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A Simulation for the Evaluation of Signal Control at Traffic Networks
Copyright © I FAC Control in Trallsportation Systems, Vi enna. Au;tria. 1986
A SIMULATION FOR THE EVALUATION OF SIGNAL CONTROL AT TRAFFIC NETWORKS M. Katakura, Sh. Mukai and Y. Sakurada /II.I/i/II/I' of /II(/II.I/riai Sri/'lIcl'. [ 'lIiln.li/),
of Tokyo. ja/)(III
Abstract. The traffic simulation program DESC was developed for evaluations of traffic responsive control in road networks. Keywords.
Traffic control; road traffic; simulation; validation .
In microscopic model, each Individual vehicle is identified and its position , acceleration and other characte risti cs are stored every unit scanning Interval . MicroscopiC models deal with 2 separate areas: streets and Intersections. On the streets . a car-following model Is usually adopted for approximation of the behavior of individual vehicle. At the intersection,pedestrlan interference and collision avoidance are usually performed. This kind of models can simulate sufficiently enough the fluctuation of traffic condition In the short term,but long simulation time and big core storage are needed.
I NTRODUCTION In recent years, as computer facilities have Improved, signal control has adopted the on -l ine real time control method . In Japan, the traffiC responsive contro l method was introdu ced In Tokyo by the National Police Agen cy In 1971. Today It is being used to operate for areas covering more than 70 intersections. In the future, more consideration will be addressed to the application of onl ine real time signal control method on the road traffic network . Thus, not only the I mprovement of computer fa c iliti es and detector reliabilIty . but also the development of tools that can eval uate the effectiveness of control of a computerized system on the traffic network in specific region is Imperative. Taking into consideration the present condit i on and expected trends In the future. the authors have developed a new road traffic network simulation model as one tool among others which can evaluate such control method as stated above.
In platoon models, vehicles are grouped Into several platoons. and the programme keeps track of the location. speed. acceleration and the size of the platoon. This kind of models are more economical In respect to computer storage and faster in execution than microscopic models . In macroscopiC models. the traffic stream Is treated as a continuous fluid. and each Individual vehicle is not identlfied.Generally ma croscopiC models are very economical In respect to computer storage and very fast In simulation. This kind of models. however, cannot describe detail traffic conditions .
MAJOR FEAT URES FOR THE MODEL Major features the model should have are considered to be as follows;
* Simulation
time should short as possible.
be as
As to the function of vehicle detection. although SCOOTS) has an signal optimization programme based on detector information. the model does not have a programme for direct simulation of detector Information. Therefore counts of volume and time occupancy by detectors are not output of the simulation itself, A simulation programme having the function of vehicle detection could not be found among existing models. On the basis of adopted concepts In previously developed models, the authors have developed a new simulation model~}4)
* The model
should trace the dynamic fluctuation of traffic stream In the short term ,
* The model should Implement the function of vehicle detection .
The first actual documented simulation were performed In 1955 with an analog computer~) Since then, many computer simUlation models have developed and are being developed to-date. The models can be grouped into 3 types as below;l) 1. 2. 3.
the
BASIC CHARACTERISTICS OF THE NEW MODEL
microscopic model platoon model macroscopic model
The authors have developed a new road traffic network simulation model named
245
:-'1. Katakllr a. Sh. :-'Iukai and Y. Sakllrad a
246
Dynamic Evalua tor of Signal Contro l (DESCJ Basic charac teristi cs of DESC are as' follow s: I. The macros coPic type model is adopte d for the simula tion of the traffic stream on lhe )'oadway In order to save comput er storag e and simula tion lime. 2.
The micros copic type model is adopte d for the simula tion of right turning vehicl e arriva l and the arriva l of indiv idual vehicl es at detect ors.
3.
The variat ion and the fluctu ation of traffic flow for the perform ance of dynami c contro l simula tion are describ ed.
4.
Detect or inform ation like traffic volume and time occupa ncy . are simula ted.
The Individ ual charac teristi CS are describe d In more detail below.
SIMULATION OF THE TRAFFIC STREAM ON THE STREET The program me assume s a traffic stream Theref ore each as a continu ous fluid. Individ ual vehicl e is not Identi fied on the street . The road is modele d as a link divide d The length of into severa l segmen ts. each segmen t is equal to the common unit cruise length . whi ch one vehicl e runs In a unit scanni ng interv al. Let the adjace nt road segmen ts denote d K and K+I be consid ered in the model. The segmen t K+ 1 is def i ned to be upstream of K. At every scanni ng interv al. a whole or a part of existin g volume at segmen t K+l • EV(K+ l,tlis advanc ed to the next segmen t The volume of vehicl e moving from K is modele d as: segmen tK+lto segmen t K AF(K.t J = mlnimum[ SFRT*NLANE. EV(K+ I.t-ll. JDS*UL*NLANE - EV(K.t -l I ... ... eq. 1 J where
AF(K.t J: arrivin g flow at seg ment K at curren t scan EV(K. t-ll: existin g volume at segmen t K at the 1as t scan SFRT: satura tion flow rate NLANE: number of lanes of the specif ic link JDS: Jam densit y UL: unit length of segmen t
Each segmen t has an upper limit for existin g volume that corresp onds to JDS*UL*NLANE. I f ex i s t i I1g vol ume i 11 segment K have reache d its upper limit . then arriva l flow AF(K.t l would be determ ined to be zero from equatio n I. Such logica l proced ure enable s the model to simula te the stoppi ng wave of the queue.
