- Email: [email protected]
Study on its Based on Self-organization Theory
STUDY ON ITS BASED ON SELF-ORGANIZA nON THEORY. ..
14th World Congress ofTFAC
Q-8e-Ol-3
Copyright © 1999 IFAC 14th Triennial World Congress, I3eijing, P.R. China
STUDY ON ITS BASED ON SELF-ORGANIZATION THEORY·
Feng Weidong
He Guoguang
Liu Bao
Systems Engineering Institute ofTianjin University, Tianjin 300072, P.R. China Tel: (86-22) 27403399. Fax: (86-22)27483164 E-mail: [email protected]. en
Abstract: In this paper, Self-organization theory and self-organization in transportation systems including ITS is reviewed firstly . Then the common ground to ITS and Self-organization Theory study is discussed. As an example to show the applications of self-organization theory in ITS, VRGS is qualitatively and quantitatively analyzed. Finally, the VRGS & TCS integrated control mode of ITS based on Self-organization Theory has been presented initially. Copyright ©1999IFAC Keywords: ITS (Intelligent Transportation Systems), self-organizing, VRGS (Vehicle Route Guidance System), integrated control.
INTRODUCTION ITS (Intelligent Transportation Systems) attracts more and more interest in Transportation Engineering field recently. ITS here means applications of advanced technologies such as information technology, image processing, and artificial intelligence in transportation engineering. In order to improve the performance of transportation systems, ITS put stress on the intelligence of roads and vehicles, on the coordination and the integration between human, road and vehicle.
In this respect more and more information technology has been applied in ITS, while the autonomy of lA in ITS should not be overlooked. Therefore, it is necessary to study ITS based on self-organization theory, which is a new branch of Systems Science.
I. SELF-ORGANIZING SYSTEMS AND SELFORGANIZA nON IN TRANSPORTA nON SYSTEMS AND ITS
1.1
ITS activities expanded rapidly but often with uncertain directions during the 1986-1995 period (French, 1995). At a certain extent it is attributed to lacking of theoretical guidance. Essentially, ITS is a complex opening system which consists innumerable "Intelligent Agent (IA)". So it is possible to study ITS by applying Self-organization Theory. On the other hand, "Intelligent" is the essential difference between ITS and traditional transportation systems. lA has some characteristics, among them the autonomy and the co-operation are the most important ones. The co-operation of lA is depending on exchanging information between IAs .
Self-organizing systems and Self-organization Theory
H. Haken has defined self-organizing systems as the systems which can acquire macro-scopic spatial, temporal, or spatio-temporal structures by means of internal processes without specific interference from the outside. "Specific" here mean that the structure or functioning is not impressed on the systems, but that the systems are acted upon from the outside in an nonspecific fashion (Haken, 1987). As a developing branch of Systems Science, Selforganization Theory focus on the study of selforganizing systems, especially on the development
• The work presented here is sponsored by NSFC (the Natural Science Foundation of China). No: 79770061.
8345
Copyright 1999 IF AC
ISBN: 008 0432484
STUDY ON ITS BASED ON SELF-ORGANIZATION THEORY. ..
14th World Congress ofIFAC
processes from non-ordered to ordered states in such systems. Generally, Self-organization theory includes Dissipative Structure theory, . Synergetics, Catastrophe theory, Chaos theory and Fractal theory.
tramntlOn. At this moment, the original dissipative mode can not meet the stability condition equation (3). Then a stack will be formed in such as transportation subsystem, and this kind of stack will compel traffic flow to search for a new dissipative way in order to stabilize itself again. At this moment, the t1uctuation in systems can not be ignored, and it even can be amplified due to existence of the nonlinear mechanism, thus impelling the system into a new dissipative state. So the equation Av = AT will be satisfied again, thereby a non-equilibrium phase transition will be accomplished and a new stable dissipative structure can be achieved.
1.2 Self-organization in transportation systems and ITS 1.2.1. Transportation system (including ITS) is a typical opening system which exchanges material, energy and infonnation with environment continuously. At the same time, it is also an nonequilibrium or even far away from equilibrium system in which Jots of uncertainties and time-varying factors existed. So transportation systems satisfY the essential conditions of self-organizing according to the dissipative structure theory
Supposed that on the condition of non-equilibrium state, a certain stable system parameter such as traffic flow counts concerned in such a subsystem is Aco/J . The input parameter in per unit time is A,mp , meanwhile the dissipated parameter is
Ad!s .
Moreover,
the relative dissipative intensity AD and the relative inputting intensity AT are defined as follows.
(I)
On the basis of Self-organization theory, the necessary condition to ensure the traffic-flow subsystem stability is (3)
Generally, the relative dissipative intensity AD is a nonlinear function of the system's state variables . The qualitative description is given as follows.
