CN106952475A - The personalized inductivity distribution method of dual path road network under user equilibrium principle - Google Patents

Abstract

The present invention relates to a kind of personalized inductivity distribution method of the dual path road network under user equilibrium principle, comprise the following steps：1) for the dual path road network to be regulated and controled, road network basic parameter is counted；2) GreenShields models and traffic flow theory are based on, the optimal separation rate under ideal conditions is asked for according to road network basic parameter, it is optimal to reach the overall traffic flow of road network；3) under the constraints of road network total optimization, the ratio compared with shortest path is travelled according to individual vehicle history, the basic constraints of personalized induction allocation strategy is set up；4) concept of vehicle priority is set up, according to this concept, using equal difference distribution principle, the personalized inductivity distribution numerical value under vehicle priority known case is calculated；5) according to step 4) determine distribution principle and vehicle history most ratio of greater inequality probability distribution, distribute induction information, meet the principle of user equilibrium to greatest extent under probability meaning, it is ensured that vehicle receive induction fairness.

Description

The personalized inductivity distribution method of dual path road network under user equilibrium principle

Technical field

The present invention relates to a kind of personalized inductivity distribution method of the dual path road network under user equilibrium principle, belong to traffic Induce optimisation technique field.

Background technology

Traditional induction information issue is published to real time information according to section real-time status on certain reception medium, two The medium that receives of class mainly is for VMS (variable information traffic sign) induced screens of colony's vehicle guidance and for personalization The car-mounted terminal of vehicle guidance.In terms of road network traffic flow macroscopic perspective, the control core variable of two class induction strategies is vehicle Separation rate in fork in the road, influence of the induction information to vehicle routing choice behavior is key issue therein.

Two class induction strategies have respective advantage and deficiency：VMS inductions can effectively regulate and control the magnitude of traffic flow of road network Distribution, it is ensured that road network total optimization, but all vehicles receive identical induction information, lacked and vehicle individual is taken into account；It is individual Propertyization induction can issue targetedly induction scheme according to the different characteristic information of individual vehicle, effectively meet the individual character of user Change demand, but often fail to consider that a large amount of vehicles receive the feedback influence to traffic flow after personalized induction information, road network is global It is optimal to be difficult to be guaranteed.

The content of the invention

Regarding to the issue above, it is an object of the invention to provide one kind based on road network is optimal, individual vehicle individual character is taken into account The personalized inductivity distribution method of dual path road network under user equilibrium principle under the user equilibrium principle of demand.

To achieve the above object, the present invention takes following technical scheme：A kind of dual path road network under user equilibrium principle There is an a sole inlet O and sole outlet D in personalized inductivity distribution method, described dual path road network, from entrance O There are two optional paths A and B to outlet D, vehicle can receive induction information when reaching entrance A, it is characterised in that：Described lures Conductance distribution method comprises the following steps：1) for the dual path road network to be regulated and controled, road network basic parameter is counted；2) it is based on GreenShields models and traffic flow theory, the optimal separation rate under ideal conditions is asked for according to road network basic parameter, with Reach that the overall traffic flow of road network is optimal；3) under the constraints of road network total optimization, travel more excellent according to individual vehicle history The ratio in path, sets up the basic constraints of personalized induction allocation strategy；4) concept of vehicle priority is set up, is utilized Poor distribution principle, calculates the personalized inductivity distribution numerical value under vehicle priority known case；5) according to step 4) determine The probability distribution of distribution principle and vehicle history most ratio of greater inequality, distributes induction information, is met to greatest extent under probability meaning The principle of user equilibrium, it is ensured that vehicle receives the fairness of induction.

The step 1) in, road network basic parameter include induction information update cycle T, magnitude of traffic flow N, current separation rate p, Path A real-time vehicle numbers N₁, path B actual vehicle numbers N₂, path A length L_A, path B length L_B, path A vehicles averagely travel Time T_Areal, path B vehicles average hourage T_Breal；Wherein, current separation rate p refers to vehicle access path A quantity percentage Than.