flo\" direct ion
existin g volwre
<::
upper limit
AF(K ,t)
~ SFRfxNLA NE
0.0
I
EV(K,t- l)
EV(K+l ,t-l) segrrent :K+l
segrrent :K Fig.l
Flow profil e in adjace nt road segmen ts denote d K and K+l
each K segmen t has a labal Next. .LABEU KI. which is set corresp onding to the curren t eXistin g volume at ea c h scanni ng Interv al. At the segmen t K.if the curren t existin g volume is equal to JDS*UL*NLANE which is the upper limit. then LABEL
------ ------- ------- ------ r----JDSX ULXNLANE AF(K ,t)
SFRI' NLANE
0.0
segment :K segrrent :K+l Fig.2
III lin the case of LABELIKI=O and LABEL< K+ 1 1=2 AF(K. tlis determ ined as SFRT*NLANE-EV(K.t-1 I (iii lin the case of LABEL(KI=2 and LABEL< K+ 1 1=1 AF(K. tlis determ ined as zero Ilvlln the case of LABEL(KI=1 and ,.I LABEL< K+ 1 1=1 AF(K. tlis determ ined as zero Such logica l proced ure enable s the model to simula te the startin g wave of the queue. In the curren t model. the vehicl e speed is assume d to be either 0 or free flow speed.
247
Signal Control at Traffic :'\let works
SI MULATI ON OF I ND I VI DUAL VEIl I CLE ARRIVAL In the DESC model. the microscopic type model is also adopted for the simulation of individual right-turn vehicle arrivals and individual vehicle arrivals at detectors. The procedures are stated below. At every scanning interval. flow profile at the intersection or the detector's locatIon is accumulated. The probability of arrival can be obtained by the linear approximated function of the cumulative value shown In Fig.3. This probability is compared to a uniform random number in order to decide if an arrival occurred or not. If the value of the probability of arrival is larger than uniform random number. then It is assumed that one vehicle has arrived. and cumulative value is reduced by 1.0. prcbability of arrival 1.0
In the current model. each variable is assumed to follow the normal distrlbution. SIMULATION OF VEHICLE DETECTION In the DESC model. the arrival of each individual vehicle is simulated by detectors as descrived above. Also the time occupancy in specific time intervals Is simulated. First of all. the travel pattern a vehicle pass through a congested area is shown on the time-distance diagram In Flg.5. The vehicle in time-distance diagram passes 5 regions. As previously mentioned. the speed of traffic flow on the street is assumed to be either 0 or free flow speed. Another logic is needed for the simulation of detector pulses actuated by vehicles passing the deceleration and acceleration region. green
--------;r--- - -
red
stopT=====jIC'~======~===;=\======~ 2.C?nges~ion \
line
\
region '\
0.0
1.0
0.0
Fig.3
cumulative value
The function of probability of vehicle arrival
SIMULATION OF RIGHT-TURN VEHICLES' BEHAVIOR
\ \ 1. free flON '\ region
~.
probability of right-turning
'\
'\
4.acceleration flON reg ion
The time-distance diagram of a congested area
1. Free flow region
The traffic stream in this region Is not directly affected by the queue. If the current detected vehicle is in a free flow region. the length of the on-pulse is modeled as;
P=P A = (L+Ao) /Vt .... eq. 2)
PA L
Ao
Vt
Fig . 4
\
,,\
distance from the stop line
where
0.0 0.0
'\
\
, 3.deceleration '\ flCMI region
Cl
Fig.S
In the DESC model. right-turn vehicles are handled as individual vehicles. In case of gap acceptance. the vehicle is able to turn only If there Is an acceptable gap in the opposing flow. The linear approximated gap acceptance function is shown in Fig.4.
'\
time
S.saturation low region
gap in the opposing flow
The function of gap acceptance
SIMULATION OF FLUCTUATION OF THE TRAFFIC FLOW
average length of the onpulse average length of a vehicle the detection area free flow speed
2. Congestion region If the current detected vehicle is in a congestion region. the length of on-pulse is modeled as the maximum length of the puis which Is assumed in this model. 3. Deceleration region
For the description of the variation and the fluctuation of traffic flow. the variables stated below are varied cycle by cycle.
