CN106355907A - Method for real-time estimation of queuing length of signalized intersection based on vehicle track - Google Patents

Abstract

The invention relates to a method for real-time estimation of the queuing length of a signalized intersection based on a vehicle track. The method comprises the following steps: (1) judging a vehicle traffic state according to real-time vehicle traffic information; (2) estimating a vehicle queue-joining key point and a vehicle queue-leaving key point according to the real-time vehicle track information, vehicle traffic state and kinematical equation; (3) identifying an upstream reached fleet according to the estimated vehicle queue-joining key point; (4) performing queuing wave and evanescent wave estimation according to the estimated vehicle queue-joining key point, the queue-leaving key point and the identified fleet; and (5) estimating the intersection signal parameter and the queuing length according to the estimated queuing wave and evanescent wave. Compared with the prior art, the method is adaptive to a data environment with low sampling frequency and low sampling rate, and has the advantages of strong robustness, high real-time performance, good accuracy and the like.

Description

Signalized crossing queue length real-time estimation method based on track of vehicle

Technical field

The present invention relates to field of traffic control, especially relate to a kind of signalized crossing based on track of vehicle and queue up Length real-time estimation method.

Background technology

Signalized intersections replace as the key component of city road network, the periodicity due to traffic lights, often can send out Raw traffic congestion, largely constrains the overall operation efficiency of City road traffic system.Queue length is handed over as evaluating The important indicator that prong runs, on the one hand can be used for the delay of indirect Estimation vehicle, stop frequency and journey time etc. and refers to Mark, on the other hand direct feedback can be used for signal timing optimization.

The existing queue length based on track of vehicle estimates that analogous technical mainly has: (1) cheng et al. is based on High-precision vehicle Track data, extracts the crucial tracing point representing vehicle-state change, so queued up using traffic wave method simulating vehicle and Evanishment, realizes queue length and estimates；(2) ban et al. differentiates vehicle delay pattern using sampling journey time, and based on not To carry out vehicle queue length estimation with delay pattern；(3) comert sets up statistical model to analyze Floating Car sample rate and row The relation of team's length accuracy, and assuming to calculate queuing queue number on the premise of upstream vehicle reaches distribution and Floating Car sample rate Term hopes；(4) Xiong Yingge et al. considers crossing Floating Car track dot density and acceleration profile feature, true using clustering method The maximum position of fixed track point average density or the position of sudden change of acceleration maximum, and the estimation as average queue length Value.

Summarize the existing queue length Estimation Study based on track of vehicle, be primarily present problems with: (1) assumes that vehicle arrives Reach (uniform or poisson arrival), this hypothesis have ignored the impact that upstream crossing reaches to vehicle；(2) assume Floating Car sampling Rate, actually Floating Car sample rate are not definite values, can over time with the change in place and change, thus affecting to estimate essence Degree；(3) assume signal parameter it is known that being in most cases actually cannot to obtain signal parameter information, particularly with adaptive Induction signal control system.

Content of the invention

The purpose of the present invention is exactly to overcome the defect of above-mentioned prior art presence to provide one kind to be based on track of vehicle Signalized crossing queue length real-time estimation method, can adapt to low sample frequency, the data environment of low sampling rate, tool There is the advantages of strong robustness, real-time are high, and accuracy is good.

The purpose of the present invention can be achieved through the following technical solutions:

A kind of comprised the following steps based on the signalized crossing queue length real-time estimation method of track of vehicle:

1) according to real-time vehicle trace information, carry out vehicle traffic condition differentiation；

2) according to real-time vehicle trace information, vehicle traffic condition and kinematical equation, carry out vehicle and add key of queuing up Put and leave the crucial point estimation of queuing；

3) vehicle according to estimation adds queuing key point, carries out fleet's identification of upstream arrival；

4) vehicle according to estimation adds queuing key point, leaves queuing key point and identified fleet, is collected Knot ripple and evanescent wave are estimated；

5) according to the assembly ripple of estimation and evanescent wave, carry out intersection signal parameter and queue length is estimated.

Described step 1) particularly as follows: obtaining track of vehicle information in real time, make i-th vehicle in t_kThe tracing point information in moment It is expressed asRepresent i-th vehicle in t respectively_kThe space coordinatess in moment, speed and acceleration, Then i-th vehicle is in t_kThe traffic behavior in momentFor:

$q_t^i\&element;\left\{\begin{array}{cc}m,& v_{t_k}^i\&greaterequal;v_{th1}\\ c,& v_{t_k}^i\&element;\&lsqb;v_{th2},v_{th1})\\ s,& v_{t_k}^i<v_{th2}\end{array}\right.$

Wherein, v_th1And v_th2For the default threshold speed for state of motion of vehicle differentiation, v_th1＜ v_th2, m, c and s divide Biao Shi not move, low speed stop-go and stop three states.

Described step 2) particularly as follows:

21) estimate that vehicle leaves queuing key point:

When i-th vehicle is in t_kAnd t_k+1The traffic status identification in moment isWithWhen, obtain corresponding Tracing point informationWith

Ifv_fFor free stream velocity, then i-th vehicle is in t_kMoment leave queuing key pointFor:

${\hat{t}}_{start}^{i,t_k}=t_{k+1}-\frac{v_{t_{k+1}}^i}{a_{acc}}$

IfThen i-th vehicle is in t_kMoment leave queuing key pointFor:

${\hat{t}}_{start}^{i,t_k}=t_{k+1}-\frac{v_{t_{k+1}}^i}{2a_{acc}}-\frac{d_3}{v_{t_{k+1}}^i}$

Wherein, a_accFor i-th vehicle in t_kAnd t_k+1Acceleration between moment, is approximately equal tod₃For i-th vehicle In t_kAnd t_k+1In the distance between moment, it is equal to

22) estimation vehicle addition queuing key point:

When i-th vehicle is in t_k-1And t_kThe traffic status identification in moment isWithWhen, obtain corresponding Tracing point informationWith

IfThen i-th vehicle is in t_kThe addition queuing key point in momentFor:

${\hat{t}}_{stop}^{i,t_k}=t_{k-1}-\frac{v_{t_{k-1}}^i-v_{th1}}{2a_{dec}}+\frac{d_2-d_1}{v_{t_{k-1}}^i}$

IfThen i-th vehicle is in t_kThe addition queuing key point in momentFor:

${\hat{t}}_{stop}^{i,t_k}=t_{k-1}+\frac{2(d_2-d_1)}{v_{t_{k-1}}^i}$

When i-th vehicle is in t_k-1And t_kThe traffic status identification in moment isWithWhen, obtain corresponding Tracing point informationWith

IfThen i-th vehicle is in t_kThe addition queuing key point in momentFor:

${\hat{t}}_{stop}^{i,t_k}=t_{k-1}-\frac{v_{t_{k-1}}^i-v_{t_k}^i}{2a_{dec}}+\frac{d_2}{v_{t_{k-1}}^i}$

IfThen i-th vehicle is in t_kThe addition queuing key point in momentFor:

${\hat{t}}_{stop}^{i,t_k}=t_{k-1}+\frac{2d_2}{v_{t_{k-1}}^i}$

Wherein, a_decFor i-th vehicle in t_k-1And t_kAcceleration between moment, is approximately equal tod₁For i-th vehicle In t_k-1The distance between starting point, d under the tracing point in moment and low speed stop-go state₂For under low speed stop-go state The distance between starting point and terminating point.

