CN106023611A - Two-stage type trunk line coordination signal control optimization method - Google Patents

Abstract

The invention relates to a two-stage type trunk line coordination signal control optimization method. The method is applied to a coordination signal control system for trunk lines with or without left-turn short lanes. According to the method, with short lane space design considered, and a cycle length, green signal ratio and short lane length optimization model is established; with the short lane space design not considered, a cycle length and green signal ratio optimization model is established; according to an optimization objective, a function form with realizing minimum total delay of vehicles or total emissions of traffic adopted an objective is put forward; according to previous research, a vehicle average delay model HCM2000, a vehicle average delay model HCM1985 and a vehicle average delay model ARRB are selected; based on the specific power of motor vehicles, a calibration method of emission factors in red and green light durations is given; based on the reference of related literatures, a phase difference optimization method is improved; technical processes using the above models and methods are put forward according to different situations; and as indicated by results, the novel method of the invention is helpful to coordinately controlling a trunk line road system in order to reduce the total delay of the vehicles and the total emissions of traffic and can be widely used in trunk line coordination signal control optimization.

Description

A kind of two-part Trunk Road Coordination signal controls optimization method

Technical field

The invention belongs to intellectual traffic control field, relate to a kind of arterial road system being applicable to there is (no) short track of turning left The two-part Trunk Road Coordination signal of system, minimizing vehicle delay and exhaust emissions controls optimization method.

Background technology

At present, many cities are perplexed by traffic congestion and environmental pollution owing to vehicle guaranteeding organic quantity increases.Reduce One of hot issue that vehicle is delayed, minimizing traffic emission is traffic administration and control field gives more sustained attention in recent years.

In urban road network, it is frequently present of several crossings on a road and there is the strongest association each other Property, now must carry out arterial road system coordination optimization in units of traffic group.Because arterial road is city road network Main framing, so the operational efficiency of arterial road system plays vital effect to the service level of whole road network.Meanwhile, The emission level of arterial road system also has crucial effect to the air quality of whole road network.Therefore, for arterial road system It is the key issue being badly in need of solving that system reduce vehicle to greatest extent to be delayed, reduce traffic emission.

In recent years, domestic and overseas correlative development focuses primarily upon:

(1) use maximum green wave band method or minimum delay method, open by adjusting the green light coordinating phase place or non-coordinating phase place Begin or finish time, reduce vehicle delay and stop frequency, its technological deficiency coordinating direction on arterial road to greatest extent It is to have ignored coordination direction and the dependency in non-coordinating direction；

(2) vehicle mounted tail gas detection technique (PEMS) is used to obtain the vehicular emission data on urban road, with different rows The average emission factors sailing operating mode is measurement index, seeks the impact on vehicular emission amount of the traffic control scheme, and its technology lacks It is trapped in the difference of motor-driven vehicle going operating mode distribution characteristics during have ignored traffic lights；

(3) utilize traffic simulation software or model of atmospheric diffusion, set up the signal timing optimization model considering traffic emission, Seeking to minimize the signal timing plan of vehicular emission amount, its technological deficiency is that emission factor used does not accounts for traffic letter Number impact；

(4) the studies above have ignored short track arrange on vehicle be delayed and the impact of traffic emission.

Having studied display, when motor vehicles is in different driving cycle, its exhaust emissions amount is widely different, and the traffic lights phase Between motor vehicles be in the distribution of various driving cycle there is notable difference.Research based on single crossing signal timing optimization becomes Really, the present invention is towards the arterial road system there is (no) short track of turning left, the emission factor during every track group traffic lights For parameter, propose the two-part Trunk Road Coordination signal that vehicle is delayed or traffic emission minimizes and control optimization method.

Summary of the invention

The invention provides a kind of vehicle that reduces to be delayed and the two-part Trunk Road Coordination signal control optimization side of traffic emission Method, reduces vehicle delay and the exhaust emissions of arterial road system to greatest extent for the transport need of phase same level.

