CN106023611B - A kind of two-part Trunk Road Coordination signal controls optimization method - Google Patents

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

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CN106023611B
CN106023611B CN201610442701.XA CN201610442701A CN106023611B CN 106023611 B CN106023611 B CN 106023611B CN 201610442701 A CN201610442701 A CN 201610442701A CN 106023611 B CN106023611 B CN 106023611B
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姚荣涵
张晓彤
许向辉
徐洪峰
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Dalian University of Technology
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Abstract

A kind of two-part Trunk Road Coordination signal control optimization method for reducing vehicle delay and exhaust emissions, suitable for the Trunk Road Coordination whistle control system there is (no) short track of turning left.Consider short track spatial design, establish cycle duration, split and short lane length Optimized model.Short track spatial design is not considered, establishes cycle duration and Split Optimization model.According to optimization purpose, it is proposed that be minimised as the functional form of target with vehicle total delay or traffic always discharge.According to early-stage Study, the average traffic delay model of tri- kinds of forms of HCM2000, HCM1985 and ARRB has been selected.Based on vehicle specific power, the scaling method of emission factor during red, green light is given.With reference to pertinent literature, phase difference optimization method is improved.For different situations, it is proposed that use above-mentioned model and the techniqueflow of method.As a result show, new method helps to coordinate to control arterial road system always to discharge to reduce vehicle total delay and traffic, can be widely used in the control optimization of Trunk Road Coordination signal.

Description

A kind of two-part Trunk Road Coordination signal controls optimization method
Technical field
The invention belongs to intellectual traffic control field, is related to a kind of arterial road system being applied to there is (no) short track of turning left System, the two-part Trunk Road Coordination signal control optimization method for reducing vehicle delay and exhaust emissions.
Background technology
At present, many cities are perplexed because vehicle guaranteeding organic quantity increases by traffic congestion and environmental pollution.Reduce Vehicle delay, reduction traffic emission are one of hot issues that traffic administration gives more sustained attention in recent years with control field.
In urban road network, be frequently present of several intersections on a road has very strong association each other Property, arterial road system coordination optimization must be now carried out 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 for being badly in need of solving that system reduces vehicle delay, reduces traffic emission to greatest extent.
In recent years, domestic and overseas correlative development focuses primarily upon：
(1) maximum green wave band method or minimum delay method are used, the green light for coordinating phase or non-coordinating phase by adjusting is opened Beginning or finish time, the vehicle delay for coordinating direction on arterial road and stop frequency, its technological deficiency are reduced to greatest extent It is to have ignored the correlation for coordinating direction and non-coordinating direction；
(2) the vehicular emission data on urban road are obtained using vehicle mounted tail gas detection technique (PEMS), not go together The average emission factors for sailing operating mode are measurement index, seek influence of the traffic control scheme to vehicular emission amount, and its technology lacks It is trapped in the difference of the motor-driven vehicle going operating mode distribution characteristics during it have ignored traffic lights；
(3) traffic simulation software or model of atmospheric diffusion are utilized, establishes the signal timing optimization model for considering traffic emission, Seek the signal timing plan of minimum vehicular emission amount, its technological deficiency is that emission factor used does not account for traffic letter Number influence；
(4) the studies above have ignored short track and set to vehicle delay and the influence of traffic emission.
Its exhaust emissions amount is widely different when existing studies have shown that motor vehicle is in different driving cycles, and the traffic lights phase Between the motor vehicle distribution that is in various driving cycles there is notable difference.Research based on single crossing signal timing optimization into Fruit, the present invention is towards the arterial road system there is (no) short track of turning left, with the emission factor during every track group traffic lights For parameter, vehicle delay or the two-part Trunk Road Coordination signal control optimization method that traffic emission minimizes are proposed.
The content of the invention
The invention provides a kind of two-part Trunk Road Coordination signal for reducing vehicle delay and traffic emission to control optimization side Method, the transport need for phase same level reduce the vehicle delay and exhaust emissions of arterial road system to greatest extent.
