CN102800194A - Ramp-factor-considered stable FVDM (Full velocity difference model) traffic flow car-following model modeling method - Google Patents

Abstract

The invention discloses a ramp-factor-considered stable FVDM traffic flow car-following model modeling method for solving the technical problem that the current FVDM microcosmic traffic flow car-following model has poor suitability to a ramp environment. The technical scheme of the method is as follows: based on the dynamic analysis of a vehicle, a new traffic model is established through the contrasting with an FVDM microcosmic traffic flow car-following model. The relevance between the traffic jam problem and the system stability is obtained through the new traffic model, and a condition of microcosmically judging whether the traffic has an probability that a jam or another abnormal phenomenon occurs on a local stability view. According to the modeling method, the basis is provided for the control and the decision of the traffic, and the modeling method can be directly applied to the processing of the traffic jam problem in the ramp environment.

Description

The FVDM traffic flow of considering the slope factor is with speeding the model stability modeling method

Technical field

The present invention relates to a kind of FVDM traffic flow with speeding model modelling approach, particularly relate to a kind of FVDM traffic flow of considering the slope factor with speeding the model stability modeling method.

Background technology

Communications and transportation is the significant problem that involves the interests of the state and the people.The advanced degree of the up-to-dateness of traffic and transportation system and traffic administration is an important symbol of weighing a modernization of the country degree.Communications and transportation whether unimpeded, to the development of urban economy, the people's quality of life, the international fame of area and even whole country all has very significant effects.But in recent years; Along with economic development; The quantity of the various vehicles increases greatly; Facility, road, the traffic control system of a lot of countries have been difficult to satisfy this speed of development in the world; Particularly the reason of many aspects such as friendship rule consciousness of the confusion of inharmonious, the traffic dispersion system disappearance of not enough, the traffic control signal of big and medium-sized cities traffic infrastructure, vehicle scheduling and management, traffic participant has caused urban transportation than jam, has caused a series of socioeconomic problems such as traffic safety, environmental pollution thus again.

Traffic flow theory is studied as one of fundamental research content of traffic problems; Be an emerging cross discipline, the purpose of research is to set up the mathematical model that can describe the actual traffic general characteristic, through parameter recognition and Computer Numerical Simulation; Seek the basic law of traffic flow; Disclose the essential characteristic of various traffic flow phenomenons, thereby for instructing traffic programme and design, development of effective traffic control and management strategy and technology provide reliable theoretical foundation.

Because traffic problems are big system problems of a complicacy; It has related to synthetical collection and network transmission technology, traffic intelligent information fusion and treatment technology, the traffic flow inductive technology of Comprehensive Control, the transport information of urban traffic network; And many-sided content such as vehicle transport intelligent dispatching method, municipal intelligent traffic planing method, traffic safety detection, traffic environment overall evaluation system; And influence each other between above-mentioned each factor, mutual restriction; Be the synthesis that correlativity is extremely strong, be difficult to unified this challenge of the form of describing portrayal; Therefore, also of all kinds to the description of traffic system, the microcosmic and the macromodel analysis traffic characteristics that wherein adopt hydromechanical viewpoint to set up are in the majority; In the microcosmic traffic flow model; Traffic flow is regarded as the complicated self-powered kinetochore subsystem of being made up of a large amount of vehicles, from the dynamic behavior of single unit vehicle, and the interaction between the research vehicle; And then obtaining the character of whole Traffic flow systems, the average behavior of vehicle collective does not highlight.Microvisual model mainly comprises with speeding model and cellular Automation Model.

Model is to be easy to obtain separating of its analytical form than a distinguishing feature of other models with speeding.Model is the microcosmic traffic flow model of a quasi-representative with speeding.When supposing that fleet goes in the bicycle road, do not allow that under the situation of overtaking other vehicles, back car is followed the vehicle ' in the place ahead, therefore be called with speeding model.With the speed v of model with vehicle of speeding, the equation that they satisfy is studied in relative velocity Δ v and space headway Δ x portrayal traffic flow.Compare with macromodel, can draw stability condition and phase transformation scheduling theory characteristic more easily, the autonomous cruise system of development vehicle is had vital role with the model of speeding.The numerical evaluation aspect, simulation is relevant with vehicle number in speed model required time and research traffic system, with numerical method choose and the discrete steps Δ x of middle space x, time t relevant with Δ t.So, be not suitable for handling the traffic problems of the traffic flow that a large amount of vehicles form with the model of speeding.

