Kelompok 2 Rek Lalulintas

7/21/2019 Kelompok 2 Rek Lalulintas

http://slidepdf.com/reader/full/kelompok-2-rek-lalulintas 1/59

Chapter 5

Link Travel Time: Simulation Analysis

5.1 Simulation description

To verify the qualitative analysis proposed in the previous section, a simple network

is modeled using VISSI ! a microscopic traffic simulation model "y #TV $%

&http'((www.english.ptv.de(). The imaginary time period is morning and the imaginary

network is a corridor towards city center.

The network is illustrated in *igure 5!1. +ach intersection is controlled "y a two!

phase fied!time signal with a cycle length of 1- s. The offset time of two consequent

intersections is / s. The signal scheme is shown in *igure 5!1. Turning rate at each

intersection is also shown in the figure.

The network is simulated for / h with time varying demands. Vehicles are generated

at origin 0ones &112, see *igure 5!1) with #oisson distri"ution. Ta"le 5!1 shows the

"ase vehicle inputs of each 0one and the temporal variation.

5/



Table 5-1. ehi!le inputs

3ase Vehicle Inputs &Veh(h) Temporal Variation

4rigin one Vehicle Inputs Time &s) #roportion of 3aseVehicle Inputs

1 1 6 .1

211 7 6 17 .2

12 5 17 28 .5

28 /9 1

/9 -5 1.2

-5 9/ 1.5

9/ 82 1

82 71 .7

71 17 .5

In the network, only the links from link 2 to link 5 are interested. *igure 5!1 shows

the data collection points &$ *), which are located at the reference points of the

entrance and eit of link. :hen a vehicle pass through any data collection points, the

vehicle I;, pass time, and spot speed of the vehicle are collected and recorded into a

log file. Then, the num"er of accesses &only through movement), mean spot speed at

upstream &only through movement), and mean travel time &only TT) of the interested

links are aggregated in every signal cycle using the log file.

5.2 Simulation result

*igure 5!2 shows the aggregated result. The num"er of accesses &only through

movement), mean spot speed at upstream &only through movement, unit' m(s), and

mean travel time &only TT) in each signal cycle are illustrated "y three solid lines. The

figure also shows the individual travel time reports &<) and the temporal variation of

vehicle inputs &dot line).

55



.No of Accesses

60 50 40 30 20 10 0

t r a v e l t i m e a c c e s s e s s p o t s p e e d

9 9 0 0

1 0 8 0 0

1 5 . 1

m e a n n o . o

f m e a n

9 0 0 0

7 2 0 0

8 1 0 0

r e s u l t " l i n k # $

4 5 0 0

5 4 0 0

6 3 0 0

S i m u l a t i o

n i m e ! s "

% l l u s t r a t i o

n o & s i m u l a t i o n

5 9

3 6 0 0

5 - # " a $ .

1 5 . 1

2 7 0 0

F i g u r e

1 3 .

3

1 8 0 0

9 0 0

0

160 140 120 100 80 60 40

ravel ime !s"



.No of Accesses

60 50 40 30 20 10 0


9 9 0 0

1 0 8 0 0

1 3 . 7

m e a n n o . o

f m e a n

7 2 0 0

8 1 0 0

9 0 0 0

r e s u l t " l i n k ' $

4 5 0 0

5 4 0 0

6 3 0 0

S i m u l a t i o

n i m e ! s "

% l l u s t r a t i o n o & s i m u l a t i o n

5 8

3 6 0 0

5 - # " b $ .

2 7 0 0

F i g u r e

1 8 0 0

1 5 . 1

9 0 0

0

120 100 80 60 40

ravel ime !s"



.No of Accesses

60 50 40 30 20 10 0

1 4 .

6


9 9 0 0

1 0 8 0 0

m e a n n o . o

f m e a n

9 0 0 0

9 . 4

7 2 0 0

8 1 0 0

r e s u l t " l i n k (

$

4 5 0 0 5 4 0 0

6 3 0 0

S i m u l a t i o n i m e ! s "

% l l u s t r a t i o n o & s i m u l a t i o n

5 7

3 6 0 0

5 - # " ! $ .

1 5 . 3

2 7 0 0

F i g u r e

1 3 .

1

1 8 0 0

9 0 0

0

200 150 100 50

ravel ime !s"



.No of Accesses

60 50 40 30 20 10 0


9 9 0 0

1 0 8 0 0

1 4 . 8

m e a n n o . o

f m e a n

9 0 0 0

1 0 .

2

6 .

2

4 5 0 0 5 4 0 0

6 3 0 0

7 2 0 0

8 1 0 0

S i m u l a t i o n i m e ! s "

% l l u s t r a t i o n o & s i m u l a t i o n r e s u l t " l i n k 5 $

5 6

3 6 0 0

5 - # " ) $ .

2 7 0 0

F i g u r e

1 3 .

4

1 8 0 0

9 0 0

0

200 150 100 50

ravel ime !s"



+ach intersection in the simulation network has same geometric properties and thus

the capacity of each intersection should "e identical. *rom *igure 5!2d, it can "e

concluded that the capacity is a"out 55 vehicle(cycle.

$s shown in *igure 5!2, when the num"er of accesses is lower than the capacity of

upstream intersection, mean travel time on link / ehi"its large variation while mean

travel times on other links are relatively sta"le. That is, though the pro"a"ility of =ase

II in #hase I is small, it still happened. In this simulation, the offset time of two

consequent intersections is set as / s and the length of the links is 5 m. Thus, when

a vehicle>s speed eceeds 19.8 m(s &9 km(h), it is possi"le that the vehicle will pass

through a link within / s and does not stop at the downstream intersection of the link

even if it through the upstream intersection of the link in the end of the green period or

in the am"er period. ?owever, when the offset time is set smaller than /s, for eample

2 s, the vehicle will stop at the downstream intersection, and the pro"a"ility of =ase II

in #hase I will increase and mean travel time will ehi"it more variation. ore

importantly, mean travel time at all links cannot trace the change of the num"er of

accesses in #hase I. That is, in #hase I, mean travel time is not a good indicator of link

performance and the num"er of accesses should "e used for tracing the change of link

performance.

$t a"out 5- s on link - and link 5, the spot speed start to decrease. The decrease

of the spot speed at upstream of a link will increase air pollution and it can "e

considered as undesira"le situation. $t same time, as shown in *igure 5!2d, the num"er

of the accesses is not reduced o"viously. =hoosing the spot speed or the num"er of

accesses as the criterion of the undesira"le situation should "e determined "ased on the

researchers> @udgment. $t this phase, mean travel time is o"viously larger than other

phase and the distri"ution of travel time tends to one peak. Therefore, it is easy to

9



identify the phase using small si0e #V reports. ?owever, as mentioned earlier, the

phase is undesira"le situation and should "e avoided.

To avoid the a"ove phase, it is important to identify the previous phase &#hase II) of

the a"ove phase. $s shown in *igure 5!2c and *igure 5!2d, in #hase II, mean travel

time increases gradually. In this phase, there are two sets in travel time reports' one

without intersection delay and with intersection delay. The proportion of the set with

delay increases and the means of the two sets also increase over time. It causes the

increase of mean travel time. Asing small si0e #V reports, it is hardly epected that the

proportion of the set with delay &or without delay) can "e estimated. ?owever, the

variance of each set is relatively small and the means of the two sets can "e estimated

"y small si0e sample. This is the key idea of the estimation method proposed in

=hapter 8.

5./ Summary of this chapter

In this chapter, the microscopic traffic simulation model VISSI is used to confirm

the qualitative analysis proposed in the previous section.

The num"er of accesses, mean spot speed at upstream &only through movement,

unit' m(s), and mean travel time &only TT) in each signal cycle are aggregated rather

than mean travel time only. The aggregation shows that &1) in #hase I, mean travel time

is not a good indicator of link performance and the num"er of accesses should "e used

for tracing the change of link performance, and &2) in #hase II, though mean travel

time can trace the link performance, individual travel time reports show that the link

travel time distri"ution is two!peak, which makes the estimation of mean travel time "y

small si0e travel time reports from #Vs difficult.

