131

Development and Design of a Signal Control Systemalong the Route 2 in Hiroshima City
Haruko Fujii＊, Hikaru Shimizu＊＊
Abstract
This paper deals with the study of a signal control system along the Route 2 in Hiroshima city from theviewpoint of a digital control for traffic flow dynamics. Time-varying characteristics of traffic flows areanalyzed to evaluate the volume balance at each signalized intersection during the cycle length for eachlane. The signal control system of the congestion length is described by a nonlinear time-varying discrete
dynamic system and synthesized by using the feedback control based on the volume balance at eachsignalized intersection. The signal control algorithm in which the three signal control parameters aresearched systematically so as to minimize the sum of congestion lengths along the arterials is presented.
From the comparison of congestion lengths between measurement values controlled by a pattern selection
method and simulation values, it is confirmed that the signal control system and the signal control
algorithm work effectively along the Route 2 in Hiroshima city, Japan.
Keywords : traffic analysis, signal control system, signal control algorithm, simulation

1. INTRODUCTION
In recent years, the congestion has increased in urban
traffic networks along with the increase of the number ofvehicles registered in Japan. Traffic control is exercisedthrough the combination of road markings, traffic signs andsignals. The signal control is an effective method to control
the congestion of traffic arterials. On-line signal control
methods such as the SCOOT［1］, decentralized controlT［2］,
MODERATOT［3］ and dynamic programming［4］ havebeen presented to control the congestion along arterials.
The common problem of the above-mentioned studies is
as follows; the three signal control parameters are notcontrolled systematically but independently to minimize
each performance criterion. Since incoming volumes andqueue lengths at each signalized intersection increase
rapidly in rush hours, the three signal control parameters
are desired to be controlled systematically andcooperatively.
This paper studies the signal control of congestion
lengths along two-way traffic arterials from adeterministic control viewpoint. The volume balance isheld at each signalized intersection of the arterials forcertain duration. Based on the volume balance at eachsignalized intersection the congestion mechanism is＊情報工学科＊＊福山大学工学部

described quantitatively. A signal control algorithm ispresented to control congestion lengths along arterials.
From the comparison between measurement values
controlled by a pattern selection method and simulation
values, it is confirmed that the proposed control algorithm
works well to control congestion lengths so as tominimize the performance criterion and to maximize thethrough band width along two-way traffic arterials.
2. TRAFFIC ANALYSIS
2.1 Volume balance
The signal control system of the congestion length issynthesized for two-way traffic arterials. The volume
balance for each lane at each signalized intersection of thearterial is written asxe ( j , m, k ) xe ( j , m, k  1)
(1)‫ޓޓޓޓޓ‬ xi ( j , m, k )  xo ( j , m, k )­ xo ( j , m, k ) [ ( j , m, k ) \ x ( j , m, k )®
¯ xe ( j , m, k ) t 0(2)

where k = k∆T denotes time, j and m denote the locationof each signalized intersection and the approach ofvehicles respectively (see Fig. 1). xe( j, m, k ), xi( j, m, k )and xo( j, m, k ) denote the excess incoming volume,
平成20年９月30日受理

132

弓削商船高等専門学校 紀要 第31号（平成21年）

j=1

2

3. SIGNAL CONTROL SYSTEM

N

m=2
m=1

In the volume balance at each signalized intersection, it
is assumed that the incoming volume x i ( j, m, k ) ismeasured, and the outgoing volume x o ( j, m, k ) is
controlled by the three signal control parameters at thesignalized intersection concerned. As the result, theoutgoing volume xo( j, m, k ) is replaced by the control
input u( j, m, k ).
The signal control system is then written byArterial

m=4
m=3

㧦Signalized intersection
Fig. 1

Two-way traffic flows along arterial.

x e ( j , m, k  1)
x i ( j , m, k )xo ( j, m , k )x e ( j , m, k )Fig. 2 Volume balance for each lane at each signalizedintersection.