1st, cycle duration, split and short lane length Optimized model
If it is considered that short track spatial design, the cycle duration established, split and short lane length Optimized model are
In formula：PI is arterial road system performance index；For intersection η phases i effective green time (s)；For Intersection η tracks group j short lane length (m)；nηFor intersection η number of phases；It is intersection η tracks group j in phase i Whether the identifier of right-of-way is had, ifOtherwisegminFor minimum effective green time (s)；CminFor most Xiao Zhou Phase duration (s)；For intersection η independent phase number；L is that average phase loses the time (s)；CmaxFor maximum cycle duration (s)；CcTo share cycle duration (s)；For average saturation headway (s)；For average parking spacing (m)；For intersection η Whether track group j is provided with the identifier in short track, ifOtherwise For intersection η and η+1 shared road Segment length (m)；For intersection η tracks group j ' whether the identifier on shared section, ifOtherwise
Phase effective green time and short lane length of the decision variable of formula (1) for each intersection.Wherein, object function (a1) represent to minimize the arterial road system performance index determined by phase effective green time and short lane length；Constrain 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, no more than highest limit value；Constraints (b3) represents that the signal period duration of all intersections is all equal (not considering binary cycle or half period here)；Constraints (b4) represents the effective green time of the track group provided with short track not Less than the time required for queuing vehicle on the short track completely release；Constraints (b5) represents that Adjacent Intersections share section On short lane length sum be no more than the length in the shared section；Constraints (c1) represents that phase effective green time is Nonnegative number；Constraints (c2) represents that short lane length is nonnegative number.
2nd, cycle duration and Split Optimization model
Discounting for short track spatial design, the cycle duration established is with Split Optimization model
Each same formula of symbolic significance (1) in formula (2), wherein decision variable be each intersection phase effective green time, mesh Scalar functions (a2) represent to minimize the arterial road system performance index determined by phase effective green time, constraints (b1), the same formula of (b2), (b3) and (c1) meaning (1).
3rd, object function selects
For formula (1) and (2), object function (a1) and (a2) concrete form include following three kinds：
Wherein：
In formula：ψ is intersection number；TDηFor intersection η vehicle total delay (s)；mηFor intersection η track group number；For intersection η tracks group j average traffic delay (s/pcu)；For Motor vehicle category number；βωFor the conversion system of ω class motor vehicles Number；For ω class motor vehicle proportions on the group j of intersection η tracks；For intersection η tracks group j demand flow rate (veh/ h)；T is analysis duration phase (h)；TEηFor intersection η vehicular emission total amount (mg)；κ is pollutant kind number； For the quality (mg) of ω class motor vehicle emission pollutants k on the group j of intersection η tracks；For ω on the group j of intersection η tracks Class motor vehicle discharges pollutants the k factor (mg/s/veh) during green light；For ω class machines on the group j of intersection η tracks Motor-car discharges pollutants the k factor (mg/s/veh) during red light；For intersection η tracks group j effective green time (s)；For the mean residence time (s) of the upper ω class motor vehicles of intersection η tracks group j；For intersection η tracks group j's Entrance driveway length (m)；For the average overall travel speed (m/s) of ω class motor vehicles on the group j of intersection η tracks.
Formula (3) represents to minimize the total delay of all vehicles；Formula (4) represents to minimize total discharge of all vehicles；Formula (5) Represent to minimize the total delay of all vehicles and total discharge simultaneously.