* saturation flow rate * jam density * average length of detector's on-pulse
CTS-I
If the current detected vehicle is in a deceleration flow region. the length of on-pulse Is modeled shown In Fig.6. At x=O and t=O. the specific vehicle of which speed is free flow speed Vt starts to decelerate. at x=Xo and t=t t. the specific vehicle of which speed is v tl is detected. At the current time of t I there might be two kinds of volum~~ in segments between the stopllne and the
M. Katakura , Sh. Mukai and Y. Sakurada
248
Thus. the length of the on-pulse can be descrlved as a linear approximated function of X which can be calculated in the current model.
x
-----CJ=---=tf------ L1:: =ngestion~Ll A - region
_stopping-:"~ - wave
- u - [j ...
'-:
Ll
eq . 7.1)
J
-~
----------~--......::;",..------
o. 0
V tl D
/0 Fig_6
t
T
1
'--_ _ _-+-_ _ __ _ _-_-_-_-_-_-~ 0.0 (L+A o ) 2
Fi g . 7
The model of a travel pattern in a congested region
Now let XSTP - Xo be X. and let XSTP be D. X Is the distance from detector to stopping location which will be passed by the detected vehicle between detected time of t 1 and stop time T. while D is the total distance of deceleration_ The relationships among these variables are given as below; d t
1
2
= = = =
1 2
x
+
1
2
V f T--dT
Vf - d t 1 Vf - dT 0 (L+AD) / V P tl where d : deceleration V t.1
( = D)
2
_. ..... eq. 3) t
l
P
=
t
l
=
(L+AD)
/J
2dX .... ... eq.
4)
As to a detected vehicle in acceleration flow region. the length of on-pulse can be modeled similarlY as; P
Pt 1
=
(L
+ AD) / V f
(L + AD)
/ Vf
2A (PM -
Vf
. {CL + AD)
..
(x >
(L
+ AD)
2
(2AP,., 2)
)
..... eq. 7-1)
P ,.,)
X + PM
2 2
>
(2AP,.,2)
X> O. 0) . : .. eq. 7-2) (X=O. 0)' ; .... eq. 7-3)
where
A=/a/ =Idl
VALIDATION AND PERFORMANCE CHECK Several outputs performed by the current model have been compared with observation datas for the validation. The selected site was Tatsuml-bashi intersection in Tokyo. which experiences one of the heaviest congestion every day. was selected as an observation site. To acquire various actual informations. 8 video cameras were used. Actual vehi c le detection pulses were also recorded from 3 d~tectors Installed at road side. L The location of such 3 detectors '1 are shown In Fig.8 ~ Observation was ~ conducted from 7:00 a.m to 9:00 a.m. A simulation was -~r---=---! also performed under the same condition as t~e observation.
) UlL S+
J~
l
r---
/J
=
(L+AD) 2aX ....... eq. 5) ( where a : acceleration) As for a detected vehicle in saturation flow region. the driving speed is assumed to be free f 10\01 V f • and the length of the on-pulse is modeled as; t1
The function of the on- pulse length
I
From these equations. the value of onpulse length at the current time of tl can be derivated as below; P
x
(2AP,., 2)
t
detector's location Ko- One is the volume packed with jam density In the congestion region. another Is the one In the deceleration flow region. At the current time of t 1. If the vehicles between the last segment of the queue.of which labal Is given in the simulation as I.and the detected vehicle are packed up to jam density behind the queue. then the stopping location XSTP at the stopping time of T of the current ly detected vehicle can be obtained_
Vf t
7 . 2)
~
Xo
detector's location
J 2AX
eq.
--- - - ----~;,,-.:-~
XSTP
( L +AD )
=
P
Ll
[j ....-..- ~- -;. -
stopping location
on-pulse length P
Cl rJ
... . . .. eq. 6)
Fig.S
site RIGHT site LEFT The location of vehicle detectors at the Tatsumibashi intersection
The ouputs are compared with each as below.
other
249
Signal Control at Traffic :\' et\\'or ks
·Saturation flow rate
*
The simulation outputs which were generated based on the analysed results are compared with observed datas In Flg.9.
Time occupancy was calculated by using detector on-pulses. The comparison Is shown in Fig.11.
_.... o
N
>< wu >z HW
""
site LEFT
><
....