1, cycle duration, split and short lane length Optimized model

If it is considered that short track spatial design, the cycle duration set up, split with short lane length Optimized model are

In formula: PI is arterial road system performance index；Effective green time (s) for crossing η phase place i；For The short lane length (m) of η track, crossing group j；n^ηNumber of phases for crossing η；For η track, crossing group j in phase place i Whether there is the identifier of right-of-way, ifOtherwiseg_minFor minimum effective green time (s)；C_minFor Xiao Zhou Phase duration (s)；Independent phase number for crossing η；L is average phase lost time (s)；C_maxFor maximum cycle duration (s)；C_cFor shared cycle duration (s)；For average saturation headway (s)；For average parking space (m)；For crossing η Whether track group j is provided with the identifier in short track, ifOtherwise Total road for crossing η Yu η+1 Segment length (m)；The whether identifier on total section for η track, crossing group j ', ifOtherwise

The phase place effective green time that decision variable is each crossing of formula (1) and short lane length.Wherein, object function (a1) expression minimizes the arterial road system performance index determined by phase place effective green time and short lane length；Constraint bar Part (b1) represents that track group effective green time is not less than minimum limit value；Constraints (b2) represents intersection signal cycle duration Not less than minimum limit value, it is not more than ceiling value；Constraints (b3) represents that the signal period duration of all crossings is the most equal (the most not considering binary cycle or half period)；Constraints (b4) represents the effective green time of the track group being provided with short track not The required time is discharged completely less than queuing vehicle on this short track；Constraints (b5) represents that Adjacent Intersections has section On short lane length sum less than the length in this total section；Constraints (c1) represents that phase place effective green time is Nonnegative number；Constraints (c2) represents that short lane length is nonnegative number.

2, cycle duration and Split Optimization model

Discounting for short track spatial design, the cycle duration set up with Split Optimization model is

$\begin{array}{ccc}\min & PI=f\left(g_{pi}^{\mathrm{\η}}\right)& \left(a2\right)\\ s.t.& \underset{i=1}{\overset{n^{\mathrm{\η}}}{\Σ}}{\mathrm{\φ}}_{ij}^{\mathrm{\η}}{g}_{pi}^{\mathrm{\η}}\≥g_{\min }& \left(b1\right)\\ & C_{\min }\≤\underset{i=1}{\overset{n^{\mathrm{\η}}}{\Σ}}{g}_{pi}^{\mathrm{\η}}+n_d^{\mathrm{\η}}l\≤C_{\max }& \left(b2\right)\\ & \underset{i=1}{\overset{n^{\mathrm{\η}}}{\Σ}}{g}_{pi}^{\mathrm{\η}}+n_d^{\mathrm{\η}}l=C_c& \left(b3\right)\\ & g_{pi}^{\mathrm{\η}}\≥0& \left(c1\right)\end{array}---\left(2\right)$

The same formula of each symbolic significance (1) in formula (2), wherein decision variable is the phase place effective green time of each crossing, mesh Scalar functions (a2) expression minimizes the arterial road system performance index determined by phase place effective green time, constraints (b1), the same formula of (b2), (b3) and (c1) meaning (1).

3, object function selects

For formula (1) and (2), the concrete form of object function (a1) and (a2) includes following three kinds:

Wherein:

In formula: ψ is crossing number；TD^ηGross vehicle for crossing η is delayed (s)；m^ηTrack group number for crossing η；Average traffic delay (s/pcu) for η track, crossing group j；For Motor vehicle category number；β_ωConversion system for ω class motor vehicles Number；For ω class motor vehicles proportion in group j of η track, crossing；Demand flow rate (veh/ for η track, crossing group j h)；T is analysis persistent period phase (h)；TE^ηVehicular emission total amount (mg) for crossing η；κ is pollutant kind number； For the quality (mg) of ω class motor vehicle emission pollutant k in group j of η track, crossing；For ω in group j of η track, crossing Class motor vehicles discharges pollutants the factor (mg/s/veh) of k during green light；For ω class machine in group j of η track, crossing Motor-car discharges pollutants the factor (mg/s/veh) of k during red light；Effective green time for η track, crossing group j (s)；Mean residence time (s) for the upper ω class motor vehicles of η track, crossing group j；For η track, crossing group j Entrance driveway length (m)；For the average overall travel speed (m/s) of ω class motor vehicles in group j of η track, crossing.

Formula (3) represents the total delay minimizing all vehicles；Formula (4) represents the total discharge minimizing all vehicles；Formula (5) Represent and minimize the total delay of all vehicles and total discharge simultaneously.