91



Chapter *

Appli!ability o& the Formulations o& the A)e+uate ,umber

The success of pro"e!"ased $TIS highly depends on the relia"ility of pro"e reports,

and the cost and capacity of the communication "etween #Vs and the operation center

impose restrictions on the num"er of #Vs. Therefore, it is impossi"le to make all

vehicles as #Vs. In other words, a set of travel time reports from #Vs on a link in a time

interval is a sample. The adequate sample si0e required to estimate mean travel time of

all vehicles &population) relia"ly has "een an imperative issue since pro"e vehicle was

recogni0ed as a method to collect traffic information and there are many literatures, for

eample 3oyce et al. &1661), =hen and =hien &2), =heu et al. &22), ?ellinga and

*u &1666), Buiroga and 3ullock &1667) and Srinivasan and Covanis &1669).

Two methods standard deviation formulation and confidence interval method are

commonly accepted, and were used as the relia"ility criterion. It should "e noted that

these formulations are "ased on =entral Dimit TheoremE that is, the result is dou"tful

when the population is severely nonnormal and sample si0e is small. This chapter will

eamine the applica"ility of the two methods on a signali0ed link.

9/



9.1 Sample si0e formulations

$ num"er of researchers have investigated the adequate num"er of #Vs at network

level and at link level. $t link level, two methods standard deviation formulation &+q.

1) and confidence interval method &+q.2) were proposed and are commonly accepted,

and were also used as the relia"ility criterion for each links in network level studies. In

the two methods, the former is used for links with normal distri"ution and the latter is

used for links without normal distri"ution.

t 2

sα (2, n#1

&1)n $

ε

x #t α ( 2,n#1 s ( n %µ% x &t α ( 2,n#1 s ( n &2)

9.2 $ssumption of travel time distri"ution

4"viously, the percentage of Set I in the queue, a""reviated as p, is a critical factor

that affects the average travel time of the vehicles in the queue &*igure -!8). Thus p is

considered as a performance indicator in this chapter, and travel time distri"ution at a

certain performance level & p F 85G is chosen @ust as an eample) is inferred "ased on

*igure -!8 and historical data descri"ed in section -.-. In the figure, it is assumed that

the vehicles spread during green period with uniform. In reality, the situation is more

comple than the illustration in the figure. There are some vehicles with other turning

movements and some vehicles partly through the link in the queue. ?owever, the

effects of these vehicles are ignored.

9-



*or p F 85G, the distri"ution can "e approimated as a composite of two normal

distri"ution and the mean and standard deviation of Set I and II can "e determined

from the historical data.

The means of %roup I and II in historical data are considered as the means of Set I

and Set II in real!time data at p F 6 G. Ander uniform assumption, when p decreases

p , the mean of Set I and Set II will increase p G &G is length of green time).

=onsequently, the mean of Set I and Set II at p F 85 G can "e calculated "y adding

15G 'G to the mean of Set I and Set II at p F 6 G, respectively. In this section, G is

set as 9 s.

Anlike historical data, the day!to!day variation is not included in real!time data and

it is reasona"le to consider that the variation of each set in real!time is smaller than the

variation in historical data. $dditionally, the adequate sample si0e is a function of the

standard deviation of link travel time, and the standard deviation is mainly contri"uted

"y the fact that there are two sets simultaneously "ut rarely contri"uted "y the variation

in each set. Thus, the standard deviations of all sets at p F 85 G are specified as one!

half of the standard deviation of %roup I.

Ta"le 9!1 summari0es the mean and the standard deviation of all and each set at p F

85 G. 3ased on the assumption of normal distri"ution in each set, the distri"ution of

travel time on the study link at p F 85 G is o"tained.

Table *-1. Travel time )istribution at p 5 /

mean &s) sd

Set I &85G) 1/5 -.92

Set II &25G) 226 -.92

$ll 157 -1.12

95



9./ $pplica"ility

$ simulation method is provided as a reference method against which the

applica"ility of standard deviation formulation and confidence interval method is

eamined. In the three methods, 15 s is selected as the pre!specified permitted error

& ), which is a"out 1 G of mean at p F 85G.

$ sample with si0e 1 is drawn from the distri"ution at p F 85 G o"tained from

previous section and is considered as the population and further sampling with sample

si0e n are performed from the population.

The simulated method is straightforward. *or each sample si0e n, 1 samples are

taken and the percentage of accepted samples is calculated. $ccepted sample means

that the sample mean fall into &µ , µ ) & is population mean). The percentage

for sample si0e from 1 to - is shown in Heference column in Ta"le 9!2. The

percentage increases as sample si0e increase and achieves 65 G when n F 28.

*or standard deviation formulation &+q. 1), / samples with sample si0e n are taken

and the formulation is eamined &α .5 ). The accepted(re@ected, the percentage of Set

I, sample mean and sample standard deviation of each sample are shown in Ta"le 9!2.

In the ta"le, the accepted samples are highlighted "y gray "ackground. :hen n 28,

there are some accepted samples. The cause is the critical underestimation of standard

deviation. The underestimation leads the right side of +q. 1 to "ecome small and the

inequality to "e satisfied. The cause of the underestimation is the sampling error. $s

shown in the ta"le, p of accepted samples is much larger than the percentage of Set I of

population &85 G). In contrast, when n JF 28, there are lots of re@ected samples. The

cause of most re@ect is the overestimation of standard deviation, and the cause of the

overestimation is also sampling error. In summary, the standard deviation

99



formulation is sensitive with sampling error and cannot provide consistent result.

*or confidence interval method , one sample is taken for each n and the

accepted(re@ected, the percentage of Set I, range of confidence interval, lower!

confidence "ound and upper!confidence "ound are calculated &Ta"le 9!2). $s shown in

the ta"le, the criterion that is the 1&1 α ) percent confidence interval calculated from

samples contains the population mean is satisfied in most n &α (.5 ). ?owever, when

n is small, the range of confidence interval is etremely large. It indicates that the a"ove

criterion is not enough to provide correct @udgment and the range of confidence interval

should "e checked. :hen n JF 28, the most confidence interval ranges are smaller than

2 and the confidence interval method with checking the confidence interval range can

"e considered as a good estimation method.

It is enough to present the shortcomings of these two methods using three times

sampling in standard deviation formulation and one time sampling in confidence

interval method . Thus further sampling is not performed in this study.

In the o"servation descri"e in the net chapter, the accesses with through movement

at Sakurayama in each signal cycle is a"out 5 vehicles and if we consider three signal

cycles as aggregation time interval the accesses is a"out 15. 3ecause we only

consider the vehicles with TT, if 7 G of accesses with through movement at %okiso,

the si0e of population is a"out 12. =onsequently, n F 28 means that a"out 22.5 G

vehicles are needed as #Vs to estimate the population mean of the study link with

F 15 s.

98



Table *-#. Appli!ability o& prevalent &ormulations

n HeferenceStandard deviation formulation =onfidence interval method

Sample 1 Sample 2 Sample /&G)

$(H p mean sd $(H p mean sd $(H p mean sd $(H p range low high

1 87 1 1 1// /.5 . 8 199 -5.6 . 8 19/ --.9 1 5 1/ 1/511 88 . 72 152 /6. . 8/ 157 -5.5 . 72 152 /9.9 1 8/ 58 1// 16

12 89 . 5 172 -8.8 . 7/ 15 /7./ . 57 18/ -8.9 1 85 51 1// 17-

1/ 72 . -9 179 -8.6 . 96 19/ --.8 . 96 195 --.6 1 96 5- 1/8 16

1- 86 . 79 1-6 /5.1 . 86 158 /6.6 . 86 15- /6.6 1 86 -8 1/2 186

15 7- . 7 155 -.1 . 8/ 191 --.5 . 78 1-6 /2.- - 5- 199 2219 79 . 9/ 181 -8.7 . 96 19/ -5.8 . 96 19/ -9.8 1 96 -6 1/6 176

18 77 . 72 152 /5.7 . 77 1-- /.- . 72 151 /7.6 1 72 - 1/1 181

17 61 . 87 159 -1.2 . 7/ 15 /9.2 . 7/ 15 /8.- 1 91 -7 1-7 165

16 6 . 86 155 /7. . 97 195 -9.8 . 57 185 -8.- 1 86 /7 1/9 18-

2 61 . 8 192 -2.1 . 75 1-7 /5.2 1 85 - 1/7 1871 65 1/6 21.8

21 61 . 81 19 -5.1 . 81 191 -/.6 1 65 1-1 22.1 1 52 -/ 158 21

22 62 . 88 159 -1. 1 61 1-/ 27. . 88 158 -.6 1 72 /- 1/8 181

2/ 6/ . 91 182 -9.2 . 8 19- -/.9 . 8- 156 -/.1 1 8- /8 1-1 187

2- 6/ . 86 155 /7.6 . 81 191 -/.8 . 7/ 152 /5.6 1 77 28 1// 19

25 6/ . 97 195 --.9 . 89 157 -2.5 1 82 /9 1-/ 1861 7- 1-6 /5.

