Basic Land Use Transportation Models

Transcription

1 Advanced Urban Modelng GCU 598 (28167 or PUP 598 (28168 Arl 30, 2010 Lecture 3 Basc Land Use Transortaton Models htt:// Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

2 Outlne Entroy Maxmsng Agan and Related Measures Resdental Locaton, Modal Slt Models The London Tyndall Model: Alcatons Transortaton Modellng: The Four Stage Process Modular Modellng: Couled Satal Interacton A Smle Examle of Modularty: Lowry s Model DRAM EMPAL Style Models Demand and Suly: Maret Clearng Inut Outut: The Echenque Models Next Monday s Lecture Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

3 Entroy Maxmsng Agan and Related Measures Frst we defne entroy as Shannon nformaton and we convert all our equatons and constrants to robabltes. Shannon entroy s a measure of sread or comactness n satal systems H log We maxmse ths entroy subect to orgn and destnaton constrants or some combnaton of these but notng now that we need another constrant on travel cost whch s equvalent to energy so that we can derve a model c Cˆ Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

4 We thus set u the roblem as max H subect to c Cˆ log But note that the robabltes always add to 1, that s 1 From ths we get the Boltzmann Gbbs dstrbuton for the robabltes Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

5 By settng u a Lagrangan whch s the method of maxmsaton, then we get or T ex( c T } } A O B D } ex( c Now we can generate any model n the famly of four models unconstraned, sngly constraned (orgn or destnaton and doubly constraned by settng the redundant constrant arameters equal to zero and smlfyng the model To derve a resdental locaton model whch s orgn constraned we now the nformaton at the orgn but want to redct the flows to the destnaton and add u these flows to redct actvty at the destnaton, we Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

6 We thus set u the roblem as max H subect to c Cˆ log or ex( c And we get T D T where T A O ex( c O ex( c ex( c Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

7 Several thngs to note: There s no attractor value at the destnaton we would need to ut ths n as a constrant.e. a ece of nformaton to be ncoorated by the model Ths s a locaton model we redct actvty at the destnaton n the case of a model that redcts how many eole worng n zone O lve n zone, ths s D where the rme s the notaton for redcted Now let us ut ths model bac nto the entroy equaton and see what we get let us ut the model bac n n ts exonental form ex( c Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

8 Then what we get s H Cˆ log log ex( c ( c Cˆ What we need to note s that entroy s arttoned nto a fxed energy and free energy the fxed s the second term and the free s the frst a seres of weghted log sums and t s often thought of a nd of accessblty. In ths case t s the sum of accessbltes, one for each orgn zone. It has strong relatons to utlty n the random utlty maxmsng verson of ths nd of model whch s central to dscrete choce theory / Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

9 Resdental Locaton, Modal Slt Let me llustrate n two ways how we can buld models usng ths framewor If we say that resdental locaton deends on not only travel cost but also on money avalable for housng we argue as before that The model s sngly constraned we now where eole wor and we want to fnd out where they lve so orgns are worlaces and destnatons are housng areas The model then lets us redct eole n housng We argue that eole wll trade off money for housng aganst transort cost And we then set u the model as follows Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

10 Ths tme usng not the robablty form but the tr actvtyvolume form, we get T T leads T T to O c A O R C R ex( R ex( c Note that we now add a constrant on money avalable for housng (le rent R. We can of course fnd out from ths locaton model how many eole lve n destnaton housng zones, so agan t s a dstrbuton as well as a locaton model P T Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

11 We can extend ths model n lots of ways and we wll show some of these later. We also can thn about dsaggregatng the model nto dfferent transort modes let us call each mode and then set u the model so that we can redct T as follows The model s sngly (orgn constraned because we want to redcts how many eole travel from wor to home. Gven we now how many eole wor at orgns, and we want to redct what mode of transort they travel on. Then T T T c O F C F Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

12 And the model can be secfed as T O F ex( c F ex( c Note that the mode slt s a rato of the comettve effects of each travel cost, that s O F F ex( c ex( c T T ex( c ex( c In short the model s not only dstrbutng trs so that locatons comete but also that modes comete BUT modes do not comete er se wth locatons Now let us see how we can buld ths model for real Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

13 The London Tyndall Model: Alcatons Essentally we have bult ths model for Greater London whch s dvded nto 633 zones the area has 7.7m oulaton and about 4.3m obs we have four modes road (car, heavy ral, lght ral and tube, and bus wal/be s a resdual mode. To fx deas let me show the extent of the area frst Go to to see many mas of Greater London Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

14 Vsual Analytcs and Modellng Processes Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

15 Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

16 Modes Road Bus Heavy Ral Lght Ral All Trs Road: 38%; Bus: 12%: Heavy Ral: 12%: Lght Ral 19%; Other (Wal, Be, Fly: 19% Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

17 Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

18 Accessblty from the LUTM model Many dfferent accessblty measures, 8 n all Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

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20 Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

