美賽匯總2017獎(jiǎng)?lì)}55583

1、CForofficeuseT1 T2 T3 T4 Forofficeuse Self-drivingvehiclesWeconstructaMixedCooperationtosimulateeachoftheCForofficeuseT1 T2 T3 T4 Forofficeuse Self-drivingvehiclesWeconstructaMixedCooperationtosimulateeachofthetrafficnetworkindependentlybasedonCellularAutomata.We a me t self-driving vehicles need no

2、 safety erval compared withnon-self-drivingonesbecauseofgoodsynchronizationwiththe former vehicle. And also, we a me t the junctions have little influence on simulation because the traffic performance is continuous. OurMixedCooperationcontainsthreemaint traffic counts , in our basic ,uniformdistribu

3、tioninaday. Weknow thetrafficcountandlanesof eachsectionofthetrafficnetwork,sowecangetthetrafficdensityeach road section inriodandcontinuetousedifferentself-driving ratio to simulate the traffic flow.Next,inourtime-based,wetaketimeottrafficdensityfunctionovertimeisidenticaldual-Gaussian distribution

4、 in a day, t there are period of traffic peaks. So we can get the traffic density of each road section in each period of one day and continue to simulate similarly as the basic m .,weconstructa, consideringdedicated lanes for self-driving vehicles and con- tinue to simulate similarly as the time-bas

5、ed m,weusetheaveragevelocityofvehiclesineachsectionineachperiod toevaluatetheperformanceandcapacity. Our m s give the result of effect of self-driving on traffic performance underdifferenttrafficdensity.Furthermore,ourm spo outthe condition of needing dedicated lanes for self-driving vehicles. ernor

6、 Jay OfficeofPOBox ernor IwritetoyouonbehalfoftheMCMteam55583. Weareextremelyconcerned about the traffic condition in ernor Jay OfficeofPOBox ernor IwritetoyouonbehalfoftheMCMteam55583. Weareextremelyconcerned about the traffic condition in the Great Seattle area. Investigation the traffic flow usua

7、llyexceeds thetraffic any he Seattle, espelly during peak hours. We hope to help you improve the traffic The current traffic condition could lead to many severe problems. The problemisunacceptabledelayduringpeakhours.Duringthemorningcommuteandofthedaytheseeextremelong.Alsoitcouldleadcongestedroads,a

8、ndpotentiallyincreasetheprobabilityofoccurrenceoftraffic accidents. Congested roads could also cause problems for emergency vehicles, making them unable to respond in an appropriate amount of time.After anin-depth study of the traffic he GreatSeattle area, havecomeupwithsometcanhelpaddressthisedrivi

9、ng, cooperating cars as a solution to increase the traffic capacity without building extra lanes.Compared to human-drived cars, self-driving cars have many advantages. The biggest advantage is t it take much less time to react erms of emer- gency. Thi ually allow f-driving cars to keep a closer dist

10、ance with the car in front of it, thus it takes up much less traffic resource. In addition to this, selfdrivingcarscantunetheiraccelerationanddecelerationprofilestoconsume less fuel.Those advantages mentioned above make self-driving cars an excellent for addressing heavy traffic load. We build a to

11、simulate the traffic of the most busy he Great Seattle area and evaluate the of self-driving cars addressing the problem of heavy traffic load. The simula- tion shows promising results. The roduction of self-driving cars makes all cars among all roads he Great Seattle area go faster, it works espe l

12、ly well among busy roads during traffic peak hours. When no self-driving cars are in- troduced, the traffic goes very slow during peak hours, but after roducing approxima y 50% self-driving cars the traffic flow goes 1.5 2 times faster.In addition to making traffic flow faster, self-driving cars als

13、o make flow more stable. From our simulation, we troduction of drivingcarshelptoreducethevarianceoftrafficdelay.Thisisimportantbecause it helps to estimate times, and helps to reduce just in case time.Fortheaboveeself-drivingcarsasasolutiontotrafficheGreatSeattle.WetrafficheGreatSeattle.Wetyoudofort

14、hiscity,andlook forward to seeingitive changes. We hope you can accept out adviSincerely yoursMCM2017Team1Problem 111ement . . . . . . . . . . . . . . . . . . . . . . . . . . . Related. . . . .1Problem 111ement . . . . . . . . . . . . . . . . . . . . . . . . . . . Related. . . . . . . . . . . . . .

15、. . . . . . . . . . . . . . . . 2Amptionsand222mptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3MTheself-driving,cooperatingcar334666. . . . . . . . . . . . . . . Themixed,dynamicroad. . . . . . . . . . . .