The changing of AT is generally continuous and smooth during the process of unbalance phase transition for a practical transportation system. But on the other side, the dissipative ability is limited for a concrete dissipative mode. When A D "# AT' traffic flow tends toward the critical point of phase
1.2.2. H. Haken had indicated that traffic flow worked as an order parameter when vehicles was going on a congested road, and each driver placed himself in a huge self-organizing system so he can not has his own way (Haken, 1987).
I. 2. 3. It can be founded in practice that vehicles and pedestrians can choose their group behavior in a very "clever" way (Feng W.D, et aI., 1998). Due to the extensive t1uctuation factors existing in traffic flow, the transportation systems can "test" all kinds of collective behaviors. As a result, that collective behavior which can perform the transportation task more efficiently will keep existing, because only this kind of collective behavior ( in corresponding to the order parameter) can increase with time while other kinds of group patterns will decrease even if they appeared in a short tenn .
1.2.4. It has been shown by traffic simulation with Cellular Automation (CA) models that the selforganization exists in traffic t10w evolution processes. For example, a sharp jamming transition was found that separates between the low-density dynamically phase in which all cars move at maximal speed and the high-density jammed phase in which they are a\l stopped (Biham, et aI., 1992).
1.2.5. Chaos and fractal in transportation systems It is well-known that traffic flow is a typical non-
stationary process. So Fast Fourier Transform (FFT) is not suitable for analyzing traffic dynamics, while Wavelets analysis which is well localized in space and time simultaneously and is more suitable for nonstationary process. Therefore wavelets analysis can be used as a main mathematical tool for detecting chaos and fractality in transportation system. This work was first developed by Feng (1998), who demonstrated that chaos and fractality exist in transportation systems, and it is believed that the long-term dependence and memory in transportation systems are the source of fractality and chaos ( Feng W .D ., et aI., 1998).
8346
Copyright 1999 IF AC
ISBN: 0 08 043248 4
STUDY ON ITS BASED ON SELF-ORGANIZA nON THEORY. ..
14th World Congress ofTFAC
destination. 1.2 6. Self-organization in ITS As a typical transportation system, it is believed that ITS also have self-organizing characteristics just as mentioned above in general transportation systems.
2. THE COMMON GROUND TO ITS AND SELF-ORGANIZA nON THEORY STUDY There are a lot of common ground between ITS and Self-organization Theory study. • The common research object of study As mentioned above, the existence of lA (vehicledriver individual) result in the self-organization in traffic flow, and this kind of intelligent agent is just the focus of ITS study. • The common research key point the autonomy and the co-operation between lA. • The common conditions - opening systems and exchanging of information • The common systems aim - ordered state of system It is stated that ITS emphasizes the coordination between intelligent vehicle, intelligent highway and driver in order to construct a more safety, high-speed, comfortable and efficient transportation system. In Self-organization Theory (especially in Synergetics), a main research content is how the individual can be well coordinated to form an ordered structure. Further more, ITS emphasizes the system opening and the information exchange. Similarly, opening is the essential condition to form a dissipative structure. There are a lot of control variables in ITS, and the exchanges of infolTI1ation are increasingly exponential So it is difficult to deal with them. But the Slaving Principle in Synergetics can be used for extracting the critical variables ( the order parameters), thus simplifying the control of ITS.
3. QUALITATIVE AND QUANTITATIVE ANALYSIS ON VRGS BASED ON SELFORGANIZATION THEORY
3.1
Qualitative analysis based on self-organization theory
VRGS ( Vehicle Route Guidance System) is an important subset of ITS. In the current study, besides real-time traffic infOlTI1ation, VRGS ( such as A TlS, LlSB, AUTOGUIDE etc. ) will be able to provide users the route guidance infonnation which show the optimum routes from ones' current position to their
From the view of Self-organization Theory, traffic flow is a stochastic process in which exist lots of uncertainties. So transportation system is located in high-entropy state. If transportation system could get more information from the outside environment, the certainty can increase. Therefore, as an important function of VRGS, it is useful to input real-time traffic information namely "negative entropy flow" in order to construct a more orderly and efficient transportation system. But as the other function of VRGS which provide the concrete route guidance commands is not necessary. For example, the designers of the VRGS hope that most ofthe vehicles being navigated should follow the route that VRGS has provided. If not, the route guidance of VRGS is meaningless. But in fact, an new "man-made" congestion may be resulted if most of the vehicles follow the same guidance commands. On the other hand, although the "classical" route optimizing in VRGS includes the shortest routing length plan and the shortest driving time plan, these plans can not satisfy all the requirements that each driver pursue individual's utility maximum. It is believed that traffic flow has the self-organizing ability. Therefore, it is enough for VRGS to provide some more detail and real-time traffic information, and it is not possible and necessary to make a decision instead of the individuals themselves. Furthermore, VRGS can not force the vehicle being navigated to follow the guidance advice entirely. The guidance can be treated as a kind of non -specific interference for the vehicle being navigated. So selforganization theory is suitable for the study of drivers' behavior in responding the VRGS. As an example to show how the self-organization theory can be used in VRGS (or ATlS), the drivers' route choice behavior in response to the real-time traffic information provided by VRGS (or A TIS) is mode led explicitly as follows.
