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Unformatted text preview: CHAPTER I s Enimdsetésn is Meeeis We now discuss modeiéng concepts so emphasize what is impomam in bufiding transposmtioa models. If we are thinking, for example, about deveioping 2: sransportation mode} ofthe Boston metropolitan area, we can reiatévely quickly come up with any number of modding issues we wouid have to deal with in representing transportation in Boston. For example, we have so decide aeout {he scaie at which to stuciy Bosion. How many nodes do we represent Boston wish? 5? 58*? 500? 5,000? How many iinks? At the link ievei, we have modeling choices: do we represent traffic as a set 05 individual vehicles (discrete meek-:3) or as a flow {eontinuoos modei}? A: the node levei, we can represens a bus tennimi, for example, as a deierministic (Edgy function or we. can model it as a eos‘nyiex microwsémulation, which gives us a profiabiiéstic regiment-soon of delay for each veiséeie. Whaz are the impficatiom of these decisions? How many digerent modes do we consscier in éeveioping this mode} ofBosion transportation? it is clear tint we would have separate modes for automobiles and transit, but do we need a separase mode for waEkess and bicyclists? Shouéd these modal mocieis 211% be insercon—n neared? Or, should we have inciependeni: models representieg each of these modes? $10an we consider the flows on the networks as smtéc, or shouid we represent flows dynamieaflywas a function of time? Shouid we consider short: run or tong mu issues? Do we aiiow for changes is: laudnuse? Do we consider equfiibsiom? We talk about equfiibrfium as a way to think about transportation systems, and we 211i beiieve is; however, it is interesting how many models we come up with the: are usefu} bu: ignore egofiibrfiom. $36 MGfifiLENS CONCEP?S Emmy, x 1.1 Hierarchy (firrlodds. filerarthies a? Mofiels 5’). key nmdcling conccpt is that ofl'licmrchics 0fn-mcicls (see: Figure 11;): Very of‘ecn we have modsls efcomponems {hat dcscrihe ihc blahavior 95 individual links or DGdCS. They desm’ilve how a traffic intersectien or a highway link perfbrms. We might have rclationsi‘zigs that describe fiew fuel is consumtd anti haw emissions are produced by a vehicle as. a fimctfion of velocity and accclcmtéon. We have models that (icsmlxg how customcrg cheese among trausportazion moécs laasecl (m Elnpifigai data. All ofthcse models {it together in some hierarchical way that gives 30:11:: broader represenmtion of a regicm iikc {fie Boston area This might lead {0 models of cconemic growih, of landmusgl of nciwork behavior, all of which are based cm l9w~levcl, more detailed moclcls dealing with fuel consumption, vchicle emissigng, link bahavior, 0: node ljchavior. Thoae dctailacl medcls ofcompgnem bchavmr lead as $0 an apprapriam macroscopic medal of evemfl systci'n behavior. fifiafigfing¥ssues There are many modcling issues on which m focus. Through expe— rlcncc, Wt: have learned ahat the fellowing issues are imperial: in deciding how {:9 develop a sransportation model, gougejaries The first issue is boundaries. Eran chi: field of struczuml cugincefing, we have the concept of frembedy diagrams (see Figure E12}. We take an claimant: and isolate: it from the rest of the structure; we analyze it by representmg the entire rest of the. structure as a set of farms azlé moments an that element~se it is a free boéyc Macroscopic madei of aysiem behavmr Detailed models of compeaené‘ behavier .EN'I‘EHJSJULL'I'aQN T0 TRANSPORTATION SYS‘rEMS Fist ere ; Piazza A com when? lN'rR Kids (sec: Figurs: 11$), scribe the behavior of :43}: intersection 0; a :ips that éescribe how :ed by a which as a medals that describe less bascci or; empiricaé rchicai way that gives Eiosmn arm. gmwth, 0f haciwuse, on Eowwicvei, mars a, which? Emissions, nodc‘is ofcemponsm éc made} 0%" overaii acus. Thmagh expa— 165 are. important in :uctura} enginecfing, figure 11.2). We take: um; W5 analyza it by a 565: if forces and mafia} havéar flTEO-N SYSTEMS INTRODUC‘I‘EON