incoming volume and outgoing volume (see Fig. 2).
ψx( j, m, k ) denotes the net traffic flow rate and ξ( j, m, k )is evaluated by taking the value of dividing xo( j, m, k ) byψx( j, m, k ) under any traffic flow conditions.
2.2 Congestion mechanism
The congestion mechanism which plays an essential
role to control congestion lengths is described
quantitatively based on the volume balance at eachsignalized intersection given by Eq.(1).
i ) The congestion at each signalized intersection
occurs at the time when the excess incoming volume
becomes greater than zero, i.e.

xe ( j , m, k  1)xe ( j , m, k  1) ! 0‫ޓޓޓ‬andxe ( j , m, k  1)  xi ( j , m, k ) d xo ( j , m, k )(4)iii) It continues so long as the excess incoming volume
is positive, i.e.

xe ( j , m, k  1) ! 0‫ޓޓޓ‬andxe ( j , m, k  1)  xi ( j , m, k ) ! xo ( j , m, k )NJ a (k )4¦¦ g ( j, m, k )(7)

j 1 m 1

where N denotes the number of signalized intersections
along the direction for j, the function g( j, m, k ) and thecontrol error e( j, m, k ) are defined by using reference
input lr( j, m, k )(3)ii) It disappears at the time when the excess incoming
volume becomes less than or equal zero, i.e.

(6)where the upper limit of the control input is determinedby Eq.(2) and shown in Fig. 3. The observation equationof the congestion length yc( j, m, k ) is described in such a
way that the state variable is multiplied by atransformation factor lm( j, m, k ).
The signal control system of the congestion length isconsidered on the arterials; in this control system, thereference input, control input and output are given by thepermitted congestion length lr( j, m, k ), the three signal
control parameters and the congestion length respectively.
In this way, the signal control system of the congestion
length is synthesized using the feedback control at eachsignalized intersection (see Fig. 4). The purpose of thesignal control system of two-way traffic arterials is to findsuch control input that it makes the following
performance criterion Ja(k) minimizeg ( j , m, k )0‫ޓޓޓ‬andxi ( j , m, k ) ! xo ( j , m, k )­ xe ( j , m, k ) xe ( j , m, k  1)°
 xi ( j , m, k )  u ( j , m, k )®‫ޓޓޓޓޓ‬° y ( j , m, k ) l ( j , m, k )  x ( j , m, k )me¯ c­0 ‫ޓޓޓޓޓ‬e( j , m, k ) t 0®
¯| e( j , m, k ) | ‫ޓ‬e( j , m, k )  0

u ( j , m, k )Ƕ( j , m, k )u \ x ( j , m, k )0(5)Fig. 3Ƕ( j , m, k )xe ( j, m, k  1)

u \ x ( j , m, k ) xi ( j, m, k )Characteristic of control input.

(8)

Development and Design of a Signal Control System along the Route 2 in Hiroshima City（Fujii・Shimizu）

Step 4. The net traffic flow rate for each lane at thesignalized intersection is evaluated by

Signalcontrolalgorithm

Controller parameters+l r ( j , m, k )Signalcontrollere( j, m, k )­\ xl ( n ) ( j , m, k ) rgl ( n ) ( j, m, k )  c xl ( j , m, k )
° (n)
(n)
°°\ xs ( j , m, k ) rgs ( j , m, k )  c xs ( j , m, k )
(11)
® (n)
(n)
°\ xr ( j , m, k ) rgr ( j , m, k )  c xr ( j , m, k )
° (n)
(n)
¯°\ xsl ( j , m, k ) rgsl ( j , m, k )  c xsl ( j , m, k )Trafficflowu ( j , m, k )y c ( j , m, k )Fig. 4 Signal control system of congestion length at eachsignalized intersection.

