Count and percentage of estimated split failures over 24 hours.

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10-0008

Intersection 1002 had slightly more split failures than intersection 1001 (252 vs. 236), which is
perhaps unexpected given that intersection 1001 had a slightly higher XC distribution (Figure 4a).
The reason for this inconsistency is that XC is a macroscopic performance measure. It does not
use green time, but only considers volumes on the critical path. In the XC calculation (Equation
2), each left turn phase volume is coupled with a through phase volume. If one phase is
oversaturated and the other is unsaturated, their contribution to XC will tend to suggest a
moderate level of saturation. In other words, a lower XC does not imply that there are no
individual phase capacity problems. This illustrates why it is essential to examine individual
phase performance in addition to overall intersection performance.

DATA TO SUPPORT SPLIT REBALANCING
Identification of Correctable Split Failures
Combining information about individual split performance with XC allows estimated split
failures to be categorized with respect to a threshold value XT, as follows (3):


Correctable split failures are those that take place during a cycle when XC < XT. Enough
spare capacity in the system should exist to allow phases to be rebalanced.



Non-correctable split failures take place during a cycle when XC ≥ XT.

The threshold XT represents the level of saturation beyond which it is assumed there is not
sufficient capacity to support rebalancing splits. Thus, for cycles where XC exceeds this value,
split adjustments alone are unlikely to resolve capacity problems. The selection of XT is a policy
decision to be made by the individual agency. To help make this concept more tangible, Table 1
presents estimates of the minimum amount of slack green time for various cycle lengths, for
given values of XT. A lost time of 20 seconds is assumed. The minimum slack green (gs,min) is
calculated from
g s,min  C  L1  X T , 0  X T  1 .

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Equation 4

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10-0008

This equation is derived as follows. Assuming that XC approximately represents the proportion of
cycle time that is used by vehicles and lost time, then (1 – XC) represents the unused proportion.
The amount of slack green time is therefore equal to gs = (C – L)(1 – XC). All values of XC < 1
theoretically provide some slack green time, but as XC approaches 1, gs approaches 0. The
threshold value of XT indicates the maximum XC to be considered for split rebalancing, and
implies the minimum amount of gs.
Table 1. Table of estimated minimum slack green time based on given values of XT.
Cycle Length
(sec)
50
60
70
80
90
100
110
120
130
140
150
160
170
180

Lost Time
(sec)
20
20
20
20
20
20
20
20
20
20
20
20
20
20

XT = 0.5
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
55.0
60.0
65.0
70.0
75.0
80.0

Estimated Minimum Slack Green Time
XT = 0.65
XT = 0.75
XT = 0.85
10.5
7.5
4.5
14.0
10.0
6.0
17.5
12.5
7.5
21.0
15.0
9.0
24.5
17.5
10.5
28.0
20.0
12.0
31.5
22.5
13.5
35.0
25.0
15.0
38.5
27.5
16.5
42.0
30.0
18.0
45.5
32.5
19.5
49.0
35.0
21.0
52.5
37.5
22.5
56.0
40.0
24.0

XT = 0.95
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0

For example, given C = 120 and L = 20, selecting XT = 0.75 implies that we prefer to have at
least 25 seconds of (estimated) slack green time in the cycle to consider phase rebalancing, while
XT = 0.85 suggests that we would be willing to work with 15 seconds of slack. Selecting a value
of XT that is too low will lead to excluding cycles when split rebalancing could have solved
problems. Conversely, selecting a value that is too high will lead to excessive effort in moving
very small increments of time between phases. In reality, the amount of slack green time might
be less than the values in Table 1, because the lower bounds on phase times are limited by
minimum green times, pedestrian intervals, barrier constraints, and coordination constraints.
However, Table 1 helps give more tangible meaning of XT.

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Figure 7 shows plots of XC for intersections 1001 and 1003 over 24 hours, with 20-point moving
average lines corresponding to those in Figure 3. The points in Figure 7 represent values of XC
during cycles that experienced split failures, with symbols corresponding to the phase that was
estimated to have a capacity deficiency. Some cycles experienced deficiencies on multiple
phases, indicated by overlapped symbols. These plots illustrate the distribution of split failures
throughout the day, and their status as correctable or non-correctable. Horizontal lines are drawn
at XC = 0.75 and XC = 0.85 indicating candidate values of XT. At Intersection 1001, the number
of split failures considered to be correctable is sensitive to this selection. Using XT = 0.75
excludes most of the split failures from further analysis, while XT = 0.85 includes almost all of
the split failures except for those during the AM and PM peak periods. In contrast, Intersection
1003 has XC values well below 1.0 throughout the entire day, and most of its split failures would
be considered correctable at either XT = 0.75 or XT = 0.85.

