CN107730931A - Vehicle formation control and signal optimization method under vehicle-road cooperative environment - Google Patents

Vehicle formation control and signal optimization method under vehicle-road cooperative environment Download PDF

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CN107730931A
CN107730931A CN201710856347.XA CN201710856347A CN107730931A CN 107730931 A CN107730931 A CN 107730931A CN 201710856347 A CN201710856347 A CN 201710856347A CN 107730931 A CN107730931 A CN 107730931A
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mrow
msubsup
msup
speed
car
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CN107730931B (en
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王庞伟
蒋依伦
倪浩原
王力
李颖宏
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North China University of Technology
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North China University of Technology
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    • GPHYSICS
    • G08SIGNALLING
    • G08GTRAFFIC CONTROL SYSTEMS
    • G08G1/00Traffic control systems for road vehicles
    • G08G1/07Controlling traffic signals
    • G08G1/081Plural intersections under common control
    • GPHYSICS
    • G08SIGNALLING
    • G08GTRAFFIC CONTROL SYSTEMS
    • G08G1/00Traffic control systems for road vehicles
    • G08G1/22Platooning, i.e. convoy of communicating vehicles

Abstract

The invention provides a method for coordinating and controlling trunk lines of urban road sections and optimizing signals based on the characteristics of a vehicle-road collaborative environment. The method comprises the steps of firstly determining influence factors of a vehicle road coordination environment on vehicles, and analyzing occurrence rules of traffic flow and vehicle running states in trunk line coordination. Then, the speed of the head car is guided based on the signal period and the phase difference. The method comprises the steps of determining the running mode of formation vehicles in trunk line coordination control, optimizing intersection signal timing in real time through vehicle formation information, improving the traffic capacity of other phases of an intersection on the premise of ensuring that trunk line traffic basically does not stop passing through the intersection, and achieving the purposes of solving traffic jam and improving the service level of a traffic system.

Description

Vehicle formation control and its signal optimizing method under a kind of bus or train route cooperative surroundings
Technical field
The present invention relates to intelligent transportation, bus or train route collaboration field, and in particular to one kind is directed to main line under bus or train route cooperative surroundings Coordinate the control method that intersection carries out wagon control and signal control.
Background technology
It was found from the overview of domestic and international Arterial Coordination Control method, at present, existing Arterial Coordination Control method is with regard to its root Originally it is the part optimization to conventional rail tuning algorithm, i.e., by assuming that the average speed of driving vehicle is known and solid on section It is fixed, the calculating of green wave band phase difference is carried out in this, as design speed.There are phase difference that this kind of mode calculates and timing scheme very Difficulty produces a desired effect, and its basic reason is that the transport condition of main line wagon flow has randomness, can be by road condition, other The influence of travel condition of vehicle, there is certain uncertainty, non-main line wagon flow, which produces, has randomness, and this randomness can be right Main line wagon flow causes large effect.Affected its travel speed of main line wagon flow is difficult the travel speed with expected design It is identical, so as to cause green wave band effect to be difficult satisfactory.Thus propose under a kind of bus or train route cooperative surroundings vehicle formation control and Its signal optimizing method.
Bus or train route cooperative system is the mainstream development direction of world today's traffic, and it relies on the intellectuality of automobile and joined with net Change, realize truck traffic and bus or train route communication in road network.Traffic relevant information is set quickly to be circulated in each net connection automobile, profit With.The OD that these information arrive greatly road network is distributed, telecommunication flow information, overall traffic behavior, weather, and road conditions are small to arrive each intelligence The real-time speed of net connection vehicle, discharge, the currently performed timing scheme of signal control facility, all information can be in this kind Environment is newly circulated, and provides corresponding strategy and scheme based on this for the optimization of whole urban transportation.
Currently the traffic control method both at home and abroad based on car networking environment is directed to Single Intersection mostly.By to signal facility Performed timing scheme carries out real-time judge and carries out speed guiding according to the current position of vehicle, vehicle is not stopped as far as possible Car passes through intersection.This control method causes the wagon flow relation between intersection separate, not in view of Adjacent Intersections Between vehicular movement correlation.The more control modes with Trunk Road Coordination in arterial highway of living of urban transportation carry out traffic signals simultaneously Control, with reference to the fast development of current car networking technology, it is to have to propose that a kind of Arterial Coordination Control based on the environment is taken precautions against very much It is necessary.
