2017 MCM/ICM Merging Area Designing Model for A Highway Toll Plaza Summary Sheet


 Belinda Kelley
 1 years ago
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1 Team#55307 Page 1 of 25 For office use only T1 T2 T3 T4 Team Conrol Number Problem Chosen B For office use only F1 F2 F3 F MCM/ICM Merging Area Designing Model for A Highway Toll Plaza Summary Shee Too much aenion has been aached o he former par of barrier olls, for people consider ha he main cause of delay happens when cars wai o be serviced in ollboohs. Besides he number of ollboohs, he condiions and siuaions afer he barrier olls also need our consideraions. Because cars have o fan in from he larger number of ollbooh egress lanes o he smaller number of regular ravel lanes. Safey risk and delay also exis when cars ry o change heir lanes. Insead of somewha specific mehod used in curren researches, we focus on he merging area of he oll, which is he area following he B oll barriers, ending a he L ougoing raffic lanes. The merging area of oll differs from hree pars: shape, size and merging paern. We selec safey, hroughpu and cos as our main consideraions. Firsly we selec five curren barrier olls o analyze heir shape, size and merging paerns. We can sum up several imporan poins vary from safey, hroughpu, delay, cos, line shape and raffic demand. These poins help us esablish models and design our soluions. Then we combine carfollowing model and gap inerpeneraion model o find he relaionship beween safey and he shape, size of he merging area. Wih our firs model, we can evaluae wheher he oll areas of differen oll saions are safe enough and we can use he model o calculae he heoreically limi lengh of he merging lane. Addiionally, we analyze hroughpu and we have drawn a conclusion ha he merging area will never be he boleneck if B and L mach each oher, for i can hold more vehicles per hour han he olls. Delay as a very imporan index in ransporaion engineering should also be considered for i has a close relaionship wih ime cos and efficiency of he merging area. Therefore, we se up delay model and based on which we build up cos model. Moreover, we design hree differen paerns based on former resuls, analysis of curren paerns and basic road design heories. Using VISSIM, he raffic simulaion sofware, we evaluae he safey and delay of hree differen paerns which show ha a he maximum volume, he delay and variance of speed of Paern 1 are he smalles. Finally we es our soluions under differen condiions: wih ligh and heavy raffic, wih more auonomous vehicles and wih differen ypes of ollboohs. We find all of our hree soluions perform well in he es, while Paern 1 works he bes under he volume es, and when we add more auonomous vehicles, Paern 2 or 3 is more suiable. When differen ypes of ollboohs are aken ino consideraion, we add some modificaions o our soluions. In conclusion, Paern 1 works bes when errain condiions are good and he proporion of rucks and buses is high. Paern 3 has he bes effec when errain condiions are limied and he proporion of rucks and buses is high is low. Specific choice depends on governmen planning, consrucion mehods, and raffic composiion.
2 Team#55307 Page 2 of 25 Resaemen of he Problem Insead of somewha specific mehod used in curren researches, we focus on he merging area of he oll, which is he area following he B oll barriers, ending a he L ougoing raffic lanes. The merging area of he oll differs from hree pars: shape, size and merging paern. We selec safey, hroughpu and cos as our main consideraions and we should se up reasonable models o deermine he shape, size and merging paern of he area. Wih he models we se up and analysis of curren ollbooh, we can design an appropriae soluion. Moreover, we should es our soluion under differen condiions: wih ligh and heavy raffic, wih more auonomous vehicles and wih differen ypes of ollboohs. Definiions and Key Terms Merging area. The area following he oll barrier in which vehicles fan in from B ollbooh egress lanes down o L lanes of raffic. Delay. The exra ime for a car o raverse merging area han i pass he area wih ideal speed. Time headway. A measuremen of he minimum possible disance or ime beween vehicles in a ransi sysem, wihou a reducion in he speed of vehicles. Merging lane. The lane on which cars desire o change lane. Merged lane. The lane which is merged by cars from oher adjacen lanes. Acceleraion lane. The lane on which cars accelerae. Speed limi. The maximum speed of he road. Available gap. The minimum gap allows cars o merge. Lane balance. The heory used in road engineering. I suggess ha each ime he number of lanes can only decrease one. Capaciy. The maximum amoun of cars pass he crosssecion per hour. Time cos. People's ime has alernaive uses ha are valuable. General Assumpions Make assumpions abou he homogeneiy of cars and ollboohs, cars are all sandard passenger cars and he service raes of ollbooh are he same. The moion of a car in he merging area in erms of safey consideraions and reacion ime. The weaher is fine, drivers are all moderae drivers and no accidens happen. The flow of vehicles leaving he barrier oll is discree. The given consan B, L are reasonable. They mach each oher and funcion well ogeher. Take B=6, L=3 as example for our research. (Based on he conclusion of essay For whom he booh olls ) In he merging area, if here is no lane change behavior, he car is doing homogeneous acceleraion moion wih iniial velociy 0 unil reaching he speed limi. There is no congesion or flow limiaion on he segmen afer he merging area.