16、. . . . . . . Performance evaluationcriteria . . . . . . . . . . . . . . . . . . . . CarVelocityv . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , Daily. . . . . . . . . . . . . . . . . . . . . 4Mand7788Problem1: Theeffectsofauto-drivingrafficnetwork . . . Car Velocity/Performance . . . . . .

17、 . . . . . . . . . . . SpaceDailyEquilibria. . . . . . . . . . . . . . . . . . 2s. . . . . . . . . . . . . . . . . . . . . . Problem2: Thedifferenteffectsonpeak/averagehours . . . . . . TrafficDensityDistributionofTime . . . . . . . . . . . . . Simulation . . . . . . . . . . . . . . . . . . . . . .

18、. . . . . . . . . . . . . . . . . . . . . . . . . . . . Problem3: Dedicatedlane. . . . . . . . . . . . . . . . ysis . . . . . . . . . . . . . . . . . . . . . . . 5StrengthsandStrengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19、 . . . . . . Future. . . . . . . . Future. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Appendix Appendix AppendixCellularautomataprogram:Createnewvehicles Page1of1Problem Traffic capacity is anyregions of the United es due to the ber of lanes of roads. For he Greater Seattle area dr

20、ivers encelongdelaysduringpeaktraffichoursbecausethePage1of1Problem Traffic capacity is anyregions of the United es due to the ber of lanes of roads. For he Greater Seattle area drivers encelongdelaysduringpeaktraffichoursbecausethevolumeoftrafficexceeds the designed capacity of the road networks. T

21、his is particularly pronounced on es 5, 90, and 405, as well as Se Route 520, the roads of particular in- terest for this problem. Self-driving, cooperating cars have been proed asa solutiontoincreasecapacityofhighwayswithoutincreasingnumberoflanesor roads. The behavior of these carseracting with th

22、e existing traffic flow and each other is not welderstood at this po. Based on the road listed above hurston, Pierce, King, and Snohomish counties, we considered how the ef- fects would change as the percentage of self-driving cars increases from 10% 50% to 90%, and the well as the where changesmark

23、edly.Alsowetunderwhatconditions,ifany,lanes be dedicated to these cars. Based on our m,welistedseveralpractical suggestions to the localRelated Traffic flow has been researched for a long time by many people.We can get somebasicm saboutrelationshipamongtrafficdensity,speedandthrough- put5.When traff

24、ic density is medium, there is a linear relationship:traffic um Speed (1 Speed um densityWhentrafficdensityisnearlyfull,thereisalogarithmicum )umSpeedlnSpeed traffic Whentrafficdensityisverylow,thereisaexponentialum um Speed (1 expSpeed traffic Self-driving has entered our and maybe he future.The ra

25、cy and safety have been improved a lotnks to the development of artifi- elligence.One of the most important pois the sensors on the vehicle1, which can detect the motion sdistanceandacceleration.So,inours,wetself-drivingeepthesamemotionewiththeformer one,withoutPage2ofmptions and AWemakethefollowing

26、basic of our mptionsisjustifiedandisconsistentwiththebasicTime consumed on thecrossroads and toll on the roadsisnotin consid- eration. We sup e t the cars are he same speed and ignored the wasted time due to the road conditions.ThetrafficPage2ofmptions and AWemakethefollowingbasic of our mptionsisju

27、stifiedandisconsistentwiththebasicTime consumed on thecrossroads and toll on the roadsisnotin consid- eration. We sup e t the cars are he same speed and ignored the wasted time due to the road conditions.Thetrafficcountsonthespecificroadswillnotchangeaftercertain day or certain hours the t need to c

28、ertainroadwillnotchange because ofour No lane changing situation is considered. This mption will be plainedin3.1whenweillustrate theself-driving, cooperating car.The capacitiesand sizesofdifferent kindsof cars willnotbe ated. To simplify our m, we atall the car inour m thesame regularlength 4mandreg

29、ularwidthfor onecar aTheiontablecontainsalltheionswehisinstantaneousspeedofatheresponsetimeofahumanunitlengthofablockinCellularAutomatonm lane counts of a certain road sectionthe distance betn two adjacent cars thewholelengthofacertainroadsectionequalsequalsum ta car canTC during a TC24 is a traffic

30、countduringa ime cartheaveragecarpassingcarvelocityvarianceduringdifferentperiodinaday car velocity variance among different road sectionstssibility of a self-driving car to show up sibilityofanon-self-drivingcartoshowupTable1:Page3ofThe self-driving, cooperating car Fromarticle1and2,wec four potent