29 6- 1 75 1-7 //.7 . 71 152 /7.2 . 95 198 -5.5 1 75 27 1/8 195

28 65 . 8- 156 -2.5 . 8 19- --.6 1 76 1-5 27.- 1 71 / 1/5 199

27 69 1 79 1-6 /1.- . 85 157 -1./ . 86 155 /6.6 1 85 /2 1-/ 18526 69 . 99 198 -5.6 . 99 197 -9.5 . 99 198 -9.9 1 86 26 1/6 197

/ 69 . 98 199 -5.5 . 58 185 -5.9 . 88 157 -.7 1 98 /- 1-6 17/

/1 65 . 81 191 -/.- 1 95 /5 151 1791 7- 151 /5.5 1 88 158 -.

/2 68 . 82 19 -/./ 1 85 157 -./ 1 71 152 /8.2 1 71 28 1/6 198

// 68 1

89 156 -.9 1

89 157 -.2 .

8 19- --.8 1 72 29 1/7 195/- 68 . 59 189 -7.1 . 81 19/ --.2 1 81 192 -2.5 1 72 25 1/7 19-

/5 67 . 99 198 -5. . 81 192 --./ 1 8- 156 -2.5 1 81 26 1-8 189

/9 67 1 7/ 25 1/6 19/1 82 19 -/.8 1 82 191 -/.6 1 71 155 -.2

/8 67 1 8/ 156 -2.7 . 92 181 -9.5 1 89 157 -1.8 1 71 29 1- 199

/7 67 1 86 155 /6.8 1 89 157 -1.- . 9/ 196 -9.2 1 99 / 15/ 17/

/6 67 1 98 / 152 1711 82 192 -2.8 1 8- 156 -2. 1 86 15- /7.7

- 66 1 7/ 151 /5.2 1 7 15/ /7.6 1 8/ 19 -/.- 1 7 25 1-2 198

97



9.- Summary of this chapter

Though standard deviation formulation and confidence interval method are

considered as good estimation methods for the adequate num"er of #Vs at link level

and are used in several network level studies, this chapter shows that these methods are

not availa"le for a signali0ed link due to travel time has multi!peak distri"ution. The

standard deviation formulation is sensitive with sampling error and cannot provide

consistent result, and the confidence interval method is needed to add additional

criterion to provide correct @udgment.

96



Chapter

0er&orman!e stimation

+ven if the time period is very short &e.g., 5 min), the travel times of all vehicles on

a signali0ed link always can "e divided into several groups "y turning movements at

upstream and downstream intersection and the delay at downstream intersection, and

each group has different travel time characteristics. #ro"e reports on a link within a

time interval are considered as a sample. :hen the proportion of #Vs is different over

these su"groups, sampling error arises and "ecomes serious in small si0e sample.

This chapter introduces a new performance indicator and proposes a method to

estimate the new performance indicator using small si0e pro"e reports on signali0ed

link. The new performance indicator is essentially equivalent to conventional time!

"ased performance indicators such as mean travel time or space!mean speed and has

some desira"le features.

8.1 #erformance indicator

3y pro"e vehicle technique, route or link travel time can "e o"tained directly.

Therefore, time!"ased performance indicators such as mean travel time or space!mean

81



speed are commonly suggested for pro"e!"ased $dvanced Traveler Information

Systems &$TIS). Buiroga &2) also indicated that time!"ased indicators are

etremely powerful, versatile and desira"le. ?e compared three commonly used

categories of performance indicators &highway capacity manual &?=) "ased,

queuing!related and time!"ased) and provided the reasons why time!"ased

performance indicators are preferred.

Though time!"ased performance indicators have numerous advantages, it is difficult

to estimate the conventional time!"ased indicators relia"ly "y limited num"er of #Vs

as shown in the previous chapter.

Therefore, this chapter introduces a new performance indicator and proposes a

method to estimate the new performance indicator using small si0e pro"e reports on

signali0ed link. *urther, it will "e shown that the new performance indicator is

essentially equivalent to conventional time!"ased performance indicators such as mean

travel time or space!mean speed and has some desira"le features.

:hen demand eceeds capacity at a link>s upstream intersection &e.g., morning

peak), it is reasona"le to assume that the vehicles with through movement will access

the link with uniform distri"ution over each green period. If we further assume that the

vehicles with TT also access the link with uniform distri"ution, the ratio "etween the

num"er of Set I and the num"er of vehicles with same access green period, p, can "e

considered as a performance indicator &+q. /).

N Set I

p ( N Set I & N Set II &/)

where N Set I and N Set II represent num"ers of vehicles in Set I and Set II,

respectively. The performance indicator has some desira"le features.

82



*irstly, as a performance indicator, p is essentially equivalent to conventional time!

"ased performance indicators such as mean travel time or space!mean speed. $s p

decreases, mean travel time increases and space!mean speed decreases monotonously.

Secondly, using p and information a"out traffic signal &such as cycle length, green

time and offset time "etween downstream and upstream intersections), corresponding

travel time distri"ution can "e calculated approimately. *or a given p, the distri"ution

can "e approimated as a composite of two normal distri"utions. +q. - 7 provide a

possi"le form of formulations to calculate the means of two normal distri"ution and

total mean using p and traffic signal. These formulations are acquired from *igure 8!1,

which is illustrated "ased on uniform assumption. The vehicles with through access

movement and left(right departure movement will queue in left(right turning lanes at

downstream intersection and thus the length of queue of vehicles with TT at

Figure -1. A +ueue o& vehi!les that a!!ess a link in same green perio)

8/



downstream will "ecome shorter than the length at upstream. The in +q. - 5

reflects the reduction of the length and is dependent on the ratio of the vehicles with

through access movement and left(right departure movement to the vehicles with TT.

In this study, is simply specified as .8 and the variation with space and time are

not discussed precisely due to lack of real data for several links in road network. *or

δ ,

an estimated value is given "ased on an o"servation in net section. The variances

of two normal distri"utions are in!queue variance and can "e treated as constant. In

contrast, mean travel time or space!mean speed has no a"ility to calculate the

Head Set I ,Head Set II



distri"ution.

µSet I

( Head Set I #.5 '&1#α ) ' p ' EGin

&-)

(offset & EGout #α ' p ' EGin #.5 '&1 #α ) ' p ' EGin

µSet II

( Head Set II #.5'&1#α ) '&1# p) ' EGin

&5)(offset &cycle # p ' EGin #.5'&1#α ) '&1# p) ' EGin

µall ( p 'µSet I &&1 # p) 'µSet II &9)

EGin (Gin &δ &8)

EGout (Gout &δ &7)

where

p ( performance indicator

(travel times of head in Set I and Set II

µSet I , µSet II , µall (mean of Set I, Set II, all

cycle,offset (signal length and signal offset "etween upstream and

downstream instersection

Gin ,Gout (green time of upstream and downstream intersection

for through movement

α (reduction rate of length of vehicles with TT "etween

downstream and upstream

δ (constant

8-



Thirdly, using the knowledge a"out distri"ution, it is possi"le to develop a method

that can minimi0e the effect of the sampling error arisen from intersection delay and

efficiently estimate p from small sample. $ simple estimation method is presented in

the su"sequent section.