11/13/2009
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Day, Sturdevant, and Bullock

10-0008

P1

P2

P3

P4

P5

P6

P7

P8

1

Degree of Intersection Saturation

X C = 0.85
X C = 0.75

0.75

0.5

0.25

0
00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00
Time of Day

(a) Intersection 1001.
P1

P2

P3

P4

P5

P6

P7

P8

1

Degree of Intersection Saturation

X C = 0.85
X C = 0.75

0.75

0.5

0.25

0
00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 00:00
Time of Day

(b) Intersection 1003.
Figure 7. XC plotted over 24 with split failures by phase shown.

11/13/2009
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1:39:48 PM
Paper revised from original submittal.

Day, Sturdevant, and Bullock

10-0008

While Figure 7 is illustrative of the concept of filtering by XT, it is rather difficult to determine
what time periods require action based on this graph. By aggregating the points plotted in Figure
7, it is possible to produce a distribution of split failures by time of day as shown in Figure 8.
This figure shows the number of split failures per hour for each phase of the four intersections on
the arterial. The vertical lines show when timing plans change (0600; 0900; 1100; 1300; 1700;
and 2200). While the high number of split failures at Intersections 1001, 1002, and 1004 during
the 1500-1900 PM peak period are not unexpected, the rather high number of split failures at
Intersection 1003 during the 1100-1300 midday period is noteworthy and warrants further
investigation.

45

45

Ring 1

Int. 1001

Ring 1

30

30

15

15

0

0

15

15
30

30

Ring 2

Ring 2
45

45
0:00

45

Int. 1003

6:00

12:00

18:00

24:00

0:00

6:00

12:00

18:00

24:00

45

Int. 1002

Ring 1

Ring 1

30

30

15

15

0

0

15

15

Int. 1004

30

30

Ring 2

Ring 2
45

45
0:00

6:00

12:00

Phase1
Phase5

18:00

24:00

0:00

Phase2
Phase6

6:00

Phase3
Phase7

12:00

18:00

24:00

Phase4
Phase8

Figure 8. Split failures per hour by phase.

11/13/2009
TRB 2010 Annual Meeting CD-ROM

Page 21 of 31

1:39:48 PM
Paper revised from original submittal.

Day, Sturdevant, and Bullock

10-0008

Figure 9 filters these bar graphs by removing out all points where XC > 0.85 (equivalent to
selecting XT = 0.85). This leaves only those split failures during cycles where there was
significant slack available to rebalance the splits (indicated by XC < 0.85). Thus, Figure 9 shows
the distribution of split failures that are theoretically correctable. Compared to Figure 8, the
distributions are somewhat lower, particularly for the PM peak period at intersections 1001,
1002, and 1004. However, there remain a number of correctable split failures even during those
peak periods at those intersections. The 1100-1300 midday period at Intersection 1002 stands out
as an candidate for split rebalancing. Additionally, the distribution for intersection 1003 is
identical in Figure 8 and Figure 9, because it never experienced any XC > 0.85 at any time in the
day.

45

45

Ring 1

Int. 1001

Ring 1

30

30

15

15

0

0

15

15
30

30

Ring 2

Ring 2
45

45
0:00

45

Int. 1003

6:00

12:00

18:00

24:00

0:00

6:00

12:00

18:00

24:00

45

Int. 1002

Ring 1

30

Ring 1

Int. 1004

30

a

15

15

0

0

15

15

b

30

30

Ring 2

Ring 2
45

45
0:00

6:00

12:00

Phase1
Phase5

18:00

24:00

0:00

Phase2
Phase6

6:00

Phase3
Phase7

12:00

18:00

24:00

Phase4
Phase8

Figure 9. Split failures per hour by phase that are theoretically correctable, filtered using XT =
0.85.

11/13/2009
TRB 2010 Annual Meeting CD-ROM

Page 22 of 31

1:39:48 PM
Paper revised from original submittal.