4, it is delayed formula to select

For formula (1) and (2), the formula calculating every track group average traffic delay includes that following three kinds (are omitted crossing to compile Number):

$d_j=\frac{0.5C_c{\left(1-{\mathrm{\λ}}_j\right)}^2}{1-\min \left(1,x_j\right){\mathrm{\λ}}_j}\×{\mathrm{PF}}_j+900T\[\left(x_j-1\right)+\sqrt{\left(x_j-1\right)+\frac{8{\mathrm{KI}}_j{x}_j}{c_{j}T}}\]+1800q_j\left(1+u_j^{\′}\right)t_j^{\′}/\left(c_{j}T\right)---\left(6\right)$

$d_j=\frac{0.38C_c{(1-{\mathrm{\λ}}_j)}^2}{(1-{\mathrm{\λ}}_j{x}_j)}+173{x_j}^2\[(x_j-1)+\sqrt{{(x_j-1)}^2+16x_j/c_j}\]---\left(7\right)$

$d_j=\left\{\begin{array}{cc}\frac{C_c{(1-{\mathrm{\λ}}_j)}^2}{2(1-y_j)}+\frac{c_j{x}_{j}T}{4q_j^{\′}}\[(x_j-1)+\sqrt{{(x_j-1)}^2+\frac{12(x_j-x_{0j})}{c_{j}T}}\],& x_j>x_{0j}\\ \frac{C_c{(1-{\mathrm{\λ}}_j)}^2}{2(1-y_j)},& x_j\≤x_{0j}\end{array}\right.---\left(8\right)$

Wherein:

In formula: d_jAverage traffic delay (s/pcu) for track group j；PF_jSignal linkage correction factor for track group j；r′_jFor Fleet's ratio of track group j；f_jThe correction factor that queue arrives is become for vehicle during the group j green light of track；K is signal Control Cooling Delay correction factor；I_jUpstream regulation incremental delay correction factor for track group j；X_jThere is tribute all upstreams for track group j Offer wagon flow and be weighted the saturation of gained by flow；Q_jFor analyzing initial queuing vehicle number (pcu) in group j of track；u′_jFor The delay parameter of track group j；t′_jThe time (h) of transport need can not be met for analyzing phase inside lane group j；c_jFor track group j The traffic capacity (pcu/h)；λ_jSplit for track group j；x_jSaturation for track group j；y_jFlow-rate ratio for track group j； SF_jComplete track saturation volume rate (pcu/h) for track group j；The identifier in short track whether it is provided with for track group j, ifOtherwiseSS_jShort track saturation volume rate (pcu/h) for track group j；L_jShort lane length for track group j (m)；g_jEffective green time (s) for track group j；G_jDisplay green time (s) for track group j；l_sFor front lost time (s)；E is post-compensation time (s)；q′_jStandard car demand flow rate (pcu/s) for track group j；S′_jWorking as track group j Amount saturation volume rate (pcu/s)；x_0jThe saturation of track group j when queuing is approximately 0 is overflowed for average.

Formula (6)～(8) are respectively HCM2000, HCM1985 and ARRB and are delayed formula.

5, during traffic lights, emission factor is demarcated

As follows for the calibration formula of emission factor during formula (1) and (2), traffic lights:

Wherein:

In formula:Discharge pollutants the quality (mg) of k for vehicle ζ in moment t crossing η track group j；For ω class The emission factor (mg/s/veh) of pollutant k when the specific power of motor vehicles is positioned at subregion γ；τ is adopting of car speed and acceleration The resolution (s) of sample time interval；For sailing out of the ω class of stop line during green light in moment t crossing η track group j Motor vehicles number (veh)；For sailing out of the ω class motor vehicles number of stop line during red light in moment t crossing η track group j (veh)；O_ηThe absolute green time difference (s) for crossing η；Green light for η track, crossing group j plays bright moment (s)；For Green light finish time (s) of η track, crossing group j；For the category attribute of vehicle ζ in moment t crossing η track group j；For the specific power (kW/t) of vehicle ζ in moment t crossing η track group j；LVSP_ω,γDivide for ω class vehicle specific power The lower limit (kW/t) of district γ；UVSP_ω,γThe upper limit (kW/t) for ω class vehicle specific power subregion γ；Intersect for moment t The speed (m/s) of vehicle ζ in group j of mouth η track；For the acceleration (m/s of vehicle ζ in moment t crossing η track group j²)；Road grade (°) for η track, crossing group j.

