An iterative approach to an integrated land use and transportation planning tool for small urban areas

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1 Journl of Modern Trnsportton Volume 20, Number 3, September 2012, Pge Journl homepge: mt.swtu.edu.cn DOI: /BF An tertve pproch to n ntegrted lnd use nd trnsportton plnnng tool for smll urbn res Mewu AN 1, Me CHEN 2* 1. Snt Lous County Deprtment of Hghwys nd Trffc nd Publc Wors, 121 South Mermec Avenue, 8th Floor Snt Lous, Mssour 63105, USA 2. Deprtment of Cvl Engneerng, Unversty of Kentucy, Lexngton, KY , USA Abstrct: There hs been ncresng nterests n developng lnd use models for smll urbn res for vrous plnnng pplctons such s r qulty conformty nlyss. The output of lnd use model cn serve s mor nput to trnsportton model; conversely, trnsportton model output cn provde crtcl nput to lnd use model. The connecton between the two models cn be cheved by n ccessblty mesure. Ths pper presents n tertve pproch to solvng regresson-bsed lnd use model nd trnsportton model wth combned trp dstrbutonssgnment. A cse study usng dt from smll urbn re s presented to llustrte the pplcton of the proposed modelng frmewor. Tests show tht the procedures cn converge, nd the modelng frmewor cn be vluble tool for plnners nd decson-mers n evlutng lnd use polces nd trnsportton nvestment strteges. Key words: ntegrted lnd use nd trnsportton model; urbn model; trvel demnd model; combned trp dstrbuton nd ssgnment model; urbn plnnng 2012 JMT. All rghts reserved. 1. Introducton T he growth of Amerc s urbn res hs been ccompned by deterortng trffc condtons. Metropoltn Plnnng Orgnztons (MPOs) hve been formed to oversee the comprehensve plnnng process for urbnzed res wth populton of more thn Regonl or urbn trvel demnd models hve been creted for medum nd lrge MPO res; they serve s tools for better evluton of the long-term consequences of vrous lnd use nd trnsportton polces. Hvng seen the growth ssocted problems encountered by lrger metropoltn res, ctzens n smller urbn or MPO res hve been dvoctng for the preservton of the smll town tmosphere. However, the exstng tools for modelng the ntercton between lnd use nd trnsportton system my not be pplcble to these res. ITLUP nd TELUM re grvty-bsed ntegrted urbn models tht hve been deployed n mny urbn res [1-4]. It ssumes tht the subect re s closed system,.e., most obs n the study re re held by resdents of the re; nd most worers from locl house- Receved Mr. 2, 2012; revson ccepted My 28, 2012 * Correspondng uthor. E-ml: mchen@engr.uy.edu (M. CHEN) 2012 JMT. All rghts reserved do: /.ssn X holds wor n the sme re. Whle ths stnds for lrge metropoltn regons, t my not be the cse n smller urbn res. For exmple, Woodford County, Kentucy, the smll urbn re studed n ths pper, s locted n centrl Kentucy between Lexngton (the second lrgest cty n Kentucy) nd Frnfort (the stte cptl). Sttstcs show tht 48% of the totl obs n the re re held by worers resdng outsde the re; bout 55% of totl worers n locl households wor outsde the county. However, Woodford County does not belong to ether one of the trnsportton mngement or MPO n the regon. A tool s needed to ccommodte the needs of res le. MEPLAN nd PECAS, nother type of ntegrted urbn models, were developed on the bss of nput-output economc frmewor [5-7]. Its use of regonlzed nputoutput models for economc nd populton dstrbuton mes t better suted for nter-urbn thn ntr-urbn pplctons [8]. Its modelng structure suggests tht ts pplcton on smll urbn res s questonble [9]. The recently developed opertonl urbn model UrbnSm requres n extensve mount of dt t dsggregted levels sptlly [10-12]. Very few regons or metropoltn res routnely collect ll the dt needed by UrbnSm, not to menton smller urbn res. Trnsportton system s n mportnt element n the urbn systems sgnfcntly ffects the urbn form. Its ntercton wth urbn ctvtes hs been well docu-

