JOURNAL OF TRANSPORTATION
SYSTEMS ENGINEERING AND INFORMATION TECHNOLOGY
Volume 8, Issue 2, April 2008
Online English edition of the Chinese language journal
RESEARCH PAPER
Cite this paper as: J Transpn Sys Eng & IT, 2008, 8(2), 48í57.
Analytical Approach to Evaluating Transit Signal Priority
LIU Hongchao1,*, ZHANG Jie2, CHENG Dingxin3
1 Department of Civil and Environmental Engineering, Texas Tech University, TX 79409-1023, USA
2 KBR Inc., 1444 Oak Lawn Ave, Suite 100, Dallas, TX75207, USA
3 Department of Civil Engineering, California State University, Chico, CA 95929, USA
Abstract: Successful deployment of transit signal priority (TSP) systems requires thorough laboratory evaluation before field
implementation. Traffic simulation is a powerful tool in this regard; however, it requires tremendous efforts toward network coding,
data collection, and model calibration. Besides, simulation models tend to be project specific, and the models developed for one
project are often discarded upon the completion of that project. In this paper, it is shown that the impacts of two fundamental TSP
strategies (early green and extended green) can be evaluated using an analytical approach. The impacts of the above two strategies
on both the prioritized and the nonprioritized approaches are illustrated using graphical as well as analytical methods. A simulation
study is then conducted for comparison analyses, followed by a statistical approach for the test of generality.
Key Words:
1
traffic signal system; bus priority; traffic simulation; signal timing
Introduction
The importance of public transportation in providing
sustainable mobility is being recognized by researchers and
transportation authorities as well as the traveling public in the
United States. Transit signal priority (TSP) has shown promise
in improving the performance of in-service transit vehicles by
ensuring schedule adherence and reducing delay and
operational cost. The simulation approach has commonly been
used for evaluating TSP strategies as well as their impacts on
ˉ
other vehicles[1 3]. However, the efforts required for network
coding, data collection, and model calibration make the
simulation approach extremely tedious and time consuming.
Basic requirements for simulating TSP involve emulating
the logic of fixed time/actuated traffic signals under normal
operation and during transit signal priority, detection of a bus
at the check-in and check-out points, priority generator,
priority server, communication links between buses and traffic
signals, bus movements in the traffic stream, and dwelling
time at bus stops. Advanced features that need to be modeled
include, but are not limited to adaptive signal control,
Automatic Vehicle Location (AVL) systems, bus arrival time
predictor, and checking or monitoring bus schedule online [4,5].
As pointed out by Liu[6], most simulation models currently
available lack most of the characteristics and capabilities for
realistically modeling TSP systems.
In addition, the development of TSP simulation models has
been approached differently by researchers and traffic
engineers on the basis of their specific needs, and the
interpretations of simulation outputs vary significantly from
project to project. Recent examples include the works of
ˉ
Balke, Davol, Shalaby, Dion, and Ngan et al.[6 11].
Unfortunately, these models could not be used by other
users. Sunkari et al.[12] has presented an interesting modeling
approach, in which a simple evaluation model was developed
using the delay equation from the 1985 Highway Capacity
Manual. However, this method was oversimplified and did not
lead to practical application.
In the latest report by ITS America[13] and Smith et al.[14], it
is concluded that Early Green and Extended Green are the two
most commonly applied operational strategies in such systems.
These two strategies are identical in the sense that both rely on
shortening the green time of the opposing approaches to
obtain extra green time for the prioritized approach. A major
concern with regard to the “2E’s” operation is the possible
negative impact it might have on other vehicles.