Bus or train route cooperative system realizes truck traffic, bus or train route communication, and the running status of vehicle can be perceived and induce, intersect The state of message number control facility can be perceived and adjust in real time.The environment is the basis of novel traffic signal control method, can Wagon flow is realized by the analysis to road grid traffic distribution situation and the analysis of travel condition of vehicle, the bidirectional optimistic of signal, improved The traffic capacity of urban road intersection.
Traffic signal optimization includes single crossing control, multi-intersection Arterial Coordination Control method.Single crossing control System, is optimized by existing control algolithm such as genetic algorithm, model prediction etc. to traffic timing, intersects message by adjusting Number cycle duration, split, intersection vehicles delay, queuing time etc. are reduced, so as to intersection efficiency.Multi-intersection is done Signal coordination control method, Arterial Coordination Control method are traffic control methods that is a kind of very common in urban transportation and using, It is used for major urban arterial highway.By the fixed cycle and phase difference between crossing is adjusted, makes Some vehicles not parking by intersection, with This improves intersection efficiency.
Speed guides and platooning's method, and the speed guiding of Current vehicle and platooning are all by the automatic of vehicle What cruise function was realized.There is the cruise function of vehicle to realize the guiding of speed, and pass through the cruise active work(of more cars Can, cooperated by sensors such as radar, infrared detectors with vehicle-mounted computer realize vehicle with speeding.Multiple vehicles it is automatic Cruise function can realize the effect of speed control and platooning, but this platooning requires higher to condition of road surface, commonly uses Travelled in length, there is larger limitation in urban road.
Prior art deficiency
1st, algorithm related to the control method of Trunk Road Coordination in the research for the control method that current relevant bus or train route cooperates with compared with Few, it is essentially the Single Intersection signal control method under bus or train route cooperative surroundings.Further for Arterial Coordination Control method also very The correlation between its vehicle running state and phase difference is considered less.
2nd, for less to vehicle formation control method under bus or train route cooperative surroundings in traffic control method, while not formation The pattern of traveling is associated with signal optimization.
The content of the invention
For the deficiency of existing correlation technique, the present invention makes full use of the technical advantage of bus or train route cooperative system, proposes a kind of Arterial Coordination Control method under bus or train route cooperative surroundings.Guided by speed, the mode of platooning and signal optimization realizes friendship Logical control, reaching main line wagon flow can the not parking purpose reduced by intersection, non-main line wagon flow delay.This method specifically uses Following steps:
Step 1:Intersection region division under bus or train route cooperative surroundings
The region of upstream intersection j-1 stop lines to downstream intersection j stop lines is divided into buffering area and speed guiding is compiled Area of team;Buffer length isLane-change is freely exercised and fulfiled ahead of schedule for vehicle;Speed guiding formation section length be For completing guiding and the platooning of speed;
Step 2:The speed control of platooning is divided into four-stage:It is free travel phase, the speed adjusting stage 1, even Fast travel phase, speed adjusting stage 2;
In free travel phase, in buffering area, incorrect car carries out speed induction for head parking stall, and head car is freely travelled and shifted to an earlier date Lane-change is completed, free travel phase terminates when car rolls buffering area away from right overhead;Head car be in free travel phase running time Operating range isSpeed when car leaves buffering area right overhead is
In the speed adjusting stage 1, head car is needed current vehicle speedAdjust to guiding speedThe value of acceleration is A, when speed adjust complete when the speed adjusting stage 1 terminate;Running time is head car at this stageOperating rangeShould Stage terminates rear speedWherein
In at the uniform velocity travel phase, head car is with speedAt the uniform velocity travel, running time is head car at this stageTraveling DistanceWherein
In the speed adjusting stage 2, speed can be by guiding speedAdjust to regulation speed vmax, the value of acceleration is a, Car is with fixing speed v right overheadmaxWhen passing through stop line when green light plays bright in j intersections, the speed adjusting stage 2 terminates, this stage head Car running timeOperating rangeWherein
Step 3:To guiding speedCalculated,
In formulaPhase difference for j intersections relative to j-1 intersections, C are common period, and k is nonnegative integer;
It can be obtained by formula (1)-(6)
Take all feasibleMiddle maximum guides speed as head car.