6, phase difference optimization method

After the formula of use (1) obtains the best of breed of shared cycle duration, split and short lane length, or make Obtain the best of breed sharing cycle duration and split by formula (2) after, following method is used to optimize phase contrast:

$\begin{array}{cc}\min & D_{\mathrm{\η}+1}^d+D_{\mathrm{\η}+1}^u=f\left(o_{\mathrm{\η},\mathrm{\η}+1}\right)\end{array}---\left(10\right)$

Wherein:

In formula:Fleet for crossing η+1 descending coordination direction is delayed (s)；For the up coordination of crossing η+1 The fleet in direction is delayed (s)；O_η,η+1For the descending coordination direction crossing η+1 green time difference (s) of ideal relative to η；s_η,η+1For handing over Stop line spacing (m) of prong η to η+1；v_η,η+1Descending speed (m/s) for crossing η to η+1；o_η,η+1For descending coordination side To crossing η+1 green time difference (s) of the reality relative to η.

IfWhenDescending coordination direction Fleet be delayed beWhenThe fleet in descending coordination direction is delayedWhenThe fleet in descending coordination direction is delayed

In formula:Fleet's head car due in for crossing η+1 descending coordination direction is the reddest The time interval (s) of lamp finish time；Fleet vehicle number (pcu) for crossing η to η+1；For crossing η+1 time Row coordinates the saturation volume rate (pcu/s) in direction；Standard car demand flow rate for crossing η+1 descending coordination direction (pcu/s)；Effective green time (s) for crossing η+1 descending coordination direction；For crossing η+1 time Row coordinates effective red time (s) in direction.

IfIfOrderWhenUnder Row coordinates fleet's delay in directionWhenDescending The fleet's delay coordinating direction isWhen The fleet in descending coordination direction is delayed

In formula:Red light for crossing η+1 descending coordination direction opens bright Moment is to the time interval (s) of fleet's trailer due in.

The fleet in up coordination direction is delayedComputational methods similar with descending coordination direction.

7, techniqueflow

If it is considered that short track spatial design, idiographic flow is as follows: (I), for each control time, uses formula (1) to determine Optimal shared cycle duration, split and short lane length；(II) by day part optimize short lane length maximum or 85% quantile, as the design load of short lane length, determines space, short track；(III) on the basis of (II), for each Control time, uses formula (2) to determine optimal shared cycle duration and split；(IV) on the basis of (III), for each Control time, uses formula (10) to determine optimal phase contrast.

Discounting for short track spatial design, idiographic flow is as follows: (I), for each control time, uses formula (2) true Fixed optimal shared cycle duration and split；(II) on the basis of (I), for each control time, use formula (10) true Fixed optimal phase contrast.

Without arranging short track, making short track saturation volume rate is 0, and idiographic flow is as follows: when (I) is for each control Section, uses formula (1) or (2) to determine optimal shared cycle duration and split；(II) on the basis of (I), for each control Period processed, formula (10) is used to determine optimal phase contrast.

If object function uses formula (4) or (5), before the formula of use (1) or (2), need use formula (9) for every Track group demarcates the emission factor during traffic lights.

Accompanying drawing explanation

Fig. 1 is arterial road system schematic.

Fig. 2 is that single crossing track arranges schematic diagram.

Fig. 3 (a) is East and West direction special left turn phase design schematic diagram.

Fig. 3 (b) is the straight left Signal Phase Design scheme schematic diagram of East and West direction entrance driveway.

Fig. 3 (c) is the preposition left-hand rotation of East and West direction+rearmounted left turn phase design schematic diagram.

Fig. 3 (d) is the special left-hand rotation of East and West direction+preposition left turn phase design schematic diagram.

Fig. 4 is intersection signal phasing scheme schematic diagram.

As a example by Fig. 1, arterial road system is made up of 3～8 crossings on arterial road, and each intersection type is three Road, four roads or five tunnels, every road can be all or part of one way traffic.

As a example by simple intersection shown in Fig. 2, equal canalization 1 left-hand rotation short track, 1 left-hand rotation special-purpose vehicle on every entrance driveway Runway is mixed on road, 1 Through Lane and 1 straight right side.Assuming that be all not provided with right-hand rotation special signal lamp on all entrance driveway, enter westerly Mouth starts, in the direction of the clock to the left turn traffic in Fig. 2 numbered M1, M3, M5 and M7, the straight right wagon flow conflicted with it respectively Numbered M2, M4, M6 and M8 respectively.Any entrance driveway in this crossing, short track of turning left, left-hand rotation dedicated Lanes or Through Lane can With more than 1, it is also possible to without short track of turning left, left-hand rotation dedicated Lanes, Through Lane or straight right lane, it is also possible to there is right-hand rotation specially Use track.