2 Journl of Modern Trnsportton (3): mented. In lrge urbn res, trvel demnd models re vlble for the plnners to evlute the user nd system mpct of demogrphc nd socoeconomc chnges s well s vrous nfrstructure nvestment decsons. To ntegrte lnd use nd trnsportton plnnng, these models need to nterfce wth lnd use modules n the urbn model. For exmple, under the ITLUP settng, the locton choce models for household nd employment nd the trnsportton model te ech other s output s nput, nd feedbc loop should contnue untl the process converges. However, due to lmted resources, the tertve feedbc process s rrely executed even n lrge urbn pplctons [3]. The development nd mntennce of such urbn models requre substntl resource tht smll urbn res typclly do not hve. Ths pper presents n tertve pproch to n ntegrted lnd use nd trnsportton plnnng model. The modelng frmewor s composed of lnd use model nd trnsportton model. The former s regressonbsed model for household nd employment dstrbuton forecstng; the ltter s combned trp dstrbuton nd ssgnment model. Ech model uses the outputs of the other s nput for the next run. Ths frmewor does not mplctly requre closed system, nd t s smple enough for smll urbn re pplctons. The concept s tested usng dt collected from Woodford County, Kentucy. 2. Dt Wth populton of nd totl of households n the yer 2000, Woodford County, Kentucy, s consdered smll urbn re. It contns 191 squre mles mostly covered by rollng frmlnd nd tmber stnds. There re 78 nternl trffc nlyss zones (TAZ) nd 22 externl TAZs, s shown n Fg. 1, whch lso contns the re rod networ. Whle dcent to Lexngton, Woodford County s not prt of the Lexngton re MPO. Socoeconomc dt, ncludng populton nd employment, ws obtned t the census bloc level nd ggregted to the TAZ level. Populton nd household dt ws extrcted from the 2000 Census dt; employment dt ctegorzed by stndrd ndustrl clssfcton codes ws obtned from Dun & Brdstreet employment survey dt for the Commonwelth of Kentucy. In 2000 whch s consdered s the bse yer, there were obs n the county, whle mny resdents wored n the dcent ctes of Lexngton nd Frnfort. Fg. 1 Zones nd rod networ of the study re

3 162 Mewu AN et l. / An tertve pproch to n ntegrted lnd use nd trnsportton plnnng tool for 3. Lnd use model In ths study, lnd use model ws developed to estmte household nd employment dstrbutons. Exstng urbn lnd use models re usully bsed on plnnng zones tht re much lrger thn TAZs, whch mes them unsutble for pplcton n smller urbn res whose szes re usully very lmted. The lnd use model developed n ths study uses TAZs s the plnnng zones for smll urbn res. The setup enbles the preservton of reltvely detled demogrphc nd socoeconomc ttrbutes of ech zone. To normlze the effect of the zonl sze, household nd employment denstes rther thn the ctul numbers of households nd obs were used s ndctors of ther dstrbutons. The densty s defned s the number of households (or employees) per unt re. Ltertures hve shown tht these denstes re correlted wth two mor groups of fctors; they re lnd use vrbles nd trnsportton mesures. The dentfcton nd nlyss of these fctors s dscussed next followed by the modelng process. 4. Vrble specfcton Locl lnd use dt used n ths study nclude lnd use types t the prcel level. Some of these types re resdentl, grculture, ndustrl, commercl, professonl offce, vcnt, etc. Ths nformton s vlble from the locl plnnng/zonng gences. In ddton, lnd use mx ndex (lso nown s lnd use blnce, or entropy) ws ncluded to explore the potentl effect of lnd use mx. Ths ndex s defned s n 1 MxIndex Frln( Fr), (1) ln( n) where n s the totl number of lnd use types under consderton nd Fr s the frcton of lnd use type. The lnd use mx ndex s functon of the lnd use frctons; ts vlue rnges from 0 to 1, where 0 ndctes tht TAZ hs only one type of lnd use nd 1 ndctes tht ll types of lnd uses hve the sme shre n TAZ [13]. Trnsportton mesures to be consdered shll be developed bsed on the chrcterstcs of the study re. Such mesures often nclude dstnce to mor hghwys, trvel tme to downtown nd nerby employment centers. In ddton, generl ccessblty term tht mesures the degree to whch resdents n zone cn rech or be reched by ctvtes s used. There hve been severl wys to defne the ccessblty [14]. For exmple, n the household densty model, ccessblty mesures the degree of ese wth whch the resdents n zone me trps to other zones n order to prtcpte n relevnt ctvtes. It s drectonl proportonl to the rechble opportuntes t the destnton zones nd nversely proportonl to the trvel costs ncurred n rechng those opportuntes. A smlr formulton to Wllm [14] ws used n ths study: ACCH c E e, (2) where E s the number of obs n zone of the study re; s n emprclly determned coeffcent n the trp dstrbuton functon; nd c s the congested trvel tme between zones nd of the study re. 5. Lnd use model form The correlton between household/employment denstes nd lnd use/trnsportton mesures were then explored. Vrous trnsformtons such s logrthm, nverse, squre, nd exponentl trnsformtons were tested to fnd the one tht fts best wth ech of the explntory vrbles n the lnd