U
0
..;
~r...
observed data
simulation output
o
0
E-<::l ":0 ..:l~
Time series of the occupancy
site LEFT
Z
P,
::la UlI)
U
2000.0 1000.0 SAT. FLOW RATE [ VEH/HR J
2000.0 1000.0 SAT. FLOW RATE ( VEH/HR} EAST Approach
a
WEST Approach
24
72 TIt1E (MINl
120
74
24
72 TIt1E (MIN)
120
24
72 TIME (MIN)
120
o
....o
lOOO.O 2000.0 SAT. FLOW RATE ( VEH/HR l
1000.0 2000.0 SAT. FLOW RATE r VEH/HR J
NORTH Approach
SOUTH Approach
72 TIME ( min)
120
o
o
.... site RIGHT
site RIGHT
><
u
simulation observed ~ output distribution ~
g;
Fig.9
Distribution of saturation flow rate
• Counts of volume o
o
H
site LEFT
::;;
a
24
o
....o
Z ....
u u
site THROUGH
lI)
72 TIME (tUN 1
Fig . ll
72 TIME ( min)
24
120
Time series of occupancy
'-.
~
::la ..:lll)
In the DESC model. queue length and delay can also be calculated. Relationships between time occupancy and delay. between time occupancy and queue length are described as below.
o lI)
§;
o
za
H ....
::;;
lI)
TIME (Sminl
U Q)
TIME (Smi n l
a•
Ul 0 -1.0
site RIGHT
~
'-.
W
....
..:l
::;;
W
observed data
::l ..:la all)
o
W
>
-D-
Fig.lO
Time series of counts of volume
•
;200
simulation output
TIME (Sm in l
o
\.90 W
> ..:
1.0 2 . 0 3.0 AVERAGE ON-PULSE LENGTH ( sec /ve h / Smin)
1 . 0 2.0 3 . 0 AVERAGE ON-PULSE LENGTH ( sec /v eh / Smin)
250
!\I. Kalakllra ,
Sh. !\!lIkai and Y. Sakllracla
SIMULATION OF THE SIGNAL CONTROL IN A TRAFFIC NETWORK
RESULTS
Having used the DESC model. a simulation of traffic responsive program selection control in a traffic network covering 35 intersections was performed.
Total
The simulation site was selected in Tokyo In this network traffic responsive program selection control is actually performed. The procedure is stated below. The network is divided into several subareas. Each sub-area has one major Intersection. and several detectors are installed around this major intersection. Each sub-area Is controled under the common cycle length which is determined according to the control index. Such control Index Is calculated by using the detector Information every unit control interval. control index
Cl = a*O
+
The total delay in the network under the pretimed control was reduced by 17 % due to the traffic responsive control.
Table.l
TOTAL
DELAY
NO OF SUBAREA
1
simulation
is
* Input datas Length of link. number of lane. detector location and input traffic volume were given by actual datas. * Signal control parameters In the simulation. the effectiveness of the traffic responsive program selection control was compared with the one of the single program pretime control. As for the pretime control. cycle length of each intersection was set corresponding to the maximum saturation degree. and split was set In proportion to the saturation degree of the phases. As for the program selection control. 6 values of cycle length and split were prepared for each major intersections. In the simulation split was selected every 5 minutes. and cycle length was selected every i5 minutes. * Simulation time
4
TRAFFIC RES PONS gE .. OR [VEil' SEC (Dr.:.R R)IOP*100
397093.1 810855.0 211978.5 350205,1
[X]
13.3
14.3
5
6
OP
261576.7 342895,0
OR
105946.0 271005.4
(OP-OR)/OP*100
59.5
27.7
2.3
21.0
SUMMARY AND FUTURE A new vehicular traffic simUlation programme DESC was developed. This model was newly developed especlaly for the evaluation of traffic responsive control in road traffic networks. But we are not sure that the model can describe the traffic condition correctly enough, More validation checks are considered to be needed in the near future, REFERENCES 1) r.Ross and D.Gibson : Review
of Road Traffic Network Simulation Models, Transp.Rec. 644. pp36-41 .1977
2) J.K.Matthewson. D.L.Trautman and D.L. Gerlough : Study of Traffic Flow by Simulation, Proc .• HRB. Vol.34. pp522529 3) Haruo Ozaki A Simulation of the Evaluation of Signal Control, Tokyo Oniv .. master's thesis.1984 4)
Youichi Sakurada : Evaluation of the Signal Control in Road Traffic Network through Simulation. Tokyo Univ .. master's thesis.1985
5)
P.B. Hunt.D. I.Robertson.R.D.Bretherton and R. I .Winton : SCOOT - a traffic responsive method of coordinating signals. TRRL Laboratory Report 1014. 1981
2 hours
The network was divided into 6 sub-areas.
3
457896.6 946258.5 293157.6 358557.2
b*V
In the each sub-area. the cycle length corresponding to the control index is selected from among several values which was set In advance and is used for control. AS for the major intersections. the value of split also be selected every unit control interval.