East and West direction or north-south to any crossing, signal phase scheme can select special left-hand rotation (Fig. 3 a), import Road directly left (Fig. 3 b), preposition left-hand rotation+rearmounted left-hand rotation (Fig. 3 c) or special left-hand rotation+preposition any one mode of left-hand rotation (Fig. 3 d), as Shown in Fig. 3 (as a example by East and West direction).If a certain crossing expands to five crossings, tunnel, its wagon flow number may increase, signal phase Position scheme may be more complicated.If a certain crossing is reduced to situation or the three-way intersection of one way traffic, wagon flow number will reduce, Signal phase scheme may be simpler.

Fig. 4 is that intersection signal phasing scheme, East and West direction and north-south all use special left-hand rotation+preposition left-hand rotation mode.Real On border, each intersection signal phasing scheme should be configured according to crossing flow distribution feature.

Detailed description of the invention

1, transport need and vehicular emission data are gathered

Assuming that certain arterial road system comprises 3 crossings, each intersection channelizing scheme and signal phase scheme are the most such as Shown in Fig. 2 and 4, entrance driveway length is 50m, and the gradient of every road is 0, traffic flow consist of 70% car, 10% In-between car and 20% bus.Table 1 is hour flow of the per share wagon flow in each crossing and peak 15min flow rate in certain period.Respectively Import track saturation volume rate is determined by traffic study or practical experience, sets the full of left turn lane, Through Lane and straight right lane It is respectively 1810,1850 and 1810pcu/h with flow rate.

2, reference signal timing scheme is obtained

Use the traffic demand data in table 1, use Robert Webster method to calculate and coordinate signal control parameter.Table 2 is listed Shared cycle duration, each track group effective green time and each crossing phase contrast.

3, pollutants emission characteristics during traffic lights is demarcated

For the transport need in table 1, use the reference scheme in table 2, utilize VISSIM software to set up Traffic Flow Simulation Model, the real-time speed of each car and acceleration in acquisition system.Consider tri-kinds of common contaminant of CO, HC and NOx, according to motor-driven Car specific power partitioned parameters demarcates all kinds vehicle emission factor during traffic lights.Here simulation time takes 4200s, adopts Sample time interval takes 1s, and system warm-up time takes 600s, starts to gather data from 601s until 4200s.Use many operational modes Emulate and eliminate random factor impact for 5 times.For each type motor vehicles, various during calculating traffic lights respectively according to formula (9) The emission factor of pollutant, result is listed in table 3.

Table 3 shows, every kind of pollutant emission factor during green light is above its emission factor during red light, this One rule is unrelated with crossing, track group and motor vehicles type；Two class emission factors show extremely strong stability, and it is absolute Value is strongly depend on motor vehicles type.

Hour flow of the per share wagon flow in each crossing of table 1 and peak 15min flow rate

The reference scheme that signal controls coordinated by table 2

The emission factor of each pollutant during table 3 traffic lights

The emission factor (continued) of each pollutant during table 3 traffic lights

4, setting model parameter

The calibration value of each parameter involved during table 4 lists model optimization and in traffic simulation experimentation.

Parameter in table 4 model optimization and traffic simulation sets

5, the time-space distribution allocative decision of motor vehicles total release is minimized

As a example by object function selecting type (4), based on two class emission factors in table 3, formula (1) is used to obtain phase place effective Green time and the best of breed of short lane length, then use formula (10) to obtain optimum phase difference.Table 5 illustrates delay formula It is respectively adopted the optimal time-space distribution allocative decision of HCM2000, HCM1985 and ARRB gained.

Table 5 minimizes the time-space distribution allocative decision of motor vehicles total release

6, the signal timing optimization scheme of motor vehicles total release is minimized

According to table 5, set a length of 50m in every short track here.As a example by object function selecting type (4), based on table 3 In two class emission factors, use formula (2) obtain optimal phase place effective green time, then use formula (10) to obtain optimal phase Potential difference.Table 6 illustrates delay formula and is respectively adopted the Optimal Signals timing scheme of HCM2000, HCM1985 and ARRB gained.