Described i-th vehicle is in t_k-1The tracing point in moment and the distance between starting point under low speed stop-go state d₁ Meet below equation:

$d_2=x_{t_k}^i-\frac{3(v_{th1}+v_{th2})}{2}-x_{t_{k-1}}^i$

Starting point and the distance between terminating point d under described low speed stop-go state₂Meet below equation:

$d_1=\frac{3(v_{th1}+v_{th2})}{2}.$

Described step 3) particularly as follows:

31) queuing key point is added to the vehicle of estimationI=1 ..., n, n are the sum of vehicle, carry out ascending order row Sequence；

32) after obtaining ascending sort, Adjacent vehicles add the time difference of queuing key point and range difference, meet below equation:

$\mathrm{\&delta;}{\hat{t}}_i={\hat{t}}_{stop}^{i,t_k}-{\hat{t}}_{stop}^{i-1,t_k}$

${\mathrm{\&delta;x}}_i=x_{t_k}^i-x_{t_k}^{i-1}$

Wherein,Represent the time difference of i-th vehicle and the addition queuing key point of rear Adjacent vehicles,δx_iRepresent the range difference of i-th vehicle and the addition queuing key point of rear Adjacent vehicles；

33) carry out fleet's identification of upstream arrival, particularly as follows:

Ifθ is fleet's judgment threshold, then i-th vehicle and rear Adjacent vehicles belong to a fleet, instead It, do not belong to a fleet.

Described step 4) particularly as follows:

41) queuing estimation point and identified fleet are added according to estimating the vehicle that obtains in time interval j, to assembling ripple Carry out piecewise linear model matching, meet below equation:

$\begin{array}{cc}\underset{j}{\min }& \underset{m=1}{\overset{\left|\right|n_j^s\left|\right|}{\mathrm{\&sigma;}}}\underset{{\hat{t}}_{stop}^{i,t_k}\&element;\&lsqb;{\hat{t}}_{stop,m},{\hat{t}}_{stop,m+1}\&rsqb;}{\mathrm{\&sigma;}}{\&lsqb;x_{t_k}^i-({\mathrm{\&omega;}}_{j,m}^s\&centerdot;{\hat{t}}_{stop}^{i,t_k}+{\mathrm{\&beta;}}_{j,m}^s)\&rsqb;}^2\\ & s.t.\\ & \begin{array}{cc}({\hat{t}}_{stop}^{i,t_k},x_{t_k}^i)\&element;n_j^s& \&forall;m=1,...,\left|\right|n_j^s\left|\right|\end{array}\\ & x_m-({\mathrm{\&omega;}}_{j,m}^s\&centerdot;{\hat{t}}_{stop,m}+{\mathrm{\&beta;}}_{j,m}^s)=0\\ & t_c^r\&le;{\hat{t}}_{stop}^{i,t_k},l_{stop-bar}\&greaterequal;x_{t_k}^i\\ & \left\{\begin{array}{cc}{x}_{t_k}^i-({\mathrm{\&omega;}}_{j,m}^s\&centerdot;{\hat{t}}_{stop}^{i,t_k}+{\mathrm{\&beta;}}_{j,m}^s)\&greaterequal;-\mathrm{\&epsiv;}& \&forall;q_{t_k}^i\&element;m\\ x_{t_k}^i-({\mathrm{\&omega;}}_{j,m}^s\&centerdot;{\hat{t}}_{stop}^{i,t_k}+{\mathrm{\&beta;}}_{j,m}^s)\&le;\mathrm{\&epsiv;}& \&forall;q_{t_k}^i\&element;c\&cup;s\end{array}\right.\end{array}$

Wherein,Add the set of queuing estimation point, set for vehicles all in time interval jMiddle basis identifies Fleet be divided intoIndividual fleet, m represents the numbering of fleet,Represent m, m+1 fleet's headstock car respectively Addition queuing key point, x_mRepresent and correspond toVehicle space coordinatess, It is respectively the in time interval j The m section slope assembling ripple to be estimated and intercept,Open bright moment, l for corresponding entrance driveway red light_stop-barRepresent that stop line is located Position, ε is positive adjusting parameter, for adjustment constraint hardness；

Then assemble ripple expression formula in time interval jFor:

$y_j^s=\left\{\begin{array}{cc}{w}_{j,1}^{s}t+{\mathrm{\&beta;}}_{j,1}^s,& t<{\hat{t}}_{stop,1}\\ \&centerdot;& \\ \&centerdot;& \\ \&centerdot;& \\ w_{j,m}^{s}t+{\mathrm{\&beta;}}_{j,m}^s,& t\&greaterequal;{\hat{t}}_{stop,m}\\ \&centerdot;& \\ \&centerdot;& \\ \&centerdot;& \\ w_{j,\left|\right|n_j^s\left|\right|}^{s}t+{\mathrm{\&beta;}}_{j,\left|\right|n_j^s\left|\right|}^s,& t\&greaterequal;{\hat{t}}_{stop,\left|\right|n_j^s\left|\right|}\end{array}\right.,m=1,...,\left|\right|n_j^s\left|\right|$

Wherein, t represents the moment；

42) queuing estimation point is left according to the vehicle estimating in time interval j to obtain, method of least square is carried out to evanescent wave Linear fit, meets below equation:

$\begin{array}{c}\underset{j}{\min }\mathrm{\&sigma;}{\&lsqb;x_{t_k}^i-({\mathrm{\&omega;}}_j^g\&centerdot;{\hat{t}}_{start}^{i,t_k}+{\mathrm{\&beta;}}_j^g)\&rsqb;}^2\\ s.t.\\ ({\hat{t}}_{start}^{i,t_k},x_{t_k}^i)\&element;n_j^g\\ \left\{\begin{array}{cc}{x}_{t_k}^i-({\mathrm{\&omega;}}_j^g\&centerdot;{\hat{t}}_{start}^{i,t_k}+{\mathrm{\&beta;}}_j^g)\&greaterequal;-\mathrm{\&epsiv;}& \&forall;q_{t_k}^i\&element;s\\ x_{t_k}^i-({\mathrm{\&omega;}}_j^g\&centerdot;{\hat{t}}_{start}^{i,t_k}+{\mathrm{\&beta;}}_j^g)\&le;\mathrm{\&epsiv;}& \&forall;q_{t_k}^i\&element;m\end{array}\right.\end{array}$