Step 4:Complete platooning
After head car enters intersection, second car existsMoment, withSpeed enters intersection formation area, and ByComplete to form into columns with head car after time, subsequent vehicle is completed to form into columns by that analogy;
It is that object function establishes model that it is most short, which to form the time formed into columns, with rear car and front truck
In formulaIt is the time required for (x+1)th car is formed into columns with xth formation car composition;
In formula, hsFor the safe bus head spacing when two Adjacent vehicles speed are consistent,For xth parking stall move- Time graph,For xth vehicle speed-time graph,At the time of entering buffering area for xth car;
Displacement-time graph of (x+1)th car is drawn by formula (8) and formula (9)And speed-time graphIt can not be formed when entering formation area or (x+1)th car without (x+1)th car with front truck when forming into columns, record motorcade length
Step 5:Signal timing optimization
It is by the time used in the stop line of j intersections by the fleet j-1 intersections:
It is the time required to by the fleet j+1 intersections
In formula,The motorcade length set out for j-1 intersections,The motorcade length set out for j+1 intersections,
The long green light time of mains phase on all intersections is adjusted according to platooning's length and its fleet's speed:
In formulaRepresent the long green light time of the i-th phase of j intersections, i=1 is mains phase, GmaxFor maximum long green light time,Bicycle road flow larger in the i phases of j intersections is indicated, n is signal phase number, and Y is the total losses time in cycle;
According to formula (12), (13) can solve the long green light time of the non-mains phase under bus or train route cooperative surroundings(i= 2...n)。
Brief description of the drawings
Fig. 1 is the bus or train route cooperative system schematic diagram of the present invention.
Fig. 2 is intersection and section region division schematic diagram under bus or train route cooperative surroundings.
Fig. 3 is speed guiding and timing designing flow chart
Fig. 4 is speed seeker vehicle speed change in displacement schematic diagram
Fig. 5 is vehicle group schematic diagram.
Embodiment
As shown in figure 1, the present invention carries out vehicle guiding by implementing the data of collection, so as to reach system optimal.Dry During line coordination, the running status of section vehicle can be obtained in real time by bus or train route cooperative surroundings.Speed is carried out to vehicle to draw Lead and the formation of vehicle
(1) the guiding speed computational methods based on bus or train route collaboration
Step 1:Intersection region partitioning method under bus or train route cooperative surroundings.
As shown in Fig. 2 using upstream intersection stop line as starting point to downstream intersection stop line.Be classified as buffering area and Speed guiding formation region.Buffer length isIt can freely be exercised its role is to vehicle and fulfil lane-change ahead of schedule, avoided There is lane-change situation in speed guiding formation area.Vehicle completes guiding and the platooning of speed in speed guiding formation section length, Its length isRegion division enters control area to each vehicle after terminating guides, boot flow such as Fig. 3 institutes Show.
Step 2:As shown in figure 4, equally by taking the crossing of jth -1 and jth crossing as an example, when playing bright with the intersection of jth -1 green light Carve as zero point, do not consider that a Chinese herbaceous peony has queuing vehicle, to being divided into A, B, C by transport condition, D totally 4 stages:
Stage A:Free travel phase
Head parking stall carries out speed induction in buffering area, incorrect car at this stage, and head car is freely travelled and fulfiled ahead of schedule and changes Road.When vehicle rolls buffering area away from, the stage terminates.Running time is head car at this stageOperating range isWork as car Speed when leaving buffering area isWhereinDetected in real time by car networking system.
Stage B:The speed adjusting stage 1
At this stage, vehicle is needed current vehicle speedAdjust to guiding speedThe value of acceleration is a.Work as car The stage terminates during velocity modulation whole completion.Running time is head car at this stageOperating rangeThe stage terminates rear car Speed should be
Stage C:At the uniform velocity travel phase
At this stage, vehicle is with speedAt the uniform velocity travel.Running time is head car at this stageOperating range
Stage D:The speed adjusting stage 2
At this stage, speed can be by guiding speedAdjust to regulation speed vmax, the value of acceleration is a.Its reason exists In vehicle with vmaxSpeed when passing through stop line, it is possible to reduce the green light of this phase is let pass the time, and standard is done for follow-up timing designing It is standby.
Car is with fixing speed v right overheadmaxWhen passing through stop line when green light plays bright in j intersections, the stage terminates.This stage Head car running timeOperating range
In summary, to guiding speedCalculated., can correct car when leaving buffering area under car networking environment TimeSpeedRecorded.Known to the acceleration a of speed change;Buffer lengthFormation section length It is known.Head car is with the admissible maximal rate v in sectionmaxBy stop line, then can obtain
In formulaPhase difference for j intersections relative to j-1 intersections, C are common period, and k is nonnegative integer.
Limited according to kinematics formula and speed, formula (1) to formula (5) is substituted into formula (6) to obtain
For any k (k=0,1,2) in formula (7), take all feasibleMiddle maximum guides speed as head car.