This paper presents the analytical fundamentals underlying
the Early Green and Extended Green operations. The
analytical approach provides a useful tool for predicting and
evaluating the performance of a common TSP system in a
Received date: Jan 21, 2008; Revised date: Mar 6, 2008; Accepted date: Mar 11, 2008
*Corresponding author. E-mail: hongchao.liu@ttu.edu
Copyright © 2008, China Association for Science and Technology. Electronic version published by Elsevier Limited. All rights reserved.
systematic fashion. The advantages of an analytical approach
also lie in its simplicity and generality. Most data (e.g., bus
dwelling time, pedestrian demand, and vehicle speed) required
by simulation models become unnecessary for the analytical
method. The tremendous time and effort spent on coding
network geometries and calibrating simulation models can
also be saved.
where,
C=cycle length in second;
i=the prioritized phase;
Ri=red interval of phase i in second;
Ȝi=traffic demand on lane group i in vehicle/s;
U Oi / s i ;
ȡi=flow ratio of the lane group i, i
Si=saturation flow rate of lane group i in vehicle/s.
And the delay reduction per vehicle is
Ei ['(delay / veh)]
T (2 Ri T )
2C (1 U i )
ȝt
1
Ȝ
Analytical fundamentals of transit signal
priority
The intersection delay is composed of uniform delay,
random delay, and residual queue delay. The issue of concern
toward TSP is often the additional delay it might bring to the
general traffic, i.e., the ǻdelay. If we assume that operation of
TSP does not significantly change the randomness of traffic
flow, the random delay should remain unchanged before and
after the TSP. Hence, attention can be focused on the delay
changes in the uniform delay and the residual queue delay.
This will be presented in the following sections with graphical
illustrations.
2.1 Early green
Early Green applies if the signal is in red phase at the time
of detection for point detection based systems or will be in red
phase at the time when the bus is predicted to arrive at the
intersection for the zone and area detection based systems.
First, the impact of Early Green on the prioritized and
nonprioritized approaches is illustrated.
2.1.1 Impact of early green on prioritized approach
Figure 1 shows graphically an undersaturated case where
the approach arrivals do not exceed the capacity. When Early
Green is not operational, the green phase is started at point A,
and the corresponding deterministic delay can be easily
calculated by the first term of Webster’s formula. If Early
Green is present, the actual start time is at point B because of
the early start of the green interval. The small time interval T
(in seconds) in between A and B is the total amount of green
time obtained from the nonprioritized phases, i.e., T ¦j t j ,
where tj is the green time “borrowed” from the phase j. The
reduced intersection delay is thus the area of the shaded part,
which is
Oi T (2 Ri T )
(1)
E i ['delay ]
2(1 U i )
Ȝt
BB
AA
TT
s
1
R
R
C
C
CC
RR
time
Fig. 1 Impact of early green on prioritized approach
1
Cumulative vehicles
2
Cumulative vehicles
LIU Hongchao et al. / J Transpn Sys Eng & IT, 2008, 8(2), 48í57
tj
1
R
C
R
C
time
Fig. 2 Impact of early green on nonprioritized approaches
2.1.2 Impact of early green on nonprioritized approaches
The green interval T for the prioritized approach is obtained
by shortening the green intervals of preceding phases. Its
possible negative impact is one of the major concerns of the
traffic engineers regarding the TSP. This impact can also be
quantified. As shown in Fig. 2, when an otherwise
undersaturated signal phase is truncated before the queue on
the associated approach is cleared, the total increased delay is
composed of three elements if the assumption that TSP would
not change the randomness of traffic flows is valid.
The small triangle ǻ1 represents the initial queue delay
caused by the residual queue because of the truncation of the
phase; whereas ǻ2 represents the additional delay caused by
the increased traffic arrivals during the prolonged red interval
in the subsequent cycle; and ǻ3 is the delay under normal
operation when there is no truncation.
The average initial queue delay E j [ ' 1 delay ] is calculated
by
2
2
s j >R j (C t j )(1 U j )@
(3)
E j ['1delay ]
2O j (1 U j )
The induced delay during the extended red interval is
E j [' 2 delay ]
(2)
O j t j (2R j t j )
2(1 U j )
Rj
(4)
sj[
(C t j )](R j t j )
1 U j
where tj=the amount of green time “borrowed” from phase j.