3 Team#55307 Page 3 of 25 Exposiion of Variable Table 1 Variables, definiions and unis Variable Definiion Unis L V V 0 S 0 x l Pl () c V Q 1 l Q f Q r l i I V s L S 1i V i 2i 1 2 3i 3 a a d N M N p Lengh of line Velociy of saring merge Iniial velociy Acceleraion disance Posiion of merging vehicle Travel disance of merging vehicle Probabiliy of successful merge Safe ime gap Safe difference of velociy Arrival rae Volume of lane afer merging Gap of ravel disance Volume of Merging lane Volume of Merged lane The No. i Uniform moion disance Number of merging Expeced velociy Lengh of merging area The No. i uniform moion ime The No. i velociy of saring merge The No. i merging acceleraing ime Sum of Sum of The No. i normal acceleraing ime Sum of The oal ime passing hrough he merging area Average 1i 2i 3i a m m/s m/s m m m uniless s m/s uniless pcu/h m pcu/h pcu/h uniless uniless m/s m s m/s Average delay s Design capaciy of road segmen wihou plane inersecion s pcu/h affec The basic raffic capaciy of a moorway pcu/h 2 si m Area of he No. i lane s 2 q L i L 0 p Area of merging area Volume of single lane Lengh of he No. I lane The disance beween wo rows of olls Average passengers on each car s s s s s s s m pcu/h m m uniless
4 Team#55307 Page 4 of 25 Table 2 Consans, definiions and unis Consan Meaning Uins B L a f c f n f w f p f b Number of olls Number of lanes Acceleraion coefficien coefficien coefficien Road grade facor for moor vehicles Moor vehicle number correcion facor Moorway Widh Correcion Facor Driver Correcion Facor Bicycle Correcion Facor Moivaion and Jusificaion for he Model uniless uniless uniless uniless uniless uniless uniless uniless uniless uniless uniless In his model, safey, hroughpu and cos are hree facors aken ino consideraion, wih safey as he op prioriy. Therefore, we sar wih building a model o sudy he relaionship beween paerns of merging area and safey. Then we plan o esablish models for hroughpu and cos. Delay as a very imporan index in ransporaion engineering should also be considered for i has a close relaionship wih ime cos and efficiency of he merging area. Curren Case Sudy Picure1 Curren Siuaion of Barrier Toll Boohs
5 Team#55307 Page 5 of 25 Above are he examples of barrier oll boohs from China and America. Two picures in he lef upper corner are from US and he ohers are in China. As he problem saemen says, basically he number of olls (B) is larger han he number of lanes (L). However, we can sill see difference and feaures among he five examples. The number of olls (B) is larger han he number of lanes (L); The American designer end o divided he elecronic olls and nonelecric olls apar, while he olls in china are usually arranged in a sraigh line; Some oll saions have a grea number of olls even four or five imes of he number of lanes and need larger area; Tolls in he picure a he boom lef corner separae small cars from rucks and buses and charge hem separaely; Some of hem may only ake he capaciy of volume ino consideraion (Eg. he picure a he boom lef corner); Mos oll barrier has smooh lines shape which no only provide beer view bu also improving driving comfor; Through he saus quo analysis, we can sum up some imporan poins for designing he plaza and esablishing he model: Safey: Traffic safey is he basic requiremens of ravel, and usually measured by he relaive mean speed beween wo adjacen lanes as well as he variance of velociy among one single cross secion. There are many facors affecing safey such as he merging paern, lengh of acceleraion lanes, urning radius and so on; Throughpu: Throughpu show he capaciy of he oll plaza. The capaciy of he plaza has o mach wih he olls, or i is more likely o ge congesed. However, according o laer calculaions, we find he capaciy of he plaza is usually far beyond ha of olls; Delay: Delay means he difference beween ravel ime under ideal condiions and ravel ime under pracical condiions; Cos: Cos includes land cos and also ime cos which is deermined by he area of he oll plaza, he local housing price, delay and he average local income; Line Shape: Line shape includes he urning radius, he shape of ransiion curve beween wo Circular curves and so on. However, we only discuss he shape, size and merging paern of he oll plaza and ignore he influence of line shape. Traffic demand: Traffic demand direcly reflec he value of volume. And he number of olls as well as lanes all depend on his parameer. However, we only consider oll plazas wih six olls and hree lanes because i is he mos common form and Only when he values of B and L are deermined can he quaniaive calculaion be carried ou. Probabiliy Model of Vehicle Merging Safey Main Idea and Procedure
6 Team#55307 Page 6 of 25 Our model involves he Forced change road and he Auonomous change road. Firs, he higher speed he vehicle have, he longer disance he vehicle require o merge. Through building Probabiliy Model of Vehicle Merging Safey, we can achieve ge under he differen volume, Probabiliy disribuions regular paern of vehicle s merging. And he lengh of each lane can be deermined by deducing he lengh of ravel required o mee all he merging vehicles safey. Expecaions of Our Model Funcion1: We can use he model o evaluae he probabiliy of acciden prevenion in differen merging areas. Funcion2: We can use he model o calculae he heoreically limi lengh of he merging lane. Picure 2 procedure of funcion1 Addiional Assumpions and Definiions Picure 3 procedure of funcion2 V is he saisical safe speed difference. V =2.5m/s.() Taking he behavior characerisics of difference drivers and he disribuion of vehicles on he merged lane ino accoun, he merging vehicle may ravel a disance. When is velociy reachesv, i sars o merge. A his ime he velociy difference should be less han V. The minimum ravel disance of he merging
7 Team#55307 Page 7 of 25 vehicle is as follows: V V S0 2a Afer he merging vehicle s velociy reaching V, i mainains a consan velociy. Se up he model Suppose ha when he merging vehicle s velociy is V( V=2.5m/s), is posiion is x 0.Afer reachingv, is posiion is x L S.From x 0 o 0 x L S, he 0 probabiliy of successful merging is Pl ().As he picure shows: When x 0, Pl ( ) 0. Picure 4 Schemaic of he variables Afer he merging vehicle s velociy reaches V a posiion x l( l S0), he accepable merging ime gap ( =2.16s)occurs. The probabiliy of he accepable c c merging ime gap on he merged lane is randomly disribued. The probabiliy disribuion funcion can be se as follows: P( h ) F( ) When he volume of lane is ligh, vehicle s ineracion is very small, vehicle raveling can be seen as independen, his ime headway disribuion have grea randomness, can generally use he negaive exponenial disribuion or displacemen of negaive exponenial disribuion o describe is random feaures: P( h ) e Q 1 /3600 When he volume of lane is heavy, closed o he capaciy of he case, ime headway basically mainained a a sable value: 3600 Q 1
8 Team#55307 Page 8 of 25 A condiion of, P( h ) 1; A condiion of c, P( h ) 0 ;( is ime c headway) When he volume of lane is a he middle level, some vehicles on he road are independen of each oher, he oher par is muual influenced. A his ime, he ime headway disribuion model is he Korder Erlang disribuion model: k 1 P( h ) ( k) i 0 i e i! Here we choose he second order Erlang disribuion model: Wheher he merging vehicle can mee c a x l or no depends on is relaive velociy and relaive displacemen wih he merged vehicle. Boh of which can be convered o he ime ha afer merging vehicle s velociy reachesv, i coninues o ravel in he original lane. Because he ime is coninuously variable, i can be