The step 2) in, under " optimal " is the overall average hourage minimum criterion with vehicle, ideal conditions Optimal separation rate to ask for process as follows：

GreenShields models are pointed out, in certain scope, have linear relationship between speed v and vehicle density ρ, Its expression formula is as follows：

In formula, v_freeRepresent section Maximum speed limit, ρ_jamVehicle most high-density is represented, wherein：

N_maxBetween representing that the maximum appearance of vehicle amount of road, L represent that road section length, l represent that average length of car, d represent that vehicle is minimum Away from for different paths, average length of car and vehicle minimum spacing are identicals, i.e. vehicle most high-density ρ_jamIt is solid Definite value；

Further according to the definition of vehicle density

In formula, N_tripPresent road vehicle number is represented,

It is final to draw vehicle average hourage T_tripWith road section length L and present road vehicle number N_tripRelation：

The new vehicle that reaches receives induction information and selected behind path, and two section vehicle numbers are expected

E(N_A)=N₁+Np-N_1out

E(N_B)=N₂+N(1-p)-N_2out

In formula, N represents the magnitude of traffic flow, N_A、N_BRepresent that the new vehicle that reaches receives induction information and access path A, path respectively B vehicle number, E (N_A)、E(N_B) represent that the new vehicle that reaches receives induction information and access path A, path B vehicle number respectively Expect, p represents separation rate, N₁Represent path A current real-time vehicle number, N₂Path B current real-time vehicle number is represented, wherein N_1out,N_2outRepresent the vehicle flowrate left in an information updating cycle from two paths；

Expect expression formula according to two section vehicle numbers, obtain vehicle overall travel time on the paths of A, B two and expect expression Formula

Wherein only p is variable；

Minimum is asked for the formula, optimal separation rate p is drawn_bestExpression formula

Wherein

In formula, N_freeA、N_freeBFor intermediate variable, represent to assume that vehicle fully enters B path, now path A, path B points The maximum vehicle number that can not accommodate, v_free1v_free2Path A and path B Maximum speed limit is represented respectively.

The step 3) in, the process for setting up the basic constraints of personalized induction allocation strategy is as follows：

A basic constraints of customized information issue is obtained according to the expression formula of optimal separation rate：

Wherein p_iRepresent that vehicle i receives the probability that path A is selected after personalized induction information, also referred to as vehicle i's Inductivity；

Assuming that current time optimal path is A paths, above-mentioned condition can be formulated as：

In formula, p_iRepresent vehicle i inductivity, p_jVehicle j inductivity is represented, rate (i) represents vehicle i history most Ratio of greater inequality, rate (j) represents vehicle j history most ratio of greater inequality；

Above-mentioned two formula constitutes the basic constraints of personalized inductivity distribution.

The step 4) implementation process it is as follows：

First, the concept of priority is defined, if the rate (i) of i-th car is ordered as kth greatly in all vehicles, The priority of the vehicle is called k, and the history most ratio of greater inequality of this car is accordingly denoted as rate (i_(k)), in addition, priority is k vehicle Inductivity apportioning cost is designated as p_k, it is clear that vehicle priority is bigger, inductivity apportioning cost p_kIt is bigger；

According to the concept of above-mentioned vehicle priority, according to priority k sizes, successively decreased determination inductivity, use with arithmetic progression Formula is expressed as：

p_k+1-p_k=p_k+2-p_k+1=Δ

The expression formula of the comprehensive formula and optimal separation rate, is obtained：

Minimum inductivity p only need to be provided₁, then tolerance Δ can be obtained, and then determine the inductivity of each priority.

The step 5) in, the determination process of the allocative decision of induction information is as follows：

Note n=N-i is does not reach vehicle number, and in this n+1 car, the probability that vehicle i priority is k is：

In formula, P (rate (i)) represents that any vehicle priority that do not reach is higher than the probability for having reached vehicle i, and this is one Only with rate (i) about and with the unrelated values of j；

According to total-expectation formula, can obtain vehicle i should distribute the desired value of inductivity, under probability meaning, and this is most Excellent allocative decision；It is formulated as：

Wherein E (p_k| rate (i)=rate (i_(k))) to represent vehicle i priority be inductivity apportioning cost p under conditions of k_k's Conditional expectation；

In step 4) described in arithmetic progression allocation rule under, inductivity apportioning cost p_kIt is only relevant with vehicle priority k, i.e., Once it is determined that vehicle priority, p_kJust it is to determine and known, therefore has：

