The Analysis of Mutual Beneficial Cooperation among Urban Traffic Modes

FAN Wen-ting, WANG Ren-yin, HUANG Zhong-xiang School of Transportation Engineering, Changsha University of Science and Technology,

Changsha, 410076, P. R. China E-mail:fanwenting.yspa@163.com

Abstract

As the lack of researches of present literatures about the cooperative relation among traffic modes, in this paper, we establish a mutual beneficial cooperation model among urban traffic modes by using LV model which is proposed for simulating population dynamic relation in ecology. Then we preliminary discuss the inherent dynamics relation and evolution mechanism of the harmonious developments among different kinds of traffic modes from the perspective of theory by doing steady-state stability analysis and simulation to it. The simulation study indicates that the evolvement directions of the cooperation system have multi-possibility and the evolvement results of it have close relationship with the cooperation effect. The urban traffic system can be developed rapidly and coordinately by the magnification of the cooperative effects. 1. Introduction

The urban traffic structure is the proportion that people choose different traffic modes in the urban transportation systems in certain times. The urban transportation is an open and complicated system in the nature, and its complexity is not only on the structures of the system, but also on the nonlinear relations among the system’s elements. Thus we can not be limited in just one traffic mode when studying the urban transportation, and should study the inherent relations of different traffic modes wholly and completely. Then we should also choose the possible communication facilities and combine them properly to make all traffic modes complementary and coordinated. Consequently, we can make full use of the supply of the limited roads and different traffic mode’s advantages to undertake the heavy responsibility of urban transportation and to form an orderly transportation system.

But until recently, researches about the coordinated allocation of traffic structures are little; especially the documents are about the mutually beneficial cooperation among various traffic modes and their evolutions. Therefore, this paper will construct the model of the urban traffic modes according to the theories and methods of systematic dynamics of the related research results, then adding LV model which is used to simulate the population dynamic relation in ecology based on Logistic Equation. Some new thoughts and suggestions will be provided to the research of urban traffic modes by equilibrium analysis and computer simulation. 2. The cooperation model building of traffic modes

Suppose there are two traffic modes M1 and M2 in a city, both follow the Logistic law when they developed individually, then we define x1(t) and x2(t) are the respective developing scale of two traffic modes on t, (which using the crowd scale of traffic mode to determine); r1, r2 are the respective inherent growth rate which are got by its ability. And if r1>0, r2>0, that is we do not consider the stagnation or retrogression of the traffic mode’s development; N1, N2 are defined as the threshold when the two traffic modes develop respectively by themselves when resources are short. Assume M1, M2 provide transportation services in a way of mutual beneficial cooperation, and their existence have promoting effect to each other, and with the development of M1 and M2, the scale must be changed, then we define the influence leading the situation as “ability of coordination” . From all above, we can build the Logistic Model [4] [7]:

]1[)(2

21

1

1111 N

xNx

xrtx σ+−=•

(1)

]1[)(1

12

2

2222 N

xNx

xrtx σ+−=•

(2)

2008 International Conference on Intelligent Computation Technology and Automation

978-0-7695-3357-5/08 $25.00 © 2008 IEEE

DOI 10.1109/ICICTA.2008.441

516

Here the ratio 1σ is linear with the scale of traffic modes on t, which means the increasing of M2 also brings increases of passengers volume or services level

of M1, and in a word, )1(2

21 N

xσ+ is the reflection of

the increasing effect that the consumption of M2’s limited resources on M1’s passengers volume.

2σ , )1(1

12 N

xσ+ are the same, 0122

11 >> σNxNx

,

0211

22 >> σNxNx

.

We can find from equations (1) and (2), after introducing the cooperator, the development of the traffic mode scale is not only effected by the retardant effect of its development ,but also by the cooperator’s promoted effect, the positive effect to each other. It is beneficial to the quick develop of both of them, and the promoted effect’s scale depends on the cooperators’ scale, capacity of the environment, and also the ability of the coordination.

3. The steady-state stability of the model

The equation when the two traffic modes reach

balance is: ⎪⎩

⎪⎨

⎧

==

==

0),(

0),(

121

121

dtdx

xxQdtdx

xxP (3)

From the equation (3) we can get four steady-state solutions:

)0,0(1A , )0,( 12 NA , ),0( 23 NA ,

)11

,1

1(

21

21

21

114 σσ

σσσ

σ−+

−+

NNA

After analysis, )0,0(1A isn’t a stable point,

)0,( 12 NA and ),0( 23 NA are saddle points.

)11

,1

1(

21

21

21

114 σσ

σσσ

σ−+

−+

NNA is a saddle point

when 121 >σσ ;And when 121 <σσ , it has two conditions of stable and unstable . 4. The analysis of the model

Different modes have advantages cross in the economy and technology characteristic, which show every mode has its superiority field. However, traffic

demand (on the quantity and the quality) dose not strictly correspond with its advantage field. Moreover, by the changing of the traffic demand, the level of correspondence is becoming less and less. It certainly will arise “combined supply” alongside the competence, to supply each other, and get a better way to satisfy the traffic demand by combining two or more modes. So it provides an extensive choice for traffic demand to improve the satisfaction rate generally, which also makes up the fault of different modes on the economy and technology, and making the characteristic of transportation supply continually. The rail transit cannot cover the whole area, buses cannot reach every destination and customer, but some other transportation facilities do it, such as cars and bicycles. In addition, the transportation facilities, modes and processes of transportation’s changing demand the modes to cooperation based on division of labor, coordination and closely connect.