considered ha he probabiliy disribuion funcion of he merging vehicle encounering c a he posiion x l is he geomeric disribuion of he waiing ime a he posiion. Using he differenial mehod o solve: Suppose ha he probabiliy of successful merging a he crosssecion x l l is P( l l) : P( l l) P( l) [1 P( l)] F( c( l )) k l V P( l l) P( l) P( l)] F( ( l)) F( ( l)) c c l V V On boh sides of he derivaivel : F( ( l)) c Ql () V P'( l) Q( l) P( l) Q( l) Q Q() l is he expeced value of he disribuion funcion Ql (): When he volume of lane is ligh: When he volume of lane is heavy Q1 c () l 3600 e Q V
9 Team#55307 Page 9 of 25 1 ( () l ) or Q 0 ( () l ) Q V When he volume of lane is a he middle level: According o he HCM 2000: e Q c Q 1c( l ) Q1 c( l ) Q c() l e 3600 V Q Q Q f 3 r c, 1 2, 3 can be obained hrough field daa or simulaion. The general soluion of differenial equaion can be obained: Because x<0, Pl () =0, we can ge C=1. Ql Ql P( l) e ( e C) P( l) 1 e Ql So he probabiliy of ha he merging vehicle can ravel l in he original lane: P ( l) 1 (1 e Ql ) e f Ql A he posiion x=l, he probabiliy of successful merging is: P( l) 1 e Ql We can ge Probabiliy Model of Vehicle Merging Safey: 0,(0 l S ) 0 Pl () ( 0 ) 1 e Q l S,( S l L) 0 To secure he probabiliy of successful merging is 95%, he lengh of merging lane: ln(1 P) l S Q 0 Throughpu For manual oll saions, when he vehicle passes he driver needs o park, prepare he money, pay he bills, ake he invoice and sar, which basically akes an average of 15 seconds based on our experience. The capaciy of one single ollbooh is 240 pcu/h. Taking he limi siuaion ino accoun, we se he service rae as 12 s/pcu and he capaciy is 360 pcu/h. The unidirecional raffic capaciy of he road no affeced by he inersecion is calculaed by he following formula: Nm=fc fn fw fp fb Np
10 Team#55307 Page 10 of 25 According o he formula and parameers able on Highway Capaciy Manual (HCM2000), under ideal condiions, we can calculae capaciy of merging area values more han 3000 pcu/h far beyond he max capaciy of six olls which values 2160 pcu/h. Meanwhile, he vehicles don arrive a he oll plaza (behindoll area) a he same ime resriced o he conrol of service rae of olls. In conclusion, ideally, he capaciy of merging area is no he cause of congesion under normal design condiions. The real reason why he merging area always ge congesed is ha he capaciy of he segmen or road nodes doesn mach wih he capaciy of he merging area or he olls. The road capaciy depends on he capaciy of boleneck raher han he max capaciy of one single segmen. Since he merging area can hold more vehicles per hour han he olls, he merging area will never be he boleneck. Delay Model Addiional Assumpions and Definiions j is vehicle number. Se up he model Before he vehicle merges No. i ino he merged lane, is Uniform moion ime. 1i li V i The No. i merging acceleraing ime: B L 1 1i i 1 2i 2al2i Vi a The No. i normal acceleraing ime: When i 1: Wheni=2,3,4.(i I ): 3i B L 2 2i i 1 31 V i V 1 a V a ( i 1)
11 Team#55307 Page 11 of 25 a B L 3 3i i Considering he limi, here are vehicles passing hrough he B olls a he same ime. Then he average ime: Delay: a B a L d a V S s Cos Model Area cos We number he lanes from lef o righ i( i 1,2,3... i B) No. i lane occupies an area si Lib Toal area s si B i 1 According o he average of New Jersey s land price of $2,000 per square meer,he area cos is 2000 s Time cos According o he average of income of US residens is $7.25 per hour, he ime cos is 7.25 pdbq 3600 Merging Paern The Merging Paerns ha we designed involve hree differen ypes: Paern 1:merging all from ouside Wih his paern, cars a he wo inside lanes will no be affeced by merging cars. All merging poins lie a ouside lanes. And he join mehod of wo direcions lanes is symmerical along he inner lane.