E(p_k| rate (i)=rate (i_(k)))=p_k

In the continuous arrival process of vehicle, respective path is selected respectively with vehicle has been reached, optimal separation rate is in In being continually changing, it is assumed that when i-th car reaches crossing, preceding i-1 car selects the quantity of A paths and B path according to allocation rule Respectively n₁And n₂, then obviously it is not changed into by the road network optimal constraint conditionses of crossing vehicle now：

According to arithmetic progression allocation rule, can obtain the vehicle guidance rate apportioning cost that priority is k should meet condition, use Formula is expressed as：

Wherein Δ is constant, and for the inductivity tolerance of setting, this tolerance should ensure that the minimum inductivity and highest of vehicle Inductivity in the reasonable scope, takes

Further solve, can show that the vehicle guidance rate apportioning cost that priority is k is：

According to above-mentioned solution, i-th car inductivity apportioning cost optimal under probability meaning is obtained：

Wherein：

The step 5) solution to P (rate (i)), when there is enough prioris, just according to statistical information pair The optimal ratio distribution of history of vehicle is fitted, when priori is not enough, then it is assumed that the history of vehicle most ratio of greater inequality obeys normal state Distribution, now：

Wherein μ, δ are the average and standard deviation of normal distribution, and x is the symbol of stochastic variable.

The present invention is due to taking above technical scheme, and it has advantages below：1st, the present invention is solved by traffic flow theory Optimized overall Vehicles separation rate, the serious road sections part vehicle of congestion is adjusted to the lighter section of congestion level, it is ensured that road network is imitated The maximization of rate simultaneously avoids congestion status from shifting repeatedly as far as possible.2nd, the present invention is on the premise of road network total optimization is ensured, simultaneously Take into account the individual demand of individual vehicle, it is ensured that the harmony of individual consumer's trip.3rd, the present invention combines colony's induction and individual The advantage of propertyization induction, it is to avoid the deficiency of colony's induction and personalized induction, both ensure that the personalization of induction, it is contemplated that To the feedback effect of road network after vehicle guidance so that the advantage of two kinds of induction strategies is given full play to.

Brief description of the drawings

Fig. 1 is the topological structure schematic diagram of dual path road network.

Embodiment

The present invention is described in detail with reference to the accompanying drawings and examples.

The present invention proposes the personalized inductivity distribution method of dual path road network under a kind of user equilibrium principle, dual path The topological structure of road network has two as shown in figure 1, road network has a sole inlet O and sole outlet D from entrance O to outlet D Bar optional path A and B, vehicle can receive induction information when reaching entrance O points, and select path according to induction information.The present invention Method comprises the following steps：

1) for the dual path road network to be regulated and controled, road network basic parameter is counted, including induction information update cycle T, Magnitude of traffic flow N, current separation rate (vehicle access path A number percent) p, path A real-time vehicle numbers N₁, path B it is actual Vehicle number N₂, path A length L_A, path B length L_B, path A vehicles average hourage T_Areal, path B vehicles are when averagely travelling Between T_Breal。

In above-mentioned parameter, path A length L_A, path B length L_BClearly known constant, path A real-time vehicle numbers N₁And road Footpath B actual vehicle numbers N₂Can by way of in road network setup of entrances and exits detector indirect gain, known quantity can also be considered as.

2) GreenShields models and traffic flow theory are based on, is asked for according to road network basic parameter under ideal conditions Optimal separation rate, it is optimal to reach the overall traffic flow of road network.Wherein, " optimal ", is minimum with the overall average hourage of vehicle For criterion.

GreenShields models are pointed out, in certain scope, have linear relationship between speed v and vehicle density ρ, Its expression formula is as follows：

In formula, v_freeRepresent section Maximum speed limit, ρ_jamVehicle most high-density is represented, be can be generally considered as

N_maxBetween representing that the maximum appearance of vehicle amount of road, L represent that road section length, l represent that average length of car, d represent that vehicle is minimum Away from for different paths, average length of car and vehicle minimum spacing may be considered identical, i.e. vehicle most high-density ρ_jamFor fixed value.