2
PRETIME ... OP [VEII·SEC]
where(o:occupancy V:counts of volume a.b:constant
Next condition of the given as below.
delay in each sub-area is shown in
Table.l,
A SIMULATION FOR THE EVALUATION OF SIGNAL CONTROL AT TRAFFIC NETWORKS M. Katakura, Sh. Mukai and Y. Sakurada /II.I/i/II/I' of /II(/II.I/riai Sri/'lIcl'. [ 'lIiln.li/),
of Tokyo. ja/)(III
Abstract. The traffic simulation program DESC was developed for evaluations of traffic responsive control in road networks. Keywords.
Traffic control; road traffic; simulation; validation .
In microscopic model, each Individual vehicle is identified and its position , acceleration and other characte risti cs are stored every unit scanning Interval . MicroscopiC models deal with 2 separate areas: streets and Intersections. On the streets . a car-following model Is usually adopted for approximation of the behavior of individual vehicle. At the intersection,pedestrlan interference and collision avoidance are usually performed. This kind of models can simulate sufficiently enough the fluctuation of traffic condition In the short term,but long simulation time and big core storage are needed.
I NTRODUCTION In recent years, as computer facilities have Improved, signal control has adopted the on -l ine real time control method . In Japan, the traffiC responsive contro l method was introdu ced In Tokyo by the National Police Agen cy In 1971. Today It is being used to operate for areas covering more than 70 intersections. In the future, more consideration will be addressed to the application of onl ine real time signal control method on the road traffic network . Thus, not only the I mprovement of computer fa c iliti es and detector reliabilIty . but also the development of tools that can eval uate the effectiveness of control of a computerized system on the traffic network in specific region is Imperative. Taking into consideration the present condit i on and expected trends In the future. the authors have developed a new road traffic network simulation model as one tool among others which can evaluate such control method as stated above.
In platoon models, vehicles are grouped Into several platoons. and the programme keeps track of the location. speed. acceleration and the size of the platoon. This kind of models are more economical In respect to computer storage and faster in execution than microscopic models . In macroscopiC models. the traffic stream Is treated as a continuous fluid. and each Individual vehicle is not identlfied.Generally ma croscopiC models are very economical In respect to computer storage and very fast In simulation. This kind of models. however, cannot describe detail traffic conditions .
MAJOR FEAT URES FOR THE MODEL Major features the model should have are considered to be as follows;
* Simulation
time should short as possible.
be as
As to the function of vehicle detection. although SCOOTS) has an signal optimization programme based on detector information. the model does not have a programme for direct simulation of detector Information. Therefore counts of volume and time occupancy by detectors are not output of the simulation itself, A simulation programme having the function of vehicle detection could not be found among existing models. On the basis of adopted concepts In previously developed models, the authors have developed a new simulation model~}4)
* The model
should trace the dynamic fluctuation of traffic stream In the short term ,
* The model should Implement the function of vehicle detection .
The first actual documented simulation were performed In 1955 with an analog computer~) Since then, many computer simUlation models have developed and are being developed to-date. The models can be grouped into 3 types as below;l) 1. 2. 3.
the
BASIC CHARACTERISTICS OF THE NEW MODEL
microscopic model platoon model macroscopic model
The authors have developed a new road traffic network simulation model named
245
:-'1. Katakllr a. Sh. :-'Iukai and Y. Sakllrad a
246
Dynamic Evalua tor of Signal Contro l (DESCJ Basic charac teristi cs of DESC are as' follow s: I. The macros coPic type model is adopte d for the simula tion of the traffic stream on lhe )'oadway In order to save comput er storag e and simula tion lime. 2.
The micros copic type model is adopte d for the simula tion of right turning vehicl e arriva l and the arriva l of indiv idual vehicl es at detect ors.
3.
The variat ion and the fluctu ation of traffic flow for the perform ance of dynami c contro l simula tion are describ ed.
4.
Detect or inform ation like traffic volume and time occupa ncy . are simula ted.
The Individ ual charac teristi CS are describe d In more detail below.
SIMULATION OF THE TRAFFIC STREAM ON THE STREET The program me assume s a traffic stream Theref ore each as a continu ous fluid. Individ ual vehicl e is not Identi fied on the street . The road is modele d as a link divide d The length of into severa l segmen ts. each segmen t is equal to the common unit cruise length . whi ch one vehicl e runs In a unit scanni ng interv al. Let the adjace nt road segmen ts denote d K and K+I be consid ered in the model. The segmen t K+ 1 is def i ned to be upstream of K. At every scanni ng interv al. a whole or a part of existin g volume at segmen t K+l • EV(K+ l,tlis advanc ed to the next segmen t The volume of vehicl e moving from K is modele d as: segmen tK+lto segmen t K AF(K.t J = mlnimum[ SFRT*NLANE. EV(K+ I.t-ll. JDS*UL*NLANE - EV(K.t -l I ... ... eq. 1 J where
AF(K.t J: arrivin g flow at seg ment K at curren t scan EV(K. t-ll: existin g volume at segmen t K at the 1as t scan SFRT: satura tion flow rate NLANE: number of lanes of the specif ic link JDS: Jam densit y UL: unit length of segmen t
Each segmen t has an upper limit for existin g volume that corresp onds to JDS*UL*NLANE. I f ex i s t i I1g vol ume i 11 segment K have reache d its upper limit . then arriva l flow AF(K.t l would be determ ined to be zero from equatio n I. Such logica l proced ure enable s the model to simula te the stoppi ng wave of the queue.