12 Team#55307 Page 12 of 25 Picure 5 Schemaic diagram of paern 1 Paern 2:merging from boh side Compared o Paern I, only one lane a he middle will no be affeced by merging cars. Merging poins lie a boh side. Wha s more, we ake he lane balance ino consideraion, move wo ollboohs L 0 ahead so ha each ime we make lanes decrease only one. The lanes of wo direcions are symmerical a he cener poin, jus as he picure shows below: Picure 6 Schemaic diagram of paern 2 Paern 3:Firs mergence in oll barrier area As we se he assumpion ha all he ollbooh are humansaffed, he service ime for each car is usually quie a long ime. And i is very common ha he gap beween wo successive cars is oally enough for he car a he adjacen lane o merge in. Wih his paern, cars a he ouermos and innermos lanes will merge in he adjacen lane jus afer hey leave he oll. The following par is similar o Paern2. The lanes of wo direcions are also symmerical a he cener poin o save land, jus as he
13 Team#55307 Page 13 of 25 picure below: Picure 7 Schemaic diagram of paern 3 Evaluaion of Differen Paerns Acciden prevenion By calculaing he ideal lengh of safe driving and acciden rae o deermine wheher he oll saion is safe and reasonable. Through he buil model, we can ge specific probabiliy disribuion and ideal size. If he size does no mach, hen he acciden rae will increase Cos Cos consiss of area cos and ime cos. Specific algorihm has been shown above. Paern Simulaion Model simulaion Through VISSIM5.0, raffic simulaion sofware, he hree design mehods menioned in his paper are simulaed and processed. Vissim does no have a oll saion for his ransporaion faciliy, and if here is no maerial for a shor ime can no be esablished oll saion 3DMAX maerial. Therefore, he use of raffic lighs on he oll saion simulaion. Parameers calibraion Before he simulaion, calibrae he raffic parameers:
14 Team#55307 Page 14 of 25 Table 3 Parameer calibraion Propery Value Explanaion Signal Cycle 10s The cycle of signals is 10s Red End Time 8s The red ligh ime ges over a he eighh second of a cycle Green End Time 10s The green ligh ime ges over a he enh second of a cycle and make sure one oll can only pass one vehicle in a single cycle Offse 0s All he six signal lighs urn o green a he same ime o es he capaciy Composiion of Traffic Flow Passenger Car 100% The volume only consiss of sandard car VolumeGernerae 3600(pcu/h) Se his propery high o es he capabiliy he oll plaza Simulaion seps: Draw he hree oll plazas in VISSIM according o he design dimensions; Se 6 signal lighs as well as sauraed volume on each merging paern; Se daa deecion poins before and afer each lane reducion on every lane o obain such daa as he maxspeed, minspeed, maxacceleraion, minacceleraion, number of vehicles; Se ravel ime deecors a he oll and he end of las lane reducion o obain he ravel ime and delay. Picure 8 Simulaion diagram Picure 9 daa deecion poins disribuion
15 Team#55307 Page 15 of 25 Picure 10 simulaion screenshos According o he daa colleced by he daa deecion poins, we can analyze he variaion of speed and he disribuion of number of vehicle passing each crosssecion. Variaion(mean & variance) of Acceleraion and Speed Diagram
16 Team#55307 Page 16 of 25 Deecion resuls: Table 4 Delay & ravel ime & volume paern delay(s) ravel ime(s) num of vehicles(pcu) Safey evaluaion The keys o raffic safey evaluaion are he difference of acceleraion and speed and he difference of variance of acceleraion and speed in he adjacen lanes. In oher words, he smaller of he relaive speed beween wo adjacen lanes and he variance of speed and acceleraion among one crosssecion, he safer i is. Because in his case, he inerference beween vehicles is smaller, he impac of energy release occurs when he smaller. Speed and acceleraion analysis As vehicles moving forward, he speed is more and more divergen in paern 2 and paern 3 while he difference of speed is geing smaller in paern 1. The variance of he maximum velociy and he minimum velociy of paern1 converge coninuously. The variance of paern2 and 3 increases firs and hen decreases, and he maximum is obained a he second secion. As for he variance of average speed, he hree are basically he same. The gap beween max and min acceleraion is larger and larger Delay and ravel ime analysis Paern 1 has he leas delay and ravel ime as well as he mos volume among he hree designs while Paern 3 has he mos delay and ravel ime as well as he leas volume among he hree designs