Hence, the total increased delay because of the early
termination is
LIU Hongchao et al. / J Transpn Sys Eng & IT, 2008, 8(2), 48í57
(5)
And the issue of concern, i.e., the increased delay per
vehicle is approximately
E j ['delay / veh]
E j [ 'delay ]
(6)
O jC
The impact of the early green on minor approaches is
sensitive to the flow ratio of the affected approach and the
amount of green time taken from the associated phase. It is
evident that E j [' 1 delay ] 0 gives the upper threshold of tj,
which is the maximum available green time that can be
“borrowed” for the prioritized phase without causing cycle
failure at the associated phase. The t j (optimal ) yields
t j (optimal) C Rj
(7)
1 U j
This provides an additional guidance in TSP planning while
determining the extent to which a minor phase can be
shortened under specific traffic and signal timing conditions.
In practice, tj should be kept less than but as close as possible
to t j (optimal ) so as to obtain maximum benefit for transit
vehicles and at the same time, keeping the truncated phases
undersaturated during and after the priority operation.
2.2 Extended green
The strategy of Extended Green is usually implemented at
the end of the requested phase when the “check-out call” from
a bus has not been received during the normal green interval.
A similar analysis is conducted in the following sections to
illustrate the impact of Extended Green on both prioritized and
nonprioritized phases.
2.2.1 Impact of extended green on prioritized approach
Consider the diagram shown in Fig. 3. If the approach is
assumed to be undersaturated and a bus is able to pass through
the intersection during the extended green interval, the actual
delay of the bus can be reduced to almost zero. The same
benefit can be obtained only by those vehicles traveling with
the bus, and the vehicles that have traversed the intersection
during the normal green interval will not benefit from the
operation. Therefore, it is intuitive that the operation of Green
Extension can bring maximum benefit to transit bus but will
not bring as much benefit as the Early Green does to other
vehicles on the same approach.
The reduction in delay, thereby saving time, by the
extended green for general vehicles can be approximately
estimated by calculating the shaded area in Fig. 3, which is
Ei ['delay] TRi Oi T 2 Oi
(1 U i )
2
Ei ['(delay / veh)]
Ei ['delay ]
Oi (C T )
(9)
2.2.2
Impact of extended green on nonprioritized
approaches
In contrast to the operation of early green where the
nonprioritized phases are treated before the start of the
prioritized phase, the minor phases are shortened during either
the priority cycle or the transitional/recovery cycle in the case
of the extended green. The negative impact of the extended
green on the affected approaches comes from two aspects,
namely, the green time of the prolonged red interval and the
truncation of the green phase. The former is the result of a
lengthened red interval because of the extension of the green
time of the prioritized green phase. The latter is because of the
early termination of the green phase during the transition,
which is similar to the operation in the early green.
Figure 4 graphically depicts the two kinds of delay induced
by the extended green. It is worthy to note that the two parts
of the delay might not apply simultaneously to all affected
phases. Some of the phases might experience only the second
part of the delay, whereas some others might experience both.
It depends largely on how the extended interval T is
“digested” among the subsequent phases.
1
Cumulative vehicles
E j ['1delay ] E j [' 2 delay ]
T
1
R
C
C
R
time
Fig. 3 Impact of green extension on the bus approach
1
Cumulative vehicles
E j ['delay ]
(8)
The average reduction in delay per vehicle is obtained by
dividing the total reduced delay by the number of vehicle
arrivals during (C+T), i.e. Oi (C T ) .
1
R
tj
C
R
C
Fig. 4 Impact of green extension on affected minor phases
time
LIU Hongchao et al. / J Transpn Sys Eng & IT, 2008, 8(2), 48í57
The delay caused by the prolonged red interval is
represented by the shaded area of ǻ1, which is
O j t j (2 R j t j ) ( j z i ,
t j  [0, T ] ) (10)
E 1j [' 1 delay ]
2(1 U j )
Hence, the issue of concern, i.e., the total increased delay
per vehicle for phase j because of the green extension is either
E 1j ['1delay / veh] or E 2j [' 2 delay / veh] , or E 1j [' 1 delay / veh]
2
+ E j [' 2 delay / veh] , depending on the specific TSP policy.
