1、Fo r o f f ice use o n l y T1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ T2 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ T3 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ T4 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Te a m Con tr o l Nu m be r 7 0 1 7 4 Probl e m Ch o sen B Fo r o f f ice use o n l y F1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ F2 _ _ _ _ _
2、 _ _ _ _ _ _ _ _ _ _ _ F3 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ F4 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 2 0 1 7 M C M /I C M Su mm a ry Sh ee t ( Yo u r tea m s s u m m ar y s h o u ld b e in clu d ed as th e f ir s t p ag e o f y o u r elec tr o n ic s u b m i s s io n .) Type a sum m a ry o f yo ur re sul ts o n
3、 t h is pa ge. D o n o t i n clude th e n a m e o f y o ur sc h o o l, a d viso r, o r tea m m em be rs o n t h is pa ge. L o n g l in es a n d h ea vy c o n g estio n a re m a j o r pr o b lem s t h a t a re f a ce d a t tol l boo th p la z a s a cr o ss th e coun tr y. In pa rticula r, th e Ne w J
4、 er sey T urnp ik e is i n f a m o us f o r i ts h ea vy tr a f f ic. Thi s pa pe r pr o p o ses a m etho d f o r d ev el o pin g a n d ev a lua tin g n o ve l p la z a d esig n s wh ich i n corp o ra tes th e ef f ec ts o f va ryin g leve ls o f tra f f ic, to ll bo o t h p a ym ent m eth o d s, a
5、s well a s th e ef f ec t of a n in cr ea si n g n um be r o f a uto n o m o us, self - d rivi n g c a rs. Fi rst a m o d el o f t h e pla z a is cr ea ted in Ne tLogo , a n a gent - ba sed m o d eli n g s o f tw a re . A gent - ba sed m o d eli n g is a n a tura l cho ice f o r si m ula t in g a pr
6、 o blem suc h a s th i s, si n ce it a ll o w s ca rs to si m ul a te h um a n i n ter a ctio n s i n tr a f f ic. With th is f o un d a ti o n o ur robu st m o d el is a ble to ev a lua te m ult iple re a li z a tio n s o f a wi d e ra n ge o f va ria bles in f luen ci n g c u st o m sa ti sfa ctio
7、 n o f th e pla z a . Thi s r ep o rt a lo n e a n a ly z es o ve r 7 0 0 pos si ble com bi n a ti o n s o f th ese va ria ble s, ra n gi n g f rom la n e d rop d esig n a n d n u m b er o f h ig h wa y la n es t o d riv er pa tien ce a s well a s th e p a ra m ete rs m enti o n ed ea rlier . It wa
8、s f o un d th a t a sy m m etr ic d es ig n wa s d esire d to m a xim iz e th e sa tis f a cti o n a s well a s e f f iciency o f th e pla z a . A d d iti o n a ll y, th e ef f ec t of th e n u m be r o f ele ctr o n ic tra n spo n d er o n ly la n es wa s si gn ifica n t, wi t h a h ig h er n um be
9、 r o f s uch la n es corr esp o n d i n g t o a h ig h er o ve ra ll sa tis f a ctio n ra tin g. It wa s a ls o f o u n d th a t the ef f ec t of s elf - d rivin g ca rs wa s ne gl ig i ble, th o u gh t h is m ig h t b e ex pe cte d a s th ey s h o u ld o pe ra te clo se t o h u m a n o pe ra te ve
10、h icles. It wa s f o un d t h a t a cr o ss pa ra m ete rs, th e a bili ty t o re d uce th e a m o u n t of st o p - a n d go tra f f ic ma d e th e gre a test im pa ct o n th e sy st e m . Thi s m o d el is ve ry ve rsa til e a n d is a ble to be a pplied to cha n gi n g tr a f f ic d is pos iti o
11、n s ( i.e . a gg re ss ive vs. d ef ens ive) , to ll bo o t h types, a n d h ig h w a y spe ed s e n ter in g a n d ex it in g t h e pla z a . Proper use o f th i s m o d el wi ll lea d to in va lua ble a n a l ys es t h a t c a n a id in ea si n g t h e co n gest in g of m a j o r t o ll pla z a s
12、a cr o ss th e U n ited S t a tes. An Agen t-Based Mo del for Dev eloping and Ev aluatingE cien t T oll Plaza DesignsMCM Problem B: Merge after T ollT eam 70174Jan uary 23, 20171P age 2T eam 70174T o the New Jersey T urnpik e Authorit y:The New Jersey T urnpik e is one of the mos t notab le roads in