17 Team#55307 Page 17 of 25 Cos analysis Cos of Paern 1 Area cos s m s m s m s s s 4s m The area cos is 2000s = = 6,232,500$ Time cos d Bq = = $/h Cos of Paern 2 Area cos s m s m s 2s 4s m 1 2 The area cos is 2000s = = 1,530,000$ Time cos d Bq = = $/h Cos of Paern 3 Area cos s m s m s 2s 4s m
18 Team#55307 Page 18 of 25 The area cos is 2000s = = 1,155,000 $ Time cos d Bq = = $/h Analysis The above hree paerns have heir own advanages and disadvanages. All of hem can make heir ime cos and area cos achieve he bes a he same ime. Paern 1 works bes when errain condiions are good and he proporion of rucks and buses is high. Paern 3 has he bes effec when errain condiions are limied and he proporion of rucks and buses is high is low. Specific choice depends on governmen planning, consrucion mehods, and raffic composiion. Tes our soluion under differen condiions Ligh and Heavy Traffic Safey analysis Under he condiion ha he expeced merging speed of he vehicle is consan and he iniial speed is consan, he effec of he flow rae on he failure probabiliy of he vehicle s merging wihou sopping is shown in Picure 11: Ql 300 pcu / h Ql pcu / h Ql pcu / h Ql pcu / h S 0 Picure 11 QFailure Merge Probabiliy Picure 12 Discrepancy In which he vehicle is in he phase of S 0, since he vehicle speed does no reach he speed a which he driver expecs o merge, so he vehicle fails o merge. Afer S 0, wih he increase in raffic, in he case of nonsop, he curve of failure possibiliy rises as a whole. If drivers force o merge, raffic accidens have a good chance o occur, and safey can be guaraneed. And wih he increase of raffic, he maximum merging disance increases, resuling in decreasing in safey. To make he success rae of 95
19 Team#55307 Page 19 of 25 percen or more, i is necessary o increase he lengh of he acceleraion lanes. When raffic increases o he capaciy of he oll saion, headway ends o be raher small. In order o successfully merge, c mus be limied o a lower level, a he expense of safey change he lane, oherwise he driver mus sop and wai for anoher chance. According o Picure 12,when he headway disribuion is in accordance wih he second order Erlang, When he singlelane flow is reduced from pcu / h o pcu / h, he flow change is 16.7% and he acciden prevenion probabiliy decreases by 3.91%.From he abovemenioned probabiliy model, he decrease of acciden prevenion probabiliy ends o be sable wih he decrease of flow rae. And he merging paern we designed, in all he size of raffic, are o mee cerain securiy. Delay Analysis: Table 5 delay comparison volume (pcu/h*lane) paern1 delay(s) paern2 paern From he able, wih he longiudinal comparison, he delay increases as he flow rae increases. However, according o he simulaion resuls, here is a cerain convergence of delay increase, which is consisen wih he realiy. Bu he rae of increase in differen syles of delay is differen. Auonomous Vehicles Since we only ake auonomous ino accoun, when he basic condiions such as charging mode, road shape and so on remain he same, he driving rule of he auopilo vehicle ino he oll plaza is equal o he driving rule of manual driving. The only difference beween he Auonomous and manual vehicles is driving behavior. Followings are some assumpion for he auonomous: All auopilo vehicles have he same vehicle sandards, he homogeneiy of he auonomous vehicle; The auonomous vehicles have beer driving skills hen he normal ones and provide beer safey; Wih more auonomous cars, he average ime headway become smaller; When muliple auonomous vehicles have he same desinaion, hey form small group in column. Inside he group, and ime head way disance beween each oher is far smaller han manual cars. Bu hey also can choose no o join i; The auonomous vehicles are jus like manual cars when hey drive alone on he road wihou oher auonomous cars; They can pass all kinds of olls freely; The mos wo significan changes are he appearance of groups of vehicles in