Further according to the definition of vehicle density

In formula, N_tripPresent road vehicle number is represented, vehicle average hourage T can be finally drawn_tripWith road section length L and present road vehicle number N_tripRelation：

The new vehicle that reaches receives induction information and selected behind path, and two section vehicle numbers are expected

E(N_A)=N₁+Np-N_1out (5)

E(N_B)=N₂+N(1-p)-N_2out (6)

In formula, N represents the magnitude of traffic flow, N_A、N_BRepresent that the new vehicle that reaches receives induction information and access path A, path respectively B vehicle number, E (N_A)、E(N_B) represent that the new vehicle that reaches receives induction information and access path A, path B vehicle number respectively Expect, p represents separation rate, N₁Represent path A current real-time vehicle number, N₂Path B current real-time vehicle number is represented, wherein N_1out,N_2outThe vehicle flowrate left in an information updating cycle from two paths is represented, its expression formula can be according to traffic flow Theory is solved and drawn.

According to (5), (6) formula, vehicle overall travel time on the paths of A, B two can be obtained and expect expression formula

Wherein only p is variable, and its residual value is considered known constant.

Minimum is asked for (7) formula, optimal separation rate p can be drawn_bestExpression formula

Wherein

In formula, N_freeA、N_freeBFor intermediate variable, represent to assume that vehicle fully enters B path, now path A, path B points The maximum vehicle number that can not accommodate, v_free1v_free2Path A and path B Maximum speed limit is represented respectively.

3) under the constraints of road network total optimization, the ratio compared with shortest path is travelled according to individual vehicle history, set up The basic constraints of personalization induction allocation strategy.

Traffic flow obtained in previous step, in the optimal separation rate of fork in the road, can be crossing VMS induction informations Issue provides a basic control parameter.In fact, for the road network of same structure, the issue of VMS information and customized information The core control parameter of issue is the Vehicles separation rate at crossing, regardless of whether being which kind of control strategy, its purpose is by adjusting Control the separation rate of vehicle so that the distribution of road network vehicle reaches optimal result in some sense.Wherein, the standard of optimal solution is Vehicle average hourage reaches minimum.

When road network input flow rate is constant and known, optimal total separation rate and the VMS information of customized information issue are issued Optimal separation rate it is identical, its expression formula is (8) formula.

Different from VMS colonies inductions, in personalization induction, each vehicle can be distributed according to the different situations of vehicle in itself Different inductivities, control different vehicle selects path with different probability.The optimal separation rate tried to achieve according to (8) formula, can be obtained The basic constraints issued to customized information：

Wherein p_iRepresent that vehicle i receives the probability that path A is selected after personalized induction information, also referred to as vehicle i's Inductivity.

In recent years, with the development of intelligent bus or train route cooperative system, by the communication of vehicle and roadside device, dress can be obtained It is loaded with the individual vehicle information of communication equipment, including vehicle running history record.Therefore, for the vehicle at each arrival crossing I, ratio (hereinafter referred to as " history most ratio of greater inequality ") rate (i) that the optimal section number of times of its history traveling accounts for total degree may be considered It is known.In this data basis, personalized induction information can be recorded according to the traveling of individual vehicle, and issue specific aim is lured Lead information, it is ensured that vehicle selects the fairness of optimal path.I.e. vehicle history travel optimal section number of times account for total degree ratio compared with Hour, personalized induction information should cause the optimal path that the vehicle has bigger probability to choose current time.Assuming that when current Quarter, optimal path was A paths, and above-mentioned condition can be formulated as：

In formula, p_iRepresent vehicle i inductivity, p_jVehicle j inductivity is represented, rate (i) represents vehicle i history most Ratio of greater inequality, rate (j) represents vehicle j history most ratio of greater inequality.

Comprehensive (10) (11) two formula, the inductivity of reasonable distribution each car so that on the premise of road network total optimization, take into account Individual vehicle selects the fairness of optimal path.(10) (11) two formulas constitute the basic constraint bar of personalized inductivity distribution Part.

4) concept of vehicle priority is set up, according to this concept, using equal difference distribution principle, vehicle priority has been calculated Personalized inductivity distribution numerical value in the case of knowing.