The average increased delay per vehicle because of the
enlarged green interval is
3
E1j ['1 (delay / veh)]
t j (2 R j t j ) (
j z i,
2C (1 U j )
t j  [ 0, T ] )
(11)
The delay caused by the early termination of the phase
during the transition is depicted by the shaded area ǻ2, which
is
2
E j [' 2 delay ]
O j t j ' (2R j t j ' )
2(1 U j )
Rj
sj[
(C t j ' )](R j t j ' )
1 U j
( j z i , t 'j  [0, g j ] )
(12)
Where tj=the amount of green time “cut” from phase j (for
return to coordination); gj = the green interval of phase j;
The increased delay per vehicle is
E 2j [ ' 2 delay / veh]
E 2j [' 2 delay ]
(13)
O jC
Example applications and simulation test
3.1 Analytical method
The example uses a typical signalized intersection with
common lead-lag phases. Signal priority applies to the
coordinated phases 2 and 6. As shown in Table 1, all one
needs is the signal timing plan and the traffic demand.
To begin with, let’s consider the early green. The easiest
but least effective way is to terminate all preceding minor
phases right after their minimum green interval is processed.
For illustrative purpose, the “minimum green” strategy is
evaluated in this example. Note that the v/c ratios of phase 4
and 8 as well as phase 5 are already high and it is very likely
that their associated approaches might become oversaturated
after TSP operation. The quantitative results are summarized
in Table 2.
Table 1 Traffic and signal timing information
Phases
Movements
Ȝ (veh/h)
S (veh/h)
144
1 800
102
1 800
120
1 800
180
1 800
1 (4,8)
2 (3,7)
3a (2,5)
3b (2,6)
3c (1,6)
160
1 800
2 160
5 400
1 840
5 400
2 160
5 400
1 840
5 400
108
1 800
Green time (s)
Lost time (secs)
Degree of saturation
20
4
0.57
10
14
4
1.00
6
10
14
26
44
62
6
10
14
Min
Avg.
Max
8
14
6
Cycle (secs)
0.89
100
0.74
4
0.63
Table 2 Impact of early green
(secs)
T
(secs)
Increased delay/veh./cycle
(secs)
Reduced
delay/bus/cycle
(secs)
Avg.
delay/ veh.
Degree
of
saturation
6
6.5
u
0.0
u
40.2
1.00
2 (3,7)
4
0.0
u
22.1
u
67.1
1.67
3a (2,5)
4
1.3
u
17.7
u
62.1
1.48
3b (2,6)
u
u
14
u
14
9.8
0.59
3c (1,6)
u
u
u
0.0
u
43.1
0.63
tj
(secs)
t j (optimal )
1 (4,8)
Phases
Movements
LIU Hongchao et al. / J Transpn Sys Eng & IT, 2008, 8(2), 48í57
Table 3 Impact of extended green
Phases
Movements
T (secs)
tj (secs)
1 (4,8)
u
8
2 (3,7)
u
3a (2,5)
t 'j
(secs)
Increased delay/vehicle (secs)*
Reduced delay/bus (secs)
4
7.8+0=7.8
u
4
4
4.1+18.8=22.9
u
u
u
u
u
u
3b (2,6)
8
u
u
u
44.5
3c (1,6)
u
0
0
0.0
u
*: In the form of E1[' delay / veh] E 2[' delay / veh]
j
1
j
2
For a phase terminated at the time of “minimum green”, tj is
the difference between the phase length and the minimum
green interval. The sum of tj of each minor phase is T, which
is 14 s in this case. It is shown from the result that when tj is
close to t j (optimal ) , e.g., the phases (4, 8), the increased
delay on the associated approach is very low. Otherwise, the
delay might increase significantly (e.g., for the movements of
the phase (3, 7) and phase 5).