e( j , m, k )133

lr ( j, m, k )  yc ( j, m, k )(9)because degrees of saturation are different to approaches
at signalized intersections.
4. SIGNAL CONTROL ALGORITHM
A balance control algorithm is applied to control thecongestion length along two-way traffic arterials. Thebalance control of the congestion length means that the
maximum values of congestion lengths which cross eachother on a road are controlled so as to become equal, andthe three signal control parameters are systematically andsequentially searched so as to minimize the performance
criterion Ja(k).
Step 1. The initial values, upper and lower limits andincrement of signal control parameters are set foreach signalized intersection. The approach ofvehicles is set as m=1.
Step 2. The incoming volume xi(n)( j, m, k ) is inputted
and the duration ∆T is equally set to the cycle
length cy(n)( j, m, k ). The symbol(n) denotes therepetition times of computation.
Step 3. The incoming volumes of congestion cases arerecalculated by­ x il ' ( n ) ( j , m, k ) x il ( n ) ( j , m, k )° x el ( j , m, k  1)°‫ޓޓޓޓޓޓޓ‬° x ' ( n ) ( j , m, k ) x ( n ) ( j , m, k )is° is°°‫ޓޓޓޓޓޓޓ‬ x es ( j , m, k  1)
® (n)
(n)
° x ir ' ( j , m, k ) x ir ( j , m, k )(n)°‫ޓޓޓޓޓޓޓ‬ x er ( j , m, k  1)°
° x isl ' ( n ) ( j , m, k ) x isl ( n ) ( j , m, k )°(n)°¯‫ޓޓޓޓޓޓޓ‬ x esl ( j , m, k  1)

where cxl( j, m, k ), cxs( j, m, k ), cxr( j, m, k ),cxsl( j, m, k ) are the capacities and rgl( j, m, k ),rgs( j, m, k ), rgr( j, m, k ), rgsl( j, m, k ) are thegreen splits, of left-turn-, straightforward-, rightturn- and straightforward-left-turn-lanes
respectively.
Step 5. The green time of each lane are evaluated bymultiplying the cycle length by the green split.
Step 6. The excess incoming volume xe(n)( j, m, k ) isevaluated based on the volume balance(n)x el ( j , m, k )x il ' ( n ) ( j , m, k )‫ޓޓޓޓޓޓޓ‬ x ol(n)­° xol ( n ) ( j , m, k ) [ ( j , m, k ) \ xl ( n ) ( j , m, k )® (n)°̄ xel ( j , m, k ) t 0(n)x es ( j , m, k )x is ' ( n ) ( j , m, k )(n)‫ޓޓޓޓޓޓޓ‬ x os ( j , m, k )­° xos ( n ) ( j , m, k ) [ ( j , m, k ) \ xs ( n ) ( j , m, k )® (n)°̄ xes ( j , m, k ) t 0(n)x er ( j , m, k )x ir ' ( n ) ( j , m, k )‫ޓޓޓޓޓޓޓ‬ x or(n)( j , m, k )x isl ' ( n ) ( j , m, k )‫ޓޓޓޓޓޓޓ‬ x osl

where xil(n)( j, m, k ), xis(n)( j, m, k ), xir(n)( j, m, k ),xisl(n)( j, m, k ) are incoming volume, of left-turn-,
straightforward-, right-turn- and straightforwardleft-turn-lanes respectively.

(n)­° xor ( n ) ( j , m, k ) [ ( j , m, k ) \ xr ( n ) ( j , m, k )® (n)°̄ xer ( j , m, k ) t 0
x esl ( j , m, k )(10)( j , m, k )(n)( j , m, k )­° xosl ( n ) ( j , m, k ) [ ( j , m, k ) \ xsl ( n ) ( j , m, k )® (n)°̄ xesl ( j , m, k ) t 0

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

where xol(n)( j, m, k ), xos(n)( j, m, k ), xor(n)( j, m, k ),xosl(n)( j, m, k ) are outgoing volume, of left-turn-,
straightforward-, right-turn- and straightforwardleft-turn-lanes respectively.
Step 7. The congestion length yc(n)( j, m, k ) is evaluated
by