Wherein,Leave the set of queuing estimation point for vehicles all in time interval j,Respectively to be estimated The slope of evanescent wave and intercept；

Then assemble ripple expression formula in time interval jFor:

$y_j^g=w_j^{g}t+{\mathrm{\&beta;}}_j^g.$

Described step 5) particularly as follows:

51) obtain red light, green light in time interval j and open the bright momentWithMeet below equation:

$t_j^r=\frac{l_{stop-bar}-{\mathrm{\&beta;}}_{j,1}^s}{w_{j,1}^s}$

$t_j^g=\frac{l_{stop-bar}-{\mathrm{\&beta;}}_j^g}{w_j^g}$

Wherein, l_stop-barFor stop line position,Assemble the slope of ripple for first paragraph in time interval j And intercept；

52) obtain intersection signal parameter: the signal period t in time interval j_jWith respective inlets road green time pt_j, Meet below equation:

Or

${\mathrm{pt}}_j=t_j^g-t_j^r$

Wherein,Open the bright moment for the green light in time interval j-1,When opening bright for the red light in time interval j-1 Carve；

53) obtain the maximum queue length in current cycle estimatorAnd its correspond to the momentMeet below equation:

$q_j^{\max }=l_{stop-bar}-w_j^g\frac{{\mathrm{\&beta;}}_j^g-{\mathrm{\&beta;}}_{j,\left|\right|n_j^s\left|\right|}^s}{w_{j,\left|\right|n_j^s\left|\right|}^s-w_j^g}+{\mathrm{\&beta;}}_j^g$

$t_j^{\max }=\frac{{\mathrm{\&beta;}}_j^g-{\mathrm{\&beta;}}_{j,\left|\right|n_j^s\left|\right|}^s}{w_{j,\left|\right|n_j^s\left|\right|}^s-w_j^g}$

Wherein,It is respectively slope and the intercept that time interval j final stage assembles ripple；

54) obtain secondary queue lengthAnd correspond to the momentMeet below equation:

$q_j^{re}=l_{stop-bar}-w_{j+1,1}^s(\frac{w_j^g(t_j^{\max }-t_j^g)}{w_j^g+v_f}+t_j^{\max }-t_{j+1}^r)$

$t_j^{re}=\frac{w_j^g(t_j^{\max }-t_j^g)}{w_j^g+v_f}+\frac{{\mathrm{\&beta;}}_j^g-{\mathrm{\&beta;}}_{j,\left|\right|n_j^s\left|\right|}^s}{w_{j,\left|\right|n_j^s\left|\right|}^s-w_j^g}$

Wherein,Assemble ripple slope for first paragraph in time interval j+1,When opening bright for red light in time interval j+1 Carve.

Compared with prior art, it is an advantage of the current invention that:

1) release known vehicle of the prior art reaches analysis, known Floating Car sample rate and known signal parameter etc. It is assumed that more practicality；

2) real-time, it is capable of the queue length detection rolling based on the cycle, accuracy is high, can not only realize Big queue length is estimated to estimate additionally it is possible to realize secondary queuing；

3) method is advanced, strong robustness, can adapt to China and adapts to low sample frequency, the data environment of low sampling rate.

4) propose to move, low speed stop-go and stopping divides for three traffic behaviors, with using three traffic shapes State obtains and adds queuing key point and queuing to leave queuing key point, can preferably react queue clearance ripple and the shape assembling ripple State, obtains the data processed result of high precision.

5) it is directed to queue up and assembles ripple, propose upstream arrival fleet and sentence method for distinguishing, obtain after piecewise fitting and assemble ripple formula Can preferably react queues up assembles the fragmentation state of ripple, provides the data precision.

Brief description

Fig. 1 is method of the present invention flow chart；

Fig. 2 is crossing macroscopic view parent map；

Fig. 3 is intersection traffic ripple schematic diagram；

Fig. 4 is intersection vehicles velocity profile；

Fig. 5 identifies schematic diagram for fleet；

Fig. 6 is to open bright phase estimate box-shaped figure based on green light；

Fig. 7 is to open bright phase estimate box-shaped figure based on red light；

Fig. 8 is queue length error analyses comparison diagram.

Specific embodiment

The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention Premised on implemented, give detailed embodiment and specific operating process, but protection scope of the present invention be not limited to Following embodiments.

The present invention is set up based on lwr traffic wave pattern and obtains, and lwr traffic wave pattern can be good at disclosing crossing Vehicle queue is formed and evanishment.As shown in Fig. 2 intersection traffic stream meets triangle macroscopic view parent map characteristic, q in Fig. 2: table Show flow (veh/h), k: represent density (veh/km), q_1,1: for representing a kind of flow status in crossing, q_1,2: for representing Crossing another kind flow status, q_m: crossing maximum stream flow, k_1,1: q_1,1Corresponding crossing density, k_1,2: with q_1,2Phase Corresponding crossing density, k_m: the density corresponding to the maximum stream flow of crossing, k_j: crossing jam density, v_1,1,: in q_1,1With k_1,1The vehicle first paragraph of corresponding statess assembles ripple velocity of wave, v_1,2: in q_1,2And k_1,2The vehicle second segment of corresponding statess assembles ripple ripple Speed, v₂: evanescent wave velocity of wave, v₃: free stream velocity.

According to lwr traffic shock wave model mechanism, because traffic lights are periodically replaced, crossing can form multiply traffic shock wave, such as Shown in Fig. 3.When red light open bright, vehicle be forced stop, formed assemble wave direction after transmit, and assemble ripple velocity of wave with upstream vehicle reach Change and change；Green light opens bright moment, and vehicle is sailed out of with saturation volume rate startup, forms backward evanescent wave.Due to backward evanescent wave Velocity of wave be more than backward assemble ripple, two traffic shock wave can intersect in c point, now reaches maximum queue length, to disappearing simultaneously before producing Scattered ripple, queuing dribbles.X in Fig. 3: represent distance, wherein intersection parking line position for 70m at, a-g: Jin Jinbiao Indicating is shown a little, a-d: represents four kinds of different traffic behaviors, i.e. 4 kinds of different flows and density.