When information of vehicles is complete and accurate, the rate size orders of all vehicles are also unique and accurate.Define one The concept of priority, if the rate (i) of i-th car is ordered as kth greatly in all vehicles, the priority of the vehicle is called K, the history most ratio of greater inequality of this car is accordingly denoted as rate (i_(k)), dictating otherwise the vehicle guidance rate apportioning cost that priority is k is p_k, it is clear that vehicle priority is bigger, inductivity apportioning cost p_kIt is bigger.

According to the concept of above-mentioned vehicle priority, according to priority k sizes, successively decreased determination inductivity, use with arithmetic progression Formula is expressed as：

p_k+1-p_k=p_k+2-p_k+1=Δ (12)

Comprehensive (8) (12) two formula, can be obtained：

Suitable minimum inductivity p need to only be provided₁, then tolerance Δ can be obtained, and then determine the inductivity of each priority.

5) according to step 4) distribution principle that determines, according to the probability distribution of vehicle history most ratio of greater inequality, reasonable distribution induction Information, meets the principle of user equilibrium to greatest extent under probability meaning, it is ensured that vehicle receives the fairness of induction.

Because colony's induction is the behavior for a large amount of vehicles, it can be considered that the history of all vehicles most ratio of greater inequality is only The vertical stochastic variable with distribution, can be according to history most ratio of greater inequality of the statistical information to vehicle when there is enough prioris Distribution is fitted, when priori is not enough, it is believed that the history of vehicle most ratio of greater inequality Normal Distribution.

Below with history most ratio of greater inequality Normal Distribution on the premise of solved, obey other points for history most ratio of greater inequality The situation of cloth, will not produce any influence, therefore can be solved according to identical step to solution procedure.

When i-th (i ＜ N) car reaches crossing, compared with not yet reaching any vehicle j (i ＜ j≤N) at crossing, preferentially The lower probability of level is：

Wherein μ, δ are the average and standard deviation of normal distribution, and x is the symbol of stochastic variable.

Obviously, this is one can be abbreviated as P (rate (i)) only with rate (i) about and with the unrelated values of j, represent times Meaning does not reach vehicle priority and is higher than the probability for having reached vehicle i.

Due to the history most ratio of greater inequality independent same distribution of all vehicles, thus reached the information of vehicle and do not reach vehicle without Close, can only consider that vehicle i does not reach vehicle with remaining, note n=N-i is does not reach vehicle number, in this n+1 car, vehicle i Priority be k probability be：

According to total-expectation formula, can obtain vehicle i should distribute the desired value of inductivity, under probability meaning, and this is most Excellent allocative decision.It is formulated as：

Wherein E (p_k| rate (i)=rate (i_(k))) to represent vehicle i priority be inductivity apportioning cost p under conditions of k_k's Conditional expectation.

In step 4) described in arithmetic progression allocation rule under, inductivity apportioning cost p_kIt is only relevant with vehicle priority k, i.e., Once it is determined that vehicle priority, p_kJust it is to determine and known, therefore has：

E(p_k| rate (i)=rate (i_(k)))=p_k(17)

In the continuous arrival process of vehicle, respective path is selected respectively with vehicle has been reached, optimal separation rate is in In being continually changing, it is assumed that when i-th car reaches crossing, preceding i-1 car selects the quantity of A paths and B path according to allocation rule Respectively n₁And n₂, then obviously it is not changed into by the road network optimal constraint conditionses of crossing vehicle now：

According to arithmetic progression allocation rule, can obtain the vehicle guidance rate apportioning cost that priority is k should meet condition, use Formula is expressed as：

Wherein Δ is constant, and for the inductivity tolerance of setting, this tolerance should ensure that the minimum inductivity and highest of vehicle Inductivity in the reasonable scope, takes

Further solve, can show that the vehicle guidance rate apportioning cost that priority is k is：

According to above-mentioned analysis and solution, i-th car inductivity apportioning cost optimal under probability meaning has been obtained：

Wherein：

The various embodiments described above are only used for having carried out further specifically the purpose of the present invention, technical scheme and beneficial effect It is bright, it is not intended to limit the invention, within the spirit and principles of the invention, any modifications, equivalent substitutions and improvements done Deng should be included within the scope of the present invention.