20 Team#55307 Page 20 of 25 column and he reducion of average ime headway boh making i harder for manual vehicles merge ino he adjacen lanes. According o our model, () l c remains consan for drivers bu he chances ha hey could mee a proper gap o merge reduce. Therefore, we may make he merging happen earlier or exend he acceleraion lanes. Paern 2 and 3 end o be more suiable for his siuaion. Proporions of Differen ollboohs Manual oll means charges are paid manually, including parking, preparing he money, paying he bills, aking he invoice and saring, which is he exac assumpion in our model and designs and according o he assumpion i can serve 360 pcu/h a mos. Auomaed ollbooh: The charging mode is charge by charging machine such as eller machine or POS machine. The charging process is also included parking, preparing money, paying he bills, aking he invoice and saring, bu here are no saff running he olls. Elecronic Toll Collecion can charge each vehicle wih special chips or oher devices. The vehicles wih such equipmen can drive direcly hrough he olls wihou parking or deceleraion According o he experience and curren daa, we canno deermine which has higher service rae beween manual and auomaed ollbooh. Therefore, we combine he wo as one form, noelecronic olls. The raffic engineers end o pu he highspeed lane in he middle of he road and he farher from he cener divider, he smaller he design speed. According o he analysis above, in order o reduce he impac of highspeed vehicles passing hrough oll saions on oher vehicles, we sugges o pu he elecronic olls in he middle of he barrier ollboohs wih isolaion measures unil all he cars reach he same speed level and no o arrange merging poins connecing lanes from differen kinds of olls due o heir huge speed difference. Conclusions We build Probabiliy Model of Vehicle Merging Safey o evaluae he probabiliy of acciden prevenion in differen merging areas and o calculae he heoreically limi lengh of he merging lane, which helps us design our paerns. Delay model and cos model along wih VISSIM simulaion enable us o evaluae our soluions and make comparison from differen perspecives. According o he resuls from VISSIM simulaion, paern 1 performs he bes for is delay and variance of speed are he smalles. All of he hree paerns can make heir ime cos and area cos achieve he bes a he same ime. Paern 1 works bes when errain condiions are good and he proporion of rucks and buses is high.
21 Team#55307 Page 21 of 25 Paern 3 has he bes effec when errain condiions are limied and he proporion of rucks and buses is high is low. When we add more auonomous vehicles, paern 2 or 3 is more suiable. Specific choice depends on governmen planning, consrucion mehods, and raffic composiion. Furher Sudy Consider he effec of heerogeneous cars, ollboohs and charging modes; Take HOV lanes ino consideraion, where only he vehicles carrying more han 2 people have he righ of way Selec real daa from New Jersey including average ime headway, vehicle Engine performance parameers, volume, peakhour volume and so on o calibrae model; Design and analyze oher merging paerns based on our model and compare he acual operaion performance and improve he model. Srenghs and Weakness Srenghs We ake safey, cos and hroughou ino consideraion, and pu safey as he primary indicaor. We combine he models of carfollowing and gap inerpeneraion models ogeher as he basis for our model. The securiy model includes boh auonomous and forced lane changes. Our model easily adaps o problems wih differen geomeries, such as differen numbers of lanes or even differen boundaries, which has grea universaliy and adapabiliy. Based on VISSIM, he model is validaed by raffic simulaion. The daa of VISSIM proves he correcness of he model. Weakness For some raffic parameers, such as flow, headway, gap, velociy disribuion and oher parameers and phenomena, we need field observaions and inducion, and parameer calibraion can be beer refleced in he model. No consideraion is given o he speed change of he vehicle a merged lane. No consideraion o oher ypes of vehicles, he model is only suiable for he same lane wih he sandard ype of vehicle. The disribuion of headway is only heoreically and has no been verified. Differences in driving behavior across counries are no aken ino accoun.