Assume that an 8-second-extended green was applied to the
phase 6 during the priority cycle. As a result, the vehicles of
the phase immediately next to the phase 6, i.e., phase (4, 8),
experienced an additional 8 s for waiting the green light. Thus,
t( 4,8) is 8 seconds in Eqs. (11) and (12) for the calculation of
E(14,8) . Unlike the case in the fixed-time control, where these 8
seconds is transferred to all subsequent phases, the extra
waiting time induced to later phases depend on the duration of
the preceding phases as well. For example, if the phase (4, 8)
2
was shortened for 4 seconds during the transitional cycle, E j
'
should also apply and t 4,8 4 s. Consequently, the phase next
to (4, 8), i.e., phase (3, 7) is subject to 4 s for the extended red
1
interval (i.e., t3,7=4 s) and E j should apply. Similarly, if the
2
phase was also cut off for, say, 4 seconds, E j should apply as
well and the transition could be finished at the end of this
phase, which incurs no impact on the following phase 5. The
result is summarized in Table 3.
A simple examination of the result is conducted by
observing the reduction of the bus delay. For an
undersaturated approach, if there is no green extension, the
bus is likely to be stopped by the signal and wait for a full red
interval until the next green phase. Hence, it is intuitive that
the reduced bus delay should be close to the red interval of the
associated phase. In this case, the average bus intersection
delay was reduced by 44.5 seconds, which is very close to the
red interval of phase 6, which is 46 seconds. Compared to the
8 seconds’ delay reduction brought by the early green, it is
obvious that the extended green is more efficient in terms of
the time saving for buses.
Note that the increased delay on the affected approaches is
1
2
given in the form of E j ['1delay / veh] E j [' 2 delay / veh] for
illustration. As previously stated, all of the minor phases
except for the phase 5 and 1 were subject to the delay of both
types in this example. The increased delay by the prolonged
red interval seems to be much smaller than that caused by the
phase truncation. Given the amount of time it saved for the
buses, it is fair to conclude that in general the operation of the
extended green is more efficient than the early green in the
case where buses can traverse the intersection during the
extended green interval.
3.2 Simulation test
VISSIM simulation[15] was used in the test. The check-out
detectors are placed at the stop bar and the distance between
the check-in and check-out detectors is 300 ft. The travel
speed of the transit buses and passenger cars is 25 mph and 35
mph, respectively, which are changed later for the generality
test. Default acceleration and deceleration rates are used for
both passenger cars and transit buses, which is 11.5 ft2/s and
–9.0 ft2/s, respectively.
VISSIM simulates the operation of early green and green
extension according to the travel time predetermined in the
NEMA editor on the basis of free flow speed. If the bus is
predicted to arrive during the green and there is still enough
time in the normal green phase, the TSP call is ignored.
Similarly, a request for the green extension might be put on
hold to the next cycle for the early green if there is no enough
green for extension. In addition, the Basic Bus TSP function
has a built-in re-service timer that prevents TSP from
occurring too often. The re-service timer will prevent TSP
calls from being placed after a previous TSP call until the zero
point of the cycle has been crossed twice. The built-in TSP
function in VISSIM is close to the control logic in the field as
described in the previous sections, which makes the
simulation test reliable.
LIU Hongchao et al. / J Transpn Sys Eng & IT, 2008, 8(2), 48í57
Table 4 Model calibration
Delays of bus priority phase (phase 6)
No TSP
Deviation
(secs/veh.)
No.1
Calculated value
(secs/veh.)
19.0
Mean simulated value
(secs/veh.)
18.4
No.2
19.0
17.7
1.3
No.3
19.0
17.5
1.5
Average
19.0
17.9
1.1
Delays of other phase (phase 4 and 8)
No TSP
0.6
Deviation
(secs/veh.)
No.1
Calculated value
(secs/veh.)
40.2
Mean simulated value
(secs/veh.)
37.1
No.2
40.2
42.3
2.1
No.3
40.2
41.1
0.9
Average
40.2
40.2
0.0
Delays of other phase (phase 3 and 7)
No TSP
3.1
No.1
Mean simulated value
(secs/veh.)