:hen demand is lower than capacity &e.g., off!peak), the uniform assumption

doesn>t hold and it is possi"le that mean travel time in peak hour is smaller than that in

off!peak. =onsequently, the proposed performance indicator is not applica"le in off!

peak and in distinguishing peak and off!peak situation.

8.2 4"servation of vehicle accesses at upstream intersection

The o"servation was made on Kovem"er 7th, 25 &Tuesday). The link from

Sakurayama intersection to %okiso intersection &north "ound only) is chosen and the

two intersections are investigated &*igure 8!2). The link is a primary arterial link in

Kagoya, Capan. The link has three lanes and is a"out 65m. Kagoya has a high density

road network and there are five signali0ed intersections on the link ecept Sakurayama

and %okiso intersections. Such link is fundamental element of arterial road and the

o"servation spot

Sakurayama

. 1 2

m

%okiso

;H!Dink Type

$rterial Hoad

inor Hoad

Figure -#. Stu)y link an) observation spot



85



properties are important.

The green, am"er and red time of Sakurayama for through movement is 5/ s, / s and

7- s, respectively and the %okiso is 91 s, - s and 85 s, respectively. The cycle length of

the two intersections is 1- s and the offset time is 12/ s. The signal time is an

o"servation of one day and day!to!day variation is unknown. In peak hour, the traffic

signals should operate in optimi0ed scheme and the variation may "e very small.

The access times of all vehicles during 7' 6' am &29 signal cycles) were

o"served at the o"servation spot shown in *igure 8!2. Then the access times are

organi0ed "y signal cycle &green starting for through movement as cycle starting). The

num"er of accesses, through accesses and left(right turnings &the sum of left and right

turning) are summari0ed in each signal cycle and the access times are converted to the

offset times from the corresponding signal cycle "eginning. *igure 8!/ shows the

num"er of accesses, through accesses and left(right turnings in each signal cycles.

3ecause these flows decrease during the last half, only the fist 12 cycles are used in the

8 0

6 0

r a

f f i c ) l o *

4 0

2 0

0

1 2 3 4 5 6 7 8 9

All+rou,+

-eft./i,+t

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

sclende

Figure -'. Tra&&i! &low o& ea!h signal !y!les



89



Table -1. Summary o& a!!esses o& signal !y!les

sclende All -/ ffset time from

1 76 58 18 101112...5961: -

2 72 54 18 111213...6162: -

3 66 50 16 91011...6161: -

4 72 58 14 91112...6162: -

5 67 54 13 81112...5959: -

6 68 52 16 8910...5859: -/

7 73 57 16 6810...6161: -/

8 70 56 14 91012...6162: -

9 66 54 12 81011...5858: -

10 73 56 17 9911...6061: -

11 60 48 12 91113...6166: -12 68 48 20 91213...5859: -

Avera,e 70 54 16 ;e,innin, of 9 s

simulation, which needs sta"le flow input to keep a certain performance level. Ta"le 8!

1 shows the flows and offset times of the first 12 cycles and the average. The offset

time in the ta"le are separated into two groups "y turning movement' through

movement &T) and left(right turning &D(H). In *igure 8!/ and Ta"le 8!1, the cycle inde

of o"servation is termed 4"sL=ycleLInde and is distinguished from the cycle inde of

simulation used in the net section, which is termed SimL=ycleLInde.

8./ Simulation at performance levels

To o"tain travel times of vehicles with TT across a link at different performance

levels, a simple network that consists of a link &link 2 in *igure 8!-), upstream and

downstream intersections, and ad@acent links are modeled in a simulation developed

"ased on an o"servation.

*igure 8!- shows the position of reference points of entrance and eit of link 2. $t

these reference points, the access and departure of a vehicle can "e @udged easily and

88



Figure -(. Simulation network

thus the time of access and departure can "e measured accurately. *urthermore,

acceleration process of vehicle is mostly finished at the reference points and running

time and intersection delay are included "etween two reference points completely.

The "ehaviors of vehicles at the entrances of link 2 and link / are considered similar,

and an o"servation at entrance of a real link is used to model the "ehaviors at the

entrances of link 2 and /. The entrance of link / is also the eit of link 2 &*igure 8!-).

The o"servations of each signal cycle, that consists of the num"er of accesses,

through accesses and left(right turnings and the offset times from the corresponding

signal cycle, are used on the two intersections &I and II) in the simulation. It is

equivalent to that the signals of the two intersections are set as same as the signal of

Sakurayama &cycle F 1- s, green F 5/ s, am"er F / s, and red F 7- s). The offset time

of the two intersections is set as same as the offset time "etween Sakurayama and

%okiso &offset F 12/ s).

Three levels of performance & p is 1G, 85G and 5G, respectively) are simulated.

That is the range of p is from 1 G to 5 G and the resolution of performance level is

25 G. In each performance level, the simulation is run for 25 signal cycles and the

vehicles that have TT and access link 2 during first 2- signal cycles are analy0ed.

87



In the simulation program, each link is considered as *I*4 &*irst In, *irst 4ut)

queue M a type of data structure. 3efore running simulation for each performance

level, the ad@acent links at upstream intersection &id' 1, -, and 5) are initiali0ed "y

sufficient num"er of vehicles to provide the vehicles that access link 2 within 25

signal cycles. Dink 2 is also initiali0ed "y different num"er of vehicles to reali0e three

performance levels. $ll initiali0ed vehicles are specified a unique numeric identifier.

The signal of upstream intersection &id' I) for through movement is switched to

green at &&k #1) 1- sec &k is SimL=ycleLInde of intersection I and 1 25).

The o"servations of 12 signal cycles are repeated 2 times to determine the num"er of

through accesses & N T , from link 1 to link 2), left(right turnings & N RL, from link -, 5 to

link 2) and offset times for each k . *or eample, the 2nd o"servation in 12 signal

cycles are used for k F 2 and /rd o"servation is used for k F 15. $t green starting of

each cycles & &&k 1) '1- sec), two operations are performed in the simulation' &1)

N T vehicles are transferred from link 1 to link 2 and the access times of the vehicles

&through movement) are calculated using the green starting and the offset times from

the relevant o"servation, and &2) N RL vehicles are transferred from link -, 5 to link 2

and the access times of the vehicles with left(right turning are set as E the travel times

from vehicles without TT is not considered in this study.

The signal of downstream intersection &id' II) for through movement is switched to

green at 12/ && #1) '1- sec & is SimL=ycleLInde of intersection II and 1 25).

The o"servations of 12 signal cycles are repeated as descri"ed a"ove. The num"er of

departures & N all , link 2 to link /, 9, 8) and the num"er of through departures & N T , link 2

to link /) in the simulation are determined using the num"er of accesses and through

accesses in the o"servation, respectively. $t green starting of each cycles, N all vehicles

are moved out from link2, then N T vehicles are chosen randomly and moved into link /

86



&through movement) and remainder are moved into link 9, 8 &left(right turning). The

departure times of vehicles with through movement are calculated using the green

starting and the offset times and the departure times of vehicles with left(right turning

are set as .

:hen the simulation of each performance level is terminated, vehicle id, access

cycle inde, and travel time of each vehicles with TT &from link 1 to link /) are

recorded into a file.

8.- The simulation output

*igure 8!5 illustrates the mean of Set I, the mean of Set II, and performance

indicator p of each signal cycle for first -7 cycles from simulation for p F 85G. The

minimum value and maimum value of Set I and Set II are also illustrated "y dot line.

N all , N T , N RL change over signal cycles in the simulation, so p is not invariant and

varies around the mean of p as shown in the figure.

r a v e l i m e ! s "

mean of Set mean of Set p

1 3 5 7 9 11 14 17 20 23 26 29 32 35 38 41 44 47 Simclende

Figure -5. Travel times an) p "Simulation &or p 5/$

7



0 . 0

8

100<Set Set

0 . 0

6

75<50<

e n s i t

0 . 0

450<

d

75<

0 . 0

2

0 . 0

0 100<

100 120 140 160 180 200 220 240

ravel ime !s"

Figure -*. Link travel time )istribution " p 122/3 5/3 an) 52/$

*igure 8!9 illustrates the travel time distri"utions for p F 1 G, 85 G, and 5 G

using travel time reports during 2- cycles. $s shown in the figure, link travel time

distri"ution at a certain performance level can "e approimated as a composite of two

normal distri"utions. The figure also shows that as p decreases, the proportion of the

set with delay increases and the means of the two sets increase. =onsequently, mean

link travel time increases as p decreases.