13、 the nation. Unfortunately , its notoriet yis lik ely a case of infam y . The New Jersey T urnpik e is a toll road, and toll roads often frustrate tra v elerswith their long lines. In addition, toll plazas are often dangerous, esp ecially when cars are forced to mergequic kly after a tollb o oth. Ho
14、 w ev er, there ma y b e hop e f o r the public image of the NJT. If a m or e e cien ttollb o oth plaza design w as implemen ted, the NJT could see a reduction in tra c and an increase in safet y .W e ha v e dev elop ed a mo del to sim ulate the mo v emen t of cars and tra c on the toll plazas of th
15、e NewJersey T u rnpik e (NJT), and w e hop e that it can b e of some use to y ou . Our mo del w as dev elop ed in Ne tL-ogo, a soft w are program that is of te n used to mo del ph ysical and so cial phenomenon. O ur mo del considersindividual driv ers on the NTJ. In our mo del, individual cars mak e
16、 c hoices that aggr e gate to form groupdynamics. Th us, the mo del can sim ulate tra c and queueing on toll plazas of v arious sizes. In addition,it c an b e easily altered to consider div e r s e scenarios relev an t to the NJT, including di eren t lev els of tra co w, self driv en cars, and the d
17、i eren t pa ymen t metho ds that tra v elers use on y our roads.Of particular in terest to us is the cost, w ait time, safet y , and throughput of the toll plazas on the NJT.It has b een theorized that manipulations of the merging strip after a toll plaza could increase the e ciencyand s af e t y of
18、 the NJT. W e ha v e b een in v estigating that claim, and ha v e some preliminary results. So far, i tapp ears that toll plazas are most e ectiv e if lanes decrease from their increased width to normal road sizesymmetrically . It ap p ears to remain true regardl e ss of total lane coun t or tra c d
19、ensit y .Another in teresting result of our mo del is that the patience of individual driv ers h a s a great impact onthe system. In our m o del, whenev er cars came to a complete stop, they su ered a loss of patience, meaningthat they w ere frustrated and more willing to mak e risky driving decisio
20、ns. In ligh t of this, e orts should b emade to preserv e the patience of driv ers on the NJT. P erhaps something as simple as decreasing the sp eedlimit on the p ortion of the high w a y leading up to the toll plazas, so that cars are driving for longer, insteadof stopping, w ould mak e the system
21、more e cien t and safe o v erall.W e ha v e not y et in v estigated man y of our theorized toll plaza des i gns, but w e w an ted to pass the mo delalong to y ou. The mo del is equipp ed with a v ery user friendly in terface, whic h y ou can use to in v estigate an ysituation immediately in te r e s
22、ting to y ou while w e conduct our o wn researc h. W e ha v e c hec k e d the robustnessof the mo del, and it pro vides trust w orth y results.W e sincerely hop e that our rep ort and its m o del pro v e useful to y ou, and that it pro vides suggestionsthat mak e the NJT more pro table, as w ell as
23、safer and more e cien t for those who tra v el on it.Sincerely ,MCM team 70174P age 3T eam 701741 In tro ductionT ollroads are seen all o v er Ame r ic a, with 42 states, D.C., and Puerto Rico all ha vin g some sort of toll road. 9 .T oll plazas, where tolls are collected, t ypically con tain more l
24、anes than the roads leading in to them. Thiscon guration requires cars to merge on to a cond e n s ed lane after pa yin g their toll. It is p ossible that a certaincon guration of merging lanes, as w ell as the ad dition of more automated tolls, migh t increase the e ceincyof the toll plaza, raising
25、 the satisfaction of tra v elers o v erall.An analysis of this t yp e is esp e cially p ertin e n t in New Jersey , home to the infamous New Jersey T urn-pik e (NJT), a 148 mile toll road. 5 A recen t study sho w ed that New Jersey is the only state that is d is l ik edmore than it is lik ed. 6,7 .