use models. Vrous combntons of these vrbles were tested n the development process of lnd use model usng methods such s forwrd selecton, bcwrd elmnton, nd stepwse selecton. The followng equton ws chosen s the household densty model wth coeffcent of determnton (Adusted R Squre) It s ndcted tht 87% of vrton n household densty cn be explned by Household Densty= Frcton of Resdentl Lnd 0.224Accessblty. One needs to be cutous when pplyng ths model, snce ech of these two explntory vrbles hs ts own physcl menng n the urbn plnnng envronment. For exmple, ccessblty mesure s lwys postve, whch cretes stuton where the estmted vlue of household densty for zone s lwys lrger thn zero even when there s no resdentl prcel t ll n ths zone. To vod the nconsstency, ths model s only ppled to the zones wth resdentl lnd use. For the zones wthout resdentl lnd prcel, household densty s set to zero. The totl number of households n zone cn be estmted s H Are (64.762X E e ). (3) For the employment densty model, dstnce to mor hghwys ppers to be strongly correlted wth employment densty. However, t s mportnt to note tht employment dstrbuton typclly hs hstorcl trend, or t s more exogenous thn endogenous n the context c

4 Journl of Modern Trnsportton (3): of urbn plnnng. For exmple, the ITLUP lloctes employments nto ech plnnng zone bsed on prevous employment dstrbuton. Anlyss on the Woodford County dt showed tht the current employment dstrbuton (n yer 2000) s strongly correlted wth tht n the prevous perods. Menwhle, the correlton between employment densty nd lnd use/trnsportton fctors re not very sgnfcnt. Therefore, n ths study, the employment densty ws treted s n externl nput to the ntegrted lnd use nd trnsportton modelng frmewor. Dependng on the plnnng horzon, one cn obtn employment estmtes from prevous yers. It s lso recommended tht model results should be screened by locl plnnng professonl before they re put nto trnsportton models. The proected household nd employment were then used s nput to the estmton of trp generton. The nterzonl trvel tme ( c ) term n the ccessblty functon s obtned from the trnsportton model whch wll be dscussed n the next secton. 6. Trnsportton model 6.1. Formulton The trnsportton model n ths study ws formulted s combned trp dstrbuton nd ssgnment model. Ths formulton hs been studed extensvely [15-17], nd s consdered to hve performnce dvntge n some cses [18]. Effort hs been mde to ncorporte lnd use fctor nto trnsportton model. For exmple, Meng et l. [19] extends the combned trp dstrbuton nd ssgnment model by lnng Lowrybsed lnd use model to model home-bsed wor trps. Ths pper dopts the formulton of combned trp dstrbuton nd ssgnment model nd presents cse of complete clbrton nd pplcton bsed on prctcl networ, ncludng ll trp purposes such s homebsed wor trps, home-bsed other trps, nd nonhome-bsed trps. s.t. 1 Mn ( )d ( ln ), rr v s 0 w w t t t t O, I, t D, J, h t, I, J, r r v h, A, rr r (4) (4b) (4c) (4d) (4e) h 0, I, J, r R, (4f) r where v s defned s the trffc flow on ln, for A; A s the set of lns (rod segments) n the networ; s () s the ln performnce functon; t denotes the number of trps between orgn nd destnton for I nd J, where I nd J re the set of orgntng zones nd the set of destnton zones n the study re; O denotes the trps orgntng from zone, for I ; D denotes the trps destned to zone, for J ; R denotes the set of pths from orgn to destnton, for I nd J ; R s the set of complete pths tht connect ll OD prs n ths re. R s defned s R R, for I nd J ; h r s defned s the number of trps on pth r, for r R ; r denotes the ncdence coeffcent tht descrbes the reltonshp between pth nd ln. 1 f ln s r r on pth r ; otherwse 0, for A nd r R ; nd s the dsperson prmeter for the trp dstrbuton functon, whch s the sme s the one n ccessblty equtons. Trps wth one end outsde the re re consdered externl trps. They re treted s externl vrbles nd therefore re not ncluded n the decson vrbles n the combned dstrbuton/ssgnment problem. These trps re ssgned to the networ frst nd become the bcground trffc, whch s ncluded n the ln trvel tme functon. In ths study, typcl BPR-type functon n the form of 4 f v BG s( v) tt tt (5) CP s chosen s the ln performnce functon, n whch tt f nd tt s congested trvel tme nd free-flow trvel tme, respectvely; BG s bcground trffc flow nd CP s the cpcty of ln, for A. It hs been proved tht the soluton of the combned trp dstrbuton nd ssgnment model stsfes the user equlbrum condtons [10, 12], whch stte tht ll used pths between n OD pr hve equl trvel tme tht re shorter thn those on ll unused pths. Therefore, no rod user cn unlterlly mprove hs/her trvel tme by swtchng pths. Addng bcground trffc to the ln performnce functon hs no mpct on the optmlty condton. The trp dstrbuton functon under the optml condton of ths optmzton progrm s shown below: u t exp ( ) e u MBOD, (6) where,, nd u re the Lgrnge multplers for equtons 4(b), 4(c), nd 4(d); M e / O nd