31、ial benefits:ttheself-driving,cooperatingcarsPage3ofThe self-driving, cooperating car Fromarticle1and2,wec four potential benefits:ttheself-driving,cooperatingcarsFewer accidents. Driverless car can dramatically reduce the accident duetodrivers More productive commutes. Driverless cars would enable

32、the unproduc- tivehoursandminutestobeconverted oproductiveworkand/orleisure time. In other word, self-driving car can help reduce the useless waste on Environmental friendliness. Autonomous cars and trucks can tune their acceleration and deceleration profiles to reduce wasted fuel.Fewer traffic jams

33、. Driverless carswould bebetter adapted to highervol- umesoftraffic,astheywouldbeabletotravelathigherspeedswhilekeep- ing shorter distan bet n vehicles.In our ,aid lattentionto theforth benefitand considered lotabouttheself-drivingcarseffectsontrafficA self-driving, cooperating car is guided ernal c

34、omputers and nalsensors,anditcancommunicateandexchangedataswithotherself-cooperating cars as it decides what to do. In our , we think self-cooperating cars can betterdeal with emergent situation and almost dont thereactionthuman takeinface ofFrom article 3 we can see on the one hand, when cars pull

35、over or over- take, they may have trouble recognizing lane markers espe lly in low light, badweather,oncurves,andatforksandmerginglanes.Ontheotherhand,lane changepredictionofself-drivingcarsmaynotbeaccurateenough,andthetime itwilltakeforacompleteturnoverofallcarstoself-drivingcarsmakesplanning for i

36、t more n a little premature. So we reasonably a me t in our m , no lane changing situation is considered.Here is the structural difference bet non-self-driving cars.n self-driving, cooperating cars Page4of(a)non-self-drivingFigure1:Thedifferencebet emergency situations(b)self-drivingnself-drivingand

37、non-self-drivingcarsinfaceDefinition 1. erval is the shortest distance from thePage4of(a)non-self-drivingFigure1:Thedifferencebet emergency situations(b)self-drivingnself-drivingandnon-self-drivingcarsinfaceDefinition 1. erval is the shortest distance from the former car to the safety, considering t

38、he current speed and response time of a human driver. And we can compute it as follows:erval= vins When twocarsdistanceisntheerval,driverswillslowand keep distance with the former car, which is just as the Figure 1(a) above.Butforself-drivingcooperatingcars,theyarecontrolledbyystem and they ways ime

39、 when the speed of the car changes. So these cars donnot need to keep erval and they can followtheformercar atbest,whichis shownin Figure1(b) The mixed, dynamic road In order to better reproduce the dynamic road traffic flow , we CellularAutomatontosimulatetheReal-TimeTrafficofeveryroadsection. foll

40、owing Figure2 shows the improved Cellular Automaton m used in We update the data every second. Every he CA represents lane on the road. Every volume block represent a unit length to represent length of a car and the distance bet n adjacent cars. As shown in Figure 2, the yellow-colored blocks repres

41、ents the self-driving cars and the blue-colored blocksrepresentthenon-self-drivingcars.Thefollowinglistcontainsallthepa- rameters and procedures in our CA based road m .Unit length lu: For convenience, the unit length = 4m, equals the ofaregularLanes count Because the two directions on each road hav

42、e no difference, andwill notdisrupteach other aswell. Soweregardthem Page5ofFigure2: TheCellularAutomatonbasedroadsame in our ,andthelanesnumberistheadditionoflanecountsthesetwoPage5ofFigure2: TheCellularAutomatonbasedroadsame in our ,andthelanesnumberistheadditionoflanecountsthesetwonl = nleft +Adj

43、acentcarsdistanced: wedefinethenumberofunitlengthncars the distance from the rear end of the car to the head of next former latter dRoad section length For every section of the road, the length of sectionisthenumberof unitL Rum speed Vmax: we define the speed by how many unit lengths car has gone pe

44、r second.Speed limit is /h, which is about 27 namely, 7unitlength persecond.Vmax = 7 Humanresponsetimetresponse: wedefinehumanresponsetimeasthewhich need to start to slow down the car after he or she foundemergency.Commonly,responsetimeisfrom0.3secondsto1.5sec- onds.Here we define tresponse = 1Insta

45、ntaneous velocity of cars The instantaneous speed of this sponding cardecides how manyblocks the car will move forward at next second. And the unit of vins is blocks per secondTrafficCountsTC: Duringsometime, theamountofthecarsreachingthe end of road section is the TC of this road section duringt lo