134

弓削商船高等専門学校 紀要 第31号（平成21年）­ ycl ( n ) ( j , m, k ) lm ( j , m, k )  xel ( n ) ( j , m, k )
° (n)
(n)
° ycs ( j , m, k ) lm ( j , m, k )  xes ( j , m, k )
(20)
® (n)
(n)
° ycr ( j , m, k ) lm ( j , m, k )  xer ( j , m, k )(n)° ( n)¯ ycsl ( j , m, k ) lm ( j , m, k )  xesl ( j , m, k )where ycl(n)( j, m, k ), ycs(n)( j, m, k ), ycr(n)( j, m, k ),ycsl(n)( j, m, k ) are congestion length, of left-turn-,
straightforward-, right-turn- and straightforwardleft-turn-lanes respectively.
Step 8. The green time and green splits are evaluated for
all approaches based on the phase at eachsignalized intersection.
Step 9. If the following control index
(N )

(Z )

1
FirstStep
level

Fig. 5

Hierarchical structure of balance control algorithm.

Table. 1

Performance criteria of balance control algorithm.

Step
Level

(21)

max{ e (N ) ( j ,1, k ) , e (Z ) ( j ,2, k ) , e ( P ) ( j ,3, k ) ,
(22)

H !0

­rgl ( n1) ( j , m, k ) rgl ( n ) ( j , m, k )  'rgl ( j , m)
° ( n1)( n)°°rgs ( j , m, k ) rgs ( j , m, k )  'rgs ( j , m)
(23)
® ( n1)( n)°rgr ( j , m, k ) rgr ( j , m, k )  'rgr ( j , m)
° ( n1)(n)°¯rgsl ( j , m, k ) rgsl ( j , m, k )  'rgsl ( j , m)
If, rgs(n+1)( j, m, k ) > rgs, max then proceed to Step11.
If, rgs(n+1)( j, m, k ) ≤ rgs, max then return to Step4.
Step 11. The cycle length is corrected by( n 1)( j , m, k )(n)c y ( j , m, k )  'c y ( j , m)

(24)

If, cy(n+1)( j, m, k ) > cy, max then proceed to Step12.
If, cy(n+1)( js, m, k ) ≤ cy, max then return to Step2.
Step 12. By using the optimal values of the green splits
and cycle length, the balance offset which
maximizes a through band width along the,arterial is evaluated by the Fieser s method.
In this algorithm, the cycle length and the green splits
are corrected starting from the lower limits to the upper
limits by their increments. This control algorithm is
executed sequentially from k=1 to k=kf and from j=1 to
j=N. The hierarchical structure and the performancec y , rg , toff

Minimize J a (k )rg , toffcriteria of the balance control algorithm are shown in Fig.
5 and Table 1. From the relation of the offset control, themaximum values of cycle lengths at N signalizedintersections are set in common, and the green split andthe offset at each signalized intersection are calculated
again.

then the green splits whose approach of vehicles
take the maximum control error are corrected
using

cy

Minimize J a (k )SecondStep level
2

H !0

‫ޓޓޓ‬
e ( O ) ( j ,4, k ) } ! H

Performance criteria

Steplevel1Firstis satisfied, we apply the green splits and thecycle length at optimum time values and proceed
to Step12.
Step 10. Otherwise

C2 ̖ CN

㧦Signalized intersection

max{ e ( j ,1, k ) , e ( j ,2, k ) , e ( j ,3, k ) ,‫ޓޓޓ‬e ( j ,4, k ) } d H

C1

Cj 㧦Signal controller

(P)

(O )

Arterial

2
SecondStep
level

5. SIMULATION RESULTS
The balance control algorithm of the congestion length
for two-way traffic arterials is simulated at signalizedintersections during evening rush hours in Hiroshima city,
Japan (see Fig. 6 to Fig. 9). The parameters and theincoming volumes are arranged for the simulation at
signalized intersections based on measurement data. The
incoming volumes for each lane vary randomly cycle bycycle at signalized intersections as shown in Fig. 10. The

N

Link length (m)
j=1
2

3

480

345
50

50
Legal speed (km/h)

Lane number㧦Signalized intersection

2 lanes
3 lanes
4 lanes㧦Signalized intersection with channelizing island

Fig. 6 Arterial consisting of three signalized intersections in
Hiroshima city.