3.2 Quantitative analysis on drivers' route choice behavior in VRGS based on self-organization theory Considering VRGS which only provide real-time traffic infonnation displayed by roadside electronic signs such as VMS (Variable Messages Signs, outlined in Figure 1), this paper focus on the evolution of drivers' route choice behavior, and assume that: • all the drivers before the separated point A have the same trip characteristics, including destinations, trip purpose, drivers' intra characteristics, etc. • all the drivers before point A tend to follow the
8347
Copyright 1999 IF AC
ISBN: 008 0432484
STUDY ON ITS BASED ON SELF-ORGANIZA nON THEORY. ..
14th World Congress ofTFAC
guidance advice. • the vehicle queues accumulated near point C can not go beyond the point A, which means the queues can not overflow back when congestion occurs.
Ai
= exp(U;) M
= exp(wjQ +
H
WilL C1.,",Stm + WLJ3ih D i2
m~]
ih)
(8)
h~l
where U i is the visible measurement of the drivers' utility function. Comprehensively considering the static and dynamic characteristics of route i, Stm are the static index of route i while Dih are the dynamic index including infonnation such as travel time, length of congestion, occupancy, which can he achieved by VMS in VRGS, Figure 1
Consequently, the equilibrium solutions of the model mentioned above can be given by
Drivers' route choice in responding to VRGS
Thus, the drivers' route choice behavior is detennined mainly by the static and dynamic characteristics of route 1 or route 2.
(9)
The corresponding phase portrait is sketched Figure 2-1.
More specifically, the choice set of the drivers in Figure I is Q = {route I, route 2}. Suppose the number of vehicles who choose route i is n i (i=I, 2),
III
and let n] + n2 = n. Then typical self-organization model---Fokker-Planck equation can be expressed as follows.
(5)
Figure 2-1 where
x,
=!!..i..-
namely the proportion of route
n
choice i, and
E
1
= - «
n
From Figure 2-1, the dynamics of the drivers' behavior in responding to VRGS can be described as follows. point (1,0) and (0, I) are non-equilibrium nodes, which shows that it is impossible in practice that all the drivers choose route 1 or route 2.
I.
The probability distribution p(x, ,t) is introduced for the choice-configuration to be in state i at time t. K(x;) is a drift coefficient which is defined as K(x,)
Q(x t )
=
Figure 2·2
kn A] +A2
2 [A]x, -(A2 +A])x; 1
(AI' A2 ) is an attracting fixed point (stable
A]
(6)
point), where Al = ----'-- is the attraction of route A] + A2 . ] whlle 'A 2 =
is a fluctuation coefficient which can be
A2
is the attraction of route 2.
A] +A2
defmed as
(A] ,A 2) is the equilibrium point of traffic flow assignment. Obviously, the drivers' route choice behavior in macroscopic evolves toward a stable equilibrium point under real-time traffic infonnation provided by VRGS. So the system is self-organizing during this process. What VRGS does is just to input real-time
A, can be defined as the attraction of the route i in self-organization theory, and can be given by
8348
Copyright 1999 IF AC
ISBN: 008 0432484
14th World Congress oflFAC
STUDY ON ITS BASED ON SELF-ORGANIZATION THEORY ...
Moreover, the macroscopic average value H can be defined as follows.
information by VMS. As a result, an equilibrium point can be achieved autonomously. In other words, traffic flow in VRGS can perform the assignment of traffic flow by means of self-organization.
n
H(x, (t) :::; E( -In Xi (t» = -
Further more, (I' 1,A 2 ) is time-varying in practice due to the complexity of route. So the attracting fixed point
XI (t)
real-time traffic volume of i section is F;(t). Then
x2
the degree of congestion x, (t) can be given.
x;(t) =
X'+j
~
x~ (t)
C; (t) , where
Then a function can be define as 1= f(x; (t») , which
(13)
112,
(I) =
Ct)
,u2 , ... , Uj ), .. . ,
U[,
(i) =
x'+j_1
(10)
I, F; (t) the congestion will happen possibly.
UJ '
= hi+j(U 1 ,U2 , ... , Ui ), . ••
= h~ (U)o u2'''', U j)
is the order parameter, and j« n.
II j
Putting all these into equation (12) yields
describes the traffic-flow ordered degree of section i . Here it is assumed that when I ~ 0 the transportation system is ordered; conversely, when I < 0 the transportation system is not ordered. So the function / should satisfY the following conditions.