Table 6 minimizes the signal time distributing conception of motor vehicles total release

Claims (1)

1. the two-part Trunk Road Coordination signal reducing vehicle delay and exhaust emissions controls optimization method, it is characterised in that Following steps:

(1) implementation condition

(1) the arterial road system being made up of 2 or more than 2 crossings；

(2) intersection type is three tunnels, four roads or five tunnels, and every entrance driveway arranges 2 or more than 2 tracks；

(3) it is not provided with controlling the independent signal of right-hand rotation wagon flow；

(4) each crossing arranges 2 or the signal phase of more than 2；

(2) cycle duration, split and short lane length Optimized model

For design space, short track, the cycle duration set up, split with short lane length Optimized model are

In formula: PI is arterial road system performance index；Effective green time (s) for crossing η phase place i；For intersecting The short lane length (m) of mouth η track group j；n^ηNumber of phases for crossing η；For η track, crossing group j in phase place i whether There is the identifier of right-of-way, ifOtherwiseg_minFor minimum effective green time (s)；C_minDuring for the minimum period Long (s)；Independent phase number for crossing η；L is average phase lost time (s)；C_maxFor maximum cycle duration (s)；C_c For shared cycle duration (s)；For average saturation headway (s)；S is average parking space (m)；For η track, crossing Whether group j is provided with the identifier in short track, ifOtherwise Total section for crossing η Yu η+1 is long Degree (m)；The whether identifier on total section for η track, crossing group j ', ifOtherwise

The phase place effective green time that decision variable is each crossing of formula (1) and short lane length；Wherein, object function (a1) Represent and minimize the arterial road system performance index determined by phase place effective green time and short lane length；Constraints (b1) represent that track group effective green time is not less than minimum limit value；Constraints (b2) represents intersection signal cycle duration not Less than minimum limit value, it is not more than ceiling value；Constraints (b3) represents that the signal period duration of all crossings is the most equal；About Bundle condition (b4) represents that the effective green time of the track group being provided with short track is released completely not less than queuing vehicle on this short track Put the required time；Constraints (b5) represents that the short lane length sum that Adjacent Intersections has on section is total to less than this There is the length in section；Constraints (c1) represents that phase place effective green time is nonnegative number；Constraints (c2) represents short car Road length is nonnegative number；

(3) cycle duration and Split Optimization model

For not designing space, short track, the cycle duration set up with Split Optimization model is

$\begin{array}{ccc}\min & PI=f\left(g_{pi}^{\mathrm{\η}}\right)& \left(a2\right)\\ s.t.& \underset{i=1}{\overset{n^{\mathrm{\η}}}{\Σ}}{\mathrm{\φ}}_{ij}^{\mathrm{\η}}{g}_{pi}^{\mathrm{\η}}\≥g_{\min }& \left(b1\right)\\ & C_{\min }\≤\underset{i=1}{\overset{n^{\mathrm{\η}}}{\Σ}}{g}_{pi}^{\mathrm{\η}}+n_d^{\mathrm{\η}}l\≤C_{\max }& \left(b2\right)\\ & \underset{i=1}{\overset{n^{\mathrm{\η}}}{\Σ}}{g}_{pi}^{\mathrm{\η}}+n_d^{n}l=C_c& \left(b3\right)\\ & g_{pi}^{\mathrm{\η}}\≥0& \left(c1\right)\end{array}---\left(2\right)$

The same formula of each symbolic significance (1) in formula (2), wherein decision variable is the phase place effective green time of each crossing, target letter Number (a2) represents and minimizes the arterial road system performance index determined by phase place effective green time, constraints (b1), (b2), the same formula of (b3) and (c1) meaning (1)；

(4) object function selects

For formula (1) and (2), the concrete form of object function (a1) and (a2) includes following three kinds:

Wherein:

In formula: ψ is crossing number；TD^ηGross vehicle for crossing η is delayed (s)；m^ηTrack group number for crossing η；For The average traffic delay (s/pcu) of η track, crossing group j；For Motor vehicle category number；β_ωConversion factor for ω class motor vehicles； For ω class motor vehicles proportion in group j of η track, crossing；Demand flow rate (veh/h) for η track, crossing group j；T is Analysis persistent period phase (h)；TE^ηVehicular emission total amount (mg) for crossing η；κ is pollutant kind number；For intersecting The quality (mg) of ω class motor vehicle emission pollutant k in group j of mouth η track；Motor-driven for ω class in group j of η track, crossing Car discharges pollutants the factor (mg/s/veh) of k during green light；Exist for ω class motor vehicles in group j of η track, crossing Discharge pollutants during red light the factor (mg/s/veh) of k；Effective green time (s) for η track, crossing group j；For The mean residence time (s) of the upper ω class motor vehicles of η track, crossing group j；Entrance driveway for η track, crossing group j is long Degree (m)；For the average overall travel speed (m/s) of ω class motor vehicles in group j of η track, crossing；

