Modeling and Simulation of Bus Priority Oriented Urban Road Network Elastic Equilibrium

As the poor applicability of rail transit and elevated road limited by economy, population and many other factors, the waste of road resources caused by bus lane, maximizing application of available road resources and bus facilities, reducing the environmental pollution is the critical issue faced by current situation of urban transportation development in China. Guided by Bus Priority Oriented, utilized comprehensive techniques, such as ABC classification, bi-level programming model, sensitivity analysis, this paper constructed a theoretical frame of elastic equilibrium based on system optimization. Taking time and environment as optimized objectives, This paper established the Bi-Level multiobjective programming model based on travel time, and programmed with MATLAB for the calculation. Finally, the case study is illustrated. the software VISSIM was adopted to realize the simulation of the volume before and after the implementation of elastic plan in urban areas of PingDingshan. The simulation results showed the validity and feasibility of the modeling and simulation of Bus Priority Oriented urban road network elastic equilibrium.


Introduction
The elastic traffic is a great interesting topic of research at present and also the direction of future traffic development. Based on the Bus Priority Theory, the elastic traffic has all the strategic merits of the bus priority, is the allocation of resources, an effective way to solve the traffic jam problem in cities, will contribute to the solution of problems such as "energy emergency" and"environmental pollution" as well.
Many measures had been taken on trip during peak hours currently, they focused on questions for the moment. It is urgent to establish the theory system of elastic traffic to alleviate and improve urban transportation.

Bi-Level multi-objective programming model based on travel time
From the application of relative theories, the final optimization results of system can be reflected in the following three aspects.
(1)Minimum of total service time Targeting at optimization of density, maximization of volume and idealization of speed under elastic equilibrium, model will reaches the anticipated goal of the minimum of total service time.
(2) Maximum of environmental benefits (3) Minimum of users' travel time This study divides influence factors into three categories--A (subjective measures), B (objective macrography ) and C (others, such as economy ,planning). Class C was not discussed for its uncertainty.
The model can satisfy user and system optimal, formulated as follows [1] : (U2) minE=α∑F(x a (y),y a )+β∑P(x a (y),y a ) (2) s.t. y a ≧0 (3) Parameters above can be solved by the functions belows:  Upper question has two objective functions, U1 is the network design of elastic equilibrium, which analysis of elastic demand and measures were conducted. U2 is the design of environmental optimizing.
Lower question L1 is users' equilibrium assignment. The travelers' behavior conform to user optimum principle based on the travel time budget.
The steps of Algorithm based on sensitivity is as follows [2] : Step 1: Set initial solution y 0 , the capacity increment, and set iterations n=0.
Step 2: Solve lower question according to given y n , obtain the OD demand q n . OD demand.
Step 5: If max|y a n+1 -y a n |≤ ε stop, Where ε is the iterative precision. Or set n=n+1,back to step 2.
Algorithm ends.

Case Analysis
The elastic equilibrium of bi-level programming model was validated by public transportation system in PingDingshan (CBD).
Combined with the current situation of PingDingshan, trip mode was divided as follow: A (public transportation), B (compact car) and C (non-motor vehicle).
Bus OD demand in 2016 was Predicted by Growth Factor Method according to the survey data of current travel demand of public transportation. The result was shown as table 1. This study discussed scene one (only B takes effect) and scene two ( A and B).
In view of current traffic of PingDingshan (1, Zhongxing road north section. 2, Jianshe road west section. 3, Zhongxing road south section. 4, Jianshe road east section), the scheme was expressed as follows: (1) Increase the departure frequency Compared to 10 minutes before, add up the departure frequency to 3 minutes.
(2) Temporary bus lane JianShe Road and ZhongXing Road during the morning and evening peak hour.
(3) Linear control Optimize the signal control system of JianShe Road.
(4) LED screen Set up LED screen near the edge of the central area.
(5) prohibiting left turn, bus exclusive-use signal and bus left-turn waiting zone. Now considering the five kinds of measures above as the influencing factors of A only, apply the given conditions to the bi-level programming model, build raw data network as table 2 shown. Where t 1 signifies original runtime of the bus on sections for the whole network, t 2 signifies original runtime of the compact car on sections for the whole network, T signifies total runtime for whole system [3,4] . The optimized in the road network is shown as table 3. Where: t 1 ' signifies improved runtime of the bus on sections for the whole network, t 2 ' improved signifies original runtime of the compact car on sections for the whole network, T ' signifies improved the total runtime for whole system, T-T ' signifies decrement of total time.

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Advances in Intelligent Transportation System and Technology Be seen from the chart, travel time of compact car user decreases 0~3 minutes averagely, 0~2 minutes to bus.
Then consider the second objective environmental optimum in upper model. The result was shown as table 4 via calculation, where F signifies the decrement of energy, units by L/(km×h). P signifies the decrement of pollution, namely the emissions of every ton standard coal, units by t/(km×h) [5] . Through the contrast and statistical analysis, it can be found that after those Elastic Equilibrium measures, the traffic congestion gets relief, the amount of compact car effectively decreases, the amount of large-capacity traffic tools increases "Bus Priority" promotes, the energy consumption and emissions of pollutant caused by traffic congestion both decrease, system achieves equilibrium.

Results and Discussion
The summary of innovations in this dissertation is as following: 1) Application of ABC classification, trip mode and the influence factors were split by ABC classification, to divide of elastic equilibrium and discuss respectively according to the specific situations.
2) The optimization of time and environment. The minimum of system time and environmental optimization as the upper objective functions of bi-level programming model, and minimum of users time as the lower.
3)Application of "Elastic Equilibrium". "Elastic Equilibrium" is defined as the new balanced subjected to some elastic factors. The study builds elastic equilibrium system of the urban traffic oriented to "Bus Priority" and showed the expected effect through modeling and simulation. 4)VISSIM simulation. The software VISSIM was adopted to realize the simulation of the volume before and after the implementation of elastic plan in urban areas of PingDingshan.