We can summarize from the analysis of steady-state stability, when the cooperation of M1 and M2 are mild, or one is mild and the other one is active, namely the coordination ability coefficients’ product of M1 and M2 is less than 1, the two modes can reach a steady balanced condition, and within a threshold value at last. This is also a prerequisite of the urban transport integration.

At the first, when two modes differ greatly on scale, one is main mode, and the other is the minor mode, 1σ is very small but 2σ is large. Generally, transfer passengers that the main mode supplies to the minor one occupy a great part and even all of them, but the minor one’s supply only occupies a little part. So the contribution rate of the main mode to the minor is larger than that of the minor one to the main one. Now,

121 <σσ shows the condition when the two mutual beneficial cooperated modes reach balance

is 1211

22 >> σNxNx

, 11 <σ . In fact this demands the

main mode’s scale to be large and the level of work division to be high.

When the two modes are similar on grade of scale, characteristics of economy and technology, and the ability of service , the contribution rates to each other are about the same, and the condition of mutual beneficial cooperated balance can only be 12 <σ , 11 <σ .The economical explanations are: the two modes share their projects of infrastructure, technology and information, reasonably divide work to expand the ability of transport and the scale of market, reduce cost, and raise the efficiency and benefit of transport, then supply better service to the customers.

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At the balanced point of system evolution 4A , the

two modes’ share ratio in the market is 22

11

)1()1(NN

σσ

++

,

the structure of the market is determined by the coordinate ability of the modes and the threshold when each of the mode develop separately , and has nothing to do with the mode’s growth rate, this has been proved by computer simulation too. When N1=N2 or N1≈N2, (when the scale level and transportation recourses of the two modes are alike), the structure of the market is determined by the coordinate ability of the modes. Larger the ability of coordinate is, more share will occur when the related markets are balanced. So, if a mode needs to occupy more interest in the competition, it must make a breakthrough within its limitations, to cooperate but not to compete only, use the way of cooperate to improve the ability of compete and innovate, only cooperation is “the best both beneficial strategy “.

The cooperated model which mentioned above can be expanded into a more general condition that contains n different modes. The way to deal with this kind of condition is as follow:

]1[,1∑

≠=

•+−=

n

ijj j

jij

i

iiii N

xNx

xrx σ (4)

In it, ijσ indicates the jth mode’s relative coordinate ability coefficient to the ith. 5. Case analysis

For researching the mechanism which is described in the cooperation system of urban traffic modes, we combine the MATLAB program language to simulate the track of evolution when parameters have changed. The initial values of the two modes are selected from Beijing 2006 annual report of transportation development, bus transit x10=44.98, rail transit x20=6.80 (the unit is: hundred million person).

1. Two cooperated modes are very active, namely 11 >σ , 12 >σ , by choosing different parameters and simulating it by computer , we can get the results in Fig.1.

Fig.1 The evolutionary of stability about x1(t) and x2(t)

The operation results indicate: when M1 and M2 cooperate actively, both of them can reach their threshold finally. Suppose r1=0.1, r2=0.12, and other situations maintain, the simulation results don’t change, which indicates the model’s results have nothing to do with the mode’s increase ratio, and only do something with the condition of cooperate and the largest scale they can reach.

2. Two cooperated modes are mildly, namely 11 <σ , 12 <σ , by choosing different parameters and simulating it by computer, we can get the results in Fig.2:

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Fig.2 The evolutionary of stability about x1(t) and x2(t)

The operation results indicate: when M1 and M2 both cooperate in mild ways, they can also reach the threshold finally, and steady at a limit value.

3. One mode is active and the other one is mild, namely 11 >σ , 12 <σ or 11 <σ , 12 >σ , by choosing different parameters and simulating it by computer, we can get the results in Fig.3, which is similar with condition2.

Fig.3 The evolutionary of stability about x1(t) and x2(t)

6. Conclusion

In this paper, we structured a mutual beneficial cooperation model between two urban traffic modes by using the LV model which is proposed for simulating population dynamic relation in ecology. Then we analyze the model’s structures and stability, show the evolution of two traffic modes, and have expanded it with n kinds of modes. The analysis of the evolution shows: in the process of evolution of urban traffic system, due to the relations of cooperation of different traffic modes, the development of one traffic mode will have effects on another which associated with it more or less, and will put the light fluctuation of some changeable factors to the whole urban traffic system, which will lead the high fluctuation and change the whole suddenly and formed a more harmonious and new structure. So we should try our best to enlarge the function of cooperation in system and lead it develop to the right direction, then we can improve the services standard of traffic system completely and maximize the interests of traffic system and make city developed rapidly. Of course, we still need the government’s policies to coordinate and realize the mechanism of the cooperation in the system for different traffic modes have different benefits in the real cooperation under the effect of operating speed, comfortable level, transport capacity, the trip feature and social economics. Acknowledge

This research is sponsored by the National Natural Science Foundation of China under grant number 50578019 . References [1] Lin Zhen, and Yang Hao, “Optimization Model Analysis for Urban Transport Structure”, China Civil Engineering Journal, China Civil Engineering Society, Beijing, 2005.38(5), pp.100-104. [2] Qiu Yuzhuo, and Chen Senfa, “A Nonlinear Dynamic Model for Mutualism of Transportation Modes”, System Engineering, Hunan Institute of Systems Engineering, Hunan, 2006.7 (24), pp.8-12. [3] Li Zhenhua, and Zhao Liming, “Dynamic Modeling of the Self-Organizing Evolvement Process of the “Coopetition” System”, Journal of Tianjin University(Science and Technology), Tianjin University, Tianjin, 2006.6(39), pp.293-297. [4] He Jishan, and Dai Weiming, “The Equilibrium of Industrial Clusters: From an Ecological Perspective”, Journal

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