"
H == -Lxi (I) In x, (I)
= -[hI (u[, U2 " " , 11)
In hI (* )+" +hi - 1 (uJ' u2'''', uJ ) In hj _ 1 (*) +u,lnu/+,,+u j lnuj +h;+j(uj,U2," ' ,uj
10 is the monotone decreasing function of •
f(x;(t))::?:O,
whenx ; (t) ~ 1
(12)
(t)
= hi (u) , u2' "', u J ),
(t) = h2 (u)
-'>'+1
~
Xi
Now suppose that a certain transportation system can represented by state vector be X(t) = {x) (t),x 2 (t), .. · ,xi (t),. .. ,xn(t)} . According to the Slaving Principle of Synergetic, it is possible to find out j parameters as the order parameter. Here j « n ( generally, the dimensions decreasing is the essential way to self-organizing). A typical order parameter equation then reads
In practice, a certain transportation subsystem R can be divided into n sections. Suppose that at t moment the capacity of i section is Cl (t) , and the
(t)
(t) In
4.2 The optimization o/the order parameter
4.1 Definition o/the traffic-jlow entropy
XI
Xj
This formula is similar to the fonnula of information entropy, especially when Xi (t) is treated as "probability". Here H is defined as traffic-flow entropy, which describes the traffic-flow ordered degree in transportation system R.
4. THE VRGS & TCS INTEGRATED CONTROL MODE OF ITS BASED ON SELFORGANIZATION THEORY
It is well known that when
L
x, (t);
)
(14)
+.. +hn(uj, u2 , " ' , u j ) In hn (*)]
otherwise .
=
G(ul, Uz ," ' , u j
)
f(Xi (t)) < 0 ;
• /(x; (t)) = 00 , when x; (t) = 0
;
It can be proved that the function which can satisfY the above-mentioned conditions is
Based on the idea of minimum entropy ( MinH), the order parameters can be optimized by solving the differential equations (k = 1,2, · ·· j)
(15)
I(xi(t» = - logxi (t) , or I(x, (t» = -In x , (t)
(11)
Suppose the solution of the equations above is
8349
Copyright 1999 IFAC
ISBN: 0 08 043248 4
STUDY ON ITS BASED ON SELF-ORGANIZA nON THEORY. ..
u' =(ut,u;, ... ,u;), then
u
.
can
14th World Congress ofTFAC
dX(t) = f(X(t), u)dt + dw(t)
satisfy the
optimal object MinH(x, (t), u·).
Generally, process.
4.3 Jriformatioll (negative entropy flow)
H(x, (t), le) = -le + H(x, (t») n
w(t) represents the Wiener stochastic
On the other hand, from the point of the ITS, it can be also regarded that the integration of organization components as TCS , while the integration of selforganization components regarded as VRGS. Then an integrated control mode of TCS and VRGS ( Figure 3), is proposed. Moreover, it satisfies the requirement of systems optimizing in ITS.
When the inputting infonnation from VRGS environment is considered, the traffic-flow entropy can be rewritten as:
=-1. - LxrCt)lnx,(t)
(17)
(16)
5. CONCLUSIONS where le represent the negative entropy flow ( infonnation ) from the outside environment.
As above-mentioned, ITS implies the idea of Selforganization Theory. Then Self-organization Theory can be applied to the study of ITS and provide efficient support for development of ITS, which is jus.t the original intention of this paper.
4.4 The VRGS & TeS integrated control mode of iTS based on Self-organization Theory ITS emphasizes the coordination between Intelligent Vehicle, Intelligent Highway and driver. So considerable research has been accomplished in the integration of ITS, such as the integration of VRGS and TCS (Traffic Control Systems) . In the current study, more and more attention are paid to system optimizing instead of route optimizing only. Correspondingly, the study based on Selforganization emphasizes the integration of organiz.ation and self-organiz.ation. From this point, the VRGS & TCS integrated control mode of ITS based on Self-organization Theory has been presented initially. Its essential frame is shown by Figure 3. where the traffic-flow self-organization process can be described by Ito stochastic equation.
REFERENCES French, R. L. (1995). From the 1986 Caltrans Conference to the 1995 World Congress: A Decade of Global Progress in Intelligent Transportation, Proceedings of 3rd World Congress on ITS, pp. 2280-2288 Haken, H.( 1987). Information and Self-organization, Springer, Berlin. Feng W.O., He G.G. and B. Liu (1998). Study on Traffic flow based on Self-organization Theory, Journal of Systems Engineering, P.R. China, Vol 13, No. 4, pp. 100- 104. Biham, O. and A. A. Middleton (1992). Selforganization and a Dynamical Transition in Traffic Flow Models, Physical Review, 46A. No. 10, pp. 46-52.