43.0
No.2
45.0
43.0
2.0
No.3
45.0
43.9
1.1
Average
45.0
43.3
1.7
Delays of phase 5
4
Statistical test
T-test is used for the proof of generality for the same case
with different random seeds. Enough simulation runs were
made by using different random seeds. Ten different random
seeds are tested and the results are summarized in Table 7.
For the prioritized phase (phase 6) and phase (4, 8), the
hypothesis is accepted at the 95% confident level. For phase
(3, 7) and phase 5, the hypothesis is rejected. This is
reasonable because the analytical method is more accurate for
the undersaturated situation. The degree of saturation is 1.67
for phase (3, 7) and 1.48 for phase 5.
Deviation
(secs/veh.)
Calculated value
(secs/veh.)
45.0
No TSP
simulation result, the speed of the passenger cars was changed
from 35mph to 45mph and the speed of transit buses from
25mph to 35mph, and no significant effect was found.
2.0
Deviation
(secs/veh.)
No.1
Calculated value
(secs/veh.)
44.4
Mean simulated value
(secs/veh.)
49.9
No.2
44.4
53.6
9.2
No.3
44.4
57.0
12.6
Average
44.4
53.5
9.1
5.5
The calibration of the simulation model was conducted by
comparing the simulation result with that of the analytical
approach. In accordance with the analytical analysis, the
random delays were excluded from the simulation. As shown
in Table 4, the uniform delay and the residual queue delay
from simulation are close to the calculated values when there
is no TSP. The average deviations for phase 6, phase (3, 7),
and phase (4, 8) are 1.1, 0.0, and 1.7, which indicates a less
than 6% range between the analytical calculation and
simulation values. For phase 5, the deviation is 9.1, which is
still acceptable.
Statistical analysis was conducted to furthermore evaluate
these results. The impact of early green was derived from
simulation runs and compared with the calculation results in
Table 5. The average deviations for phase 6, phase (3, 7),
phase 8 and 5 are 1.5, 7.3, 7.2, and 2.8 secs. The most
significant error is 7.3 sec in phase (4, 8), which is still in
18.2% range. Table 6 gives the result for the simulated and
calculated values with the Green Extension. Similar to the
case of the Early Green, the results agree with each other
fairly well. To evaluate the impact of the vehicle speed to the
Table 5 Comparison between the analytical method and simulation
with early green
Delays of bus priority phase (phase 6)
Early green
Deviation
(secs/veh.)
Calculated value
(secs/veh.)
Simulated value
(secs/veh.)
No.1
9.8
8.5
1.3
No.2
9.8
8.2
1.6
No.3
9.8
8.2
1.6
Average
9.8
8.3
1.5
Impact to other phase (phase 4 and 8)
Early green
Deviation
(secs/veh.)
Calculated value
(secs/veh.)
Simulated value
(secs/veh.)
No.1
40.2
37.1
3.1
No.2
40.2
42.3
2.1
No.3
40.2
63.1
22.9
Average
40.2
47.5
7.3
Impact to other phase (phase 3 and 7)
Early green
Deviation
(secs/veh.)
Calculated value
(secs/veh.)
Simulated value
(secs/veh.)
No.1
67.1
55.4
11.7
No.2
67.1
54.9
12.2
No.3
67.1
69.5
2.4
Average
67.1
60.0
7.2
Impact to phase 5
Early green
Deviation
(secs/veh.)
Calculated value
(secs/veh.)
Simulated value
(secs/veh.)
No.1
62.1
70.9
8.8
No.2
62.1
43.5
18.6
No.3
62.1
63.5
1.4
Average
62.1
59.3
2.8
LIU Hongchao et al. / J Transpn Sys Eng & IT, 2008, 8(2), 48í57
Table 6 Comparison between the analytical method and simulation
with green extension
Calculated value
(secs/veh.)
Simulated value
(secs/veh.)
Deviation
(secs/veh.)