The basic applicable elements of the inventive method are as follows:

1) in same intersection vehicles queuing number of times not over twice；

2) no oversize vehicle, such as lorry and buses etc. in queuing vehicle.

As shown in figure 1, a kind of based on the signalized crossing queue length real-time estimation method of track of vehicle include with Lower step:

1) according to real-time vehicle trace information, carry out vehicle traffic condition differentiation；

2) according to real-time vehicle trace information, vehicle traffic condition and kinematical equation, carry out vehicle and add key of queuing up Put and leave the crucial point estimation of queuing；

3) vehicle according to estimation adds queuing key point, carries out fleet's identification of upstream arrival；

4) vehicle according to estimation adds queuing key point, leaves queuing key point and identified fleet, to dissipation Ripple velocity of wave segmentation/queuing is assembled ripple and is estimated, is obtained with evanescent wave velocity of wave according to the assembly ripple obtaining and assembles ripple and evanescent wave；

5) according to the assembly ripple of estimation and evanescent wave, intersection signal parameter (periodic signal etc.) and queue length are carried out Estimate.

Step 1) if particularly as follows: i-th vehicle velocity profile in crossing is as shown in figure 4, i-th vehicle is in t_kWhen Carve tracing point information beRepresent i-th vehicle in t respectively_kThe space coordinatess in moment, speed Degree and acceleration, space coordinatess are obtained by the latitude and longitude information of vehicle, then i-th vehicle is in t_kThe traffic behavior in momentFor:

$q_t^i\&element;\left\{\begin{array}{cc}m,& v_{t_k}^i\&greaterequal;v_{th1}\\ c,& v_{t_k}^i\&element;\&lsqb;v_{th2},v_{th1})\\ s,& v_{t_k}^i<v_{th2}\end{array}\right.$

Wherein, v_th1And v_th2For the default threshold speed for state of motion of vehicle differentiation, v_th1＜ v_th2, m, c and s divide Biao Shi not move, low speed stop-go and stop three states.

I.e. whenVehicle belongs to kinestate, once car speedThen enter low speed to stop walking state, when When vehicle is in low speed stop-go state, its speed is in [v_th2,v_th1) scope；Work as car speedLess than v_th2When, vehicle Enter dead ship condition.In Fig. 4, x₁-x₄: represent the space coordinatess of 4 track samples；d₁-d₃Expression is two-by-two between the sample point of track Travel.

Step 2) particularly as follows:

21) estimate that vehicle leaves queuing key point:

When i-th vehicle is in t_kAnd t_k+1The traffic status identification in moment isWithWhen, obtain corresponding Tracing point informationWith

Ifv_fFor free stream velocity, that is, vehicle is in t_k+1Moment, then i-th vehicle was in t still in acceleration mode_k Moment leave queuing key pointFor:

${\hat{t}}_{start}^{i,t_k}=t_{k+1}-\frac{v_{t_{k+1}}^i}{a_{acc}}$

IfI.e. vehicle is in t_k+1Moment, then i-th vehicle was in t still in uniform speed motion state_kThe leaving of moment Queuing key pointFor:

${\hat{t}}_{start}^{i,t_k}=t_{k+1}-\frac{v_{t_{k+1}}^i}{2a_{acc}}-\frac{d_3}{v_{t_{k+1}}^i}$

Wherein, a_accFor i-th vehicle in t_kAnd t_k+1Acceleration between moment, is approximately equal toCan value i-th Vehicle is in t_k+1Moment accelerationd₃For i-th vehicle in t_kAnd t_k+1In the distance between moment, it is equal to

22) estimation vehicle addition queuing key point:

When i-th vehicle is in t_k-1And t_kThe traffic status identification in moment isWithWhen, obtain corresponding Tracing point informationWith

IfI.e. vehicle is in t_k-1Moment, then i-th vehicle was in t still in uniform speed motion state_kThe addition in moment Queuing key pointFor:

${\hat{t}}_{stop}^{i,t_k}=t_{k-1}-\frac{v_{t_{k-1}}^i-v_{th1}}{2a_{dec}}+\frac{d_2-d_1}{v_{t_{k-1}}^i}$

IfI.e. vehicle is in t_k-1Moment, then i-th vehicle was in t still in retarded motion state_kThe addition in moment Queuing key pointFor:

${\hat{t}}_{stop}^{i,t_k}=t_{k-1}+\frac{2(d_2-d_1)}{v_{t_{k-1}}^i}$

When i-th vehicle is in t_k-1And t_kThe traffic status identification in moment isWithWhen, obtain corresponding Tracing point informationWith

IfI.e. vehicle is in t_k-1Moment, then i-th vehicle was in t still in uniform speed motion state_kThe addition in moment Queuing key pointFor:

${\hat{t}}_{stop}^{i,t_k}=t_{k-1}-\frac{v_{t_{k-1}}^i-v_{t_k}^i}{2a_{dec}}+\frac{d_2}{v_{t_{k-1}}^i}$

IfI.e. vehicle is in t_k-1Moment, then i-th vehicle was in t still in retarded motion state_kThe addition in moment Queuing key pointFor:

${\hat{t}}_{stop}^{i,t_k}=t_{k-1}+\frac{2d_2}{v_{t_{k-1}}^i}$

Wherein, a_decFor i-th vehicle in t_k-1And t_kAcceleration between moment, is approximately equal tod₁For i-th vehicle In t_k-1The distance between starting point, d under the tracing point in moment and low speed stop-go state₂For under low speed stop-go state The distance between starting point and terminating point.

I-th vehicle is in t_k-1The tracing point in moment and the distance between starting point under low speed stop-go state d₁Meet Below equation:

$d_2=x_{t_k}^i-\frac{3(v_{th1}+v_{th2})}{2}-x_{t_{k-1}}^i$

Starting point and the distance between terminating point d under low speed stop-go state₂Meet below equation:

$d_1=\frac{3(v_{th1}+v_{th2})}{2}.$

Step 3) particularly as follows:

31) queuing key point is added to the vehicle of estimationI=1 ..., n, n are the sum of vehicle, carry out ascending order row Whether sequence (because this is single-lane road, is ranked up processing and does not interfere with result that is to say, that the addition of previous car The queuing key point necessarily little addition queuing key point of later, that is,)；

32) after obtaining ascending sort, Adjacent vehicles add the time difference of queuing key point and range difference, meet below equation:

$\mathrm{\&delta;}{\hat{t}}_i={\hat{t}}_{stop}^{i,t_k}-{\hat{t}}_{stop}^{i-1,t_k}$

${\mathrm{\&delta;x}}_i=x_{t_k}^i-x_{t_k}^{i-1}$

Wherein,Represent the time difference of i-th vehicle and the addition queuing key point of rear Adjacent vehicles, δ x_iRepresent The range difference of the addition queuing key point of i-th vehicle and rear Adjacent vehicles；

33) carry out fleet's identification of upstream arrival, particularly as follows:

Ifθ is fleet's judgment threshold, then i-th vehicle and rear Adjacent vehicles belong to a fleet, IfThen do not belong to a fleet and (it is believed that vehicle i is the head car of another fleet, be also believed to upstream vehicle Arrival rate finds change), recognition effect is as shown in Figure 5.