4th, it is delayed formula selection
For formula (1) and (2), calculating the formula of every track group average traffic delay includes following three kinds (omission intersection volumes Number)：
Wherein：
In formula：djFor track group j average traffic delay (s/pcu)；PFjFor track group j signal linkage correction factor；r′jFor Track group j fleet's ratio；fjFor the correction factor that vehicle reaches into queue during the group j green lights of track；K is signal Control Cooling Delay correction factor；IjFor track group j upstream regulation incremental delay correction factor；XjThere is tribute all upstreams for track group j Offer the saturation degree that wagon flow is weighted gained by flow；QjTo analyze the queuing vehicle number (pcu) in beginning on the group j of track；u′jFor Track group j delay parameter；t′jThe time (h) of transport need can not be met for analysis phase inside lane group j；cjFor track group j's The traffic capacity (pcu/h)；λjFor track group j split；xjFor track group j saturation degree；yjFor track group j flow-rate ratio； SFjFor track group j complete track saturation volume rate (pcu/h)；The identifier in short track whether is provided with for track group j, ifOtherwiseSSjFor track group j short track saturation volume rate (pcu/h)；LjFor track group j short lane length (m)；gjFor track group j effective green time (s)；GjFor track group j display green time (s)；lsFor the preceding loss time (s)；E is the post-compensation time (s)；q′jFor track group j standard car demand flow rate (pcu/s)；S′jFor working as track group j Measure saturation volume rate (pcu/s)；x0jFor the average saturation degree for overflowing track group j when queuing is approximately 0.
Formula (6)~(8) are respectively HCM2000, HCM1985 and ARRB delay formula.
5th, emission factor is demarcated during traffic lights
For formula (1) and (2), the calibration formula of emission factor is as follows during traffic lights：
Wherein：
In formula：Discharge pollutants k quality (mg) for vehicle ζ on moment t intersection η track group j；For ω classes Pollutant k emission factor (mg/s/veh) when the specific power of motor vehicle is located at subregion γ；τ is adopting for car speed and acceleration The resolution ratio (s) of sample time interval；To sail out of the ω classes of stop line during green light on moment t intersection η track group j Motor vehicle number (veh)；To sail out of the ω class motor vehicle numbers of stop line during red light on moment t intersection η track group j (veh)；OηFor the intersection η absolute green time difference (s)；Bright moment (s) is played for intersection η tracks group j green light；For Intersection η tracks group j green light finish time (s)；For the category attribute of vehicle ζ on moment t intersection η track group j；For the specific power (kW/t) of vehicle ζ on moment t intersection η track group j；LVSPω,γFor ω classes vehicle specific power point Area γ lower limit (kW/t)；UVSPω,γFor the ω class vehicle specific power subregions γ upper limit (kW/t)；Intersect for moment t Vehicle ζ speed (m/s) on mouth η track group j；For the acceleration (m/s of vehicle ζ on moment t intersection η track group j2)；For intersection η tracks group j road grade (°).
6th, phase difference optimization method
After the best of breed for sharing cycle duration, split and short lane length is obtained using formula (1), or make After the best of breed for sharing cycle duration and split is obtained with formula (2), optimize phase difference using following methods：
Wherein：
In formula：It is delayed (s) for the descending fleets for coordinating direction of intersection η+1；For+1 up coordinations of intersection η Fleet's delay (s) in direction；Oη,η+1The preferable green time difference (s) for descending coordination direction intersection η+1 relative to η；sη,η+1To hand over Prong η to η+1 stop line spacing (m)；vη,η+1For intersection η to η+1 descending speed (m/s)；oη,η+1For descending coordination side The green time difference (s) of reality to intersection η+1 relative to η.
IfWhenDescending coordination direction Fleet delay beWhen The descending fleet for coordinating direction, which is delayed, isWhenDescending association The fleet in tune direction, which is delayed, is
In formula：It is the descending fleet's head car due ins for coordinating direction of intersection η+1 to red The time interval (s) of lamp finish time；For intersection η to η+1 fleet vehicle number (pcu)；For under intersection η+1 Row coordinates the saturation volume rate (pcu/s) in direction；For the descending standard car demand flow rates for coordinating direction of intersection η+1 (pcu/s)；For the descending effective green times (s) for coordinating direction of intersection η+1；For under intersection η+1 Row coordinates effective red time (s) in direction.
IfIfOrderWhenUnder The fleet in row coordination direction, which is delayed, isWhenUnder The fleet in row coordination direction, which is delayed, isWhenThe descending fleet for coordinating direction, which is delayed, is
In formula：Opened for the descending red lights for coordinating direction of intersection η+1 bright Moment to fleet's trailer due in time interval (s).