flo\" direct ion
existin g volwre
<::
upper limit
AF(K ,t)
~ SFRfxNLA NE
0.0
I
EV(K,t- l)
EV(K+l ,t-l) segrrent :K+l
segrrent :K Fig.l
Flow profil e in adjace nt road segmen ts denote d K and K+l
each K segmen t has a labal Next. .LABEU KI. which is set corresp onding to the curren t eXistin g volume at ea c h scanni ng Interv al. At the segmen t K.if the curren t existin g volume is equal to JDS*UL*NLANE which is the upper limit. then LABEL
------ ------- ------- ------ r----JDSX ULXNLANE AF(K ,t)
SFRI' NLANE
0.0
segment :K segrrent :K+l Fig.2
III lin the case of LABELIKI=O and LABEL< K+ 1 1=2 AF(K. tlis determ ined as SFRT*NLANE-EV(K.t-1 I (iii lin the case of LABEL(KI=2 and LABEL< K+ 1 1=1 AF(K. tlis determ ined as zero Ilvlln the case of LABEL(KI=1 and ,.I LABEL< K+ 1 1=1 AF(K. tlis determ ined as zero Such logica l proced ure enable s the model to simula te the startin g wave of the queue. In the curren t model. the vehicl e speed is assume d to be either 0 or free flow speed.
247
Signal Control at Traffic :'\let works
SI MULATI ON OF I ND I VI DUAL VEIl I CLE ARRIVAL In the DESC model. the microscopic type model is also adopted for the simulation of individual right-turn vehicle arrivals and individual vehicle arrivals at detectors. The procedures are stated below. At every scanning interval. flow profile at the intersection or the detector's locatIon is accumulated. The probability of arrival can be obtained by the linear approximated function of the cumulative value shown In Fig.3. This probability is compared to a uniform random number in order to decide if an arrival occurred or not. If the value of the probability of arrival is larger than uniform random number. then It is assumed that one vehicle has arrived. and cumulative value is reduced by 1.0. prcbability of arrival 1.0
In the current model. each variable is assumed to follow the normal distrlbution. SIMULATION OF VEHICLE DETECTION In the DESC model. the arrival of each individual vehicle is simulated by detectors as descrived above. Also the time occupancy in specific time intervals Is simulated. First of all. the travel pattern a vehicle pass through a congested area is shown on the time-distance diagram In Flg.5. The vehicle in time-distance diagram passes 5 regions. As previously mentioned. the speed of traffic flow on the street is assumed to be either 0 or free flow speed. Another logic is needed for the simulation of detector pulses actuated by vehicles passing the deceleration and acceleration region. green
--------;r--- - -
red
stopT=====jIC'~======~===;=\======~ 2.C?nges~ion \
line
\
region '\
0.0
1.0
0.0
Fig.3
cumulative value
The function of probability of vehicle arrival
SIMULATION OF RIGHT-TURN VEHICLES' BEHAVIOR
\ \ 1. free flON '\ region
~.
probability of right-turning
'\
'\
4.acceleration flON reg ion
The time-distance diagram of a congested area
1. Free flow region
The traffic stream in this region Is not directly affected by the queue. If the current detected vehicle is in a free flow region. the length of the on-pulse is modeled as;
P=P A = (L+Ao) /Vt .... eq. 2)
PA L
Ao
Vt
Fig . 4
\
,,\
distance from the stop line
where
0.0 0.0
'\
\
, 3.deceleration '\ flCMI region
Cl
Fig.S
In the DESC model. right-turn vehicles are handled as individual vehicles. In case of gap acceptance. the vehicle is able to turn only If there Is an acceptable gap in the opposing flow. The linear approximated gap acceptance function is shown in Fig.4.
'\
time
S.saturation low region
gap in the opposing flow
The function of gap acceptance
SIMULATION OF FLUCTUATION OF THE TRAFFIC FLOW
average length of the onpulse average length of a vehicle the detection area free flow speed
2. Congestion region If the current detected vehicle is in a congestion region. the length of on-pulse is modeled as the maximum length of the puis which Is assumed in this model. 3. Deceleration region
For the description of the variation and the fluctuation of traffic flow. the variables stated below are varied cycle by cycle.