Step 4) particularly as follows:

41) queuing estimation point and identified fleet (time interval are added according to estimating the vehicle that obtains in time interval j In j, only one vehicle of a car adds queuing estimation point and a vehicle to leave queuing estimation point), carry out segmentation to assembling ripple Linear model matching, meets below equation:

$\begin{array}{cc}\underset{j}{\min }& \underset{m=1}{\overset{\left|\right|n_j^s\left|\right|}{\mathrm{\&sigma;}}}\underset{{\hat{t}}_{stop}^{i,t_k}\&element;\&lsqb;{\hat{t}}_{stop,m},{\hat{t}}_{stop,m+1}\&rsqb;}{\mathrm{\&sigma;}}{\&lsqb;x_{t_k}^i-({\mathrm{\&omega;}}_{j,m}^s\&centerdot;{\hat{t}}_{stop}^{i,t_k}+{\mathrm{\&beta;}}_{j,m}^s)\&rsqb;}^2\\ & s.t.\\ & \begin{array}{cc}({\hat{t}}_{stop}^{i,t_k},x_{t_k}^i)\&element;n_j^s& \&forall;m=1,...,\left|\right|n_j^s\left|\right|\end{array}\\ & x_m-({\mathrm{\&omega;}}_{j,m}^s\&centerdot;{\hat{t}}_{stop,m}+{\mathrm{\&beta;}}_{j,m}^s)=0\\ & t_c^r\&le;{\hat{t}}_{stop}^{i,t_k},l_{stop-bar}\&greaterequal;x_{t_k}^i\\ & \left\{\begin{array}{cc}{x}_{t_k}^i-({\mathrm{\&omega;}}_{j,m}^s\&centerdot;{\hat{t}}_{stop}^{i,t_k}+{\mathrm{\&beta;}}_{j,m}^s)\&greaterequal;-\mathrm{\&epsiv;}& \&forall;q_{t_k}^i\&element;m\\ x_{t_k}^i-({\mathrm{\&omega;}}_{j,m}^s\&centerdot;{\hat{t}}_{stop}^{i,t_k}+{\mathrm{\&beta;}}_{j,m}^s)\&le;\mathrm{\&epsiv;}& \&forall;q_{t_k}^i\&element;c\&cup;s\end{array}\right.\end{array}$

Wherein,Add the set of queuing estimation point, set for vehicles all in time interval jMiddle basis identifies Fleet be divided intoIndividual fleet, m represents the numbering of fleet,Represent m, m+1 fleet's headstock respectively The addition queuing key point of vehicle, x_mRepresent and correspond toVehicle space coordinatess, It is respectively in time interval j The m section slope assembling ripple to be estimated and intercept,Open bright moment, l for corresponding entrance driveway red light_stop-barRepresent stop line institute In position, ε is positive adjusting parameter, for adjustment constraint hardness；

Then ripple is assembled according to the Subsection Queue Disposal after piecewise fitting, obtain assembling ripple complete expression in time interval jFor:

$y_j^s=\left\{\begin{array}{cc}{w}_{j,1}^{s}t+{\mathrm{\&beta;}}_{j,1}^s,& t<{\hat{t}}_{stop,1}\\ \&centerdot;& \\ \&centerdot;& \\ \&centerdot;& \\ w_{j,m}^{s}t+{\mathrm{\&beta;}}_{j,m}^s,& t\&greaterequal;{\hat{t}}_{stop,m}\\ \&centerdot;& \\ \&centerdot;& \\ \&centerdot;& \\ w_{j,\left|\right|n_j^s\left|\right|}^{s}t+{\mathrm{\&beta;}}_{j,\left|\right|n_j^s\left|\right|}^s,& t\&greaterequal;{\hat{t}}_{stop,\left|\right|n_j^s\left|\right|}\end{array}\right.,m=1,...,\left|\right|n_j^s\left|\right|$

Wherein, t represents the moment,Segmentation depend onSize, has identified that upstream reaches fleet's number；

42) queuing estimation point is left according to the vehicle estimating in time interval j to obtain, method of least square is carried out to evanescent wave Linear fit, meets below equation:

$\begin{array}{c}\underset{j}{\min }\mathrm{\&sigma;}{\&lsqb;x_{t_k}^i-({\mathrm{\&omega;}}_j^g\&centerdot;{\hat{t}}_{start}^{i,t_k}+{\mathrm{\&beta;}}_j^g)\&rsqb;}^2\\ s.t.\\ ({\hat{t}}_{start}^{i,t_k},x_{t_k}^i)\&element;n_j^g\\ \left\{\begin{array}{cc}{x}_{t_k}^i-({\mathrm{\&omega;}}_j^g\&centerdot;{\hat{t}}_{start}^{i,t_k}+{\mathrm{\&beta;}}_j^g)\&greaterequal;-\mathrm{\&epsiv;},& \&forall;q_{t_k}^i\&element;s\\ x_{t_k}^i-({\mathrm{\&omega;}}_j^g\&centerdot;{\hat{t}}_{start}^{i,t_k}+{\mathrm{\&beta;}}_j^g)\&le;\mathrm{\&epsiv;},& \&forall;q_{t_k}^i\&element;m\end{array}\right.\end{array}$

Wherein,Leave the set of queuing estimation point for vehicles all in time interval j,Respectively to be estimated The slope of evanescent wave and intercept, ε is positive adjusting parameter, for adjustment constraint hardness；

Then according to the queue clearance ripple after least square linear fit, obtain assembling ripple complete expression in time interval jFor:

$y_j^g=w_j^{g}t+{\mathrm{\&beta;}}_j^g.$

Step 5) particularly as follows:

51) obtain red light, green light in time interval j and open the bright momentWithMeet below equation:

$t_j^r=\frac{l_{stop-bar}-{\mathrm{\&beta;}}_{j,1}^s}{w_{j,1}^s}$

$t_j^g=\frac{l_{stop-bar}-{\mathrm{\&beta;}}_j^g}{w_j^g}$

Wherein, l_stop-barFor stop line position,Assemble the slope of ripple for first paragraph in time interval j And intercept,It is respectively slope and the intercept of evanescent wave；