26、Though there are man y f ac tor s in uencing publi c opinion of the state, it is lik elythat one of them is the NJT. The NJT is kno wn, and not fondly , for its long w aits and high fees. If a new tollplaza design could decrease costs and w ait times, it is p ossbile that New J e rsey could impro v
27、e its p ublic image.In addition, there is a push in New Jersey for the automation of toll roads through the addition of au-tomated tollb o oths. 10 . While automated tollb o oths promise p oten tial sa vings to b oth the go v ernmen t andconsumers, they also th reate n the job securit y of h undreds
28、 of Americans. It seems necesarry to compare thecosts and b e n e ts of all sc enar ios b efore making a decision.2 Analysis of the ProblemThe problem prompt asks us to consider a toll plaza, where L lanes fan out in to B L tollb o oths and thencondense bac k in to L lanes. The strip of r oad after
29、the toll plaza, where cars are exp ected to condense tofew er lanes, can tak e man y shap es. These shap es a ect the abilit y of cars to merge on to the high w a y safelyand e cien tly .W e are ask ed nd the “b est“ design for a tollb o oth plaza. This solution should consider suc h things asaccide
30、n t prev en tion, the throughput of the toll plaza, and the cost of the plaza. W e are a l s o ask ed to con-sider our solution in a n um b er of di eren t conditions, suc h as ligh t or hea vy tra c.T o address this c hallenge, w e will use NetLogo, an agen t based mo deling soft w are 2 , to sim u
31、late theoret-ical toll plazas. These plazas will ha v e v ariab le n um b ers of lanes-in, L, and to olb o oths, B, with v aryingpatterns in the merge strip after the toll. The tollb o oths will accept di eren t pa ymen t metho ds (electronic,cash, exact c hange). The cars driving through th e plaza
32、s will b e a mixture of automated or h uman driv en.The res u lts of these sim ulations wil l b e ev aluated using a de ned satisfaction metric that g i v es equal w eigh tto cost, w ait time, an d safet y . After determining a few optimal designs, w e will ev aluate ho w thes e ideal tollplazas pre
33、form in v aried conditions, lik e ligh t or hea vy tra c, or a higher prop ortion of automated cars.3 Assumptions and Justi cationsAssumption: There are more toll lanes than incomi n g tra c lanes.Assumption: Cars alw a ys go to b o oths of their assigned pa ymen t metho d.P age 4T eam 70174Justi ca
34、tion: When driving on toll road s , p eople are t ypically v ery careful to c ho ose an appropriatelane. Moreo v er, if cars en ter the wrong lane, there are usually pro cedures in place to ensure o w is notdisrupted. F or instance, on the NJT, if a c ar en ters an EZ pass lane without an EZ pass, t
35、he driv er isbilled later th rough the mail. 11Assumption: The cost of restructuring a toll plaza will b e ab out the same.Justi cation: W e are more in teres ted in a long-term analysis of toll-b o oth p erformance as w ell assatisfaction. Moreo v er, hiring a construction crew and pa ying for mate
36、rials will b e similar for B-Lcom binations that are the same. The real cost comes from ha ving to emplo y w ork ers to man th etollb o oths.Assumption: Cars alw a ys c ho ose the shortest lane of their pa ymen t t yp e, so long as theyare able to merge in to that lane.Assumption: Self driving cars
37、are p erfectly patien t.Justi cation: The tec hnology on self driving cars is orien ted to w ards acciden t prev en tion, e.g.,correcting lane drift and detecting p ossible ob jects in a collision path. 8 Th us, it seems that self d rivingcars practice defensiv e, rather than aggressiv e, driving. I