* saturation flow rate * jam density * average length of detector's on-pulse
CTS-I
If the current detected vehicle is in a deceleration flow region. the length of on-pulse Is modeled shown In Fig.6. At x=O and t=O. the specific vehicle of which speed is free flow speed Vt starts to decelerate. at x=Xo and t=t t. the specific vehicle of which speed is v tl is detected. At the current time of t I there might be two kinds of volum~~ in segments between the stopllne and the
M. Katakura , Sh. Mukai and Y. Sakurada
248
Thus. the length of the on-pulse can be descrlved as a linear approximated function of X which can be calculated in the current model.
x
-----CJ=---=tf------ L1:: =ngestion~Ll A - region
_stopping-:"~ - wave
- u - [j ...
'-:
Ll
eq . 7.1)
J
-~
----------~--......::;",..------
o. 0
V tl D
/0 Fig_6
t
T
1
'--_ _ _-+-_ _ __ _ _-_-_-_-_-_-~ 0.0 (L+A o ) 2
Fi g . 7
The model of a travel pattern in a congested region
Now let XSTP - Xo be X. and let XSTP be D. X Is the distance from detector to stopping location which will be passed by the detected vehicle between detected time of t 1 and stop time T. while D is the total distance of deceleration_ The relationships among these variables are given as below; d t
1
2
= = = =
1 2
x
+
1
2
V f T--dT
Vf - d t 1 Vf - dT 0 (L+AD) / V P tl where d : deceleration V t.1
( = D)
2
_. ..... eq. 3) t
l
P
=
t
l
=
(L+AD)
/J
2dX .... ... eq.
4)
As to a detected vehicle in acceleration flow region. the length of on-pulse can be modeled similarlY as; P
Pt 1
=
(L
+ AD) / V f
(L + AD)
/ Vf
2A (PM -
Vf
. {CL + AD)
..
(x >
(L
+ AD)
2
(2AP,., 2)
)
..... eq. 7-1)
P ,.,)
X + PM
2 2
>
(2AP,.,2)
X> O. 0) . : .. eq. 7-2) (X=O. 0)' ; .... eq. 7-3)
where
A=/a/ =Idl
VALIDATION AND PERFORMANCE CHECK Several outputs performed by the current model have been compared with observation datas for the validation. The selected site was Tatsuml-bashi intersection in Tokyo. which experiences one of the heaviest congestion every day. was selected as an observation site. To acquire various actual informations. 8 video cameras were used. Actual vehi c le detection pulses were also recorded from 3 d~tectors Installed at road side. L The location of such 3 detectors '1 are shown In Fig.8 ~ Observation was ~ conducted from 7:00 a.m to 9:00 a.m. A simulation was -~r---=---! also performed under the same condition as t~e observation.
) UlL S+
J~
l
r---
/J
=
(L+AD) 2aX ....... eq. 5) ( where a : acceleration) As for a detected vehicle in saturation flow region. the driving speed is assumed to be free f 10\01 V f • and the length of the on-pulse is modeled as; t1
The function of the on- pulse length
I
From these equations. the value of onpulse length at the current time of tl can be derivated as below; P
x
(2AP,., 2)
t
detector's location Ko- One is the volume packed with jam density In the congestion region. another Is the one In the deceleration flow region. At the current time of t 1. If the vehicles between the last segment of the queue.of which labal Is given in the simulation as I.and the detected vehicle are packed up to jam density behind the queue. then the stopping location XSTP at the stopping time of T of the current ly detected vehicle can be obtained_
Vf t
7 . 2)
~
Xo
detector's location
J 2AX
eq.
--- - - ----~;,,-.:-~
XSTP
( L +AD )
=
P
Ll
[j ....-..- ~- -;. -
stopping location
on-pulse length P
Cl rJ
... . . .. eq. 6)
Fig.S
site RIGHT site LEFT The location of vehicle detectors at the Tatsumibashi intersection
The ouputs are compared with each as below.
other
249
Signal Control at Traffic :\' et\\'or ks
·Saturation flow rate
*
The simulation outputs which were generated based on the analysed results are compared with observed datas In Flg.9.
Time occupancy was calculated by using detector on-pulses. The comparison Is shown in Fig.11.
_.... o
N
>< wu >z HW
""
site LEFT
><
....