The up fleet's delay for coordinating directionComputational methods with it is descending coordination direction it is similar.
7th, techniqueflow
If it is considered that short track spatial design, idiographic flow are as follows：(I) each control time is directed to, is determined using formula (1) Optimal shared cycle duration, split and short lane length；(II) by day part optimization short lane length maximum or Design load of 85% quantile as short lane length, determine short track space；(III) on the basis of (II), for each Control time, optimal shared cycle duration and split are determined using formula (2)；(IV) on the basis of (III), for each Control time, optimal phase difference is determined using formula (10).
It is as follows discounting for short track spatial design, idiographic flow：(I) each control time is directed to, it is true using formula (2) Fixed optimal shared cycle duration and split；(II) it is true using formula (10) for each control time on the basis of (I) Fixed optimal phase difference.
If being not provided with short track, it is 0 to make short track saturation volume rate, and idiographic flow is as follows：(I) when for each control Section, optimal shared cycle duration and split are determined using formula (1) or (2)；(II) on the basis of (I), for each control Period processed, optimal phase difference is determined using formula (10).
If object function uses formula (4) or (5), it is necessary to be directed to every using formula (9) before using formula (1) or (2) Emission factor during the group demarcation traffic lights of track.
Brief description of the drawings
Fig. 1 is arterial road system schematic.
Fig. 2 is that single crossing track sets schematic diagram.
Fig. 3 (a) is the special left turn phase design schematic diagram of East and West direction.
Fig. 3 (b) is East and West direction entrance driveway directly left Signal Phase Design scheme schematic diagram.
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.
By taking Fig. 1 as an example, arterial road system is made up of 3~8 intersections on arterial road, and each intersection type is three Road, four tunnels or five tunnels, every road can be all or part of one way traffic.
1 turn left short track, 1 left-hand rotation special-purpose vehicle are canalized by taking simple intersection shown in Fig. 2 as an example, on every entrance driveway The straight right mixed runway of road, 1 Through Lane and 1.It is assumed that being not provided with right-hand rotation special signal lamp on all entrance driveway, enter westerly Mouthful start, it is M1, M3, M5 and M7 that the left turn traffic in Fig. 2 is numbered respectively in the direction of the clock, the straight right wagon flow to conflict with it Numbering is M2, M4, M6 and M8 respectively.Any entrance driveway in the intersection, turning left short track, left-hand rotation dedicated Lanes or Through Lane can More than 1, can also can also exist and turn right specially without short track, left-hand rotation dedicated Lanes, Through Lane or the straight right lane of turning left Use track.
East and West direction or north-south to any intersection, signal phase scheme can select special left-hand rotation (Fig. 3 a), import Road straight left (Fig. 3 b), preposition left-hand rotation+rearmounted left-hand rotation (Fig. 3 c) or special left-hand rotation+preposition left-hand rotation (Fig. 3 d) any one mode, such as Shown in Fig. 3 (by taking East and West direction as an example).If a certain intersection expands to five tunnel intersections, its wagon flow number may increase, signal phase Position scheme may be more complicated.If a certain intersection is reduced to the situation or three-way intersection of one way traffic, wagon flow number will be reduced, Signal phase scheme may be simpler.
Fig. 4 is intersection signal phasing scheme, and East and West direction and north-south are using special left-hand rotation+preposition left-hand rotation mode.It is real On border, each intersection signal phasing scheme should be configured according to intersection flow distribution feature.
Embodiment
1st, transport need and vehicular emission data are gathered
It is assumed that certain arterial road system includes 3 intersections, each intersection channelizing scheme and signal phase scheme are respectively such as Shown in Fig. 2 and 4, entrance driveway length is 50m, and the gradient of every road is 0, and traffic flow composition is 70% car, 10% In-between car and 20% bus.Table 1 is the hour flow of each per share wagon flow in intersection and peak 15min flow rates 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.