Day, Sturdevant, and Bullock

10-0008

On further inspection of the phase composition of the bars in Figure 9, some phases persistently
report correctable split failures throughout the day. At Intersection 1002, phase 1 appears
frequently, and is prominent in the 1100-1300 period (Figure 9, a). At Intersection 1004, phase 4
has the most deficiencies and reports several correctable split failures during each hour of the
day from 0600 to 2200 (Figure 9, b).
Table 2 summarizes the information presented graphically in Figure 8 and Figure 9. The number
of estimated split failures taking place for each phase at all four intersections in the system is
shown, with the numbers of theoretically correctable split failures at XT = 0.75 and XT = 0.85.
The total number of split failures in the system was 702. Selecting the rather optimistic XT =
0.85, we find that 560 or 80% of these are theoretically correctable. Using the slightly less
aggressive threshold (XT = 0.75) suggest 353 or ~50% of all split failures may be correctable.
This data can also be tabulated by TOD plan period, as shown in Table 3 for XT = 0.85. This
shows the same information as Figure 9 in tabular format.

11/13/2009
TRB 2010 Annual Meeting CD-ROM

Page 23 of 31

1:39:48 PM
Paper revised from original submittal.

Day, Sturdevant, and Bullock

10-0008

Table 2. Table of split failures by intersection and phase.
Intersection

Phase

1
2
3
4
1001
5
(SR 37 & SR 32)
6
7
8
Total
1
2
3
4
1002
(SR 37 & Pleasant
5
St.)
6
7
8
Total
1
2
3
4
1003
5
(SR 37 & Town and
Country Blvd.)
6
7
8
Total
1
2
3
4
1004 (SR 37 &
5
Greenfield Ave.)
6
7
8
Total
Arterial System Total

11/13/2009
TRB 2010 Annual Meeting CD-ROM

Movement

Total Split
Failures

SBLT
NB
WBLT
EB
NBLT
SB
EBLT
WB

1
4
58
72
79
6
16
0
236
74
11
10
29
39
1
50
42
256
3
0
31
0
5
0
25
5
69
0
0
5
81
23
5
20
7
141
702

NBLT
SB
WBLT
EB
SBLT
NB
EBLT
WB
NBLT
SB
WBLT
EB
SBLT
NB
EBLT
WB
NBLT
SB
WBLT
EB
SBLT
NB
EBLT
WB

Page 24 of 31

Theoretically Correctable
Split Failures
XT ≤ 0.75
XT ≤ 0.85
Criteria
Criteria
1
1
0
1
16
38
27
44
34
61
1
2
5
11
9
0
93
158
44
65
1
7
2
9
15
24
12
33
0
0
18
38
11
33
103
209
3
3
0
0
31
31
0
0
5
5
0
0
25
25
5
5
69
69
0
0
0
0
4
5
63
75
5
19
3
4
10
17
3
4
88
124
353
560

1:39:48 PM
Paper revised from original submittal.

Day, Sturdevant, and Bullock

10-0008

Table 3. Numbers of theoretically correctable split failures by intersection, phase, and TOD
using XT = 0.85.
Time of Day Plan Period
Intersection Phase
Total
1
2
3
4
5
6
7
8
0000 0600 0900 1100 1300 1500 1900 2200
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
3
0
4
3
11
2
17
1
0
38
4
0
2
4
5
12
14
7
0
44
5
1
10
14
13
5
18
0
0
61
1001
6
0
1
0
1
0
0
0
0
2
7
1
2
0
1
2
5
0
0
11
8
0
0
0
0
0
0
0
0
0
Total
2
20
21
31
21
55
8
0
158
1
1
6
4
34
4
16
0
0
65
2
0
0
2
0
5
0
0
0
7
3
0
0
1
2
1
5
0
0
9
4
0
2
4
3
0
15
0
0
24
5
0
3
3
1
1
24
1
0
33
1002
6
0
0
0
0
0
0
0
0
0
7
0
0
1
17
1
15
4
0
38
8
0
1
1
1
1
27
2
0
33
Total
1
12
16
58
13
102
7
0
209
1
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
3
4
0
0
4
2
12
8
1
31
4
0
0
0
0
0
0
0
0
0
5
0
0
0
4
0
1
0
0
5
1003
6
0
0
0
0
0
0
0
0
0
7
0
0
0
7
0
18
0
0
25
8
0
1
0
1
0
2
1
0
5
Total
4
1
1
16
4
33
9
1
69
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
3
0
0
0
1
0
0
5
4
0
17
8
12
7
25
6
0
75
5
0
0
0
1
0
18
0
0
19
1004
6
0
0
0
0
2
0
2
0
4
7
0
1
0
5
1
8
1
1
17
8
0
1
0
0
0
3
0
0
4
Total
1
22
8
18
10
55
9
1
124
System Total
8
55
46
123
48
245
33
2
560

11/13/2009
TRB 2010 Annual Meeting CD-ROM

Page 25 of 31

1:39:48 PM
Paper revised from original submittal.