Ta"le 8!2 summari0es the output of the 2- signal cycles. The ta"le presents the mean

of all & !all ), the mean of Set I & !Set I ) and the mean of Set II & !Set II ). The difference of !all

"etween two consecutive performance levels is a"out / s. The space!mean speed is also

presented. In the ta"le, the items with hat are the result from +q. -7 and

Table -#. Summary o& simulation output

p Speed&km(h)µ

all

µSet I

µSet II

µNall

µNSet I

µNSet II

1G 28 126 126 M 1/1 &!2) 1/1 &!2) M

85G 21 191 1- 22/ 192 &!1) 1-2 &!2) 222 &1)

5G 17 16/ 151 2/- 16/ &) 15/ &!2) 2// &1)

71



the red values are the difference from the simulated values. EGin in *igure 8!1 is the

range of offset times for through movement in each signal cycle and the average is 52 s

from Ta"le 8!1E that is δ F 1 s. In +q. -7, α .8 are used and the formulations provide

good estimates.

8.5 #roposed estimation method

Several studies estimated the smallest num"er of #Vs that are required to estimate

link travel time relia"ly' link level studies &Buiroga and 3ullock, 1667E ?ellinga and

*u, 1666) and network level studies &Srinivasan and Covanis, 1669E =hen and =hien,

2E =heu et al., 22). In these studies, sample mean &pro"e link travel time reports)

is directly compared to population mean &travel times of all vehicles). *or instance, if

estimation error &the difference "etween sample mean and population mean) is small

than allowa"le error &e.g., 1 G of population mean), it is considered that the

estimation result is relia"le.

*igure 8!9 and Ta"le 8!2 show that as performance "ecome worse &as p decreases),

mean link travel time increases and the means of the two sets &without delay and with

delay) also increase. It indicates that performance level can "e estimated "y the means

of the two sets of a sample &pro"e travel time reports) ecept sample mean of link

travel time. The essential of the proposed method is estimating performance level using

the means of the two sets of a sample instead of sample mean.

The travel time reports in each signal cycle o"tained from the simulation at

performance level 85G is treated as a population. Samples are taken from these

populations for each sample si0e n &2- times for each sample si0e n). *or each sample,

+q.6 &proposed method) and +q.1 &conventional method) are used to @udge the

72



Table -'. Comparison between propose) an) prevalent metho)

Sample si0e #roposed method #revalent method

/ 22 &6.2 G) 1/5 &59./ G)

5 6 &/.7 G) 76 &/8.1 G)

1 9 &2.5 G) -1 &18.1 G)

15 8 &2.6 G) 26 &12.1G)

2 - &1.8 G) 18 &8.1 G)

estimated performance level' these equations are eamined for p F 85 G and the two

ad@acent performance levels & p F 1 G and p F 5 G) &O p,Set I, O p,Set II, O p,all are

o"tained from Ta"le 8!2) and the p" that minimi0es these equations is considered as

the estimated performance level. If the performance level p F 85G is concluded "y a

sample, it is considered as success and if others & p F 5 G or 1 G) it is considered as

failed. Ta"le 8!/ shows the failed times and the error rate at five levels of sample si0e.

In +q.6, each set of sample and population are compared respectively. 3y this, the

influence of the sampling error arisen from intersection delay is eliminated. ;ue to the

o"vious difference "etween Set I and Set II, it is easy to @udge which set a sample case

"elongs to.

e p

(&µ # xSet I

)2 &&µ # xSet II

)2

&6) p,Set I p,Set II

where

e p

µ p,Set I , !

p,Set II

xSet I

, x

Set II

(the sum of the square of deviation of the means of the two sets of a sample

from the means of the two sets of a performance level p

(mean of Set I and Set II of a performance

level (mean of samples in Set I and Set II

#opulation mean at p F 85 G is different from the means of two ad@acent

7/



performance levels & p F 1 G and p F 5 G) a"out / s &see Ta"le 8!2). Thus, for

conventional method, if the difference "etween sample mean and population mean is

larger than 15 s &a"out 1 G of mean at p F 85 G), it will "e concluded that the

estimated performance level is p F 1 G or p F 5 G &failed).

e p

(&µ # x)2&1)

p,all

where

e p (the square of deviation of sample mean from true mean of a performance level p

µ p,all (mean of a performance level

x (mean of samples

$s shown in Ta"le 8!/, at sample si0e /, the error rate of proposed method is lower

than 1 G while the error rate of conventional method is higher than 5 G. +ven if the

sample si0e increases to 15, the conventional method can not provide the same quality

as proposed method at sample si0e /. In the simulation, average num"er of vehicles

with TT in each cycle is /9 &range' 25 -5). If 1 G is regarded as accepta"le error

rate, the adequate #V rate is a"out 7 G. The conventional method needs a"out -2 G to

o"tain the same quality. If traffic condition is considered invaria"le in consecutive three

signal cycles, the adequate #V rate in proposed method "ecomes a"out /G and in

conventional method "ecomes a"out 19 G. 4"viously, the adequate #V rate is affected

"y the resolution of performance level &e.g., 25 G in this study). ?igher resolution &e.g.,

1 G) needs more #Vs.

8.9 Summary of this chapter

It is epected that link travel time can "e estimated relia"ly "y relatively small

7-



num"er of #Vs in #ro"e!"ased $TIS. ?owever, when sample si0e is small, sampling

error makes difficult to estimate population mean using sample mean directly.

Sampling error arises from two sources' turning movement and intersection delay.

This study suggests that the effect of sampling "ias from the former should "e

eliminated "y redefining the population to only travel times from vehicles with TT.

?owever, the latter is inevita"le and this chapter proposes a new estimation method

that minimi0es sampling error from the latter.

$s mentioned in =hapter - and =hapter 5, as link performance decreases, the

proportion of the group with delay increases and the means of the two groups also

increase. *or estimating link performance, it is needed to estimate the proportion or the

means of the two groups or "oth. In the proposed estimation method, the means of the

two groups is estimated directly using pro"e reports instead of the proportion or mean

travel time. The failure rate of the proposed method is lower than 1 G at sample si0e /

and the conventional method can not provide the same quality even if sample si0e

increases to 15.

:hen the link performance was identified, mean link travel time can "e estimated

"y the means of the two groups and the relationship of the proportion and the means of

the two groups. *or estimating mean travel time, it is needed to estimate "oth the

proportion and the means of the two groups. *ortunately, when traffic signal is known

and under uniform assumption, the relationship "etween the proportion and the means

of the two groups can "e identified &see +q. - 7). The proportion can "e o"tained

indirectly "y the relationship and then the mean travel time can "e estimated.

$ new performance indicator is introduced and a set of formulations is proposed to

o"tain link travel time distri"ution at a certain performance level using information

a"out traffic signal and the new performance indicator. In the formulations, there is a

75



parameter & ) and the parameter might "e link specific. *urther research is needed to

verify the availa"ility of the formulations in different links.

79



Chapter 4

ehi!le-to-ehi!le Travel Time ariability

Travel time varia"ility plays an important role in travel decision and there is a

growing attention to travel time varia"ility measurement &%raves et al., 2E Di et al.,

29E 4h and =hung, 29). Travel time varia"ility has two components' one from the

varia"ility of performance level, and another from the varia"ility of vehicle!to!vehicle

at certain performance level. The performance levels of each link in a road network

may vary over day!to!day and time!to!time. It can "e measured "y traffic detectors

such as loop detector, video camera and pro"e vehicle. $t a certain performance level,

vehicle!to!vehicle varia"ility still arises from driver "ehaviour such as aggressiveness

and lane choice &Di et al., 29) and from intersection delay. In peak time period, the

"ehaviour of individual driver will "e limited and the intersection delay "ecomes the

ma@or source of vehicle!to!vehicle varia"ility.