Document " Full velocity difference model for a car-following theory [J] .Physical Review E.2001,64:017101) " discloses a kind of Full velocity difference model (hereinafter to be referred as FVDM) microscopic traffic flow with speeding model

$\frac{d^2{x}_n\left(t\right)}{{\mathrm{dt}}^2}=a[V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)-\frac{{\mathrm{dx}}_n\left(t\right)}{\mathrm{dt}}]+\mathrm{\λa}\frac{\mathrm{d\Δ}{x}_n\left(t\right)}{\mathrm{dt}}.$

This model be people such as Jiang Rui based on the optimal speed model, consider that new microscopic traffic flow that relative speed difference constitutes is with speeding model.In the formula, x _n(t) be n car position of moment t,

Be the speed of n car of moment t, Δ x _n(t) be space headway between the continuous two cars, V () is the optimal speed function, and a is driver's a sensitivity coefficient, and λ a is the response parameter of relative speed difference.Compare with the OV model, the FVDM model has overcome the too high hastening phenomenon that above model exists.The FVDM model not only can be portrayed the characteristic of Nonlinear Wave Propagation, and can describe the non-linear phenomenas such as variation of traffic flow under the microvariations, and more closing to reality traffic flow has developed the OV model to a certain extent.

Yet above-mentioned FVDM microscopic traffic flow is with model and the present many actual conditions of following the model of speeding not consider road of speeding, and a lot of regional roads of China are acclive.And the gradient has very big influence to traffic, and vehicle is prone to take place the vehicle congestion when going up a slope.Above-mentioned FVDM microscopic traffic flow model do not consider that vehicle ' is influenced by the gradient with speeding technical matters, particularly this gradient make model in practice, have certain limitation to the influence of traffic flow.

Summary of the invention

In order to overcome existing FVDM microscopic traffic flow with the deficiency of model to ramp environmental suitability difference of speeding, the present invention provides a kind of FVDM traffic flow of considering the slope factor with speeding the model stability modeling method.This method is on the basis that vehicle power is analyzed, and contrast FVDM microscopic traffic flow is set up new traffic model with speeding model.Obtain the relation of traffic jam issue and system stability through new traffic model, adopt the local stability angle to judge from microcosmic whether traffic can occur blocking up or other abnormal occurrencies.For traffic control, decision-making provide basic foundation, can be in the environment of ramp direct application processes traffic jam issue.

The technical solution adopted for the present invention to solve the technical problems is: a kind of FVDM traffic flow of considering the slope factor is characterized in may further comprise the steps with speeding the model stability modeling method:

Step 1, set up the microcosmic traffic flow model

$\left\{\begin{array}{c}\frac{d^2{x}_n\left(t\right)}{{\mathrm{dt}}^2}=a[V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)-\frac{{\mathrm{dx}}_n\left(t\right)}{\mathrm{dt}}]+\mathrm{\λa}\frac{d{\mathrm{\Δx}}_n\left(t\right)}{\mathrm{dt}},\\ V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)=\frac{v_{f,\max }\stackrel{\‾}{+}{v}_{g,\max }}{2}[\tanh ({\mathrm{\Δx}}_n\left(t\right)-h_{c,\mathrm{\θ}})+\tanh \left(h_{c,\mathrm{\θ}}\right)],\end{array}\right.$

In the formula, x _n(t) be n car position of moment t, Be the speed of n car of moment t, Δ x _n(t) be space headway between the continuous two cars, V () is the optimal speed function, and a is driver's a sensitivity coefficient, and λ a is the response parameter of relative speed difference.M is a vehicle mass, and g is an acceleration of gravity, and θ is the slope on slope, and μ is the windage friction factor, v _{F, max}And h _cBe respectively maximal rate and the safe distance of vehicle on the level land,

Be the maximal rate that vehicle is produced by gravity factor,

It is the vehicle safety spacing of considering gradient influence.Symbol "-" expression is gone up a slope, symbol "+" expression descending.

Step 2, following formula is rewritten as

$\frac{d^2\mathrm{\Δ}{x}_n\left(t\right)}{{\mathrm{dt}}^2}=a[V\left(\mathrm{\Δ}{x}_{n+1}\left(t\right)\right)-V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)-\frac{\mathrm{d\Δ}{x}_n\left(t\right)}{\mathrm{dt}}]+\mathrm{\λ}[\frac{\mathrm{d\Δ}{x}_{n+1}\left(t\right)}{\mathrm{dt}}-\frac{\mathrm{d\Δ}{x}_n\left(t\right)}{\mathrm{dt}}],$

In the formula, Δ x _n(t) be state variable.