52) obtain intersection signal parameter: the signal period t in time interval j_jWith respective inlets road green time pt_j, Meet below equation:

Or

${\mathrm{pt}}_j=t_j^g-t_j^r$

Wherein,Open the bright moment for the green light in time interval j-1,When opening bright for the red light in time interval j-1 Carve；

53) obtain the maximum queue length in current cycle estimatorAnd its correspond to the momentMeet below equation:

$\begin{array}{c}{q}_j^{\max }=l_{stop-bar}-w_j^g\frac{{\mathrm{\&beta;}}_j^g-{\mathrm{\&beta;}}_{j,\left|\right|n_j^s\left|\right|}^s}{w_{j,\left|\right|n_j^s\left|\right|}^s-w_j^g}+{\mathrm{\&beta;}}_j^g\\ t_j^{\max }=\frac{{\mathrm{\&beta;}}_j^g-{\mathrm{\&beta;}}_{j,\left|\right|n_j^s\left|\right|}^s}{w_{j,\left|\right|n_j^s\left|\right|}^s-w_j^g}\end{array}$

Wherein,It is respectively the slope that time interval j final stage assembles ripple (intersecting) with evanescent wave And intercept；

54) in the case of supersaturation, except step 53) in maximum queue length, there is also secondary queuing phenomena, then two Secondary queue lengthAnd correspond to the momentMeet below equation:

$q_j^{re}=l_{stop-bar}-w_{j+1,1}^s(\frac{w_j^g(t_j^{\max }-t_j^g)}{w_j^g+v_f}+t_j^{\max }-t_{j+1}^r)$

$t_j^{re}=\frac{w_j^g(t_j^{\max }-t_j^g)}{w_j^g+v_f}+\frac{{\mathrm{\&beta;}}_j^g-{\mathrm{\&beta;}}_{j,\left|\right|n_j^s\left|\right|}^s}{w_{j,\left|\right|n_j^s\left|\right|}^s-w_j^g}$

Wherein,Assemble ripple slope for first paragraph in time interval j+1,When opening bright for red light in time interval j+1 Carve, v_fFor free stream velocity,For step 54) the middle maximum queue length correspondence moment estimating to obtain.

Should intersection signal parameter based on real-time vehicle track method for building up of estimating model with queue length include as Lower step:

1) phantom is built

For verifying the estimation effect of inventive algorithm, the vissim5.4 micro-simulation simulator using German ptv company is set up Phantom.Impact downstream vehicle being reached for true reflection upstream crossing, this phantom comprises 3 crossings, away from From respectively 200 meters, 350 meters, the signal period is 100s, a length of 50s during thing phase place, and track flow is 1000veh/hr.

It is to make phantom have more generality simultaneously, urban intersection can be represented, by crossing speed limit in phantom Facility is 45km/h, and, in the interval of 40km/h-50km/h, emulation is in 10 different random kinds for desired speed distribution normal distribution It is separately operable 8400s, front 600s is preheating time under son.With the 3rd crossing as object of study, extract 600s to 8400s it Between track of vehicle, partial traces illustrate as shown in table 1.

Table 1 part acquisition trajectories data base illustrates table

In order to check estimation effect under different vehicle track sample rate and sample frequency for the inventive algorithm, setting 5s, 3 sample frequencys of 15s, 25s and 5% to 100%20 sample rate, form 60 test scenes altogether.It is to verify further simultaneously The effectiveness of inventive algorithm, the algorithm also being proposed with ramezani and geroliminis is compared, needed for two kinds of algorithms Parameter setting is as shown in table 2:

2 two kinds of algorithm desired parameters of table arrange table

2) simulation result

(1) Cycle Length

Under different tracks sample rate and sample frequency, statistics opens the box-shaped figure in bright moment as schemed based on green light or red light 20 times Shown in 6 and Fig. 7, count the maximum absolute error (mae) of phase estimate and the average absolute percentage under same sample frequency simultaneously Error (mape) is as shown in table 3.

Different sample frequency lower cycle estimated result contrast (unit: s) of table 3

(2) queue length

Fig. 8 is the present invention and ramezani and queue length under above-mentioned 60 test scenes for the geroliminis algorithm Illustrate with success rate.

3) analysis of simulation result

Can obtain as drawn a conclusion from phase estimate box-shaped figure and Statistical Comparison average period:

(1) it is better than based on the phase estimate result that green light opens the bright moment and bright phase estimate result is opened based on red light；

(2) for two kinds of methods of estimation, with the increase in sampling interval, its estimation difference and fluctuation also increase therewith Greatly.

The reason two above conclusion is analyzed as follows:

(1) conclusion 1 illustrates that the phase estimate method opening the bright moment based on green light has more practicality, this is because green light opens bright wink Between, queuing vehicle to sail out of close to saturation volume rate, queue clearance process stabilization, evanescent wave is close to definite value.Contrary, hot Lamp opens bright, and vehicle deceleration slowly stops, and queuing assembling process is unstable, and assembles ripple and reach change with upstream vehicle and change.

(2) conclusion 2 illustrate the increase with the sampling interval, phase estimate method accuracy of the present invention and robustness with Fall.This is because the sampling interval is bigger, estimate that the vehicle obtaining joins and departs from queuing key point precision and declines therewith.

Can obtain as drawn a conclusion from queue length error comparison diagram:

The queuing estimation difference of (1) 2 kind of algorithm is all as the increase of sample rate and declines；

(2) under low sampling rate, the estimation difference of the present invention is less than ramezani and geroliminis algorithm.But It is as the increase of sample rate, there is a marginal value so that ramezani and geroliminis algorithm is better than this Bright algorithm, and the increase with the sampling interval, threshold sampling rate is less, and (critical under 5s, 15s and 25s sampling interval is adopted Sample rate is respectively 47%, 40% and 20%).

The reason two above conclusion is analyzed as follows:

(1) conclusion 1 illustrates that two kinds of algorithms all can be made a response to the change of sample rate, under three kinds of sampling intervals, sampling The increase of rate all can provide the estimated accuracy of queue length；

(2) conclusion 2 explanation inventive algorithm is suitable for currently low sample frequency, the data environment of low sampling rate.