H(X (t))
the opti.mi~atiQIl of the oorder param eteT
r3Hldi'=O=;.u
con1rcdling 1t1fc.rmalion
X (I) VRGS (self-organization)
Figure 3
the VRGS & TCS integrated control mode of ITS based on Self-organization theory
8350
Copyright 1999 IF AC
ISBN: 008 0432484
14th World Congress ofTFAC
Q-8e-Ol-3
Copyright © 1999 IFAC 14th Triennial World Congress, I3eijing, P.R. China
STUDY ON ITS BASED ON SELF-ORGANIZATION THEORY·
Feng Weidong
He Guoguang
Liu Bao
Systems Engineering Institute ofTianjin University, Tianjin 300072, P.R. China Tel: (86-22) 27403399. Fax: (86-22)27483164 E-mail: [email protected]. en
Abstract: In this paper, Self-organization theory and self-organization in transportation systems including ITS is reviewed firstly . Then the common ground to ITS and Self-organization Theory study is discussed. As an example to show the applications of self-organization theory in ITS, VRGS is qualitatively and quantitatively analyzed. Finally, the VRGS & TCS integrated control mode of ITS based on Self-organization Theory has been presented initially. Copyright ©1999IFAC Keywords: ITS (Intelligent Transportation Systems), self-organizing, VRGS (Vehicle Route Guidance System), integrated control.
INTRODUCTION ITS (Intelligent Transportation Systems) attracts more and more interest in Transportation Engineering field recently. ITS here means applications of advanced technologies such as information technology, image processing, and artificial intelligence in transportation engineering. In order to improve the performance of transportation systems, ITS put stress on the intelligence of roads and vehicles, on the coordination and the integration between human, road and vehicle.
In this respect more and more information technology has been applied in ITS, while the autonomy of lA in ITS should not be overlooked. Therefore, it is necessary to study ITS based on self-organization theory, which is a new branch of Systems Science.
I. SELF-ORGANIZING SYSTEMS AND SELFORGANIZA nON IN TRANSPORTA nON SYSTEMS AND ITS
1.1
ITS activities expanded rapidly but often with uncertain directions during the 1986-1995 period (French, 1995). At a certain extent it is attributed to lacking of theoretical guidance. Essentially, ITS is a complex opening system which consists innumerable "Intelligent Agent (IA)". So it is possible to study ITS by applying Self-organization Theory. On the other hand, "Intelligent" is the essential difference between ITS and traditional transportation systems. lA has some characteristics, among them the autonomy and the co-operation are the most important ones. The co-operation of lA is depending on exchanging information between IAs .
Self-organizing systems and Self-organization Theory
H. Haken has defined self-organizing systems as the systems which can acquire macro-scopic spatial, temporal, or spatio-temporal structures by means of internal processes without specific interference from the outside. "Specific" here mean that the structure or functioning is not impressed on the systems, but that the systems are acted upon from the outside in an nonspecific fashion (Haken, 1987). As a developing branch of Systems Science, Selforganization Theory focus on the study of selforganizing systems, especially on the development
• The work presented here is sponsored by NSFC (the Natural Science Foundation of China). No: 79770061.
8345
Copyright 1999 IF AC
ISBN: 008 0432484
STUDY ON ITS BASED ON SELF-ORGANIZATION THEORY. ..
14th World Congress ofIFAC
processes from non-ordered to ordered states in such systems. Generally, Self-organization theory includes Dissipative Structure theory, . Synergetics, Catastrophe theory, Chaos theory and Fractal theory.
tramntlOn. At this moment, the original dissipative mode can not meet the stability condition equation (3). Then a stack will be formed in such as transportation subsystem, and this kind of stack will compel traffic flow to search for a new dissipative way in order to stabilize itself again. At this moment, the t1uctuation in systems can not be ignored, and it even can be amplified due to existence of the nonlinear mechanism, thus impelling the system into a new dissipative state. So the equation Av = AT will be satisfied again, thereby a non-equilibrium phase transition will be accomplished and a new stable dissipative structure can be achieved.
1.2 Self-organization in transportation systems and ITS 1.2.1. Transportation system (including ITS) is a typical opening system which exchanges material, energy and infonnation with environment continuously. At the same time, it is also an nonequilibrium or even far away from equilibrium system in which Jots of uncertainties and time-varying factors existed. So transportation systems satisfY the essential conditions of self-organizing according to the dissipative structure theory
Supposed that on the condition of non-equilibrium state, a certain stable system parameter such as traffic flow counts concerned in such a subsystem is Aco/J . The input parameter in per unit time is A,mp , meanwhile the dissipated parameter is
Ad!s .
Moreover,
the relative dissipative intensity AD and the relative inputting intensity AT are defined as follows.
(I)
On the basis of Self-organization theory, the necessary condition to ensure the traffic-flow subsystem stability is (3)
Generally, the relative dissipative intensity AD is a nonlinear function of the system's state variables . The qualitative description is given as follows.