135

Development and Design of a Signal Control System along the Route 2 in Hiroshima City（Fujii・Shimizu）

reference input is set as l r ( j, m, k ), =0m for all
approaches. In the signal control algorithm, the green
time defined by the product of the cycle length and thegreen split are searched so as to minimize theperformance criterion of Eq.(7). Cycle lengths arecompared between the simulation value and themeasurement value controlled by a pattern selection
method at oversaturated signalized intersections in
Fig. 11. Cycle lengths are controlled more widely andadaptively by the control algorithm. The values of green
time for straightforward vehicles are shown at the same
signalized intersection in Fig. 12. The balance offsets by,
Fieser s method are searched using the optimal values of
the cycle length and the green split so as to maximize thethrough band width (see Fig. 13). As the results, whilecongestions occur at some signalized intersections in realcircumstances, the congestion lengths are controlled so as
to become nearly zero at all signalized intersections by
the balance control algorithm (see Fig. 14).

N

Streetcar

1Ǿ

3Ǿ

2Ǿ

4Ǿ

Fig. 8 Type and phase at In front of Hiroshima City Officesignalized intersection.

N

N

Channelizing island

Overpass
1Ǿ

2Ǿ

3Ǿ

4Ǿ
1Ǿ

Fig. 7 Type and phase at Sumiyoshicho signalizedintersection.

2Ǿ

3Ǿ

Fig. 9 Type and phase at Kokutaiji signalizedintersection.

㪠㫅㪺㫆㫄㫀㫅㪾㩷㫍㫆㫃㫌㫄㪼㩿㫍㪼㪿㪆㪺㫐㪺㫃㪼㪀136

弓削商船高等専門学校 紀要 第31号（平成21年）

㪣㪼㪽㫋㪄㫋㫌㫉㫅㪪㫋㫉㪸㫀㪾㪿㫋㪽㫆㫉㫎㪸㫉㪻㪈㪍㪇㪪㫋㫉㪸㫀㪾㪿㫋㪽㫆㫉㫎㪸㫉㪻㪄㫃㪼㪽㫋㪄㫋㫌㫉㫅㪪㫋㫉㪸㫀㪾㪿㫋㪽㫆㫉㫎㪸㫉㪻㪉

㪌㪇
㪋㪇
㪊㪇
㪉㪇
㪈㪇
㪇
㪈㪍㪑㪌㪐 㪈㪎㪑㪈㪌 㪈㪎㪑㪊㪈 㪈㪎㪑㪋㪎 㪈㪏㪑㪇㪊 㪈㪏㪑㪈㪐 㪈㪏㪑㪊㪌 㪈㪏㪑㪌㪈㪫㫀㫄㪼

Fig. 13 Balance offset for straightforward vehicles at eachsignalized intersection (at k=35 cycle).

Fig. 10 Incoming volumes for m=4 at j=3 signalizedintersection.

㪪㫀㫄㫌㫃㪸㫋㫀㫆㫅㩷㫍㪸㫃㫌㪼㪚㫆㫅㪾㪼㫊㫋㫀㫆㫅㩷㫃㪼㫅㪾㫋㪿㩿㫄㪀㪪㫀㫄㫌㫃㪸㫋㫀㫆㫅㩷㫍㪸㫃㫌㪼㪤㪼㪸㫊㫌㫉㪼㫄㪼㫅㫋㩷㫍㪸㫃㫌㪼㪚㫐㪺㫃㪼㩷㫃㪼㫅㪾㫋㪿㩿㫊㪀