2nd, reference signal timing scheme is obtained
Using the traffic demand data in table 1, calculated using Robert Webster method and coordinate signal control parameter.Table 2 is listed Shared cycle duration, each track group effective green time and each intersection phase difference.
3rd, pollutants emission characteristics during demarcation traffic lights
For the transport need in table 1, using the reference scheme in table 2, Traffic Flow Simulation is established using VISSIM softwares Model, the real-time speed and acceleration of each car in acquisition system.Tri- kinds of common contaminants of CO, HC and NOx are considered, according to motor-driven Car specific power partitioned parameters demarcate emission factor of all kinds vehicle during traffic lights.Here simulation time takes 4200s, adopts Sample time interval takes 1s, and system warm-up time takes 600s, and gathered data is up to 4200s since 601s.Use more operational modes Emulate 5 times influences to eliminate enchancement factor.It is various during calculating traffic lights respectively according to formula (9) for each type motor vehicle The emission factor of pollutant, as a result it is listed in table 3.
Table 3 shows that every kind of pollutant is above its emission factor during red light in the emission factor during green light, this One rule is unrelated with intersection, track group and motor vehicle type；Two class emission factors show extremely strong stability, and its is absolute Value is strongly depend on motor vehicle type.
The hour flow of the per share wagon flow in each intersection of table 1 and peak 15min flow rates
Table 2 coordinates the reference scheme of signal control
The emission factor of each pollutant during the traffic lights of table 3
The emission factor (continued) of each pollutant during the traffic lights of table 3
4th, setting model parameter
Table 4 lists the calibration value of each parameter involved during model optimization and in traffic simulation experimentation.
Parameter setting in the model optimization of table 4 and traffic simulation
5th, the time-space distribution allocative decision of motor vehicle total release is minimized
By taking object function selecting type (4) as an example, based on two class emission factors in table 3, it is effective to obtain phase using formula (1) The best of breed of green time and short lane length, then obtain optimum phase difference using formula (10).Table 5 illustrates delay formula The optimal time-space distribution allocative decision obtained by HCM2000, HCM1985 and ARRB is respectively adopted.
Table 5 minimizes the time-space distribution allocative decision of motor vehicle total release
6th, the signal timing optimization scheme of motor vehicle total release is minimized
According to table 5, the length in every short track is set here as 50m.By taking object function selecting type (4) as an example, based on table 3 In two class emission factors, obtain optimal phase effective green time using formula (2), then obtain optimal phase using formula (10) Potential difference.Table 6 illustrates delay formula and Optimal Signals timing scheme obtained by HCM2000, HCM1985 and ARRB is respectively adopted.
Table 6 minimizes the signal time distributing conception of motor vehicle total release

Claims (1)

  1. A kind of 1. two-part Trunk Road Coordination signal control optimization method for reducing vehicle delay and exhaust emissions, it is characterised in that Following steps：
    (1) implementation condition
    (1) the arterial road system being made up of 2 or more than 2 intersections；
    (2) intersection type is three tunnels, four tunnels or five tunnels, and 2 or more than 2 tracks are set on every entrance driveway；
    (3) it is not provided with controlling the independent signal of right-hand rotation wagon flow；
    (4) each intersection sets the signal phase of 2 or more than 2；
    (2) cycle duration, split and short lane length Optimized model
    For designing short track space, the cycle duration established, split and short lane length Optimized model are
    In formula：PI is arterial road system performance index；For intersection η phases i effective green time (s)；To intersect Mouth η track group j short lane length (m)；nηFor intersection η number of phases；For intersection η tracks group j in phase i whether There is the identifier of right-of-way, ifOtherwisegminFor minimum effective green time (s)；CminFor the minimum period when Long (s)；For intersection η independent phase number；L is that average phase loses the time (s)；CmaxFor maximum cycle duration (s)；Cc To share cycle duration (s)；For average saturation headway (s)；For average parking spacing (m)；For intersection η tracks Whether group j is provided with the identifier in short track, ifOtherwise Grown for intersection η and η+1 shared section Spend (m)；For intersection η tracks group j ' whether the identifier on shared section, ifOtherwise