The changing of AT is generally continuous and smooth during the process of unbalance phase transition for a practical transportation system. But on the other side, the dissipative ability is limited for a concrete dissipative mode. When A D "# AT' traffic flow tends toward the critical point of phase
1.2.2. H. Haken had indicated that traffic flow worked as an order parameter when vehicles was going on a congested road, and each driver placed himself in a huge self-organizing system so he can not has his own way (Haken, 1987).
I. 2. 3. It can be founded in practice that vehicles and pedestrians can choose their group behavior in a very "clever" way (Feng W.D, et aI., 1998). Due to the extensive t1uctuation factors existing in traffic flow, the transportation systems can "test" all kinds of collective behaviors. As a result, that collective behavior which can perform the transportation task more efficiently will keep existing, because only this kind of collective behavior ( in corresponding to the order parameter) can increase with time while other kinds of group patterns will decrease even if they appeared in a short tenn .
1.2.4. It has been shown by traffic simulation with Cellular Automation (CA) models that the selforganization exists in traffic t10w evolution processes. For example, a sharp jamming transition was found that separates between the low-density dynamically phase in which all cars move at maximal speed and the high-density jammed phase in which they are a\l stopped (Biham, et aI., 1992).
1.2.5. Chaos and fractal in transportation systems It is well-known that traffic flow is a typical non-
stationary process. So Fast Fourier Transform (FFT) is not suitable for analyzing traffic dynamics, while Wavelets analysis which is well localized in space and time simultaneously and is more suitable for nonstationary process. Therefore wavelets analysis can be used as a main mathematical tool for detecting chaos and fractality in transportation system. This work was first developed by Feng (1998), who demonstrated that chaos and fractality exist in transportation systems, and it is believed that the long-term dependence and memory in transportation systems are the source of fractality and chaos ( Feng W .D ., et aI., 1998).
8346
Copyright 1999 IF AC
ISBN: 0 08 043248 4
STUDY ON ITS BASED ON SELF-ORGANIZA nON THEORY. ..
14th World Congress ofTFAC
destination. 1.2 6. Self-organization in ITS As a typical transportation system, it is believed that ITS also have self-organizing characteristics just as mentioned above in general transportation systems.
2. THE COMMON GROUND TO ITS AND SELF-ORGANIZA nON THEORY STUDY There are a lot of common ground between ITS and Self-organization Theory study. • The common research object of study As mentioned above, the existence of lA (vehicledriver individual) result in the self-organization in traffic flow, and this kind of intelligent agent is just the focus of ITS study. • The common research key point the autonomy and the co-operation between lA. • The common conditions - opening systems and exchanging of information • The common systems aim - ordered state of system It is stated that ITS emphasizes the coordination between intelligent vehicle, intelligent highway and driver in order to construct a more safety, high-speed, comfortable and efficient transportation system. In Self-organization Theory (especially in Synergetics), a main research content is how the individual can be well coordinated to form an ordered structure. Further more, ITS emphasizes the system opening and the information exchange. Similarly, opening is the essential condition to form a dissipative structure. There are a lot of control variables in ITS, and the exchanges of infolTI1ation are increasingly exponential So it is difficult to deal with them. But the Slaving Principle in Synergetics can be used for extracting the critical variables ( the order parameters), thus simplifying the control of ITS.
3. QUALITATIVE AND QUANTITATIVE ANALYSIS ON VRGS BASED ON SELFORGANIZATION THEORY
3.1
Qualitative analysis based on self-organization theory
VRGS ( Vehicle Route Guidance System) is an important subset of ITS. In the current study, besides real-time traffic infOlTI1ation, VRGS ( such as A TlS, LlSB, AUTOGUIDE etc. ) will be able to provide users the route guidance infonnation which show the optimum routes from ones' current position to their
From the view of Self-organization Theory, traffic flow is a stochastic process in which exist lots of uncertainties. So transportation system is located in high-entropy state. If transportation system could get more information from the outside environment, the certainty can increase. Therefore, as an important function of VRGS, it is useful to input real-time traffic information namely "negative entropy flow" in order to construct a more orderly and efficient transportation system. But as the other function of VRGS which provide the concrete route guidance commands is not necessary. For example, the designers of the VRGS hope that most ofthe vehicles being navigated should follow the route that VRGS has provided. If not, the route guidance of VRGS is meaningless. But in fact, an new "man-made" congestion may be resulted if most of the vehicles follow the same guidance commands. On the other hand, although the "classical" route optimizing in VRGS includes the shortest routing length plan and the shortest driving time plan, these plans can not satisfy all the requirements that each driver pursue individual's utility maximum. It is believed that traffic flow has the self-organizing ability. Therefore, it is enough for VRGS to provide some more detail and real-time traffic information, and it is not possible and necessary to make a decision instead of the individuals themselves. Furthermore, VRGS can not force the vehicle being navigated to follow the guidance advice entirely. The guidance can be treated as a kind of non -specific interference for the vehicle being navigated. So selforganization theory is suitable for the study of drivers' behavior in responding the VRGS. As an example to show how the self-organization theory can be used in VRGS (or ATlS), the drivers' route choice behavior in response to the real-time traffic information provided by VRGS (or A TIS) is mode led explicitly as follows.