(2) vehicle formation control and its signal optimizing method under bus or train route cooperative surroundings
Step 1:Formation control method for vehicle:
Equally by from j-1 intersections to exemplified by the direction of j intersections, to it is all using downstream intersection mains phase as outlet Its in vehicle meets that the vehicle of condition is formed into columns.
Fig. 4 is that head car and its follow-up two cars change over time curve in formation process medium velocity and displacement.Define herein When two Adjacent vehicles are consistent in speed, distance is safe bus head spacing hsWhen, it is believed that this two cars is completed to form into columns.After formation Vehicle can be dismissed with stable space headway, consistent transport condition traveling until forming into columns.
As shown in figure 5, after head car enters intersection, No. 2 cars existMoment, withSpeed is formed into columns into intersection Area, and passing throughComplete to form into columns with head car after time.No. 3 cars are similarly.
It is most short for object function that the time formed into columns is formed with rear car and front truck.Known to vehicle running state and controllable shape Under state, completing formation with the most short time can make vehicle as much as possible form formation, so as to improve the traffic efficiency in the section.
In formula (8)It is the time required for (x+1)th car is formed into columns with xth formation car composition.
In formula (9)For xth parking stall shifting-time graph,For xth vehicle speed-time graph.At the time of entering buffering area for xth car.As x=1, representative function and variable are relevant with head car.There is formula (8) And formula (9) can draw displacement-time graph of (x+1)th carAnd speed-time graphWhen without (x+1)th Car, which enters formation area or (x+1)th car, can not form with front truck when forming into columns, and record motorcade length
Step 2:Signal timing optimization
On the premise of having delay vehicle before not considering stop line, the vehicle for completing to form into columns can be with vmaxSpeed by stopping Only line, by taking j intersections as an example, it is by the time used in the stop line of j intersections by the fleet j-1 intersections:
It is the time required to by the fleet j+1 intersections
For line traffic control section, the long green light time of mains phase is according to platooning's length and its fleet on its all intersection Speed is adjusted:
Formula (12)The long green light time of the i-th phase of j intersections is represented, i=1 is mains phase.GmaxFor maximum green light when It is long.In formula (13)Bicycle road flow larger in the i phases of j intersections is indicated, n is signal phase number, and Y is cycle total losses Time.According to formula (12), (13) can solve the long green light time of the non-mains phase under bus or train route cooperative surroundings(i=2...n).

Claims (1)

1. vehicle formation control and its signal optimizing method under a kind of bus or train route cooperative surroundings, it is characterised in that comprise the following steps:
Step 1:Intersection region division under bus or train route cooperative surroundings
The region of upstream intersection j-1 stop lines to downstream intersection j stop lines is divided into buffering area and speed guiding formation area; Buffer length isLane-change is freely exercised and fulfiled ahead of schedule for vehicle;Speed guiding formation section length beFor complete Guiding and platooning into speed;
Step 2:The speed control of platooning is divided into four-stage:Free travel phase, speed adjusting stage 1, at the uniform velocity go Sail stage, speed adjusting stage 2;
In free travel phase, head parking stall carries out speed induction in buffering area, incorrect car, and head car is freely travelled and fulfiled ahead of schedule Lane-change, free travel phase terminates when car rolls buffering area away from right overhead;Head car be in free travel phase running timeTraveling Distance isSpeed when car leaves buffering area right overhead is
In the speed adjusting stage 1, head car is needed current vehicle speedAdjust to guiding speedThe value of acceleration is a, when The speed adjusting stage 1 terminates when speed adjustment is completed;Running time is head car at this stageOperating rangeThe stage Speed is after endWherein
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In at the uniform velocity travel phase, head car is with speedAt the uniform velocity travel, running time is head car at this stageOperating rangeWherein
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In the speed adjusting stage 2, speed can be by guiding speedAdjust to regulation speed vmax, the value of acceleration is a, right overhead car With fixing speed vmaxWhen passing through stop line when green light plays bright in j intersections, the speed adjusting stage 2 terminates, this stage head car traveling TimeOperating rangeWherein
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Step 3:To guiding speedCalculated,
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In formulaPhase difference for j intersections relative to j-1 intersections, C are common period, and k is nonnegative integer;
It can be obtained by formula (1)-(6)