Formula (3) represents the total delay minimizing all vehicles；Formula (4) represents the total discharge minimizing all vehicles；Formula (5) represents Minimize the total delay of all vehicles and total discharge simultaneously；

(5) it is delayed formula to select

For formula (1) and (2), the formula calculating every track group average traffic delay includes following three kinds:

$d_j=\frac{0.5C_c{(1-{\mathrm{\λ}}_j)}^2}{1-\min (1,x_j){\mathrm{\λ}}_j}\×{\mathrm{PF}}_j+900T\[(x_j-1)+\sqrt{{(x_j-1)}^2+\frac{8{\mathrm{KI}}_j{x}_j}{c_{j}T}}\]+1800Q_j(1+u_j^{\′})t_j^{\′}/\left(c_{j}T\right)---\left(6\right)$

$d_j=\frac{0.38C_c{(1-{\mathrm{\λ}}_j)}^2}{(1-{\mathrm{\λ}}_j{x}_j)}+173{x_j}^2\[(x_j-1)+\sqrt{{(x_j-1)}^2+16x_j/c_j}\]---\left(7\right)$

$d_j=\left\{\begin{array}{cc}\frac{C_c{(1-{\mathrm{\λ}}_j)}^2}{2(1-y_j)}+\frac{c_j{x}_{j}T}{4q_j^{\′}}\[(x_j-1)+\sqrt{{(x_j-1)}^2+\frac{12\left(x_j-x_{0j}\right)}{c_{j}T}}\],& x_j>x_{0j}\\ \frac{C_c{(1-{\mathrm{\λ}}_j)}^2}{2(1-y_j)},& x_j\≤x_{0j}\end{array}\right.---\left(8\right)$

Wherein:

λ_j=g_j/C_c；g_j=G_j-l_s+e；y_j=q '_j/S′_j；

x_0j=0.67+S '_jg_j/600；

In formula: d_jAverage traffic delay (s/pcu) for track group j；PF_jSignal linkage correction factor for track group j；r′_jFor track Fleet's ratio of group j；f_jThe correction factor that queue arrives is become for vehicle during the group j green light of track；K is prolonging of signal Control Cooling Correction factor by mistake；I_jUpstream regulation incremental delay correction factor for track group j；X_jThere is contribution car all upstreams for track group j Stream is weighted the saturation of gained by flow；Q_jFor analyzing initial queuing vehicle number (pcu) in group j of track；u′_jFor track The delay parameter of group j；t′_jThe time (h) of transport need can not be met for analyzing phase inside lane group j；c_jPassing through for track group j Ability (pcu/h)；λ_jSplit for track group j；x_jSaturation for track group j；y_jFlow-rate ratio for track group j；SF_jFor Complete track saturation volume rate (pcu/h) of track group j；The identifier in short track whether it is provided with for track group j, if OtherwiseSS_jShort track saturation volume rate (pcu/h) for track group j；L_jShort lane length (m) for track group j；g_jFor The effective green time (s) of track group j；G_jDisplay green time (s) for track group j；l_sFor front lost time (s)；After e is Compensation time (s)；q′_jStandard car demand flow rate (pcu/s) for track group j；S′_jEquivalent saturation volume rate for track group j (pcu/s)；x_0jThe saturation of track group j when queuing is approximately 0 is overflowed for average；

Formula (6)～(8) are respectively HCM2000, HCM1985 and ARRB and are delayed formula；

(6) during traffic lights, emission factor is demarcated

As follows for the calibration formula of emission factor during formula (1) and (2), traffic lights:

Wherein:

${\mathrm{VSP}}_{j,\mathrm{\ζ}}^{\mathrm{\η}}\left(t\right)=v_{j,\mathrm{\ζ}}^{\mathrm{\η}}\left(t\right)\[1.1a_{j,\mathrm{\ζ}}^{\mathrm{\η}}\left(t\right)+9.8sin\left({\mathrm{\θ}}_j^{\mathrm{\η}}\right)+0.132\]+0.000302{\left(v_{j,\mathrm{\ζ}}^{\mathrm{\η}}\right(t\left)\right)}^3;$

