CN102800195A - Macroscopic traffic flow model modeling method based on microcosmic OVDM (Optimal velocity difference model) car-following model - Google Patents

Abstract

The invention discloses a macroscopic traffic flow model modeling method based on a microcosmic OVDM car-following model for solving the technical problem that the current OVDM microcosmic traffic flow car-following model has poor suitability to macroscopic traffic flow. The technical scheme of the method is as follows: a new traffic model is established based on the analysis of the relevance between a space headway delta x and a vehicle average density rho. The relevance of system stability is obtained according to the new traffic model, and as the macroscopic traffic model is compared with a microcosmic traffic model, the relevance between the macroscopic traffic model and the microcosmic traffic model is obtained. And thus, the microcosmic traffic model and the macroscopic traffic model can be related to provide a basis 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 macroscopic traffic flow.

Description

Based on the macroscopic traffic flow modeling method of microcosmic OVDM with the model of speeding

Technical field

The present invention relates to a kind of macroscopic traffic flow modeling method, particularly relate to a kind of based on the macroscopic traffic flow modeling method of microcosmic OVDM with the model of speeding.

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.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.

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 macroscopic traffic flow, traffic flow is regarded as the compressible continuous fluid medium of being made up of a large amount of vehicles; 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.

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.Model is to be easy to obtain separating of its analytical form than a distinguishing feature of other models with speeding.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.

Macroscopic traffic flow is studied the equation that they satisfy with vehicle average density ρ, average velocity v and flow q portrayal traffic flow.Macroscopic traffic flow can be portrayed the collective behavior of traffic flow better than the microcosmic traffic flow model, thereby is that the traffic engineering problems such as effect that design effective traffic control strategy, simulated roadway geometry modification provide foundation.The numerical evaluation aspect, it is irrelevant that the vehicle number study in the traffic system by simulation macromodel required time and institute, with the road of studying, numerical method choose and the discrete steps Δ x of middle space x, time t relevant with Δ t.So macromodel is suitable for handling the traffic problems of the traffic flow that a large amount of vehicles form.

In view of the advantage separately of microcosmic, macroscopic traffic flow, we hope and can two class models be united in the reality, and performance advantage separately provides foundation for traffic control, decision-making better.

Document " Optimal velocity difference model for a car-following theory [J] .Physics Letters A.2011,375:3973-3977 " discloses a kind of Optimal velocity difference model (hereinafter to be referred as OVDM) microscopic traffic flow with speeding model

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

This model be people such as Peng Guanghan based on full speed degree difference model based, consider that new microscopic traffic flow that relative optimal 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, and γ a is the response parameter of optimal speed difference.Compare with the FVDM model with the OV model, the OVDM model has overcome too high acceleration and the unpractical deceleration phenomenon that above model exists.The OVDM 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 OV model and FVDM model to a certain extent.

Yet; Above-mentioned OVDM microscopic traffic flow is to judge from microcosmic whether traffic can occur blocking up or other abnormal occurrencies by the local stability angle with the model of speeding; Do not consider to judge from macroscopic view whether traffic can occur blocking up or other abnormal occurrencies, makes model in practice, have certain limitation by the global stability angle.

Summary of the invention

In order to overcome existing OVDM microscopic traffic flow with the deficiency of model to macroscopical traffic flow bad adaptability of speeding, it is a kind of based on the macroscopic traffic flow modeling method of microcosmic OVDM with the model of speeding that the present invention provides.This method is set up new traffic model on the basis of the relation of analyzing space headway Δ x and vehicle average density ρ.Obtain the relation of system stability through new traffic model, and with the contrast of microcosmic traffic flow model, obtain contact between the two.Thereby can microcosmic and macroscopic traffic flow be connected, for traffic control, decision-making provide basic foundation, can be in macroscopical traffic flow direct application processes traffic jam issue.

The technical solution adopted for the present invention to solve the technical problems is: a kind of based on the macroscopic traffic flow modeling method of microcosmic OVDM with the model of speeding, be characterized in may further comprise the steps:

The relation of step 1, space headway Δ x and vehicle average density ρ does

$\mathrm{\Δx}~\frac{1}{\mathrm{\ρ}}-\frac{{\mathrm{\ρ}}_x}{2{\mathrm{\ρ}}^3}-\frac{{\mathrm{\ρ}}_{\mathrm{xx}}}{6{\mathrm{\ρ}}^4}+\frac{{\mathrm{\ρ}}_x^2}{2{\mathrm{\ρ}}^5}+\·\·\·,$

In the formula, Δ x is the space headway between the continuous two cars, and ρ is the wagon flow average density.