Claims (7)

1. a kind of signalized crossing queue length real-time estimation method based on track of vehicle it is characterised in that include with Lower step:

1) according to real-time vehicle trace information, carry out vehicle traffic condition differentiation；

2) according to real-time vehicle trace information, vehicle traffic condition and kinematical equation, carry out vehicle add queuing key point and Leave the crucial point estimation of queuing；

3) vehicle according to estimation adds queuing key point, carries out fleet's identification of upstream arrival；

4) vehicle according to estimation adds queuing key point, leaves queuing key point and identified fleet, carries out assembling ripple Estimate with evanescent wave；

5) according to the assembly ripple of estimation and evanescent wave, carry out intersection signal parameter and queue length is estimated.

2. the signalized crossing queue length real-time estimation method based on track of vehicle according to claim 1, its It is characterised by, described step 1) particularly as follows: obtaining track of vehicle information in real time, make i-th vehicle in t_kThe tracing point letter in moment Breath is expressed as Represent i-th vehicle in t respectively_kThe space coordinatess in moment, speed and acceleration Degree, then i-th vehicle is in t_kThe traffic behavior in momentFor:

$q_t^i\&element;\left\{\begin{array}{cc}m,& v_{t_k}^i>v_{th1}\\ c,& v_{t_k}^i\&element;\&lsqb;v_{th2},v_{th1})\\ s,& v_{t_k}^i<v_{th2}\end{array}\right.$

Wherein, v_th1And v_th2For the default threshold speed for state of motion of vehicle differentiation, v_th1＜ v_th2, m, c and s table respectively Show motion, low speed stop-go and three states of stopping.

3. the signalized crossing queue length real-time estimation method based on track of vehicle according to claim 2, its It is characterised by, described step 2) particularly as follows:

21) estimate that vehicle leaves queuing key point:

When i-th vehicle is in t_kAnd t_k+1The traffic status identification in moment isWithWhen, obtain corresponding tracing point InformationWith

Ifv_fFor free stream velocity, then i-th vehicle is in t_kMoment leave queuing key pointFor:

${\hat{t}}_{start}^{i,t}k=t_{k+1}-\frac{v_{t_{k+1}}^i}{a_{acc}}$

IfThen i-th vehicle is in t_kMoment leave queuing key pointFor:

${\hat{t}}_{start}^{i,t_k}=t_{k+1}-\frac{v_{t_{k+1}}^i}{2a_{acc}}-\frac{d_3}{v_{t_{k+1}}^i}$

Wherein, a_accFor i-th vehicle in t_kAnd t_k+1Acceleration between moment, is approximately equal tod₃For i-th vehicle in t_k And t_k+1In the distance between moment, it is equal to

22) estimation vehicle addition queuing key point:

When i-th vehicle is in t_k-1And t_kThe traffic status identification in moment isWithWhen, obtain corresponding tracing point InformationWith

IfThen i-th vehicle is in t_kThe addition queuing key point in momentFor:

${\hat{t}}_{stop}^{i,t_k}=t_{k-1}-\frac{v_{t_{k-1}}^i-v_{th1}}{2a_{dec}}+\frac{d_2-d_1}{v_{t_{k-1}}^i}$

IfThen i-th vehicle is in t_kThe addition queuing key point in momentFor:

${\hat{t}}_{stop}^{i,t_k}=t_{k-1}+\frac{2(d_2-d_1)}{v_{t_{k-1}}^i}$

When i-th vehicle is in t_k-1And t_kThe traffic status identification in moment isWithWhen, obtain corresponding tracing point InformationWith

IfThen i-th vehicle is in t_kThe addition queuing key point in momentFor:

${\hat{t}}_{stop}^{i,t_k}=t_{k-1}-\frac{v_{t_{k-1}}^i-v_k^i}{2a_{dec}}+\frac{d_2}{v_{t_{k-1}}^i}$

IfThen i-th vehicle is in t_kThe addition queuing key point in momentFor:

${\hat{t}}_{stop}^{i,t_k}=t_{k-1}+\frac{2d_2}{v_{t_{k-1}}^i}$

Wherein, a_decFor i-th vehicle in t_k-1And t_kAcceleration between moment, is approximately equal tod₁Exist for i-th vehicle t_k-1The distance between starting point, d under the tracing point in moment and low speed stop-go state₂Rise under low speed stop-go state The distance between initial point and terminating point.

4. the signalized crossing queue length real-time estimation method based on track of vehicle according to claim 3, its It is characterised by, described i-th vehicle is in t_k-1The tracing point in moment and the distance between starting point under low speed stop-go state d₁ Meet below equation:

$d_2=x_{t_k}^i-\frac{3(v_{th1}+v_{th2})}{2}-x_{t_{k-1}}^i$

Starting point and the distance between terminating point d under described low speed stop-go state₂Meet below equation:

$d_1=\frac{3(v_{th1}+v_{th2})}{2}.$

5. the signalized crossing queue length real-time estimation method based on track of vehicle according to claim 3, its It is characterised by, described step 3) particularly as follows:

31) queuing key point is added to the vehicle of estimationI=1 ..., n, n are the sum of vehicle, carry out ascending sort；

32) after obtaining ascending sort, Adjacent vehicles add the time difference of queuing key point and range difference, meet below equation:

$\mathrm{\&delta;}\hat{t}={\hat{t}}_{stop}^{i,t_k}-{\hat{t}}_{stop}^{i-1,t_k}$

${\mathrm{\&delta;x}}_i=x_{t_k}^i-x_{t_k}^{i-1}$

Wherein,Represent the time difference of i-th vehicle and the addition queuing key point of rear Adjacent vehicles,δ x_iRepresent the range difference of i-th vehicle and the addition queuing key point of rear Adjacent vehicles；

33) carry out fleet's identification of upstream arrival, particularly as follows:

Ifθ is fleet's judgment threshold, then i-th vehicle and rear Adjacent vehicles belong to a fleet, conversely, Do not belong to a fleet.

6. the signalized crossing queue length real-time estimation method based on track of vehicle according to claim 5, its It is characterised by, described step 4) particularly as follows:

41) add queuing estimation point and identified fleet according to estimating the vehicle that obtains in time interval j, carry out to assembling ripple Piecewise linear model matching, meets below equation:

$\underset{j}{\min }\underset{m=1}{\overset{\left|\right|n_j^s\left|\right|}{\&sigma;}}\underset{{\hat{t}}_{stop}^{i,t_k}\&element;\&lsqb;{\hat{t}}_{stop,m},{\hat{t}}_{stop,m+1}\&rsqb;}{\&sigma;}{\&lsqb;x_{t_k}^i-({\mathrm{\&omega;}}_{j,m}^s\&centerdot;{\hat{t}}_{stop}^{i,t_k}+{\mathrm{\&beta;}}_{j,m}^s)\&rsqb;}^2$

s.t.