Delays of bus priority
phase (phase 6)
15.2
13.6
1.6
Impact to minor phase
(phase 4,8)
48.0
48.2
0.2
Impact to minor phase
(phase 3,7)
67.9
64.0
3.9
Green extension
5
priority system with the Early Green and Extended Green
operations. Through graphical illustration, it was shown that
the impact of Early Green and Extended Green on buses and
general traffic could be quantified using D/D/1 queuing
models if the issue of concern is the induced delay. A
numerical example was also presented. The result shows that
the proposed method is promising in that it requires very
limited information and provides fairly reasonable results. The
analytical approach can be used independently or as a
supplementary tool to simulation models for complicated
situations. Future researches might include a comprehensive
comparison analysis of the analytical approach with field
observation and theoretical or data proof that TSP does not
change the randomness of traffic flows, and extend the
analytical approach for analysis of other TSP treatments such
as the queue jumpers and transit phases.
Conclusions
Traffic simulation is a useful tool for the evaluation of a
transit signal priority system. However, it is well-known that
the development of simulation models has been inconsistent
and project specific. This paper presented an analytical
approach for the design and evaluation of a transit signal
Table 7 Simulation results with different random seeds
Random seed
Time point (s)
10
20
30
42
50
60
70
80
90
100
Phase 6 (E-W)
Phase 4, 8 (S-N)
Phase 3, 7 (S-W)
Phase 5 (W-N)
Cal.
Sim.
Cal.
Sim.
Cal.
Sim.
Cal.
2 368
9.8
10.1
40.2
38.8
67.1
50.8
62.1
Sim.
31.5
2 768
9.8
9.5
40.2
49.1
67.1
41.4
62.1
49.6
2 368
9.8
10.1
40.2
39
67.1
50.7
62.1
31.8
2 768
9.8
9.5
40.2
50.1
67.1
50.6
62.1
49.6
43.1
469
9.8
8.9
40.2
22.5
67.1
51.3
62.1
2 368
9.8
11.2
40.2
38.9
67.1
41.8
62.1
32.3
2 768
9.8
9.6
40.2
49.1
67.1
50.4
62.1
50.0
2 410
9.8
10.0
40.2
38.3
67.1
50.2
62.1
32.6
2 815
9.8
9.5
40.2
49.1
67.1
50.1
62.1
49.8
42.9
3 180
9.8
8.7
40.2
22.0
67.1
51.0
62.1
2 368
9.8
11.0
40.2
39.3
67.1
41.8
62.1
38.6
2 768
9.8
9.7
40.2
49.5
67.1
41.5
62.1
50.1
2 368
9.8
10.3
40.2
38.8
67.1
50.9
62.1
32.7
2 768
9.8
9.3
40.2
49.5
67.1
51.3
62.1
50.1
3 168
9.8
8.9
40.2
22.6
67.1
51.3
62.1
59.5
2 368
9.8
10.0
40.2
38.5
67.1
50.4
62.1
32.7
2 768
9.8
9.7
40.2
49.0
67.1
51.1
62.1
49.2
2 368
9.8
11.0
40.2
38.6
67.1
50.6
62.1
38.7
2 768
9.8
9.7
40.2
49.5
67.1
60.2
62.1
49.3
2 368
9.8
9.9
40.2
38.5
67.1
50.5
62.1
32.0
2 768
9.8
9.4
40.2
49.3
67.1
50.6
62.1
49.5
2 368
9.8
10.8
40.2
39.0
67.1
50.7
62.1
32.9
2 768
9.8
9.5
40.2
49.1
67.1
50.7
62.1
49.8
3 168
9.8
9.0
40.2
22.0
67.1
41.8
62.1
59.0
Table 8 Result of T-test
Phase
Cal.
95% confident interval
lower
upper
p-value
Accept or reject
6
9.8
9.5166
10.0918
0.9763
Accept
4,8
40.2
36.3476
44.4941
0.9516
Accept
3,7
67.1
47.3699
51.1051
6.12E-16
Reject
5
62.1
39.3525
47.0892
6.38E-10
Reject
LIU Hongchao et al. / J Transpn Sys Eng & IT, 2008, 8(2), 48í57
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