Step 2, set up macroscopic traffic flow

$\left\{\begin{array}{c}{\mathrm{\ρ}}_t+{\left(\mathrm{\ρv}\right)}_x=0,\\ v_t+{\mathrm{vv}}_x=a[\stackrel{\‾}{V}-v]+a{\stackrel{\‾}{V}}^{\′}[(1+2\mathrm{\γ})\frac{{\mathrm{\ρ}}_x}{2\mathrm{\ρ}}+(1+6\mathrm{\γ})\frac{{\mathrm{\ρ}}_{\mathrm{xx}}}{6{\mathrm{\ρ}}^2}-(1+4\mathrm{\γ})\frac{{\mathrm{\ρ}}_x^2}{4{\mathrm{\ρ}}^3}]\\ +{\mathrm{\λav}}_x(\frac{1}{\mathrm{\ρ}}-\frac{{\mathrm{\ρ}}_x}{2{\mathrm{\ρ}}^3}-\frac{{\mathrm{\ρ}}_{\mathrm{xx}}}{6{\mathrm{\ρ}}^4}+\frac{{\mathrm{\ρ}}_x^2}{2{\mathrm{\ρ}}^5})+(1+8\mathrm{\γ})a\frac{{\stackrel{\‾}{V}}^{\′\′}{\mathrm{\ρ}}_x^2}{8{\mathrm{\ρ}}^2}+\mathrm{\λa}\frac{v_{\mathrm{xx}}}{2{\mathrm{\ρ}}^2}\end{array}\right.$

In the formula; ρ is an average density; V is an average velocity, and V () is the optimal speed function,

a be driver's sensitivity coefficient; λ a is the response parameter of relative speed difference, and γ a is the response parameter of optimal speed difference.

${\mathrm{\ρ}}_t=\frac{\∂\mathrm{\ρ}}{\∂t},{\mathrm{\ρ}}_x=\frac{\∂\mathrm{\ρ}}{\∂x},$

${\mathrm{\ρ}}_{\mathrm{xx}}=\frac{{\∂}^2\mathrm{\ρ}}{{\∂x}^2},v_t=\frac{\∂v}{\∂t},v_x=\frac{\∂v}{\∂x},v_{\mathrm{xx}}=\frac{{\∂}^{2}v}{{\∂x}^2},{\stackrel{\‾}{V}}^{\′}=\frac{d\stackrel{\‾}{V}}{\mathrm{d\ρ}},{\stackrel{\‾}{V}}^{\′\′}=\frac{d^2\stackrel{\‾}{V}}{d{\mathrm{\ρ}}^2}.$

According to the microcosmic traffic flow model of being set up; Obtain the result of Linear Stability condition, triangle shock wave and solitary wave; And do contrast with the accordingly result of model of speeding with former microcosmic OVDM, and obtain both conclusions of equal value, set up getting in touch between microcosmic and the macroscopic traffic flow.

The invention has the beneficial effects as follows: owing on the basis of the relation of analyzing space headway Δ x and vehicle average density ρ, set up new traffic model.Obtain the relation of system stability through new traffic model, and with the contrast of microcosmic traffic flow model, obtain contact between the two.Thereby can microcosmic and macroscopic traffic flow be connected, for traffic control, decision-making provide basic foundation, can be in macroscopical traffic flow direct application processes traffic jam issue.

Below in conjunction with embodiment the present invention is elaborated.

Embodiment

It is following with the macroscopic traffic flow modeling method concrete steps of the model of speeding to the present invention is based on microcosmic OVDM:

1, considers the relation of space headway Δ x and vehicle average density ρ

$\mathrm{\Δx}~\frac{1}{\mathrm{\ρ}}-\frac{{\mathrm{\ρ}}_x}{2{\mathrm{\ρ}}^3}-\frac{{\mathrm{\ρ}}_{\mathrm{xx}}}{6{\mathrm{\ρ}}^4}+\frac{{\mathrm{\ρ}}_x^2}{2{\mathrm{\ρ}}^5}+\·\·\·,$

In the formula, Δ x is the space headway between the continuous two cars, and ρ is the wagon flow average density.

2, set up new macroscopic traffic flow

$\left\{\begin{array}{c}{\mathrm{\ρ}}_t+{\left(\mathrm{\ρv}\right)}_x=0,\\ v_t+{\mathrm{vv}}_x=a[\stackrel{\‾}{V}-v]+a{\stackrel{\‾}{V}}^{\′}[(1+2\mathrm{\γ})\frac{{\mathrm{\ρ}}_x}{2\mathrm{\ρ}}+(1+6\mathrm{\γ})\frac{{\mathrm{\ρ}}_{\mathrm{xx}}}{6{\mathrm{\ρ}}^2}-(1+4\mathrm{\γ})\frac{{\mathrm{\ρ}}_x^2}{4{\mathrm{\ρ}}^3}]\\ +{\mathrm{\λav}}_x(\frac{1}{\mathrm{\ρ}}-\frac{{\mathrm{\ρ}}_x}{2{\mathrm{\ρ}}^3}-\frac{{\mathrm{\ρ}}_{\mathrm{xx}}}{6{\mathrm{\ρ}}^4}+\frac{{\mathrm{\ρ}}_x^2}{2{\mathrm{\ρ}}^5})+(1+8\mathrm{\γ})a\frac{{\stackrel{\‾}{V}}^{\′\′}{\mathrm{\ρ}}_x^2}{8{\mathrm{\ρ}}^2}+\mathrm{\λa}\frac{v_{\mathrm{xx}}}{2{\mathrm{\ρ}}^2}\end{array}\right.$

In the formula; ρ is an average density; V is an average velocity, and V () is the optimal speed function,

a be driver's sensitivity coefficient; λ a is the response parameter of relative speed difference, and γ a is the response parameter of optimal speed difference.