i?! a: 3‘ 3% Baum 1 2,; £5. {aye—{70d}! diagram. % E; E. k. E 5: g E f E} E i i E g: E i g g Emma IL} 5: A rompiex syxtcmmm E where £5 21w éowza‘aqt? Satmfiucfion is: Maéeis ‘53? / We haw the 52:13:: isms m Eraszsporcation :‘ilodchng {scc Figure ”£1.30. What are {ha limits we impose in smdying the system? Where (in we draw the *boundasy? What is {putside anci win: is inside? An: we going £0 consider changes in technoiogy over €ime? Are we going to considar changes in iamdmse? Are we gaing :9 congider whafi our compatiiion does, or is this mafia} intended {a teli us oniy what 1:0 do in the next two h€>urs, and we. RSSEEITK‘: that our competition cannot (is aux/{hing in {bat time frama? Are: we going t0 éook at econoimc impacts, environments}? impacts, anfi grow‘ih of’m urban area? Macmsmgic Versus Micmsmgéc Madam Another modeling issue: is the levfl of demfi—macmsmpic versus 1mm scopic models. For exampEe, as we mentioned, cadier. we can modai a A pessibie system / boundary Operaiiuns . . ' Technaiogy Companion AEE quaiiiy, resourceés Land use Ewnemic growth TO TRANSPQEITATION SYSTEMS iSS MQEELING CfiNCEPTS temiinui as a Simpic L'it‘EL’l‘l'l'liiliSEiE.‘ (fishy finictien or through a migm scopic simuiuiimz. Siam Versus {Eyiiamie Mosfiais We distinguish bcmreen static and dynamic i'iiOCit‘iSA—dt) we use 1210‘};ch in which we assume the. kcy variabies are independent oftimc or {is Wt: taik about tinic—depcndeiit ”width that fly to reflcci‘ rushwhour pfigks‘ as apposed to steadywstate operations, in our study of {taxispormtimé systems? Do we assus'iie static human hehavier {31" do we model we reactions of peopie :13 situations; change? Staizhafific Vamus Qe’ierministic Moéais A fundariimtai qusstiozz is whstiicz' {0 represent transpoziation as a stochastic or a deterministic system. We. have ciiscusseci S£0£hasticiiy as a charafieristic of transportation, but i: may wail {um out in some applications rim wt? can gain some insighz 3:26 knowiedg€ 33y simpiy reprcscsizing a system as detcmiinistic. Linear Versus flaniénear Madam We taik about iinear varsus tmniiueaz‘ E‘flpffisel'iflfiifil‘lsi When we mlk about using linear programming :9 menize a sysittim, Wt: are basicaiiy assw'ning a iiiiear View ofthe world. it may be incerriici, but: iioniizicar models, while more correct, may be much mere difficuit $9 501th Lin— ear versus rmziiinear iimdcis is a gaod exampie ofthc trade—ogbctween emistmciirag iiiodcis [i135 can preduce answers reiativciy easiiy versus medals that mpmsmit the work} better but turn out to be more difficuit {a solve. flaminmus Versas DiSCieie Mmfieis We talk about cositiuuoais vsrsus :iiscmtc iizodfiis, Speaking mafizeimtb caiiy for 21 moment, WQ iconic? €31}: abom rcpréscnting the worid as a sei of difii‘rcntiai equatiens, that is, as continuous equafions; or we can rcpressnz the. W’Orid as a 36$ ofdifftrczict? equatieiis. fit 5mm: point is} an? iiws, we’ve. had some {zmciign tin: had to be intfigmtfid*—W£ iiiiii to get tin: arm under tin: curve {mm X1 {0 X2, and for whatever reasofi iNi‘EQi)U<‘:'¥EUN 1'0TRAN5POR'IATIQN SYSTEMS in '1 01” through a :13ch" :irw’ig we use medeig dent chime or do We fleet rushwheur peaks, 13d}; of transportaiion or do we modei the 1% transpcrmtéon as a name? stochasticity as fl'i {um oer in some :zmwledge by simply 30:13. When we {aik rem, We are basicafly ozrreez, but eoniénear ifficuit to soive. Lin~ 1e trademeffbetween iativeiy easiiy venue : to be more difikuit peaking nmtiwmatie eg the world as 21 set guetéons; or we can kt some. point in our megrated we had far whatever reason ”mum Sve'rnms EzGUKe 11.4, Grass representatim am! derailed‘ representefimz. [NTROEUC'i'EON inirecfiuctioe ts: Mudets $39 the function was in web a farm that :10 matter how much we looked through Our mifie ef‘imegrak, we could not find the answer {see Figure HA}. What we do in that: case is a numerical seluiion‘ We say, “Let’s break this area up into rectaugies and let’s compute the area by adding the rectangular areas." We recognize that the amount of mm: that we wili have is a function. of haw many reciangies we have. if we have a {aiziy grass representation, we may make a big mismke; if we fiave a demfled representation, we can some up with a more accurate answer. it is ihe question. between continuous amci discrete represenzatéom 0f reaiity {hat we are talking about here and how eéosely {he fiiscrege representation reflects the continuous representafien. The gross represeetation preduces quick answers-“mere are fewer rectangles. The price you pay is accuracy. The detailed representazien preduces a more accurate answer bui gakes more timema Ciasséc modeling tméemofl ifwe have a fainctéon y m {{x) that we can integrate in closed form, the way :20 get: the area under the curve is m simpiy integrate. But, ifwe have a function that we do not know haw £0 integrate (anti this is often the case), we have to 3:39 tiimugh this in a linear fashion. Ifthe horizon- taE axis is time, we are sieppmg {he model through time. TO T]{ANSPOR'£'A'}'E()N SYSTEMS 14G MOBELING GQRQEPYfi Heme 21.5 A KimM;afi02?%$!{’ppfflg a mode! Efamugh rims: Nemerieai Simuiatian Verges fisasaa $9M! Seietiea These are numerica} or sinmiation analyses; they turn m1: to be yaw 1156*qu fbr generating results because we can Virtuaiiy aiways d0 3 zmmerieal er simulation analysis. Semetimee, however, {hey can be very expensive because they take a leng time :0 {as}. An anaiytjcgg closedmform i5 better if it preperly represents reality (see Figure 11.5} We can extené this hie-.1 to stochastic sysmme (icing prebabiiise :ie simulatiom by using computer pregrams cafied randomwnumbe; generators to represen: preeabfiéstic hefiavéoy in the system of interest, Eehaviemi Verses Aggmgate Mofiais Agaether modeiing quesaen is beha‘vfioml versus aggregaie representatiom We have discrezeweizoiee models foe modding what people tie in making transportafion and relateci choiceswowcalied behavioral medels, Aggregate representatiens are possible as weil. The ‘eesi: know: example is probably the gravity mode; where we can mode} {he amomzt of flow bezween iwe geographic points as inversely prepay {ions} to some functien ofthe dismnce betWeen {hem or, mom genes aily, the resistance—wiismnce, quality 05 reads, and: so fereh. The deveiopers of the gyavity mode} dtew 11pm: the insights of Newton in the context of mechanicg; the idea is that perhaps Cities or regions within areas weriz: that way as wefl. The flow between them is inversely preportiormi H) the square ef Ehe resistance {01" same other power) iaetween chemhhence the name “gravity moeiei.” Beth behaviorai snzi aggregate medels can be useful? for particaflar appfiicaziens. §’hy$icai Verna Mathematicai Madam Another dissinc:£iox1 is between physieai and mathematicai modeis. In some areas of syssems, we can physicaliy builci 3 mociei. in fluid /‘v _ m} Time 3 Yime Time inputfuneiéone Ouiputfunciiens INTROIJUC‘i'iUN ‘E‘O TilfiNSPOR‘i‘ATiON SYSTEMS ian turn out so be vary rtually always (la a wever, they can he 3 mn. An analytical y {see Figure $1.5), 15 daing grobabiiis_ ed madam-number 2 system {sfimemss gate repsesematiens. )eoggle do in rushing ml models. . The best knGWn NE: can model the ; inversely proper— m ore more generm and so forth. The nights of Newmn gs cities or regiesss :h them is inversely sme other power) {ash behavioral am} ti<>rss. zestical models. in : moéel. in fluid M Time {st functéons lBN SYSTEMS iatroauction :9 Models 3&1 mechanics labs, we might find wave masks; it is a physical scale repre— seamtlon of reality am? we cuuici do experimems using it. Models of structures are another good example. Salusien Yaehmaues Finally, we mention solution sechniques. Gating answers from the model is fundaz'nemal ta what transportatian professianals do. We an: often dealing Wish large~sca§e problems Where we are Optimizing Complex systems, The brute force method of looking at every 9035i» hiiéty is one of the question. Transpomtien pmfessionals have billions and billions of Options, so coming up with some efficient method