㪉㪇㪇
㪈㪏㪇
㪈㪍㪇
㪈㪋㪇
㪈㪉㪇
㪈㪎㪑㪇㪇

㪤㪼㪸㫊㫌㫉㪼㫄㪼㫅㫋㩷㫍㪸㫃㫌㪼

㪊㪇㪇
㪉㪌㪇
㪉㪇㪇
㪈㪌㪇
㪈㪇㪇
㪌㪇
㪇
㪈㪍㪑㪌㪐 㪈㪎㪑㪈㪌 㪈㪎㪑㪊㪈 㪈㪎㪑㪋㪎 㪈㪏㪑㪇㪊 㪈㪏㪑㪈㪐 㪈㪏㪑㪊㪌 㪈㪏㪑㪌㪈

㪈㪎㪑㪊㪇

㪈㪏㪑㪇㪇
㪫㫀㫄㪼

㪈㪏㪑㪊㪇

㪈㪐㪑㪇㪇

Fig. 11 Comparison of cycle length between simulation
values and measurement values for j=3 signalizedintersection.

㪫㫀㫄㪼

Fig. 14 Comparison of congestion length for straightforward
vehicles between simulation values and measurement
values for m=4 at j=3 signalized intersection.

6. CONCLUSIONS㪪㫀㫄㫌㫃㪸㫋㫀㫆㫅㩷㫍㪸㫃㫌㪼㪤㪼㪸㫊㫌㫉㪼㫄㪼㫅㫋㩷㫍㪸㫃㫌㪼㪈㪋㪇㪞㫉㪼㪼㫅㩷㫋㫀㫄㪼㩿㫊㪀

㪈㪉㪇
㪈㪇㪇
㪏㪇
㪍㪇
㪋㪇
㪉㪇
㪈㪎㪑㪇㪇

㪈㪎㪑㪊㪇

㪈㪏㪑㪇㪇
㪫㫀㫄㪼

㪈㪏㪑㪊㪇

㪈㪐㪑㪇㪇

Fig. 12 Comparison of green time for straightforward
vehicles between simulation values and measurement
values for m=4 at j=3 signalized intersection.

This paper studies the development of a signal control
system along the Route 2 in Hiroshima city, Japan fromthe viewpoint of a digital control for traffic flow
dynamics. The following have been shown.
i ) A signal control system of the congestion length isdescribed by a nonlinear dynamic system based on
the volume balance for each lane at each signalizedintersection.
ii) The signal control system is synthesized for twoway traffic arterials using the feedback control.
iii) Optimal signal control parameters of the arterials aresearched systematically and sequentially by thebalance control algorithm.
iv) From the comparison between measurement values
controlled by a pattern selection method andsimulation values, it is confirmed that the signal
control system and the signal control algorithm work
effectively so as to minimize the performance
criterion along the arterial.
It is a future problem that the proposed signal control

Development and Design of a Signal Control System along the Route 2 in Hiroshima City（Fujii・Shimizu）

algorithm will be applied for more signalizedintersections along the Route 2 in Hiroshima city.
REFERENCES［1］P. G. Hunt., D. I. Robertson, R. D. Bretherton and R.
I. Winton, SCOOT−a Traffic Responsive Methodof Coordinating Signals , TRRL Laboratory Report,
pp. 1014, 1981.
［2］E. J. Davison and Ü. Özgüner , Decentralized
Control of Traffic Networks , IEEE Trans., AC-28,
No.6, pp.677-688, 1983.
［3］H. Sakakibara, T. Usami, S. Itakura and T. Tajima,
MODERATO (Management by Origin−Destination
Related Adaptation for Traffic Optimization) , Proc.
of IEEE/ IEEJ/ JSAI International Conference onIntelligent Transportation System, pp.38-43, 1999.
［4］T. H. Heung, T. K. Ho and Y. F. Fung, “Coordinatedroad-junction traffic control by dynamic
programming”, IEEE Trans. ITS-6, pp.341-350,
2005.

137