U
0
..;
~r...
observed data
simulation output
o
0
E-<::l ":0 ..:l~
Time series of the occupancy
site LEFT
Z
P,
::la UlI)
U
2000.0 1000.0 SAT. FLOW RATE [ VEH/HR J
2000.0 1000.0 SAT. FLOW RATE ( VEH/HR} EAST Approach
a
WEST Approach
24
72 TIt1E (MINl
120
74
24
72 TIt1E (MIN)
120
24
72 TIME (MIN)
120
o
....o
lOOO.O 2000.0 SAT. FLOW RATE ( VEH/HR l
1000.0 2000.0 SAT. FLOW RATE r VEH/HR J
NORTH Approach
SOUTH Approach
72 TIME ( min)
120
o
o
.... site RIGHT
site RIGHT
><
u
simulation observed ~ output distribution ~
g;
Fig.9
Distribution of saturation flow rate
• Counts of volume o
o
H
site LEFT
::;;
a
24
o
....o
Z ....
u u
site THROUGH
lI)
72 TIME (tUN 1
Fig . ll
72 TIME ( min)
24
120
Time series of occupancy
'-.
~
::la ..:lll)
In the DESC model. queue length and delay can also be calculated. Relationships between time occupancy and delay. between time occupancy and queue length are described as below.
o lI)
§;
o
za
H ....
::;;
lI)
TIME (Sminl
U Q)
TIME (Smi n l
a•
Ul 0 -1.0
site RIGHT
~
'-.
W
....
..:l
::;;
W
observed data
::l ..:la all)
o
W
>
-D-
Fig.lO
Time series of counts of volume
•
;200
simulation output
TIME (Sm in l
o
\.90 W
> ..:
1.0 2 . 0 3.0 AVERAGE ON-PULSE LENGTH ( sec /ve h / Smin)
1 . 0 2.0 3 . 0 AVERAGE ON-PULSE LENGTH ( sec /v eh / Smin)
250
!\I. Kalakllra ,
Sh. !\!lIkai and Y. Sakllracla
SIMULATION OF THE SIGNAL CONTROL IN A TRAFFIC NETWORK
RESULTS
Having used the DESC model. a simulation of traffic responsive program selection control in a traffic network covering 35 intersections was performed.
Total
The simulation site was selected in Tokyo In this network traffic responsive program selection control is actually performed. The procedure is stated below. The network is divided into several subareas. Each sub-area has one major Intersection. and several detectors are installed around this major intersection. Each sub-area Is controled under the common cycle length which is determined according to the control index. Such control Index Is calculated by using the detector Information every unit control interval. control index
Cl = a*O
+
The total delay in the network under the pretimed control was reduced by 17 % due to the traffic responsive control.
Table.l
TOTAL
DELAY
NO OF SUBAREA
1
simulation
is
* Input datas Length of link. number of lane. detector location and input traffic volume were given by actual datas. * Signal control parameters In the simulation. the effectiveness of the traffic responsive program selection control was compared with the one of the single program pretime control. As for the pretime control. cycle length of each intersection was set corresponding to the maximum saturation degree. and split was set In proportion to the saturation degree of the phases. As for the program selection control. 6 values of cycle length and split were prepared for each major intersections. In the simulation split was selected every 5 minutes. and cycle length was selected every i5 minutes. * Simulation time
4
TRAFFIC RES PONS gE .. OR [VEil' SEC (Dr.:.R R)IOP*100
397093.1 810855.0 211978.5 350205,1
[X]
13.3
14.3
5
6
OP
261576.7 342895,0
OR
105946.0 271005.4
(OP-OR)/OP*100
59.5
27.7
2.3
21.0
SUMMARY AND FUTURE A new vehicular traffic simUlation programme DESC was developed. This model was newly developed especlaly for the evaluation of traffic responsive control in road traffic networks. But we are not sure that the model can describe the traffic condition correctly enough, More validation checks are considered to be needed in the near future, REFERENCES 1) r.Ross and D.Gibson : Review
of Road Traffic Network Simulation Models, Transp.Rec. 644. pp36-41 .1977
2) J.K.Matthewson. D.L.Trautman and D.L. Gerlough : Study of Traffic Flow by Simulation, Proc .• HRB. Vol.34. pp522529 3) Haruo Ozaki A Simulation of the Evaluation of Signal Control, Tokyo Oniv .. master's thesis.1984 4)
Youichi Sakurada : Evaluation of the Signal Control in Road Traffic Network through Simulation. Tokyo Univ .. master's thesis.1985
5)
P.B. Hunt.D. I.Robertson.R.D.Bretherton and R. I .Winton : SCOOT - a traffic responsive method of coordinating signals. TRRL Laboratory Report 1014. 1981
2 hours
The network was divided into 6 sub-areas.
3
457896.6 946258.5 293157.6 358557.2
b*V
In the each sub-area. the cycle length corresponding to the control index is selected from among several values which was set In advance and is used for control. AS for the major intersections. the value of split also be selected every unit control interval.
2
PRETIME ... OP [VEII·SEC]
where(o:occupancy V:counts of volume a.b:constant
Next condition of the given as below.
delay in each sub-area is shown in
Table.l,