far mathematically seazehing through decisien 393% using optimization theory is czfiieah Sometimes? scaling dawn the problem to make it easier to solve is an appropriate serategy when we develop models to predict perfonm ance. As nosed earlier, deciding between simple sepsesentsilens using closedwfosm mathematical solutions or complex sénmlation models to generate answers is very i‘inpOfiBFit. understanding she §ystem The key is kfiewing whas‘ approximatiohs we can make in mpreset‘ztiz‘:g reality, ané this is where an understanciing ofshe system, in om: case the immsportatisn system, Games into play. We know what kinds ofsimplim fications we can make and what khsds of models we need because we uziderstand the transporsaeéon system and the kinds of questihns we want answered. We are not interested in models per se (althozsgh they are fascinatiag in and ofthemselves). We are interested in transporm fission; models help us to make trasssportation systems heater. Now, many transpertation people make inspofiam modeling advancesM—improvemenss in techniques—faster opgimizatiorz algo— rithms, superior stasistieal analyses, and so fimh. I {and others) have observed that often those advances ase achieved by people with very harcl spglications to comidermlike trazssportasian. To address ehese applications, they end Lip advancing the state of the an: in modelihg. This is an imyorzam kind efaaivity. Many find it diflfiiculewimposw sible, maybe—«t0 think about impmving modeling technique in the abstractwahsent a specific prehlem. I believe {has many mocieling ENTfiOfiUCTEON TO TRANS?ORTA'{1GN SYSTEMS m MG§£LENG CGMEEPTS advances an: nude by $269916 with inmacmble appiications about Whig}; they need answegs. How {i0 wc decide which kinds ofmodeiing concepts to use? T0 answcr (his, we have go go back to wily we mode}. We nwdcfl m L:1)derswnd~~——msigh£ modeis; WC menial to axpiaéu; WC model {0 pmdict; and we modal ti) inmmve. The fimdammm} questien we ask when ws arc: deciding what kjmi ofmedei {0 use is: WM: are we going {0 we the remlisjbr? Be the. msults; numericai or simply imights, haw are “WC“. going us: £11059 rfisuhs? That shouid gavem the way in which we Cheese :0 modei. Efwc are going to talk about a mode} that is a matter oflife and dfiaih"—"ifthC? nmdel is wreng, the astronaut gets hiked—“We have wry {iifil’reni requirements for the modal than if WE an? sémpiy looking at a modei as way cfdcvcbping a firswordcr undersmzzding efa transu pm‘tatéon network. Rcmmnber: xfila.’ madcis am: wrong. However, same are usg’fuf. Ali models are abstractions {113% diminata some rataiity. "131:: acid asst is whedxsr the zalociei pmduccs results that are uscfili in cm: areas of émcrest. Transparimimz sys‘femx are mmgiax, dynalm's, am? {mermxiiy im‘ercmmected {15 we?! as {flier/(amazed wifls other campiex aiyrrcirriia: systems (9.3, the cz-szxiros-zmer—II) {he awrwmy). N16}! vary in space) and firms (mt dgfiiérsm {in-m scaiérsjér dffiérerif componemfl Serm're is pmyia’eci m cmnpiex nezzyories. W58 systems are smdmfizéc in mime. Human darn'5iot1—rzmkerg whiz somyiex décisiarz {afcrdzk make (from; Igza? shape {he trmispormrfiozz 5313mm. INTROSUCTIUN TC) TRANSPQR'I‘A’I'IGN Sys*;*1ams IN‘E‘RQ cations about wind} :anepts to use? T3 Mic? to cxpiztin; we miammata} questien :0 use is: :r? v are: we going use ich we choose to a matter ofiife and {:6 we. have very n: simpiy looking tanding of a transw rcaiity. The acid :2qu in our area 0f -’ furmzaify ' «rompz’ex Norway}. went wr-npwzeuis). éockasti: :‘n fiafzii’a’i. mics/134i mm. um SYSTEMS issues in Mfidei Suihfifig 343 J‘s/{adding 5hr: 5mm 5}»st £3 czfinwst iricwmivaiza’e. Ow {tlmfleizge is m (110059 Wigwam sziésysfems (md made! mm appmpricztefyfor the intended purpose, mimg‘hli}; reflectirag {he boundary egffirefs affix: ammodeiad companmrs. Ifwe are considering at a made}. to use in real time we are actualiy going to comm} the real system in real t.