3.2 Quantitative analysis on drivers' route choice behavior in VRGS based on self-organization theory Considering VRGS which only provide real-time traffic infonnation displayed by roadside electronic signs such as VMS (Variable Messages Signs, outlined in Figure 1), this paper focus on the evolution of drivers' route choice behavior, and assume that: • all the drivers before the separated point A have the same trip characteristics, including destinations, trip purpose, drivers' intra characteristics, etc. • all the drivers before point A tend to follow the
8347
Copyright 1999 IF AC
ISBN: 008 0432484
STUDY ON ITS BASED ON SELF-ORGANIZA nON THEORY. ..
14th World Congress ofTFAC
guidance advice. • the vehicle queues accumulated near point C can not go beyond the point A, which means the queues can not overflow back when congestion occurs.
Ai
= exp(U;) M
= exp(wjQ +
H
WilL C1.,",Stm + WLJ3ih D i2
m~]
ih)
(8)
h~l
where U i is the visible measurement of the drivers' utility function. Comprehensively considering the static and dynamic characteristics of route i, Stm are the static index of route i while Dih are the dynamic index including infonnation such as travel time, length of congestion, occupancy, which can he achieved by VMS in VRGS, Figure 1
Consequently, the equilibrium solutions of the model mentioned above can be given by
Drivers' route choice in responding to VRGS
Thus, the drivers' route choice behavior is detennined mainly by the static and dynamic characteristics of route 1 or route 2.
(9)
The corresponding phase portrait is sketched Figure 2-1.
More specifically, the choice set of the drivers in Figure I is Q = {route I, route 2}. Suppose the number of vehicles who choose route i is n i (i=I, 2),
III
and let n] + n2 = n. Then typical self-organization model---Fokker-Planck equation can be expressed as follows.
(5)
Figure 2-1 where
x,
=!!..i..-
namely the proportion of route
n
choice i, and
E
1
= - «
n
From Figure 2-1, the dynamics of the drivers' behavior in responding to VRGS can be described as follows. point (1,0) and (0, I) are non-equilibrium nodes, which shows that it is impossible in practice that all the drivers choose route 1 or route 2.
I.
The probability distribution p(x, ,t) is introduced for the choice-configuration to be in state i at time t. K(x;) is a drift coefficient which is defined as K(x,)
Q(x t )
=
Figure 2·2
kn A] +A2
2 [A]x, -(A2 +A])x; 1
(AI' A2 ) is an attracting fixed point (stable
A]
(6)
point), where Al = ----'-- is the attraction of route A] + A2 . ] whlle 'A 2 =
is a fluctuation coefficient which can be
A2
is the attraction of route 2.
A] +A2
defmed as
(A] ,A 2) is the equilibrium point of traffic flow assignment. Obviously, the drivers' route choice behavior in macroscopic evolves toward a stable equilibrium point under real-time traffic infonnation provided by VRGS. So the system is self-organizing during this process. What VRGS does is just to input real-time
A, can be defined as the attraction of the route i in self-organization theory, and can be given by
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ISBN: 008 0432484
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STUDY ON ITS BASED ON SELF-ORGANIZATION THEORY ...
Moreover, the macroscopic average value H can be defined as follows.
information by VMS. As a result, an equilibrium point can be achieved autonomously. In other words, traffic flow in VRGS can perform the assignment of traffic flow by means of self-organization.
n
H(x, (t) :::; E( -In Xi (t» = -
Further more, (I' 1,A 2 ) is time-varying in practice due to the complexity of route. So the attracting fixed point
XI (t)
real-time traffic volume of i section is F;(t). Then
x2
the degree of congestion x, (t) can be given.
x;(t) =
X'+j
~
x~ (t)
C; (t) , where
Then a function can be define as 1= f(x; (t») , which
(13)
112,
(I) =
Ct)
,u2 , ... , Uj ), .. . ,
U[,
(i) =
x'+j_1
(10)
I, F; (t) the congestion will happen possibly.
UJ '
= hi+j(U 1 ,U2 , ... , Ui ), . ••
= h~ (U)o u2'''', U j)
is the order parameter, and j« n.
II j
Putting all these into equation (12) yields
describes the traffic-flow ordered degree of section i . Here it is assumed that when I ~ 0 the transportation system is ordered; conversely, when I < 0 the transportation system is not ordered. So the function / should satisfY the following conditions.