    Phase effective green time and short lane length of the decision variable of formula (1) for each intersection；Wherein, object function (a1) Represent to minimize the arterial road system performance index determined by phase 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, no more than highest limit value；Constraints (b3) represents that the signal period duration of all intersections is all equal；About Beam condition (b4) represents that the effective green time of the track group provided with short track is released completely not less than queuing vehicle on the short track Put the required time；It is common no more than this that constraints (b5) represents that Adjacent Intersections share the short lane length sum on section There is the length in section；Constraints (c1) represents that phase 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 short track space, the cycle duration established is with Split Optimization model
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    Each same formula of symbolic significance (1) in formula (2), wherein decision variable be each intersection phase effective green time, target letter The arterial road system performance index that number (a2) expression minimum is determined by phase effective green time, constraints (b1), (b2), the same formula of (b3) and (c1) meaning (1)；
    (4) object function selects
    For formula (1) and (2), object function (a1) and (a2) concrete form include following three kinds：
    Wherein：
    In formula：ψ is intersection number；TDηFor intersection η vehicle total delay (s)；mηFor intersection η track group number；For Intersection η tracks group j average traffic delay (s/pcu)；For Motor vehicle category number；βωFor the conversion factor of ω class motor vehicles； For ω class motor vehicle proportions on the group j of intersection η tracks；For intersection η tracks group j demand flow rate (veh/h)；T is Analysis duration phase (h)；TEηFor intersection η vehicular emission total amount (mg)；κ is pollutant kind number；To intersect ω class motor vehicle emission pollutants k quality (mg) on mouth η track group j；It is motor-driven for ω classes on the group j of intersection η tracks Car discharges pollutants the k factor (mg/s/veh) during green light；Exist for ω class motor vehicles on the group j of intersection η tracks Discharge pollutants the k factor (mg/s/veh) during red light；For intersection η tracks group j effective green time (s)；For The mean residence time (s) of the upper ω class motor vehicles of intersection η tracks group j；Grown for intersection η tracks group j entrance driveway Spend (m)；For the average overall travel speed (m/s) of ω class motor vehicles on the group j of intersection η tracks；
    Formula (3) represents to minimize the total delay of all vehicles；Formula (4) represents to minimize total discharge of all vehicles；Formula (5) represents The total delay of all vehicles and total discharge are minimized simultaneously；
    (5) it is delayed formula selection
    For formula (1) and (2), calculating the formula of every track group average traffic delay includes following three kinds：
    <mrow> <msub> <mi>d</mi> <mi>j</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mn>0.5</mn> <msub> <mi>C</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;lambda;</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <mi>min</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;lambda;</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mo>&amp;times;</mo> <msub> <mi>PF</mi> <mi>j</mi> </msub> <mo>+</mo> <mn>900</mn> <mi>T</mi> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mfrac> <mrow> <mn>8</mn> <msub> <mi>KI</mi> <mi>j</mi> </msub> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mrow> <msub> <mi>c</mi> <mi>j</mi> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </msqrt> <mo>&amp;rsqb;</mo> <mo>+</mo> <mn>1800</mn> <msub> <mi>Q</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msubsup> <mi>u</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> <mo>)</mo> </mrow> <msubsup> <mi>t</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> <mo>/</mo> <mrow> <mo>(</mo> <msub> <mi>c</mi> <mi>j</mi> </msub> <mi>T</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>d</mi> <mi>j</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mn>0.38</mn> <msub> <mi>C</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;lambda;</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;lambda;</mi> <mi>j</mi> </msub> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mfrac> <mo>+</mo> <mn>173</mn> <msup> <msub> <mi>x</mi> <mi>j</mi> </msub> <mn>2</mn> </msup> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