Step 3, optimal speed function

$V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)=\frac{v_{f,\max }\stackrel{\‾}{+}{v}_{g,\max }}{2}[\tanh (\mathrm{\Δ}{x}_n\left(t\right)-h_{c,\mathrm{\θ}})+\tanh \left(h_{c,\mathrm{\θ}}\right)],$

In the formula, m is a vehicle mass, and g is an acceleration of gravity, and θ is the slope on slope, and μ is the windage friction factor, v _{F, max}And h _cBe respectively maximal rate and the safe distance of vehicle on the level land,

Be the maximal rate that vehicle is produced by gravity factor, It is the vehicle safety spacing of considering gradient influence.Symbol "-" expression is gone up a slope, symbol "+" expression descending.

According to the microcosmic traffic flow model of being set up; Draw (Δ x, two-dimensional phase planimetric map a) is according to the result of Linear Stability condition and kink-anti-ripple of twisting together; Obtain coexistence curve and indifferent equilibrium curve respectively, the two-dimensional phase plane is divided into stabilized zone, meta zone and unstable region; Obtain critical point (h _c, a _c); Under different parameters, state, initial conditions, do phase plane and critical point.X is tending towards h when the state variable Δ _cThe time, explain that traffic flow tends towards stability; When state variable Δ x at h _cNear when fluctuating back and forth, explain that traffic flow plays pendulum.

The invention has the beneficial effects as follows: because on the basis that vehicle power is analyzed, contrast FVDM microscopic traffic flow is set up new traffic model with speeding model.Obtain the relation of traffic jam issue and system stability through new traffic model, adopt the local stability angle to judge from microcosmic whether traffic can occur blocking up or other abnormal occurrencies.For traffic control, decision-making provide basic foundation, can be in the environment of ramp direct application processes traffic jam issue.

Below in conjunction with embodiment the present invention is elaborated.

Embodiment

The present invention considers that the FVDM traffic flow of slope factor is following with the model stability modeling method concrete steps of speeding:

1, newly-established microcosmic traffic flow model does

$\left\{\begin{array}{c}\frac{d^2{x}_n\left(t\right)}{{\mathrm{dt}}^2}=a[V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)-\frac{{\mathrm{dx}}_n\left(t\right)}{\mathrm{dt}}]+\mathrm{\λa}\frac{d{\mathrm{\Δx}}_n\left(t\right)}{\mathrm{dt}},\\ V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)=\frac{v_{f,\max }\stackrel{\‾}{+}{v}_{g,\max }}{2}[\tanh ({\mathrm{\Δx}}_n\left(t\right)-h_{c,\mathrm{\θ}})+\tanh \left(h_{c,\mathrm{\θ}}\right)],\end{array}\right.$

In the formula, x _n(t) be n car position of moment t,

Be the speed of n car of moment t, Δ x _n(t) be space headway between the continuous two cars, V () is the optimal speed function, and a is driver's a sensitivity coefficient, and λ a is the response parameter of relative speed difference.M is a vehicle mass, and g is an acceleration of gravity, and θ is the slope on slope, and μ is the windage friction factor, v _{F, max}And h _cBe respectively maximal rate and the safe distance of vehicle on the level land,

Be the maximal rate that vehicle is produced by gravity factor,

It is the vehicle safety spacing of considering gradient influence.Symbol "-" expression is gone up a slope, symbol "+" expression descending.

2, the traffic flow modes that variation caused for convenient research space headway changes, and following formula is rewritten as

$\frac{d^2\mathrm{\Δ}{x}_n\left(t\right)}{{\mathrm{dt}}^2}=a[V\left(\mathrm{\Δ}{x}_{n+1}\left(t\right)\right)-V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)-\frac{\mathrm{d\Δ}{x}_n\left(t\right)}{\mathrm{dt}}]+\mathrm{\λ}[\frac{\mathrm{d\Δ}{x}_{n+1}\left(t\right)}{\mathrm{dt}}-\frac{\mathrm{d\Δ}{x}_n\left(t\right)}{\mathrm{dt}}],$

Δ x in the formula _n(t) be state variable.