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>t</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>A</mi> </msubsup> <mo>+</mo> <mo>|</mo> <mfrac> <mrow> <msubsup> <mi>v</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>l</mi> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mn>1</mn> </msubsup> </mrow> <mi>a</mi> </mfrac> <mo>|</mo> <mo>+</mo> <msubsup> <mi>t</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>C</mi> </msubsup> <mo>+</mo> <mfrac> <mrow> <msub> <mi>v</mi> <mi>max</mi> </msub> <mo>-</mo> <msubsup> <mi>v</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>l</mi> </msubsup> </mrow> <mi>a</mi> </mfrac> <mo>=</mo> <msubsup> <mi>t</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>s</mi> </msubsup> <mo>+</mo> <mi>k</mi> <mi>C</mi> <mo>,</mo> <mrow> <mo>(</mo> <mi>k</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2...</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>l</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>A</mi> </msubsup> <mo>+</mo> <mrow> <mo>|</mo> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>v</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>l</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>v</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mn>1</mn> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>a</mi> </mrow> </mfrac> <mo>|</mo> </mrow> <mo>+</mo> <msubsup> <mi>t</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>C</mi> </msubsup> <msubsup> <mi>v</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>l</mi> </msubsup> <mo>+</mo> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <msup> <mi>v</mi> <mi>max</mi> </msup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>v</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>l</mi> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>a</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>b</mi> </msubsup> <mo>+</mo> <msubsup> <mi>D</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>p</mi> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>v</mi> <mi>min</mi> </msup> <mo>&amp;le;</mo> <msubsup> <mi>v</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>l</mi> </msubsup> <mo>&amp;le;</mo> <msup> <mi>v</mi> <mi>max</mi> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
Take all feasibleMiddle maximum guides speed as head car.
Step 4:Complete platooning
After head car enters intersection, second car existsMoment, withSpeed enters intersection formation area, and is passing throughComplete to form into columns with head car after time, subsequent vehicle is completed to form into columns by that analogy;
It is that object function establishes model that it is most short, which to form the time formed into columns, with rear car and front truck
<mrow> <mi>min</mi> <mi> </mi> <mi>F</mi> <mo>=</mo> <msubsup> <mi>&amp;Delta;t</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mrow> <mi>x</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
In formulaIt is the time required for (x+1)th car is formed into columns with xth formation car composition;
In formula, hsFor the safe bus head spacing when two Adjacent vehicles speed are consistent,For xth parking stall shifting-time Curve,For xth vehicle speed-time graph,At the time of entering buffering area for xth car;
Displacement-time graph of (x+1)th car is drawn by formula (8) and formula (9)And speed-time graphWhen Entering formation area or (x+1)th car without (x+1)th car can not form with front truck when forming into columns, and record motorcade length
Step 5:Signal timing optimization
It is by the time used in the stop line of j intersections by the fleet j-1 intersections:
<mrow> <msub> <mi>g</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msubsup> <mi>L</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>x</mi> </msubsup> <msup> <mi>v</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
It is the time required to by the fleet j+1 intersections
<mrow> <msub> <mi>g</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msubsup> <mi>L</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mi>x</mi> </msubsup> <msup> <mi>v</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
In formula,The motorcade length set out for j-1 intersections,The motorcade length set out for j+1 intersections,
The long green light time of mains phase on all intersections is adjusted according to platooning's length and its fleet's speed:
<mrow> <msubsup> <mi>G</mi> <mi>j</mi> <mi>i</mi> </msubsup> <mo>=</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo>(</mo> <mrow> <msub> <mi>g</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>g</mi> <mrow> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> <mo>)</mo> <mo>,</mo> <msup> <mi>G</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msup> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>G</mi> <mi>j</mi> <mi>i</mi> </msubsup> <mo>=</mo> <mrow> <mo>(</mo> <mi>C</mi> <mo>-</mo> <msubsup> <mi>G</mi> <mi>j</mi> <mn>1</mn> </msubsup> <mo>-</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mfrac> <msubsup> <mi>Q</mi> <mi>j</mi> <mi>i</mi> </msubsup> <mrow> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> <msubsup> <mi>Q</mi> <mi>j</mi> <mi>i</mi> </msubsup> </mrow> </mfrac> <mo>,</mo> <mrow> <mo>(</mo> <mi>i</mi> <mo>=</mo> <mn>2</mn> <mo>...</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
In formulaRepresent the long green light time of the i-th phase of j intersections, i=1 is mains phase, GmaxFor maximum long green light time,Table Bicycle road flow larger in the i phases of j intersections is shown with, n is signal phase number, and Y is the total losses time in cycle;
According to formula (12), (13) can solve the long green light time of the non-mains phase under bus or train route cooperative surroundings
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