The vehicle!to!vehicle varia"ility of corridor travel time is important to pro"e!"ased

estimationE if the varia"ility is relatively small, travel time reports from #Vs can "e

aggregated at corridor level directly and corridor travel time can "e estimated "y small

num"er of #Vs.

This chapter presents vehicle!to!vehicle varia"ility on a signali0ed corridor at three

performance levels in peak time period. $ simulation is developed to model the

78



Figure 4-1. Simulation network

vehicles on the corridor and the ad@acent links. Though the simulation is very simple,

performance level and vehicle movement at intersection are considered eplicitly,

which are two critical factors that influence travel time. $ performance indicator

proposed in =hapter 8 is employed to demonstrate the sta"ility of the performance in

each three levels.

7.1 Simulation network

To o"tain travel times of all vehicles that traverse a corridor completely at different

performance levels, a simple network is modeled in a simulation that is a simple

etension of the simulation shown in section 8./ &*igure 7!1). In this figure, the

intersections are num"ered with Homan numerals and the links are num"ered with

$ra"ic numerals. The cross links are num"ered using from 11 to 2 and the access link

in the cross links are num"ered using odd num"er and the departure link in the cross

links are num"ered using even num"er. The left and right turning movements at an

intersection are not distinguished in this study and thus two access cross links are

assigned "y the same id and two departure cross links are also assigned "y the same id.

:hen a vehicle accesses link 2 from link 1 and departs link 5 to link 9, the vehicle is

77



considered as traversing the corridor completely and the travel time from link 2 to link

5 is considered as corridor travel time. The signals of the intersections and the offset

times "etween consecutive two intersections are specified equally "ased on the

o"servation shown in 8.2.

The figure also shows the positions of reference points of entrance and eit of each

links. The entrance of a link is also the eit of previous link. *or eample, the entrance

of link / is the eit of link 2.

7.2 Simulation procedure

Three levels of performance & p of link 2 5 are 1 G, 85 G, and 5G,

respectively) are simulated. In each performance level, the simulation is run for 25

signal cycles and the link travel times of vehicles with TT and the corridor travel times

are calculated.

In the simulation program, each link is simply considered as *I*4 &*irst In, *irst

4ut) queue P a type of data structure. The access links &link 1, link 11, link 1/, link 15,

link 18, and link 16) are initiali0ed "y sufficient num"er of vehicles to provide the

vehicles that access the network during 25 signal cycles. The links that compose the

corridor &link 2 5) are also initiali0ed "y different num"er of vehicles to reali0e the

three performance levels. $ll initiali0ed vehicles are specified a unique numeric

identifier.

The information of 12 signal cycles in the o"servation are repeated several times to

determine the num"er of through accesses & N T ), the num"er of left(right turning

accesses & N LR), and offset times for a cycle inde of an intersection in the simulation.

*or eample, the information of 2nd signal cycle in the o"servation is used for cycle

76



inde F 2 and /rd signal cycle is used for cycle inde F 15 in the simulation. The

num"er of left(right turning departures is specified as same as the num"er of left(right

turning accesses N LR.

$t 12/'&i #1) &1- '&ci #1) sec, the signal of cycle inde ci of intersection i for

through movement is switched to green in the simulation &ci is 1 25). $t the

moment, two operations are performed in the simulation' &1) N T # N LR vehicles are

moved out from linkQiR , then N T vehicles are chosen randomly among these vehicles

and moved into linkQi &1R and the rest of vehicles are moved into linkQ1 &2 'iR .

*or the vehicles with through movement & N T ), the departure times of upstream link and

the access times of downstream link are calculated using the green starting time and

the offset times from the relevant signal cycle in the o"servation. *or the vehicles with

left(right turning, the departure times of upstream link and the access times of

downstream link are set as E the link travel times of vehicles without TT is not

discussed in this paper. &2) N LR vehicles are transferred from linkQ1 &2 'i #1R into

linkQi &1R . The departure times of upstream link and the access times of downstream

link of these vehicles are set as .

:hen the simulation of each performance level is terminated, the result is

summari0ed "y each vehicle. *or a vehicle, the links that the vehicle traverse with TT

are identified and link id, cycle inde of access and link travel time of each link are

recorded into a file.

In this simulation, performance level and vehicle "ehavior at intersection are

considered eplicitly, which are critical factors on travel time.

6



7./ Travel time varia"ility

$%&%' Link travel time varia(ility

In this section, travel times on link 2 generated "y the simulation are presented.

*igure 7!2 illustrates mean travel time of Set I, mean travel time of Set II, and

performance indicator p for the first -7 signal cycles at three performance levels. The

minimum value and maimum value of Set I and Set II of each signal cycle are also

illustrated "y dot lines. $s shown in the figure, p fluctuates over signal cycles around

epected value of each performance level. The causes are the variation of N T and N LR

over signal cycles in the simulation, and pseudo!random num"er generated "y the

simulation. The former is consistent with the real situation. In this study, sufficient

num"er of signal cycles &25 signal cycles) is simulated to counteract the influence of

the latter on travel time distri"ution.

*igure 7!/ shows link travel time distri"utions at three performance levels, which

are o"tained using link travel times during 25 signal cycles. $s shown in the figure,

link travel time distri"ution has two peaks at each performance levels. $s p decreases,

the peak shifts towards right side and the ratio of Set II increases. =onsequently, mean

travel time on the link increases monotonously.

7.- =orridor travel time varia"ility

*igure 7!- shows corridor travel time distri"ution at three performance levels. Dink

travel time will "elong to Set I or Set II. Ta"le 7!1 shows the percentage of vehicles in

each com"ination of the num"er of Set I and Set II on the four links.

61





1 3 5 7 9 11 14 17 20 23 26 29 32 35 38 41 44 47 cle nde

p F 1 G &a)

1 2 0

1 1 0

1 0 0

p ! < "

9 0

8 0



1 3 5 7 9 11 14 17 20 23 26 29 32 35 38 41 44 47 cle nde

p F 85 G &")



1 3 5 7 9 11 14 17 20 23 26 29 32 35 38 41 44 47 cle nde

p F 5 G &c)

7 0

6 0

5 0

p ! < "

4 0

3 0

Figure 4-#. Link travel time an) per&orman!e in)i!ator

62



The distri"utions at each performance level are multi!peak distri"ution and the

difference "etween two peaks is fairly large &a"out 2 G of travel time mean). That is

travel time varia"ility is still produced even if the performance level is invaria"le and

the aggregated distance is relatively long. $s the num"er of links traversed "y vehicle

as Set II increases, there are more intersection delay and the corridor travel time

increases.

:hen performance level decreases, there are more Set II and the travel time

increases rapidly.

Table 4-1. 0er!entage o& !ombination o& the o& Set % an) Set %% on &our links "/$

- ' / ' 1 2 ' 2 1 ' / ' -

p F 1G 6.6 6.1

p F 85G 71./ 17.8

p F 5G .7 67.7 .-

0 . 0

8

100<Set Set

0 . 0

6

75<50<

e n s i t

0 . 0

450<

d

75<

0 . 0

2

0 . 0

0 100<

100 120 140 160 180 200 220 240

ravel ime !s"

Figure 4-'. Link travel time )istribution

6/



7 0 0

) r e = u e n c

5 0 0

3 0 0

1 0 0

0

450 500 550 600 650 700 750 800 850 900

ravel ime !s"

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 ) r e = u e n c

p F 1 G &a)

450 500 550 600 650 700 750 800 850 900

ravel ime !s"

p F 85 G &")

0 2 0 0 6 0 0 1 0 0 0 ) r e = u e n c

450 500 550 600 650 700

ravel ime !s"

750 800 850 900

p F 5 G &c)

Figure 4-(. Corri)or travel time



6-



7.5 Summary of this chapter

In this chapter, vehicle!to!vehicle varia"ility of signali0ed corridor travel time at

three performance levels is presented using travel times from a simulation that

considers performance level and vehicle "ehavior at intersection.