46、ng time.Page6ofPerformance evaluation From the above, the instantaneous speed is easily sible, but the velocityweusetoevaluatetheroadconditionistheaveragePage6ofPerformance evaluation From the above, the instantaneous speed is easily sible, but the velocityweusetoevaluatetheroadconditionistheaverage

47、velocityofpassedtheroadduringcerta imeslot. Theaveragecarvelocitycanwellreflect the ro erformance under different conditions. Thebigger thevelocity is, the lesscrowdedtheroadisandthusthebettertheroadcapacityis.Fromourm , there is a trick to get the average car velocity:,wecountallthecarseverysecondo

48、ntheroadsandsumthemNsum = tn(per Then,theaveragecarpassingtimeis=v 1 , Daily2 valuated the trafficnetworkequilibriafrom bothtimeaspect and space On the one hand, for a certain road section, during a single day, including peakhoursandaveragehours,ifthecarvelocitykeepsstableandchangeslittle, the time

49、daily equilibria of the traffic network is obviously better.1Definition 2. Timedaily equilibria.Wedefine it ,where 2 is the car ttvarianceduringdifferentperiodinadayforacertainroad2 m (v )tmOn the other hand, at specific time slot, if thecar velocities of different road sectionsdonotdistincttoomucho

50、rnearlysame,thespacedailyequilibriaofthe traffic network is much better.1Definition3. Spacedaily equilibria.Wedefineit ,where 2 as the car svariance at same time among different road sections.hisproblem,theroadsectionsof the particularly concerned four roads is 224.2 = 1 (v )2sPage7of4Mand osedourot

51、hreestepsandcorrespondedthemtoof all, we ignored peak hours in a day and no dedicated ed the traffic counts distribution during aday the peak hours Page7of4Mand osedourothreestepsandcorrespondedthemtoof all, we ignored peak hours in a day and no dedicated ed the traffic counts distribution during ad

52、ay the peak hours and average hours, and d our o this Lastly,weconsidereddedicatedlaneseffectandansweredthequestionUnder what condition, if any, should lanes be dedicated to these cars.Problem1: Theeffectsofauto-driving raffic Whenpeakhoursarenotoconsideration,wetthecarsrandomly at any second during

53、 a day with evenlysibilities.Soifthepropor- tion of the self-driving car is p, siblity of a self-driving car come at startof a road sectiononeachlanePself TC24h/24/3600 =and forthenon-self-drivingcar, (1 = The initial velocity of each car is randomly assigned among 0 to t is, um speed of a car is 7u

54、nits/s. Then we use the showed in Figure 3 to decide how the velocity andition will changenext second., we check if there n adjacent cars, if there ,the driversor theartifi l elligen ystemwillbrakeuntilthe velocityisthe sameasthecarinfront,so hissituation,thenewvelocityisthesameasthecar infront,andt

55、he ition willbe closelyfollowing the formerone. Meanwhile, there is , check if the distance is n erval, if not, umIf thedistance iswith he safe erval,fornon-self-drivingcar, thedriverwill decelerate considering safety, but self-driving car will still accelerating because i s the ability to adjust th

56、e speed of itself quickly according to the speed of the former car and need no response time.In other words, self-driving cars can beperfectlysynchronizedwiththeformercarautomatically,andneednoThen, wesimulated thewhole224road sections for one hourlongtime, and repeated every simulation for 100 time

57、s to eliminate accidental error.Page8ofFigure3: TheflowchartindicatinghowwedecidethevelocityPage8ofFigure3: Theflowchartindicatinghowwedecidethevelocityand the car in next seconditionCar Velocity/Performance Wesimulatesthetrafficperformancewhenthepercentageofself-driving,coop- eratingcarschangeevery

58、5%,andthe10%,50%,90%isemphasized heFigure From the result, we can safely come to steadilyincrease astheself-drivingcarpercentage t the car SpaceDailyEquilibriasThetrafficcountsdistributionoftimeisconsidered, sos isnotcomparedtFigure5belowshowsthesimulationthe space daily equilibria increase as the s

59、elf-driving, cooperating cars percent- age raises.Both this two results can t the self-driving, cooperating car can releasethetrafficre,andhelptoimprovetheroad Page9ofFigure4:Page9ofFigure4: Carvelocityv Figure5: Spacedailyvariance2 f-drivingsPage10ofSensitivity ofperformance to self-driving ratio.W

60、ith further observation of Figure 4, we t the change of performance is little and difference bet4%oftheperforman um and minimumis about 1 m/s, which isjust o, performance Page10ofSensitivity ofperformance to self-driving ratio.With further observation of Figure 4, we t the change of performance is l