22 Team#55307 Page 22 of h January 24, 2017 Recommendaion of Design and Adapabiliy Evaluaion of Toll Square o New Jersey Turnpike Auhoriy Dear Chief of New Jersey Turnpike Auhoriy, We are a eam from MCM, and we re wriing o express our suggesions abou he oll plaza o improve is level of service. The ollboohs are ofen blamed for highway congesion and regarded as he boleneck of he road ne. Wih he developmen of science and echnology as well as social progress, new charging modes, such as auomaed ollboohs and elecronic ollbooh, are becoming more and more popular hese days. On he one hand, he advanced echnology does help o expand capaciy of he olls. On he oher hand, he remaining opimizaion space is geing smaller and smaller which means we have o ake he merging area afer he olls ino furher consideraion. As paricipans of MCM, we desire o conribue our own effors o you afer exhausive on his problem. All he suggesions we provide in following have heoreical basis. Hope i would help. Firsly, we srongly recommend he following hree merging paerns. All of hem are resuls based on he model we esablished. No only did we consider safey, hroughou and consrucion cos, bu also ake ime cos ino consideraion and pu safey a he firs posiion. The hree paerns are applicable o differen siuaions: Paern 1 works bes when errain condiions are good and he proporion of rucks or buses is high. Paern 3 has he bes effec when errain condiions are limied and he proporion of rucks and buses is low. Specific choice depends on governmen planning, consrucion mehods, raffic composiion and any oher facors affecing he performance.
23 Team#55307 Page 23 of 25 Secondly, we advise you o pu elecronic olls close o he inside of he moorway wih isolaion measures unil all he cars reach he same speed level. Also, please don arrange merging poins connecing lanes from differen kinds of olls, due o heir huge speed difference. We find ha he difference of speed beween wo adjacen lanes and difference of variance of speed in one single crosssegmen are he decisive facors o safey. The higher he value of he wo kinds of difference, he more dangerous for all he vehicles. In addiion, we have analyzed he influence of auonomous vehicles on he shape, size and merging paern and have found ou ha wih selfdriving cars, he shape and size of he merging area should become larger. Wih hose cars wih highlevel driving skills, he average disance beween vehicles ends o be smaller. Therefore, manual cars need more space o change heir lanes. May all he drivers in New Jersey enjoy heir journey! Yours sincerely, MCM Team
24 Team#55307 Page 24 of 25 References Highway Capaciy Manual, Naional Research Council, Washingon, D.C., 2000 Pan Yiwei. Sudy on he Mechanism and Characerisics of Boleneck in he Confluence Zone of Expressway. Souheas Universiy Li Xun. Research on Mulilane Inducion and Conrol. Norhwesern Polyechnical Universiy Yu Wei. Sudy on he Relaionship beween Lane Change and Traffic Congesion. Souhwes Jiaoong Universiy Su Li. Sudy on Design of Toll Saion of Expressway. Changan Universiy US Average Wage Level. hps://zhidao.baidu.com/quesion/ hml Brian Camley Bradley Klingenberg Pascal Gereuer For whom he booh olls The UMAP Journal 26.3 (2005) :
25 Team#55307 Page 25 of 25 Appendices Malab code: funcion pd=myfun1(l,s0,l0,q) pd=1.*(l>0 & l<=s0)+exp(2.*q.*(ls0)).*(l>s0 & l<=l0); end funcion lf=myfun2(l0,a,v,v0,c,q,kesai) s0=((v.*v)(v0.*v0))./(2.*a); q= * *q; if kesai==1, p=exp(q*c./3600); end if kesai==0, p=exp(q.*c./3600)+q.*c/3600.*exp(q.*c./3600); end if kesai==1, =3600./(q); if >=c, p=1; else, p=0; end end qo=p./v; l=1:2:l0; pd=myfun1(l,s0,l0,qo) plo(l,pd) pdf=0.05; lf=log(pdf)./(qo)+s0; end funcion [v1,l1] = myfun3(l0,a,v0,vf,c,q1,q2,kesai) for i=1:500 v(i)=v0+(i1).*a; l1(i)=shibaihuiliu(l0,a,v(i),v0,c,q1,q2,kesai); if abs(sqr(2.*a.*l1(i)+v0)v(i))>vf, break end end [v2,a2]=sor(v,'descend'); v1=v2(1); l1=shibaihuiliu(l0,a,v1,v0,c,q1,q2,kesai); end
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