Claims (7)

1. a kind of personalized inductivity distribution method of dual path road network under user equilibrium principle, described dual path road network is present , there are two optional paths A and B from entrance O to outlet D, vehicle reaches entrance A in an one sole inlet O and sole outlet D When can receive induction information, it is characterised in that：Described inductivity distribution method comprises the following steps：

1) for the dual path road network to be regulated and controled, road network basic parameter is counted；

2) GreenShields models and traffic flow theory are based on, is asked for according to road network basic parameter optimal under ideal conditions Separation rate, it is optimal to reach the overall traffic flow of road network；

3) under the constraints of road network total optimization, the ratio compared with shortest path is travelled according to individual vehicle history, individual character is set up Change the basic constraints of induction allocation strategy；

4) concept of vehicle priority is set up, using equal difference distribution principle, the personalization under vehicle priority known case is calculated Inductivity distributes numerical value；

5) according to step 4) determine distribution principle and vehicle history most ratio of greater inequality probability distribution, distribute induction information, general The principle of user equilibrium is met under rate meaning to greatest extent, it is ensured that vehicle receives the fairness of induction.

2. the personalized inductivity distribution method of dual path road network under user equilibrium principle as claimed in claim 1, its feature It is：The step 1) in, road network basic parameter includes induction information update cycle T, magnitude of traffic flow N, current separation rate p, road Footpath A real-time vehicle numbers N₁, path B actual vehicle numbers N₂, path A length L_A, path B length L_B, path A vehicles are when averagely travelling Between T_Areal, path B vehicles average hourage T_Breal；Wherein, current separation rate p refers to vehicle access path A quantity percentage Than.

3. the personalized inductivity distribution method of dual path road network under user equilibrium principle as claimed in claim 2, its feature It is：The step 2) in, " optimal " be under the overall average hourage minimum criterion with vehicle, ideal conditions most Excellent separation rate to ask for process as follows：

GreenShields models are pointed out, in certain scope, have linear relationship, its table between speed v and vehicle density ρ It is as follows up to formula：

$v\left(\mathrm{\&rho;}\right)=v_{free}(1-\frac{\mathrm{\&rho;}}{{\mathrm{\&rho;}}_{jam}}),0<\mathrm{\&rho;}\&le;{\mathrm{\&rho;}}_{jam}$

In formula, v_freeRepresent section Maximum speed limit, ρ_jamVehicle most high-density is represented, wherein：

${\mathrm{\&rho;}}_{jam}=\frac{N_{\max }}{L}=\frac{\frac{L}{l+d}}{L}=\frac{1}{l+d}$

N_maxThe maximum appearance of vehicle amount of road is represented, L represents road section length, and l represents average length of car, and d represents vehicle minimum spacing, For different paths, average length of car and vehicle minimum spacing are identicals, i.e. vehicle most high-density ρ_jamFor fixation Value；

Further according to the definition of vehicle density

$\mathrm{\&rho;}=\frac{N_{trip}}{L}$

In formula, N_tripPresent road vehicle number is represented,

It is final to draw vehicle average hourage T_tripWith road section length L and present road vehicle number N_tripRelation：

$T_{trip}=\frac{L}{v_{free}(1-\frac{N_{trip}(l+d)}{L})}$

The new vehicle that reaches receives induction information and selected behind path, and two section vehicle numbers are expected

E(N_A)=N₁+Np-N_1out

E(N_B)=N₂+N(1-p)-N_2out

In formula, N represents the magnitude of traffic flow, N_A、N_BRepresent that the new vehicle that reaches receives induction information and access path A, path B respectively Vehicle number, E (N_A)、E(N_B) represent that the new vehicle that reaches receives induction information and access path A, the phase of path B vehicle number respectively Hope, p represents separation rate, N₁Represent path A current real-time vehicle number, N₂Path B current real-time vehicle number is represented, wherein N_1out,N_2outRepresent the vehicle flowrate left in an information updating cycle from two paths；

Expect expression formula according to two section vehicle numbers, obtain vehicle overall travel time on the paths of A, B two and expect expression formula