"
H == -Lxi (I) In x, (I)
= -[hI (u[, U2 " " , 11)
In hI (* )+" +hi - 1 (uJ' u2'''', uJ ) In hj _ 1 (*) +u,lnu/+,,+u j lnuj +h;+j(uj,U2," ' ,uj
10 is the monotone decreasing function of •
f(x;(t))::?:O,
whenx ; (t) ~ 1
(12)
(t)
= hi (u) , u2' "', u J ),
(t) = h2 (u)
-'>'+1
~
Xi
Now suppose that a certain transportation system can represented by state vector be X(t) = {x) (t),x 2 (t), .. · ,xi (t),. .. ,xn(t)} . According to the Slaving Principle of Synergetic, it is possible to find out j parameters as the order parameter. Here j « n ( generally, the dimensions decreasing is the essential way to self-organizing). A typical order parameter equation then reads
In practice, a certain transportation subsystem R can be divided into n sections. Suppose that at t moment the capacity of i section is Cl (t) , and the
(t)
(t) In
4.2 The optimization o/the order parameter
4.1 Definition o/the traffic-jlow entropy
XI
Xj
This formula is similar to the fonnula of information entropy, especially when Xi (t) is treated as "probability". Here H is defined as traffic-flow entropy, which describes the traffic-flow ordered degree in transportation system R.
4. THE VRGS & TCS INTEGRATED CONTROL MODE OF ITS BASED ON SELFORGANIZATION THEORY
It is well known that when
L
x, (t);
)
(14)
+.. +hn(uj, u2 , " ' , u j ) In hn (*)]
otherwise .
=
G(ul, Uz ," ' , u j
)
f(Xi (t)) < 0 ;
• /(x; (t)) = 00 , when x; (t) = 0
;
It can be proved that the function which can satisfY the above-mentioned conditions is
Based on the idea of minimum entropy ( MinH), the order parameters can be optimized by solving the differential equations (k = 1,2, · ·· j)
(15)
I(xi(t» = - logxi (t) , or I(x, (t» = -In x , (t)
(11)
Suppose the solution of the equations above is
8349
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ISBN: 0 08 043248 4
STUDY ON ITS BASED ON SELF-ORGANIZA nON THEORY. ..
u' =(ut,u;, ... ,u;), then
u
.
can
14th World Congress ofTFAC
dX(t) = f(X(t), u)dt + dw(t)
satisfy the
optimal object MinH(x, (t), u·).
Generally, process.
4.3 Jriformatioll (negative entropy flow)
H(x, (t), le) = -le + H(x, (t») n
w(t) represents the Wiener stochastic
On the other hand, from the point of the ITS, it can be also regarded that the integration of organization components as TCS , while the integration of selforganization components regarded as VRGS. Then an integrated control mode of TCS and VRGS ( Figure 3), is proposed. Moreover, it satisfies the requirement of systems optimizing in ITS.
When the inputting infonnation from VRGS environment is considered, the traffic-flow entropy can be rewritten as:
=-1. - LxrCt)lnx,(t)
(17)
(16)
5. CONCLUSIONS where le represent the negative entropy flow ( infonnation ) from the outside environment.
As above-mentioned, ITS implies the idea of Selforganization Theory. Then Self-organization Theory can be applied to the study of ITS and provide efficient support for development of ITS, which is jus.t the original intention of this paper.
4.4 The VRGS & TeS integrated control mode of iTS based on Self-organization Theory ITS emphasizes the coordination between Intelligent Vehicle, Intelligent Highway and driver. So considerable research has been accomplished in the integration of ITS, such as the integration of VRGS and TCS (Traffic Control Systems) . In the current study, more and more attention are paid to system optimizing instead of route optimizing only. Correspondingly, the study based on Selforganization emphasizes the integration of organiz.ation and self-organiz.ation. From this point, the VRGS & TCS integrated control mode of ITS based on Self-organization Theory has been presented initially. Its essential frame is shown by Figure 3. where the traffic-flow self-organization process can be described by Ito stochastic equation.
REFERENCES French, R. L. (1995). From the 1986 Caltrans Conference to the 1995 World Congress: A Decade of Global Progress in Intelligent Transportation, Proceedings of 3rd World Congress on ITS, pp. 2280-2288 Haken, H.( 1987). Information and Self-organization, Springer, Berlin. Feng W.O., He G.G. and B. Liu (1998). Study on Traffic flow based on Self-organization Theory, Journal of Systems Engineering, P.R. China, Vol 13, No. 4, pp. 100- 104. Biham, O. and A. A. Middleton (1992). Selforganization and a Dynamical Transition in Traffic Flow Models, Physical Review, 46A. No. 10, pp. 46-52.
H(X (t))
the opti.mi~atiQIl of the oorder param eteT
r3Hldi'=O=;.u
con1rcdling 1t1fc.rmalion
X (I) VRGS (self-organization)
Figure 3
the VRGS & TCS integrated control mode of ITS based on Self-organization theory
8350
Copyright 1999 IF AC
ISBN: 008 0432484