Day, Sturdevant, and Bullock

10-0008

Sorting this data by the number of correctable split failures allows the creation of a prioritized
list of opportunities for operational improvements in the arterial. Table 4 shows the top ten
opportunities for split rebalancing using the number of correctable split failures at XT = 0.85.
This list is dominated by phases during the 1500-1900 time period, but there are some notable
exceptions such as the top ranked opportunity (34 split failures during the 1100-1300 time period
for phase 1 at Intersection 1002).

Table 4. Top ten opportunities for split rebalancing by TOD plan period, sorted by the
number of correctable split failures using XT = 0.85.
Rank
1
2
3
4
5
6
7
8
9
10

Intersection Phase Movement
1002
1002
1004
1002
1001
1003
1004
1001
1002
1004

11/13/2009
TRB 2010 Annual Meeting CD-ROM

1
8
4
5
5
7
5
3
4
4

NBLT
WB
EB
SBLT
NBLT
EBLT
SBLT
WBLT
EB
EB

Page 26 of 31

Theoretically
Time Period Correctable
Split Failures
1100-1300
34
1500-1900
27
1500-1900
25
1500-1900
24
1500-1900
18
1500-1900
18
1500-1900
18
1500-1900
17
1100-1300
17
0600-0900
17

1:39:48 PM
Paper revised from original submittal.

Day, Sturdevant, and Bullock

10-0008

PROGRESSION QUALITY
This paper has focused on evaluation of capacity management, but in progression is also an
important aspect of arterial operations and the proportion of vehicles arriving on green (POG) is
a starting point for progression analysis with real time data:

POG 

Ng
N

Equation 5

,

where Ng is the number of vehicles arriving in green and N is the total number of vehicles
arriving in a cycle. Ng may be measured in real time on coordinated phases where advance
detectors are available (18). Low values of POG would suggest coordinated phases where offset
tuning might be recommended. Due to the interaction between signals in coordinated systems,
more detailed analysis would be needed to understand the impacts of offset changes. This is the
topic of continuing research.

11/13/2009
TRB 2010 Annual Meeting CD-ROM

Page 27 of 31

1:39:48 PM
Paper revised from original submittal.

Day, Sturdevant, and Bullock

10-0008

CONCLUSIONS
This paper investigated the network-level analysis of capacity performance measures and
demonstrated the utility of a set of performance measures in determining what specific phases in
a signalized arterial corridor are experiencing problem, and prioritizing those phases according to
need.


Figure 3 demonstrates that macroscopic performance measures such as XC can assess
overall corridor saturation, but obscure the performance of individual splits.



Combining an assessment of individual splits v/c ratios that exceed 1.0 (Figure 5 and
Equation 3) with the level of intersection saturation provides the ability to visualize
periods of the day where there is slack capacity available to correct split failures (Figure
7).



The threshold (XT) value of XC to pursue improvements with split rebalancing (illustrated
by the horizontal lines in Figure 7) is a policy decision that an agency must decide. Table
1 shows how the minimum available slack time would tend to vary according to cycle
length and XT.



Once an agency selects a threshold, Figure 8 and Figure 9 illustrate how capacity
deficiencies on a corridor can be visualized.



Lastly, Table 2 allows an agency to assess the impact of selecting various XC values for
intervention. Table 3 breaks this information down by time of day. Table 4 illustrates
how this data can be used to provide a sorted list of phases where the greatest
opportunities for improvement exist.

Future work could also incorporate aspects of pedestrian service (23) into the methodology, and
integrate split and cycle length analyses based on capacity measures (Xi and XC) with an analysis
of progression quality (based on arrival type and estimated delay).

11/13/2009
TRB 2010 Annual Meeting CD-ROM

Page 28 of 31

1:39:48 PM
Paper revised from original submittal.