${\mathrm{\ρ}}_t=\frac{\∂\mathrm{\ρ}}{\∂t},{\mathrm{\ρ}}_x=\frac{\∂\mathrm{\ρ}}{\∂x},$

${\mathrm{\ρ}}_{\mathrm{xx}}=\frac{{\∂}^2\mathrm{\ρ}}{{\∂x}^2},v_t=\frac{\∂v}{\∂t},v_x=\frac{\∂v}{\∂x},v_{\mathrm{xx}}=\frac{{\∂}^{2}v}{{\∂x}^2},{\stackrel{\‾}{V}}^{\′}=\frac{d\stackrel{\‾}{V}}{\mathrm{d\ρ}},{\stackrel{\‾}{V}}^{\′\′}=\frac{d^2\stackrel{\‾}{V}}{d{\mathrm{\ρ}}^2}.$

According to newly-established microcosmic traffic flow model; Obtain the result of Linear Stability condition, triangle shock wave and solitary wave; And do contrast with the accordingly result of model of speeding with former microcosmic OVDM; Obtain both conclusions of equal value, set up getting in touch between microcosmic and the macroscopic traffic flow, for a little useful replenishing are done in the development of three-phase traffic flow theory.

Claims (1)

1. One kind based on microcosmic OVDM with speeding the macroscopic traffic flow modeling method of model, it is characterized in that may further comprise the steps:

   The relation of step 1, space headway Δ x and vehicle average density ρ does

   $\mathrm{\Δx}~\frac{1}{\mathrm{\ρ}}-\frac{{\mathrm{\ρ}}_x}{2{\mathrm{\ρ}}^3}-\frac{{\mathrm{\ρ}}_{\mathrm{xx}}}{6{\mathrm{\ρ}}^4}+\frac{{\mathrm{\ρ}}_x^2}{2{\mathrm{\ρ}}^5}+\·\·\·,$

   In the formula, Δ x is the space headway between the continuous two cars, and ρ is the wagon flow average density;

   Step 2, set up macroscopic traffic flow

   $\left\{\begin{array}{c}{\mathrm{\ρ}}_t+{\left(\mathrm{\ρv}\right)}_x=0,\\ v_t+{\mathrm{vv}}_x=a[\stackrel{\‾}{V}-v]+a{\stackrel{\‾}{V}}^{\′}[(1+2\mathrm{\γ})\frac{{\mathrm{\ρ}}_x}{2\mathrm{\ρ}}+(1+6\mathrm{\γ})\frac{{\mathrm{\ρ}}_{\mathrm{xx}}}{6{\mathrm{\ρ}}^2}-(1+4\mathrm{\γ})\frac{{\mathrm{\ρ}}_x^2}{4{\mathrm{\ρ}}^3}]\\ +{\mathrm{\λav}}_x(\frac{1}{\mathrm{\ρ}}-\frac{{\mathrm{\ρ}}_x}{2{\mathrm{\ρ}}^3}-\frac{{\mathrm{\ρ}}_{\mathrm{xx}}}{6{\mathrm{\ρ}}^4}+\frac{{\mathrm{\ρ}}_x^2}{2{\mathrm{\ρ}}^5})+(1+8\mathrm{\γ})a\frac{{\stackrel{\‾}{V}}^{\′\′}{\mathrm{\ρ}}_x^2}{8{\mathrm{\ρ}}^2}+\mathrm{\λa}\frac{v_{\mathrm{xx}}}{2{\mathrm{\ρ}}^2}\end{array}\right.$

   In the formula; ρ is an average density; V is an average velocity, and V () is the optimal speed function,

   

   a be driver's sensitivity coefficient; λ a is the response parameter of relative speed difference, and γ a is the response parameter of optimal speed difference;

   ${\mathrm{\ρ}}_t=\frac{\∂\mathrm{\ρ}}{\∂t},{\mathrm{\ρ}}_x=\frac{\∂\mathrm{\ρ}}{\∂x},$

   ${\mathrm{\ρ}}_{\mathrm{xx}}=\frac{{\∂}^2\mathrm{\ρ}}{{\∂x}^2},v_t=\frac{\∂v}{\∂t},v_x=\frac{\∂v}{\∂x},v_{\mathrm{xx}}=\frac{{\∂}^{2}v}{{\∂x}^2},{\stackrel{\‾}{V}}^{\′}=\frac{d\stackrel{\‾}{V}}{\mathrm{d\ρ}},{\stackrel{\‾}{V}}^{\′\′}=\frac{d^2\stackrel{\‾}{V}}{d{\mathrm{\ρ}}^2};$

   According to the microcosmic traffic flow model of being set up; Obtain the result of Linear Stability condition, triangle shock wave and solitary wave; And do contrast with the accordingly result of model of speeding with former microcosmic OVDM, and obtain both conclusions of equal value, set up getting in touch between microcosmic and the macroscopic traffic flow.