mn>16</mn> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>/</mo> <msub> <mi>c</mi> <mi>j</mi> </msub> </mrow> </msqrt> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>d</mi> <mi>j</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>C</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;lambda;</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>y</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>c</mi> <mi>j</mi> </msub> <msub> <mi>x</mi> <mi>j</mi> </msub> <mi>T</mi> </mrow> <mrow> <mn>4</mn> <msubsup> <mi>q</mi> <mi>j</mi> <mo>&amp;prime;</mo> </msubsup> </mrow> </mfrac> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mfrac> <mrow> <mn>12</mn> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mn>0</mn> <mi>j</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>c</mi> <mi>j</mi> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>&gt;</mo> <msub> <mi>x</mi> <mrow> <mn>0</mn> <mi>j</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>C</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&amp;lambda;</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>y</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>&amp;le;</mo> <msub> <mi>x</mi> <mrow> <mn>0</mn> <mi>j</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    Wherein：
    λj=gj/Cc；gj=Gj-ls+e；yj=qj′/Sj′；
    x0j=0.67+Sj′gj/600；
    In formula：djFor track group j average traffic delay (s/pcu)；PFjFor track group j signal linkage correction factor；rj' it is track Group j fleet's ratio；fjFor the correction factor that vehicle reaches into queue during the group j green lights of track；K is prolonging for signal Control Cooling Correction factor by mistake；IjFor track group j upstream regulation incremental delay correction factor；XjAll upstreams for track group j contribute car Stream is weighted the saturation degree of gained by flow；QjTo analyze the queuing vehicle number (pcu) in beginning on the group j of track；uj' it is track Group j delay parameter；tj' it is the time (h) that analysis phase inside lane group j can not meet transport need；cjFor the current of track group j Ability (pcu/h)；λjFor track group j split；xjFor track group j saturation degree；yjFor track group j flow-rate ratio；SFjFor Track group j complete track saturation volume rate (pcu/h)；The identifier in short track whether is provided with for track group j, if OtherwiseSSjFor track group j short track saturation volume rate (pcu/h)；LjFor track group j short lane length (m)；gjFor Track group j effective green time (s)；GjFor track group j display green time (s)；lsFor preceding loss time (s)；After e is Compensate the time (s)；qj' standard car demand the flow rate (pcu/s) for being track group j；Sj' equivalent the saturation volume rate for being track group j (pcu/s)；x0jFor the average saturation degree for overflowing track group j when queuing is approximately 0；
    Formula (6)~(8) are respectively HCM2000, HCM1985 and ARRB delay formula；
    (6) emission factor is demarcated during traffic lights
    For formula (1) and (2), the calibration formula of emission factor is as follows during traffic lights：
    Wherein：
    <mrow> <msubsup> <mi>VSP</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>&amp;zeta;</mi> </mrow> <mi>&amp;eta;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>v</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>&amp;zeta;</mi> </mrow> <mi>&amp;eta;</mi> </msubsup> <mo>/</mo> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <mn>1.1</mn> <msubsup> <mi>a</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>&amp;zeta;</mi> </mrow> <mi>&amp;eta;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mn>9.8</mn> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <msubsup> <mi>&amp;theta;</mi> <mi>j</mi> <mi>&amp;eta;</mi> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <mn>0.132</mn> <mo>&amp;rsqb;</mo> <mo>+</mo> <mn>0.000302</mn> <msup> <mrow> <mo>(</mo> <msubsup> <mi>v</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>&amp;zeta;</mi> </mrow> <mi>&amp;eta;</mi> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mn>3</mn> </msup> <mo>;</mo> </mrow>
    In formula：Discharge pollutants k quality (mg) for vehicle ζ on moment t intersection η track group j；It is motor-driven for ω classes Pollutant k emission factor (mg/s/veh) when the specific power of car is located at subregion γ；When τ is the sampling of car speed and acceleration Between the resolution ratio (s) that is spaced；It is motor-driven to sail out of the ω classes of stop line during green light on moment t intersection η track group j Car number (veh)；To sail out of the ω class motor vehicle numbers of stop line during red light on moment t intersection η track group j (veh)；OηFor the intersection η absolute green time difference (s)；Bright moment (s) is played for intersection η tracks group j green light；For Intersection η tracks group j green light finish time (s)；For the category attribute of vehicle ζ on moment t intersection η track group j；For the specific power (kW/t) of vehicle ζ on moment t intersection η track group j；LVSPω,γFor ω classes vehicle specific power point Area γ lower limit (kW/t)；UVSPω,γFor the ω class vehicle specific power subregions γ upper limit (kW/t)；Intersect for moment t Vehicle ζ speed (m/s) on mouth η track group j；For the acceleration (m/s of vehicle ζ on moment t intersection η track group j2)；For intersection η tracks group j road grade (°)；