$\begin{array}{c}{T}_{total}=\frac{(N_1+Np-N_{1out})L_A}{v_{free1}(1-\frac{(N_1+Np-N_{1out})(l+d)}{L_A})}\\ +\frac{(N_2+N(1-p)-N_{2out})L_B}{v_{free2}(1-\frac{(N_2+N(1-p)-N_{2out})(l+d)}{L_B})}\end{array}$

Wherein only p is variable；

Minimum is asked for the formula, optimal separation rate p is drawn_bestExpression formula

$p_{best}=\frac{N_{freeA}{L}_B\sqrt{v_{free1}{L}_B}-N_{freeB}{L}_A\sqrt{v_{free2}{L}_A}}{N(L_A\sqrt{v_{free2}{L}_A}+L_B\sqrt{v_{free1}{L}_B})}$

Wherein

$N_{freeA}=\frac{L_A}{l+d}-(N_1-\frac{N_1}{L_A}{v}_{free1}(1-\frac{N_1(l+d)}{L_A}\left)T\right)$

$N_{freeB}=\frac{L_B}{1+d}-(N+N_2-\frac{N_2}{L_B}{v}_{free2}(1-\frac{N_2(l+d)}{L_B}\left)T\right)$

In formula, N_freeA、N_freeBFor intermediate variable, represent to assume that vehicle fully enters B path, now path A, path B respectively can With the maximum vehicle number of receiving, v_free1v_free2Path A and path B Maximum speed limit is represented respectively.

4. the personalized inductivity distribution method of dual path road network under user equilibrium principle as claimed in claim 3, its feature It is：The step 3) in, the process for setting up the basic constraints of personalized induction allocation strategy is as follows：

A basic constraints of customized information issue is obtained according to the expression formula of optimal separation rate：

$\underset{i=1}{\overset{N}{\&Sigma;}}{p}_i={\mathrm{Np}}_{best}$

Wherein p_iRepresent that vehicle i receives the induction of probability, also referred to as vehicle i that path A is selected after personalized induction information Rate；

Assuming that current time optimal path is A paths, above-mentioned condition can be formulated as：

$\left\{\begin{array}{c}{p}_i\&GreaterEqual;p_j;ifrate\left(i\right)\&GreaterEqual;rate\left(j\right)\\ p_i<p_j;else\end{array}\right.$

In formula, p_iRepresent vehicle i inductivity, p_jVehicle j inductivity is represented, rate (i) represents vehicle i history most ratio of greater inequality, Rate (j) represents vehicle j history most ratio of greater inequality；

Above-mentioned two formula constitutes the basic constraints of personalized inductivity distribution.

5. the personalized inductivity distribution method of dual path road network under user equilibrium principle as claimed in claim 4, its feature It is：The step 4) implementation process it is as follows：

First, the concept of priority is defined, if the rate (i) of i-th car is ordered as kth greatly in all vehicles, claiming should The priority of vehicle is k, and the history most ratio of greater inequality of this car is accordingly denoted as rate (i_(k)), in addition, priority is k vehicle guidance Rate apportioning cost is designated as p_k, it is clear that vehicle priority is bigger, inductivity apportioning cost p_kIt is bigger；

According to the concept of above-mentioned vehicle priority, according to priority k sizes, successively decreased determination inductivity with arithmetic progression, use formula It is expressed as：

p_k+1-p_k=p_k+2-p_k+1=Δ

The expression formula of the comprehensive formula and optimal separation rate, is obtained：

$p_1+\frac{N-1}{2}\mathrm{\&Delta;}=p$

Minimum inductivity p only need to be provided₁, then tolerance Δ can be obtained, and then determine the inductivity of each priority.