In formula:Discharge pollutants the quality (mg) of k for vehicle ζ in moment t crossing η track group j；Motor-driven for ω class The emission factor (mg/s/veh) of pollutant k when the specific power of car is positioned at subregion γ；When τ is the sampling of car speed and acceleration Between interval resolution (s)；Motor-driven for sailing out of the ω class of stop line during green light in moment t crossing η track group j Car number (veh)；For sailing out of the ω class motor vehicles number of stop line during red light in moment t crossing η track group j (veh)；O_ηThe absolute green time difference (s) for crossing η；Green light for η track, crossing group j plays bright moment (s)；For Green light finish time (s) of η track, crossing group j；For the category attribute of vehicle ζ in moment t crossing η track group j；For the specific power (kW/t) of vehicle ζ in moment t crossing η track group j；LVSP_ω,γDivide for ω class vehicle specific power The lower limit (kW/t) of district γ；UVSP_ω,γThe upper limit (kW/t) for ω class vehicle specific power subregion γ；Intersect for moment t The speed (m/s) of vehicle ζ in group j of mouth η track；For the acceleration (m/s of vehicle ζ in moment t crossing η track group j²)；Road grade (°) for η track, crossing group j；

(7) phase difference optimization method

After the formula of use (1) obtains the best of breed of shared cycle duration, split and short lane length, or in the formula of use (2), after obtaining the best of breed sharing cycle duration and split, following method is used to optimize phase contrast:

$\begin{array}{cc}\min & D_{\mathrm{\η}+1}^d+D_{\mathrm{\η}+1}^u=f\left(o_{\mathrm{\η},\mathrm{\η}+1}\right)\end{array}---\left(10\right)$

Wherein:

In formula:Fleet for crossing η+1 descending coordination direction is delayed (s)；For crossing η+1 up coordination direction Fleet be delayed (s)；O_η,η+1For the descending coordination direction crossing η+1 green time difference (s) of ideal relative to η；s_η,η+1For crossing Stop line spacing (m) of η to η+1；v_η,η+1Descending speed (m/s) for crossing η to η+1；o_η,η+1Hand over for descending coordination direction The green time difference (s) of the prong η+1 reality relative to η；

IfWhenThe fleet in descending coordination direction Delay isWhen The fleet in descending coordination direction is delayedWhenDescending association The fleet adjusting direction is delayed

In formula:Fleet's head car due in for crossing η+1 descending coordination direction is tied to red light The time interval (s) in bundle moment；Fleet vehicle number (pcu) for crossing η to η+1；For the descending association of crossing η+1 Adjust the saturation volume rate (pcu/s) in direction；Standard car demand flow rate (pcu/ for crossing η+1 descending coordination direction s)；Effective green time (s) for crossing η+1 descending coordination direction；For the descending association of crossing η+1 Adjust effective red time (s) in direction；

IfIfOrderWhenDescending association The fleet adjusting direction is delayedWhenDescending The fleet's delay coordinating direction isWhenUnder Row coordinates fleet's delay in direction

In formula:Red light for crossing η+1 descending coordination direction opens the bright moment Time interval (s) to fleet's trailer due in；

The fleet in up coordination direction is delayedComputational methods similar with descending coordination direction；

(8) techniqueflow

For design space, short track, idiographic flow is as follows: (I), for each control time, uses formula (1) to determine optimal being total to With cycle duration, split and short lane length；(II) by maximum or 85% point of position of the short lane length of day part optimization Number, as the design load of short lane length, determines space, short track；(III) on the basis of (II), for each control time, Use formula (2) determines optimal shared cycle duration and split；(IV) on the basis of (III), for each control time, Use formula (10) determines optimal phase contrast；

For not designing space, short track, idiographic flow is as follows: (I), for each control time, uses formula (2) to determine optimal Share cycle duration and split；(II) on the basis of (I), for each control time, formula (10) is used to determine optimal Phase contrast；

When being not provided with short track, making short track saturation volume rate is 0, and idiographic flow is as follows: (I) is for each control Period, formula (1) or (2) is used to determine optimal shared cycle duration and split；(II) on the basis of (I), for each Control time, uses formula (10) to determine optimal phase contrast；

When object function uses formula (4) or (5), before the formula of use (1) or (2), need use formula (9) for every track group Demarcate the emission factor during traffic lights.