3, optimal speed function

$V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)=\frac{v_{f,\max }\stackrel{\‾}{+}{v}_{g,\max }}{2}[\tanh (\mathrm{\Δ}{x}_n\left(t\right)-h_{c,\mathrm{\θ}})+\tanh \left(h_{c,\mathrm{\θ}}\right)],$

In the formula, m is a vehicle mass, and g is an acceleration of gravity, and θ is the slope on slope, and μ is the windage friction factor, v _{F, max}And h _cBe respectively maximal rate and the safe distance of vehicle on the level land, Be the maximal rate that vehicle is produced by gravity factor, It is the vehicle safety spacing of considering gradient influence.Symbol "-" expression is gone up a slope, symbol "+" expression descending.

According to newly-established microcosmic traffic flow model; (Δ x draws; A) two-dimensional phase planimetric map, the result according to Linear Stability condition and kink-anti-ripple of twisting together obtains coexistence curve and indifferent equilibrium curve respectively; The two-dimensional phase plane is divided into three zones, is respectively stabilized zone, meta zone and unstable region; Obtain critical point (h _c, a _c); Under conditions such as different parameters, state, input, do phase plane and critical point.X is tending towards h when the state variable Δ _cThe time, explain that traffic flow tends towards stability; When state variable Δ x at h _cNear when fluctuating back and forth, explain that traffic flow plays pendulum.

Claims (1)

1. a FVDM traffic flow of considering the slope factor is characterized in that may further comprise the steps with speeding the model stability modeling method:

Step 1, set up the microcosmic traffic flow model

$\left\{\begin{array}{c}\frac{d^2{x}_n\left(t\right)}{{\mathrm{dt}}^2}=a[V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)-\frac{{\mathrm{dx}}_n\left(t\right)}{\mathrm{dt}}]+\mathrm{\λa}\frac{d{\mathrm{\Δx}}_n\left(t\right)}{\mathrm{dt}},\\ V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)=\frac{v_{f,\max }\stackrel{\‾}{+}{v}_{g,\max }}{2}[\tanh ({\mathrm{\Δx}}_n\left(t\right)-h_{c,\mathrm{\θ}})+\tanh \left(h_{c,\mathrm{\θ}}\right)],\end{array}\right.$

In the formula, x _n(t) be n car position of moment t,

Be the speed of n car of moment t, Δ x _n(t) be space headway between the continuous two cars, V () is the optimal speed function, and a is driver's a sensitivity coefficient, and λ a is the response parameter of relative speed difference; M is a vehicle mass, and g is an acceleration of gravity, and θ is the slope on slope, and μ is the windage friction factor, v _{F, max}And h _cBe respectively maximal rate and the safe distance of vehicle on the level land,

Be the maximal rate that vehicle is produced by gravity factor,

It is the vehicle safety spacing of considering gradient influence; Symbol "-" expression is gone up a slope, symbol "+" expression descending;

Step 2, following formula is rewritten as

$\frac{d^2\mathrm{\Δ}{x}_n\left(t\right)}{{\mathrm{dt}}^2}=a[V\left(\mathrm{\Δ}{x}_{n+1}\left(t\right)\right)-V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)-\frac{\mathrm{d\Δ}{x}_n\left(t\right)}{\mathrm{dt}}]+\mathrm{\λ}[\frac{\mathrm{d\Δ}{x}_{n+1}\left(t\right)}{\mathrm{dt}}-\frac{\mathrm{d\Δ}{x}_n\left(t\right)}{\mathrm{dt}}],$

In the formula, Δ x _n(t) be state variable;

Step 3, optimal speed function

$V\left(\mathrm{\Δ}{x}_n\left(t\right)\right)=\frac{v_{f,\max }\stackrel{\‾}{+}{v}_{g,\max }}{2}[\tanh (\mathrm{\Δ}{x}_n\left(t\right)-h_{c,\mathrm{\θ}})+\tanh \left(h_{c,\mathrm{\θ}}\right)],$

According to the microcosmic traffic flow model of being set up; Draw (Δ x, two-dimensional phase planimetric map a) is according to the result of Linear Stability condition and kink-anti-ripple of twisting together; Obtain coexistence curve and indifferent equilibrium curve respectively, the two-dimensional phase plane is divided into stabilized zone, meta zone and unstable region; Obtain critical point (h _c, a _c); Under different parameters, state, initial conditions, do phase plane and critical point; X is tending towards h when the state variable Δ _cThe time, explain that traffic flow tends towards stability; When state variable Δ x at h _cNear when fluctuating back and forth, explain that traffic flow plays pendulum.