Though an artificial corridor is modeled in the simulation, the simulation can "e

used to o"tain travel time distri"ution &consequently, vehicle!to!vehicle varia"ility) for

a real signali0ed corridor. *or estimating travel time of a real corridor "y the proposed

simulation, the vehicle accesses of each link and the relationship "etween the initial

num"er of vehicles and the performance levels are needed. :hen demand eceeds

intersection capacity, the accesses of a link will "e controlled "y the signal of upstream

intersection and this is independent with performance level. That is the o"servation of

the accesses at each intersections in peak hour can "e used to identify the accesses for

several performance levels. :hen the performance levels of each link are specified, the

links can "e initiali0ed "y different num"er of vehicles "ased on the performance levels

and the corridor travel time can "e o"tained "y the simulation. The relation should "e

affected "y the geographic properties of each links and "e link!specific. The relation

"etween the initial num"er of vehicles and the performance level should "e studied in

the future.

65



Chapter

Con!lusions an) Future Stu)ies

6.1 =onclusions

)%'%' Statistical properties of link travel time

Travel time reports from #Vs should "e aggregated at link level instead of at path

level "ecause there are numerous paths in a city and the path!"ased method would

suffer from low pro"e o"servations. Though the statistical properties of link travel time

are important to implement pro"e!"ased real!time data collection system, little is

known a"out the statistical properties.

Turning movement is usually neglected in practice when aggregating traffic data at

linkE that is, all vehicles traveling a link during a time interval regardless of turning

movements at the link>s ends are defined as population. 3y the traditional definition of

link travel time, link travel time distri"ution will "e concluded as normal or

approimate normal. ?owever, it will inevita"ly accompany with large variance and it

is difficult to estimate mean link travel time using small si0e pro"e reports. Thus, the

research proposes a new definition of link travel time' only consider the vehicles with

through movement at upstream and downstream intersections.

68



3y new definition, historical pro"e reports on an arterial link show that link travel

time is two!peak distri"ution and mean travel time is larger in off!peak time period

than in peak time period. To identify the intrinsic reasons of the phenomenon, a

qualitative analysis and a simulation "ased analysis are performed and the following

conclusions are made'

1) :hen the demand is lower than the capacity of upstream intersection, for

eample in off!peak time period, mean link travel time ehi"its large variation

over time and more importantly cannot trace the change of the num"er of

vehicle accesses. That is, in this phase, mean travel time is not a good indicator

of link performance and the num"er of accesses should "e used for tracing the

change of link performance.

2) :hen demand eceeds capacity at upstream intersection, it is reasona"le to

assume that the vehicle accesses are uniform over green period. In this phase,

though mean travel time can trace the link performance, travel time

distri"ution is two!peak rather than asymptotically normal. ;espite this is not

prefera"le result, it is consistent with the o"servation from historical data and

the widely accepted "elief that link travel times "elong to at least two different

groups' one without delay at downstream intersection and the others with the

delay. $s link performance decreases, the proportion of the group with delay

increases and the means of the two groups also increase &see *igure 7!/).

Asing small si0e pro"e reports, though it is difficult to estimate the proportion

of the group with delay, it is possi"le to estimate the means of the two groups

due to their variances are relatively small. This fact is used to develop

performance estimation method using small si0e pro"e reports.

/) *or avoiding congestion, identifying the performance decrease in the second

67



phase is important.

)%'%* The formulations of the ade+uate num(er

Traditionally, it is considered that the relia"ility of pro"e!"ased estimation depends

on the num"er of the pro"e reports and the adequate sample si0e required to meet the

relia"ility has "een an imperative issue.

Two methods standard deviation formulation and confidence interval method are

commonly accepted. ?owever, these formulations are "ased on =entral Dimit Theorem

and the result is dou"tful when the population is severely nonnormal and sample si0e is

small.

The eamination descri"ed in =hapter 9 shows that these methods are not capa"le

for a signali0ed link due to travel time has multi!peak distri"ution. The standard

deviation formulation is sensitive with sampling error and cannot provide consistent

result, and the confidence interval method is needed to add additional criterion to

provide correct @udgment.

)%'%& erformance estimation

It is epected that link travel time can "e estimated relia"ly "y relatively small

num"er of #Vs in #ro"e!"ased $TIS. ?owever, when sample si0e is small, sampling

error makes difficult to estimate population mean using sample mean directly.

Sampling error arises from two sources' turning movement and intersection delay.

This study suggests that the effect of sampling "ias from the former should "e

eliminated "y redefining the population to only travel times from vehicles with TT.

?owever, the latter is inevita"le and =hapter 8 proposes a new estimation method that

66



minimi0es sampling error from the latter. The failure rate of the proposed method is

lower than 1 G at sample si0e / and the conventional method can not provide the

same quality even if sample si0e increases to 15.

$s mentioned earlier, as link performance decreases, the proportion of the group

with delay increases and the means of the two groups also increase. *or estimating link

performance, it is needed to estimate the proportion or the means of the two groups or

"oth. In the proposed estimation method, the means of the two groups are estimated

directly using pro"e reports instead of the proportion or mean travel time.

:hen the link performance was identified, mean link travel time can "e estimated

"y the means of the two groups and the relationship of the proportion and the means of

the two groups. *or estimating mean travel time, it is needed to estimate "oth the

proportion and the means of the two groups. *ortunately, when traffic signal is known

and under uniform assumption, the relationship "etween the proportion and the means

of the two groups can "e identified &see +q. - 7 in =hapter 8). The proportion can "e

o"tained indirectly "y the relationship and then the mean travel time can "e estimated.

6.2 *uture Studies

In this thesis, the statistical properties of link travel time and the transform of the

properties over the change of the traffic condition were investigated "y historical data,

qualitative analysis, and simulation "ased analysis. ?owever, the result of the analyses

should "e verified "y a field test. $ corridor that consists of several arterial links can "e

chosen as the target of the field study, such as the corridor used in simulation "ased

analysis &see *igure 5!1). *or the field test, a technique that can identify the most

vehicles &e.g., 6 G) at the entrance of each link &see *igure 8!-) is needed. $t present,

1



high!quality video camera is one of the techniques.

*or estimating path travel time, the effect of left(right turning movement should "e

studied. *urthermore, the travel time on local roads also should "e studied.

11



6e&eren!es

$sano, ., Kaka@ima, $., ?origuchi, H., 4neyama, ?., uwahara, ., oshi, .

$kahane, ?.&2/) $ real time traffic signal control "y self!evaluating delay. -ournal

of Infrastructure lannin. Revie/, 0ol%*1, No%2, pp. 786!779. &in Capanese)

3ertini, H. D.&29) Uou are the traffic @am' an eamination of congestion measures.

Transportation Research 3oard $4th 5nnual 6eetin. . 7ashin.ton, 89 .

3oyce, ;., ?icks, C. Sen, $.&1661) In!vehicle navigation system requirements for

monitoring link travel time in a dynamic route guidance system. Transportation

Research 3oard, :1th 5nnual 6eetin., 7ashin.ton, 89 .

=etin, ., Dist, %. *. hou, U.&25) *actors affecting minimum num"er of pro"es

required for relia"le estimation of travel time. TR3 *114 5nnual 6eetin. .

=hen, . =hien, S. I. C.&2) ;etermining the num"er of pro"e vehicles for freeway

travel time estimation "y microscopic simulation. Transportation Research Record

':')% TR3, National Research 9ouncil, 7ashin.ton, 8%9%, pp. 91!97.

=hen, . =hien, S. I. C.&21) ;ynamic freeway travel time prediction using pro"e

vehicle data' link!"ased vs. #ath!"ased. Transportation Research 3oard, $1th 5nnual

6eetin. .

=heu, H. D., ie, =. Dee, ;. ?.&22) #ro"e vehicle population and sample si0e for

arterial speed estimation. 9omputer;5ided 9ivil and Infrastructure En.ineerin., 18,

pp. 5/!9.

=hien, S. I. C. uchipudi, =. .&22) ;ynamic travel time prediction with real!timeand historical data. Transportation Research 3oard $'th 5nnual 6eetin. .

%raves, T. D., arr, $. *. Thakuriah, #.&2) Varia"ility of travel times on arterial

links' effects of signals and volume. National Institute of Statistical Sciences

Technical Report ''2.

?ellinga, 3. H. *u, D.&22) Heducing "ias in pro"e!"ased arterial link travel time

estimates. Transportation Research art 9< Emer.in. Technolo.ies, 1, 258!28/.