38、n our mo del, this translates to maxim umpatience.Assumption: Human op erated b o oths and exact c hange tolls (where money is giv en to amac hine) are considered equiv alen t.Justi cation: This is partially necessary to reduce complexit y i n the mo del and allo w for solv abilit y .Ho w ev er, thi
39、s is realistic in that the appro ximate time to pa y eac h is the same and t hat h uman mannedb o oths w ould b e able to tak e exact c hange.Assumption: Driv ers ha v e v aryi ng lev els of patience.Assumption: Cars that are pa ying with an electroni c sensor, suc h as an EZ-P ass, ma y gothrough a
40、n y lane.Justi cation: On the New Jersey T urnpik e, ev ery tollb o oth is equipp ed with an EZ-P ass se n s or . 5Assumption: All toll plazas use a symm etric fanning-out metho d to separa te in to tolllanes.Justi cation: This allo ws for strictly the exit strategy to b e assessed as desired. Addit
41、ionally , th isshould b e the easiest w a y to construct toll plazas in order to k eep as m uc h of the previous infrastructureas p ossible.Assumption: Ev ery toll b o oth services t w o lanes.Assumption: All autonomous driving cars are equi pp ed with the EZ-P ass pa ymen t metho d.Assumption: The
42、a v erage time to pa y at a toll b o oth is 30 seconds.Assumption: The a v erage v ehicle on the road is an SUV.P age 5T eam 701744 T oll Bo oth Plaza Mo del4.1 Mo del Dev elopmen tOur mo del is is built in NetLogo 2 , an agen t based mo d e li ng soft w are dev elop ed b y Uri Wilensky at North-w e
43、stern Univ e r s it y in Illinois. Besides its s tr e n gth and v ersatilit y , NetLogo is also freew are, making it easilyaccessible and extremely useful for the rapid creation of complex mo dels. NetLogo is v ery w ell constructedin t hat it o ers a large set of pre- d e ned metho ds that allo w f
44、or complex in teraction b et w een agen ts theen vironmen t. The mo deling in terface also allo ws the user a large range of input v ariable options makingNetLogo dep enden t on user input if nee d e d . In NetLogo, it is p oss i ble to program the b eha vior of h undredsof individually acting agen
45、ts. Ov er time, as agen ts in teract, it is p ossible to “explore the co n nec ti on b et w eenthe micro-lev el b eha vior of individuals and the macro-lev el patterns that eme r ge from their in teraction.“ 3This elemen t of agen t c hoice mak es NetLogo a natural c hoice f or our problem, where th
46、e individ ual c hoicesdriv ers mak e ab out where to direct their cars impacts the e c iency of the system o v erall. Additionally , Net-Logos b eha vior space to ol can rapidly output data b as ed on user input once the mo del is fully constructed.Although toll roads and toll pl az as exist all o v
47、 er th e coun try , this mo d e l is based o of the toll plazas ofthe New Jersey T urnpik e (NJT). This is done to ensure that this rep ort ma y b e useful to the New JerseyT urnpik e Authorit y , who this rep ort is prepared for. In addition, although our primary in terest lies in themerging patter
48、ns after tollb o oths, our mo del in c l udes the lanes b e f ore the tollb o oths. W e included this partof t he plaza so that w e c ou ld accurately sim ulate ho w p eople queue when w aiting to pa y , whic h a ects theirdisp ersal in to me rgi ng lanes after the toll . Moreo v er, this allo ws fo
49、r an easier in v estigation of a discreteproblem than statistical metho ds migh t a ord, e.g. a P oisson Distribution go v erning arriv al time of cars.In d e v eloping the mo del, w e sough t to b e able to v ary the n um b er of lanes in, L , and toll b o oths, B . Ho w ev er,w e also sough t to dev elop a m o del that c ou ld accoun t for v arious tra c lev els, pa ymen t t yp es, and cars (i.e.self-driving or h uman-op erated). T o sim ul ate realistic decisions of h uman driv ers, w e equipp e d eac h car witha unique top sp e ed, patience lev el, and servicing time. The adv an t