6. the personalized inductivity distribution method of dual path road network under user equilibrium principle as claimed in claim 5, its feature It is：The step 5) in, the determination process of the allocative decision of induction information is as follows：

Note n=N-i is does not reach vehicle number, and in this n+1 car, the probability that vehicle i priority is k is：

$p\left(rate\right(i)=rate(i_{\left(k\right)}\left)\right)=C_n^{k-1}P{\left(rate\right(i\left)\right)}^{k-1}{(1-P(rate\left(i\right)\left)\right)}^{n-k+1}$

In formula, P (rate (i)) represents that any vehicle priority that do not reach is higher than the probability for having reached vehicle i, this be one only with Rate (i) is about and with the unrelated values of j；

According to total-expectation formula, can obtain vehicle i should distribute the desired value of inductivity, under probability meaning, and this is optimal Allocative decision；It is formulated as：

$E\left(p\right(i\left)\right)=\underset{k=1}{\overset{n+1}{\&Sigma;}}p\left(rate\right(i)=rate(i_{\left(k\right)}\left)\right)E\left(p_k\right|rate\left(i\right)=rate\left(i_{\left(k\right)}\right))$

Wherein E (p_k| rate (i)=rate (i_(k))) to represent vehicle i priority be inductivity apportioning cost p under conditions of k_kCondition Expect；

In step 4) described in arithmetic progression allocation rule under, inductivity apportioning cost p_kIt is only relevant with vehicle priority k, i.e., once Determine vehicle priority, p_kJust it is to determine and known, therefore has：

E(p_k| rate (i)=rate (i_(k)))=p_k

In the continuous arrival process of vehicle, respective path is selected respectively with vehicle has been reached, optimal separation rate is in continuous In change, it is assumed that when i-th car reaches crossing, preceding i-1 car selects the quantity of A paths and B path to distinguish according to allocation rule For n₁And n₂, then obviously it is not changed into by the road network optimal constraint conditionses of crossing vehicle now：

$\underset{k=i}{\overset{N}{\&Sigma;}}p\left(k\right)=Np-n_1$

According to arithmetic progression allocation rule, can obtain the vehicle guidance rate apportioning cost that priority is k should meet condition, use formula It is expressed as：

${\mathrm{np}}_1+\frac{n(n-1)}{2}\mathrm{\&Delta;}=Np-n_1$

Wherein Δ is constant, and for the inductivity tolerance of setting, this tolerance should ensure that the minimum inductivity of vehicle and highest are induced Rate in the reasonable scope, takes

$\mathrm{\&Delta;}=\left\{\begin{array}{c}\frac{0.85p}{2n},p<0.5\\ \frac{0.85(1-p)}{2n},p>0.5\end{array}\right.$

Further solve, can show that the vehicle guidance rate apportioning cost that priority is k is：

$p_k=p_1+(k-1)\mathrm{\&Delta;}=\frac{{\mathrm{Np}}_1-n_1}{n}-\frac{n-1}{2}\mathrm{\&Delta;}+(k-1)\mathrm{\&Delta;}$

According to above-mentioned solution, i-th car inductivity apportioning cost optimal under probability meaning is obtained：

$E\left(p\right(i\left)\right)=\underset{k=1}{\overset{n+1}{\&Sigma;}}p\left(rate\right(i)=rate(i_{\left(k\right)}\left)\right)E\left(p_k\right|rate\left(i\right)=rate\left(i_{\left(k\right)}\right))$

Wherein：

$p\left(rate\right(i)=rate(i_{\left(k\right)}\left)\right)=C_{N-i}^{k-1}P{\left(rate\right(i\left)\right)}^{k-1}{(1-P(rate\left(i\right)\left)\right)}^{N-i-k+1}$

$E\left(p_k\right|rate\left(i\right)=rate\left(i_{\left(k\right)}\right))=\frac{{\mathrm{Np}}_1-n_1}{n}-\frac{n-1}{2}\mathrm{\&Delta;}+(k-1)\mathrm{\&Delta;}.$

7. the personalized inductivity distribution method of dual path road network under user equilibrium principle as claimed in claim 6, its feature It is：The step 5) solution to P (rate (i)), when there is enough prioris, just according to statistical information to vehicle The optimal ratio distribution of history be fitted, when priori is not enough, then it is assumed that the history of vehicle most ratio of greater inequality Normal Distribution, Now：

$p\left(rate\right(i)>rate(j\left)\right)=\underset{0}{\overset{rate\left(i\right)}{\&Integral;}}\frac{1}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&delta;}}{e}^{-\frac{{(x-\mathrm{\&mu;})}^2}{2{\mathrm{\&delta;}}^2}}dx$

Wherein μ, δ are the average and standard deviation of normal distribution, and x is the symbol of stochastic variable.