Day, Sturdevant, and Bullock

10-0008

ACKNOWLEDGEMENTS
This work was supported by the National Cooperative Highway Research Program, the Joint
Transportation Research Program administered by the Indiana Department of Transportation and
Purdue University, and the Federal Highway Administration’s Dwight D. Eisenhower Graduate
Transportation Fellowship. The contents of this paper reflect the views of the authors, who are
responsible for the facts and the accuracy of the data presented herein, and do not necessarily
reflect the official views or policies of the sponsoring organizations. These contents do not
constitute a standard, specification, or regulation.

11/13/2009
TRB 2010 Annual Meeting CD-ROM

Page 29 of 31

1:39:48 PM
Paper revised from original submittal.

Day, Sturdevant, and Bullock

10-0008

REFERENCES
1. National Transportation Operations Coalition. 2007 National Traffic Signal Report Card –
Technical Report. National Transportation Operations Coalition, Washington, DC, 2007.
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and T. Urbanik. Traffic Signal Timing Manual. Federal Highway Administration, Report No.
FHWA-HOP-08-024, 2008
3. Day, C.M., D.M. Bullock, and J.R. Sturdevant. “Cycle Length Performance Measures:
Revisiting and Extending Fundamentals,” Transportation Research Board Paper ID: 09-0061, in
press, 2009.
4. Bullock, D.M., J.R. Sturdevant, and C.M. Day. “Signalized Intersection Performance
Measures for Operations Decision Making,” Institute of Transportation Engineers Journal, ITE,
Vol. 78, No. 8, pp. 20-23, August 2008.
5. Day, C.M., R. Haseman, T.M. Brennan, H. Premachandra, J. Wasson, J.R. Sturdevant, and
D.M. Bullock. “Visualization and Quantitative Assessment of Arterial Progression Quality and
Travel Time Using High Resolution Signal Event Data and Bluetooth MAC Address Matching”,
Paper No. 09-0039, submitted to Transportation Research Record, July 2009.
6. Bullock, D.M. and C.M. Day, “Performance Measures for Managing Urban Traffic Signal
Systems,” Urban Transport, June 2009.
7. Miller, V.E. “Area Control by Digital Computer.” Traffic Engineering and Control, Vol.5, pp.
359-365, 1963.
8. Raynor, H.M. “Charleston’s Computerized Traffic Control System.” Traffic Engineering and
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11. Hunt, P.B. SCOOT—A Traffic Responsive Method of Coordinating Signals. Transportation
and Road Research Laboratory Report 1014, Crowthorne, Berkshire, United Kingdom, 1981.
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Algorithmic Architecture: Applying Adaptive Control System Technology to Closed-Loop

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Day, Sturdevant, and Bullock

10-0008

Traffic Control Systems.” Transportation Research Record No. 1856, Washington, DC:
Transportation Research Board, pp. 175-184, 2003.
16. Smaglik, E.J., A. Sharma, D.M. Bullock, J.R. Sturdevant, and G. Duncan, “Event-Based Data
Collection for Generating Actuated Controller Performance Measures.” Transportation Research
Record No. 2035, Washington, DC: Transportation Research Board, pp. 97–106, 2007.
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18. Smaglik, E.J., D.M. Bullock, and A. Sharma, “A Pilot Study on Real-Time Calculation of
Arrival Type for Assessment of Arterial Performance,” ASCE Journal of Transportation
Engineering, Vol. 133, No. 7, pp. 415-22, July 2007.
19. Day, C.M., E.J. Smaglik, D.M. Bullock, and J.R. Sturdevant, “Quantitative Evaluation of
Actuated Coordinated Versus Nonactuated Coordinated Phases,” Transportation Research
Record No. 2080, TRB, National Research Council, Washington, D.C., pp. 8-21, 2008.
20. Day, C.M., E.J. Smaglik, D.M. Bullock, and J.R. Sturdevant, Real-Time Arterial Traffic
Signal Performance Measures, Joint Transportation Research Program, Report FHWA/IN/JTRP2008/9, West Lafayette, IN: Purdue University, 2008.
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Signals,” Transportation Research Record, Paper ID: 08-2503, 2007.
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Report,” ITE Journal, Vol: 78, Issue: 2, February 2008.
23. Hubbard, S.M.L., D.M. Bullock, and C.M. Day, “Integration of Real-Time Pedestrian
Performance Measures into Existing Traffic Signal System Infrastrucutre,” Transportation
Research Record No. 2080, TRB, National Research Council, Washington, D.C., pp. 37-47,
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Level of Service.” Traffic Engineering, Vol. 44, No. 10, 1974.
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AB05H-11, Melbourne, Australia, August 7-10, 2005.

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