    (7) phase difference optimization method
    After the best of breed for sharing cycle duration, split and short lane length is obtained using formula (1), or using formula (2) after obtaining the best of breed for sharing cycle duration and split, phase difference is optimized using following methods：
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mi>min</mi> </mtd> <mtd> <mrow> <msubsup> <mi>D</mi> <mrow> <mi>&amp;eta;</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>d</mi> </msubsup> <mo>+</mo> <msubsup> <mi>D</mi> <mrow> <mi>&amp;eta;</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>u</mi> </msubsup> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>o</mi> <mrow> <mi>&amp;eta;</mi> <mo>,</mo> <mi>&amp;eta;</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
    Wherein：
    In formula：It is delayed (s) for the descending fleets for coordinating direction of intersection η+1；For the up coordination directions of intersection η+1 Fleet delay (s)；Oη,η+1The preferable green time difference (s) for descending coordination direction intersection η+1 relative to η；sη,η+1For intersection η to η+1 stop line spacing (m)；vη,η+1For intersection η to η+1 descending speed (m/s)；oη,η+1Handed over for descending coordination direction Prong η+1 relative to η the green time difference (s) of reality；
    IfWhenThe descending car for coordinating direction Team is delayedWhenThe descending fleet for coordinating direction, which is delayed, isWhenThe descending fleet for coordinating direction, which is delayed, is
    In formula：For the descending fleet's head car due ins for coordinating direction of intersection η+1 to red light knot The time interval (s) at beam moment；For intersection η to η+1 fleet vehicle number (pcu)；For+1 descending associations of intersection η Adjust the saturation volume rate (pcu/s) in direction；For the descending standard car demand flow rate (pcu/ for coordinating direction of intersection η+1 s)；For the descending effective green times (s) for coordinating direction of intersection η+1；For+1 descending associations of intersection η Adjust effective red time (s) in direction；
    IfIfOrderWhenDescending association The fleet in tune direction, which is delayed, isWhenUnder The fleet in row coordination direction, which is delayed, isWhenThe descending fleet for coordinating direction, which is delayed, is
    In formula：The bright moment is opened for the descending red lights for coordinating direction of intersection η+1 To the time interval (s) of fleet's trailer due in；
    The up fleet's delay for coordinating directionComputational methods with it is descending coordination direction it is similar；
    (8) techniqueflow
    For designing short track space, idiographic flow is as follows：(I) each control time is directed to, optimal be total to is determined using formula (1) With cycle duration, split and short lane length；(II) by the maximum of the short lane length of day part optimization or 85% point of position Design load of the number as short lane length, determines short track space；(III) on the basis of (II), for each control time, Optimal shared cycle duration and split are determined using formula (2)；(IV) on the basis of (III), for each control time, Optimal phase difference is determined using formula (10)；
    For not designing short track space, idiographic flow is as follows：(I) each control time is directed to, is determined most preferably using formula (2) Share cycle duration and split；(II) on the basis of (I), for each control time, determined most preferably using formula (10) Phase difference；
    In the case of short track is not provided with, it is 0 to make short track saturation volume rate, and idiographic flow is as follows：(I) for each control Period, optimal shared cycle duration and split are determined using formula (1) or (2)；(II) on the basis of (I), for each Control time, optimal phase difference is determined using formula (10)；
    When object function uses formula (4) or (5), it is necessary to be directed to every track group using formula (9) before using formula (1) or (2) Demarcate the emission factor during traffic lights.
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