21 Let us run the model I need to go to my folder >> Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

22 Run Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

23 For a very old move of all ths go to our web ste htt:// We need to retrac and say somethng more about these nds of satal nteracton models and how they can be extended Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

24 Transortaton Modellng: The Four Stage Process I should mae a bref ont about transort modellng we have ncluded transort and locaton together here but tradtonally the transort model s based on a four stage rocess that nvolves generaton, dstrbuton, modal slt and assgnment The other ssue s that n the standard transort modellng rocess, once trs are assgned to the networ, then one can assess whether the networ can tae the load ths s matchng travel demand aganst suly and f not then the model s terated to match demand to suly. Ths s another generc ssue n urban modellng demand and suly and the way the maret resolves ths. Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

25 Modular Modellng: Couled Satal Interacton Now we have a module for one nd of nteracton consder strngng these together as more than one nd of satal nteracton Classcally we mght model flows from home to wor and home to sho but there are many more and n ths sense, we can use these as buldng blocs for wder models. Ths s for next tme too What we wll now do s llustrate how we mght buld such a structure tang a ourney to wor model from Emloyment to Poulaton and then to Shong whch we structure as Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

26 Frst we have the ourney from wor to home model as T P E F ex( c, F ex( c T And then the demand from home to sho Wm ex( c m S m P, W ex( c S m S m m m m And there s a otental ln bac to emloyment from the retal sector E f ( S m m T m S m E P Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

27 A Smle Examle of Modularty: Lowry s s Model Lowry s (1964 model of Pttsburgh was a model of ths nature but t also ncororated n t or rather ts dervatves dd more formally a generatve sequence of startng wth only a orton of emloyment basc and then generatng the non basc that came from ths. Ths non basc set u demand for more non basc and so on untl all the non basc emloyment was generated, and ths sequence followed the classc multler effect that s central to nut outut models. A bloc dagram of the model follows Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

28 From htt:// Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

29 DRAM EMPAL Style Models Essentally what we have here s the noton of smultaneous deendence eone actvty generates another but that other actvty generates the frst one what came frst the chcen or the egg? Stehen Putman develoed an ntegrated model to redct resdental locaton DRAM and another to redct emloyment locaton EMPAL. In essence dfferent models are used to do each the emloyment model tends to be based on very dfferent factors t s a regresson le model of ey locaton factors not a flow model Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

30 Demand and Suly: Maret Clearng So far most of these models have been artculated from the demand sde they are models of travel demand and locatonal demand they say nothng about suly although we dd ntroduce the noton that n smulatng trs and assgnng these to the networ, we need to nvoe suly. When demand and suly are n balance, then the usual sgnal of ths s the rce that s charged. In one sense the DRAM EMPAL model confgures resdental locaton as demand and emloyment locaton as suly but most models tend to treat suly as beng relatvely fxed, gven, non modellable Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

31 However several models that coule more than one actvty together treat suly as beng balanced wth demand, often startng wth demand, seeng f demand s met, f not changng the bass of demand and so on untl equlbrum s ascertaned. Sometmes rces determne the sgnal of ths balance. If demand s too hgh, rce rses and demand falls untl suly s met and vce versa Most urban models do not attemt to model suly for suly sde modellng s much harder and less subect to generalsable behavour A strategy for ensurng balance s as follows for a model wth two sectors le the one we llustrated earler Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

32 Predct wor to home trs Assgn to networ and chec caacty Adust travel costs Predct oulaton at home Chec caacty Adust rces resd attractors Predct home to sho trs Assgn to networ and chec caacty Adust travel costs Predct retal actvty at shong centres Chec caacty Adust rces resd attractors Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

33 The decson to nest what loo nsde what other loo s a bg ssue that maes these models non unque If the suly sde s modelled searately then the way ths s ncororated further comlcates the sequence of model oeratons. In large scale ntegrated models, that we wll deal wth next tme these are crucal ssues In fact we don t have tme but there s one further structural ssue we wll deal wth when we meet next tme and ths s Inut Outut: The Echenque Models Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

34 There s some good readng of all ths materal n Google Boos n Button, K. J., Haynes, K. E., Stoher, P., and Hensher, D. A. (Edtors (2004 Handboo of Transort Geograhy and Satal Systems, Volume 5 (Handboos n Transort, Elsever Scence, New Yor htt://boos.google.com/boos?d=wmo06zfuy8c&rntsec=frontcover&dq=handboo+of+transo rt+geograhy+and+satal+systems&source=bl&ots=qvggla6_a&sg=bvoq_5befh10nsq GcCSuSNE&hl=en&e=8CraSy1AZDosQORtrSHAQ&sa=X&o=boo_result&ct=result&resnum =3&ved=0CBQQ6AEwAg#v=oneage&q&f=false Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London

35 Readng I wll ut materal u on the web tomorrow Any Questons? Centre Centre for Advanced for Advanced Satal Satal Analyss, Unversty College London