$\begin{array}{cc}({\hat{t}}_{stop}^{i,t_k},x_{t_k}^i)\&element;n_j^s& \&forall;m=1,\mathrm{...},\left|\right|n_j^s\left|\right|\end{array}$

$x_m-({\mathrm{\&omega;}}_{j,m}^s\&centerdot;{\hat{t}}_{stop,m}+{\mathrm{\&beta;}}_{j,m}^s)=0$

$t_c^r\&le;{\hat{t}}_{stop}^{i,t_k},l_{stop-bar}\&greaterequal;x_{t_k}^i$

$\left\{\begin{array}{cc}{x}_{t_k}^i-({\mathrm{\&omega;}}_{j,m}^s\&centerdot;{\hat{t}}_{stop}^{i,t_k}+{\mathrm{\&beta;}}_{j,m}^s)\&greaterequal;-\mathrm{\&epsiv;}& \&forall;q_{t_k}^i\&element;m\\ x_{t_k}^i-({\mathrm{\&omega;}}_{j,m}^s\&centerdot;{\hat{t}}_{top}^{i,t_k}+{\mathrm{\&beta;}}_{j,m}^s)\&le;\mathrm{\&epsiv;}& \&forall;q_{t_k}^i\&element;c\&cup;s\end{array}\right.$

Wherein,Add the set of queuing estimation point, set for vehicles all in time interval jMiddle according to identified fleet It is divided intoIndividual fleet, m represents the numbering of fleet,Represent adding of m, m+1 fleet's headstock vehicle respectively Enter key point of queuing up, x_mRepresent and correspond toVehicle space coordinatess, It is respectively m section in time interval j to treat Estimate to assemble slope and the intercept of ripple,Open bright moment, l for corresponding entrance driveway red light_stop-barRepresent stop line position, ε For positive adjusting parameter, constrain hardness for adjustment；

Then assemble ripple expression formula in time interval jFor:

$y_j^s=\left\{\begin{array}{cc}{w}_{j,1}^{s}t+{\mathrm{\&beta;}}_{j,1}^s,& t<{\hat{t}}_{stop,1}\\ .& \\ .& \\ .& \\ w_{j,m}^{s}t+{\mathrm{\&beta;}}_{j,m}^s& t\&greaterequal;{\hat{t}}_{stop,m}\\ .& \\ .& \\ .& \\ w_{j,\left|\right|n_j^s\left|\right|}^{s}t+{\mathrm{\&beta;}}_{j,\left|\right|n_j^s\left|\right|}^s,& t\&greaterequal;{\hat{t}}_{stop,\left|\right|n_j^s\left|\right|}\end{array}\right.,m=1,\mathrm{...},\left|\right|n_j^s\left|\right|$

Wherein, t represents the moment；

42) queuing estimation point is left according to the vehicle estimating in time interval j to obtain, method of least square is carried out to evanescent wave linear Matching, meets below equation:

$\underset{j}{\min }\&sigma;{\&lsqb;x_{t_k}^i-({\mathrm{\&omega;}}_j^g\&centerdot;{\hat{t}}_{start}^{i,t_k}+{\mathrm{\&beta;}}_j^g)\&rsqb;}^2$

s.t.

$({\hat{t}}_{tart}^{i,t_k},x_{t_k}^i)\&element;n_j^g$

$\left\{\begin{array}{cc}{x}_{t_k}^i-({\mathrm{\&omega;}}_j^g\&centerdot;{\hat{t}}_{start}^{i,t_k}+{\mathrm{\&beta;}}_j^g)\&greaterequal;-\mathrm{\&epsiv;},& \&forall;q_{t_k}^i\&element;s\\ x_{t_k}^i-({\mathrm{\&omega;}}_j^g\&centerdot;{\hat{t}}_{start}^{i,t_k}+{\mathrm{\&beta;}}_j^g)\&le;\mathrm{\&epsiv;},& \&forall;q_{t_k}^i\&element;m\end{array}\right.$

Wherein,Leave the set of queuing estimation point for vehicles all in time interval j,It is respectively dissipation to be estimated The slope of ripple and intercept；

Then assemble ripple expression formula in time interval jFor:

$y_j^g=w_j^{g}t+{\mathrm{\&beta;}}_j^g.$

7. the signalized crossing queue length real-time estimation method based on track of vehicle according to claim 6, its It is characterised by, described step 5) particularly as follows:

51) obtain red light, green light in time interval j and open the bright momentWithMeet below equation:

$t_j^r=\frac{l_{stop-bar}-{\mathrm{\&beta;}}_{j,1}^s}{w_{j,1}^s}$

$t_j^g=\frac{l_{stop-bar}-{\mathrm{\&beta;}}_j^g}{w_j^g}$

Wherein, l_stop-barFor stop line position,Assemble the slope of ripple for first paragraph in time interval j and cut Away from；

52) obtain intersection signal parameter: the signal period t in time interval j_jWith respective inlets road green time pt_j, meet Below equation:

Or

${\mathrm{pt}}_j=t_j^g-t_j^r$

Wherein,Open the bright moment for the green light in time interval j-1,Open the bright moment for the red light in time interval j-1；

53) obtain the maximum queue length in current cycle estimatorAnd its correspond to the momentMeet below equation:

$q_j^{\max }=l_{stop-bar}-w_j^g\frac{{\mathrm{\&beta;}}_j^g-{\mathrm{\&beta;}}_{j,\left|\right|n_j^s\left|\right|}^s}{w_{j,\left|\right|n_j^s\left|\right|}^s-w_j^g}+{\mathrm{\&beta;}}_j^g$

$t_j^{\max }=\frac{{\mathrm{\&beta;}}_j^g-{\mathrm{\&beta;}}_{j,\left|\right|n_j^s\left|\right|}^s}{w_{j,\left|\right|n_j^s\left|\right|}^s-w_j^g}$

Wherein,It is respectively slope and the intercept that time interval j final stage assembles ripple；

54) obtain secondary queue lengthAnd correspond to the momentMeet below equation:

$q_j^{re}=l_{stop-bar}-w_{j+1,1}^s(\frac{w_j^g(t_j^{\max }-t_j^g)}{w_j^g+v_f}+t_j^{\max }-t_{j+1}^r)$

$t_j^{re}=\frac{w_j^g(t_j^{\max }-t_j^g)}{w_j^g+v_f}+\frac{{\mathrm{\&beta;}}_j^g-{\mathrm{\&beta;}}_{j,\left|\right|n_j^s\left|\right|}^s}{w_{j,\left|\right|n_j^s\left|\right|}^s-w_j^g}$

Wherein,Assemble ripple slope for first paragraph in time interval j+1,Open the bright moment for red light in time interval j+1.