éme—~we have. to think abmzt sch/Ting the model fast anoggh {0: ii to he: useful. If we am going use flu»: modei for sensitivity anaiyses~ acid six trucks to the fleet and pmdict ievei—ofisewice change—{£16.11 we have :0 {kink abeut those sensitivity analysas as we buflé the model. We have t0 mink about fiat: knobs WE want; ti) turn on the nmdci when we build the 2110661. if we are inmrested in opiimizmg the graft}: Eight gaming in 303mm? we berm; not represent the wheie Boston tmffic Eight grid as; a single aggregate delay function. We. Wifl not get very far with that kind of {epmgenizatéon if wizat we med is :1 microscopic rcprcgentaiiim of individuai intersections, isms ii? magi Bu‘éisfiiag iN’raobucz‘ION There an: somc pragmatic issues we deal mm in modci baéldéng. is the mociei the right one? is it “true?” We paraphrase john Dfswey on the topic of how we know a moéei is “true.” Our modei @055 no: work in practice immme it i5 Hue; mike; we hold our model in be? true because? it works in, practice. “me and Reswmes Wa 1mm worry about tiny: and researces -------- money? computers, and peopie. When {has the: 33055 want the answer? What is our budget? Betta We have to think about data. What data dz) we have? What is avaiiablc t0 cafibiase {his mode} to ensure that it“ is operating correctly? How axpensive is it to colieca more? Data is aimost always 3 major considcmm Lion in real~wodd transportation systems. ‘I'U TRANSPORTATEON SYSTEMS 341$ MDQEZLENQ CGNCEPTS Designing a Suctessfui 3%}ng We ail Want m be successfili: how do ‘WL’ design a made! that is $9ng to be succcssful? By successful, we mean uscfifi and uscdm-at 50mm isveiwby the decisionmz'nakcrs for whem we designcd and 1111;316— mentcd it. SL3CC€SS in modeling i5 more at: art than a science. Here are some ways cf measuring guccess. Ease of Use The tactical ofcase ofme, dcvcigping uscrmfmcxzdly modcig is impormm flcvcloping medals that providc resuits in a farm that is consistent With the way it: which organizatiens make decisions is very important If {hrs kinds ofoutputs our made} is producing arc in some way dchrgem from the way in whicéz thc viccupresidcnt ofopcrat‘ions wants to make {icciséons about how she runs the network, the 3110ch is not going to £35 used. Coméméng Metfiais Bufidiag mode-:15; that arc convincing, that make intuitive sense to the user, is important. 6:1)th Pam Proviciing .s'noticis with a growth path that: we can modify or cxpazlé over time as Situations chaagc is impm‘tzmt t0 lengmtemi success. ifimduce Benefits Having medals that produce beacfits is fimciamcmal; we want to be 3:918 to say, “i uscd this moéci and now {he META was better.” To haw that outcome Cifiit‘r through the insights that management: gained 0: though dircct rcsuits that managenmnt was able: to use—“cozm’ng up wiih benefits-miss very important. Success breeds succe35wdevcioping a track record of useful reguits and demonstrabic benefits is important, Mmsuring Mofiei Success The ways in which people in pmctécc and {huge in academia measzufi this: success of models may (fiffar substantially. its a researcher, when i INTRODUCTION ":9 TRANSPGETAIION SYSTEMS New fievelepments Er: Moéels and Frameworks 1135 look at a model, i {look about concepts like unique solutions and assuring tho: there is a strong rheoretical base. However, when we go out to practice, geopie ask: “Does it help me in myjoh? Does it make me be a better vicempreséeleor ofMarkering than I was before i had this model?” in a some the notion is, “l Clo not care ifyou use a Ouija Board to get me these results; l do not really care about {he underlying basis ofrhis. I just wan: to Clo a beteerjo‘o.” There is a tension there berweeo {he perspeetives of rhe academic researcher and {he oerspectéves of eeople actually using morsels in the field. Sometimes the difference in priorirles leaés to some academic models not heing as useful in gracrlce as $1153; mighs: be. There are two ways that: we advance in rranspormtion. One is by advancing modeling merhoclologies—w—by thinking about: how :0 make better models for trans...
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