?ellinga, 3. *u, D.&1666) $ssessing epected accuracy of pro"e vehicle travel time

1/



reports. -ournal of Transportation En.ineerin., 0ol% '*4, No% =, pp. 52-!5/.

?origuchi, H.&22) The advantage of event!periodic data recording for pro"e vehicle

system. roceedin.s of Infrastructure lannin., 0ol% *=, 98;R>6 .&in Capanese)

?origuchi, H.&22) Strategic disposition of tai pro"e to accomplish effective data

collection for travel information provision ! a theoretical framework and its practice.

roceedin.s of Symposium on ITS *11*.

?origuchi, H. :ada, .&25) Intelligent detection of irregular congestion with an

on!"oard pro"e equipment. roceedin.s of Symposium on ITS *114. &in Capanese).

Internet ITS Coint!Hesearch %roup &22) Internet ITS research report.

uwahara, .&2/) ;emand analysis considering traffic congestion. roceedin.s of

Infrastructure lannin., 0ol% *$, 98;R>6% &in Capanese)

Dester, #.&25) $W pathfinding for "eginners.

Di, H., Hose, %. Sarvi, .&29) Asing automatic vehicle identification data to gain

insight into travel time varia"ility and its causes. Transportation Research 3oard,

$4th 5nnual 6eetin. .

Diu, .&29) =ost!effectiveness of a pro"e vehicle system at lower frequencies. ;octor

dissertation, Kagoya Aniversity, Capan.

Diu, ., Uamamoto, T. orikawa, T.&29) $n analysis of the cost efficiency of pro"e

vehicle data at different transmission frequencies. International -ournal of ITS

Research, -.

akimura, ., ikuchi, ?., Tada, S., Kaka@ima, U., Ishida, ?. Tetsuro, ?.&22)

#erformance indicator measurement using car navigation systems. Transportation

Research 3oard, $'th 5nnual 6eetin., 7ashin.ton, 89 .

iwa, T.&25) Travel "ehavior analysis in road networks "ased on pro"e vehicle data.

;octor dissertation, Kagoya Aniversity, Capan.

iwa, T. orikawa, T.&2/) $nalysis on route choice "ehavior "ased on pro"e!car

data. roceedin.s of the '1th 7orld 9on.ress on Intelli.ent Transport Systems, 98;

R>6 .

iwa, T., Sakai, T. orikawa, T.&2-) Houte identification and travel time

prediction using pro"e!car data. International -ournal of ITS Research, 2, 21!27.

ontgomery, ;. =.&166-) 5pplied statistics and pro(a(ility for en.ineers, , Cohn :iley

Sons Inc.

1-



ousa, H. .&22) $nalysis and modeling of measured delays at isolated signali0ed

intersections. ->?RN5L >@ TR5NS>RT5TI>N ENGINEERING;5S9E, 127, /-8!

/5-.

4chieng, :. U. Sauer, .&22) Ar"an road transport navigation' performance of the

glo"al positioning system after selective availa"ility. Transportation Research art 9<

Emer.in. Technolo.ies, 1, 181!178.

4h, C. S. =hung, U.&29) =alculation of travel time varia"ility from loop detector

data. Transportation Research 3oard, $4th 5nnual 6eetin. .

4ls0ewski, #.&166/) 4verall delay, stopped delay, and stops at signali0ed intersections.

->?RN5L >@ TR5NS>RT5TI>N ENGINEERING;5S9E, 116, 7/5!752.

#an, =., Du, C., :ang, ;. Han, 3.&28) $ gps!"ased arterial roadway network travel

time(delay data collection method. TR3 *11: 5nnual 6eetin.%

Buddus, . $., 4chieng, :. U., hao, D. Koland, H. 3.&2/) $ general map

matching algorithm for transport telematics applications. GS Solutions, 8, 158!198.

Buiroga, =. $.&2) #erformance measures and data requirements for congestion

management systems. Transportation Research art 9;Emer.in. Technolo.ies, 7,

278!/9.

Buiroga, =. $. 3ullock, ;.&1667a) ;etermination of sample si0es for travel timestudies. ITE -ournal, 97&7), 62!67.

Buiroga, =. $. 3ullock, ;.&1667") Travel time studies with glo"al positioning and

geographic information systems' an integrated methodology. Transportation Research

art 9< Emer.in. Technolo.ies, 9, 11!128.

Buiroga, =. $. 3ullock, ;.&1666) easuring control delay at signali0ed intersections.

-% Transp% En.r.%, 125, 281!27.

Sen, $. Thakuriah, #.&1665) +stimation of static travel!times in a dynamic route

guidance!system. 6athematical and 9omputer 6odellin., 22, 7/!11.

Sen, $., Thakuriah, #. V., hu, . B. arr, $.&1668) *requency of pro"e reports and

variance of travel time estimates. ->?RN5L >@ TR5NS>RT5TI>N

ENGINEERING;5S9E, 12/, 26!268.

Sen, $., Thakuriah, #., hu, . arr, $.&1666) Variances of link travel time estimates'

implications for optimal routes. International Transactions in >perational Research,

9, 85!78.

Srinivasan, . Covanis, #.&1669) ;etermination of the num"er of pro"e vehicles

15



required for relia"le travel time measurement in an ur"an network. Transportation

Research Record '4&:, TR3, 7ashin.ton, 8%9%,15!22.

Taylor, . $., :oolley, C. +. ito, H.&2) Integration of the glo"al positioning

system and geographical information systems for traffic congestion studies.

TR5NS>RT5TI>N RESE5R9H 5RT 9;E6ERGING TE9HN>L>GIES, 7, 258!

275.

Turner, S. . ?oldener, ;. C.&1665) #ro"e vehicle sample si0es for real!time

information' the houston eperience.

Turner, S. ., +isele, :. D., 3en0, H. C. ?oldener, ;. C.&1667) Travel time data

collection hand"ook report no. *hwa!pl!67!/5. , *ederal ?ighway $dministration,

Teas Transportation Institute.Aesugi, U., Iryo, T., 4neyama, ?., ?origuchi, H. uwahara, .&2/) +stimation of

epectation and variance for a section travel time "ased on fragmentary pro"e

tra@ectories. -ournal of Infrastructure lannin. Revie/, 0ol%*1, No%2, 62/!626,

Capanese.

Van $erde, ., ?ellinga, 3., Uu, D. Hakha, ?.&166/) Vehicle pro"es as real!time atms

sources of dynamic o!d and travel time data. roceedin.s of the 5T6S 9onference

held in St% eters(ur., @lorida, 28!2/.

Vlahogianni, +., %olias, C. and arlaftis, .&2-) Short!term traffic forecasting'

overview of o"@ectives and methods. Transport Heviews, 2-, pp. 5//!558.

:hite, =. +., 3ernstein, ;. ornhauser, $. D.&2) Some map matching algorithms

for personal navigation assistants. Transportation Research art 9< Emer.in.

Technolo.ies, 7, 61!17.

Uamamoto, T., Diu, . orikawa, T.&29) Varia"ility of travel time estimates using

pro"e vehicle data. roceedin.s of the @ourth International 9onference on Traffic

and Transportation Studies AI9TTSB, 287!278.

Uang, C., ang, S. =hon, .&25) The map matching algorithm of gps data with

relatively long polling time intervals. -ournal of the Eastern 5sia Society for

Transportation Studies, Vol.9.

ito, H., ;este, %. Taylor, . $.&1665) %lo"al positioning systems in the time!

domain ' how useful a tool for intelligent vehicle!highway systems.

Transportation Research art 9;Emer.in. Technolo.ies, /, 16/!26.

4oyama, K., Shigeta, ., atsumoto, T. and Ikenoue, .&1689)' akuritsuhensu to

19



shiteno ryoko@ikan no tokusei ni tsuite &4n the characteristics of travel time as

pro"a"ilistic varia"le), #roceedings of /rd Hesearch =onference on Traffic

+ngineering, pp. 86!72. &in Capanese)

Kelompok 2 Rek Lalulintas

Documents

Transcript of Kelompok 2 Rek Lalulintas