5 164 Mewu AN et l. / An tertve pproch to n ntegrted lnd use nd trnsportton plnnng tool for B e / D re blncng fctors tht ensure the trp nterchnge output s consstent wth the typcl form of grvty model. The trvel mpednce functon n the trp dstrbuton model s n exponentl decy n the u form of f( u ) e, where s greter thn zero Clbrton In ths study, complete clbrton process usng the dt from Woodford County ws presented to fcltte the pplcton of the ntegrted modelng frmewor. Snce the trnsportton model developed here s dly model n whch return trps should be ccounted for. Therefore, the totl orgnton trps nd destnton trps for gven zone should be equl. Orgnton nd destnton trps cn be formulted s functons of household nd employment s shown n Eq. (7). It s worth notng tht O nd D re completely dfferent from trp producton (P) nd trp ttrcton (A) n trdtonl fourstep trvel demnd model. In four-step model, trp productons refer to home-ends of trps nd trp ttrctons represents non-home ends of trps regrdless of whether home s orgnton or destnton. For exmple, for home-bsed trps, trp producton end my be the destnton. In the combned trp dstrbuton nd ssgnment model, orgnton trps drectly represent the trps whch go out of TAZ; destnton trps refer to the trps whch come to TAZ. O D H E. (7) The clbrton process mnly nvolves the determnton of the vlue of n Eq. 4(). Ths process s smlr to tht of the clbrton of grvty-type trp dstrbuton model usng the observed trp length dstrbuton n the bse yer. The convergence threshold s set to 1% reltve dfference between the two consecutve tertons. The observed men trvel tme cn be defned s C* tc / T, where c s the observed trvel tme between OD pr from nd ( I, J ), nd T s totl trps n the study re. The clbrton procedure cn be constructed s follows: (1) Intlze the vlue of s the nverse of the observed men trvel tme. (2) Apply the trp dstrbuton model (Eq. (6)) ssocted wth the gven O nd D to generte n estmted OD mtrx. (3) At terton, estmte men trvel tme C usng the sme formul s C * bsed on the new trp mtrx obtned n step 2. Compre C nd C *, f there s less thn 1% dfference between them then the convergence hs been reched nd the procedure stops. Otherwse, contnue to step 4. (4) Compute 1 ( C C* ) 1 ( C* C1) C C 1 If =1, then 2 C 1 1 / C *. Return to step 2 usng the new vlue. The terton contnues untl the convergence crteron s met. In ths study, the clbrton process stopped fter eght tertons, resultng n vlue of Lnng lnd use nd trnsportton models An tertve pproch ws estblshed to ln the lnd use nd trnsportton models. Ths pproch nvolves solvng the lnd use nd trnsportton problems tertvely usng ech other s outputs n the prevous round. Ths feedbc loop contnues untl certn convergence crter re reched. In ths study, the convergence crter were specfed s: n the two consecutve tertons, (1) less thn 5% of OD prs hve OD trps vrton of more thn 5%; (2) less thn 5% of lns hve ln flow vrton of more thn 5%; nd (3) less thn 1% of zones hve household dstrbuton vrton of more thn 5%. All three condtons need to be stsfed before the procedure cn stop. The specfc steps used re outlned below. (1) Determne E by solvng the exogenous employment dstrbuton model; (2) Set ntl vlues of 1 c. from the bse yer trnsportton model, nd set =1 where refers to the -th terton; (3) Solve the household dstrbuton model for H ; (4) Solve the combned trp dstrbuton nd ssgnment model for v, t, nd c usng E nd H s nput; (5) Chec f the convergence crter wth respect to H, v, nd t re stsfed. If yes, stop the terton; 1 otherwse replce c wth c n step 2 nd repet steps (3) (5). Ths tertve pproch ws ppled to the Woodford County lnd use nd trvel demnd models descrbed bove. The convergence crter were met fter the 3rd terton. The vrtons of mesures such s ln flows

6 Journl of Modern Trnsportton (3): nd OD volumes were trced durng the process. It ppered tht the lgorthm converged grdully durng the three tertons. No sgnfcnt oscllton of these mesures ws observed. Tble 1 shows ln flow vrton between second nd thrd tertons; Tble 2 lsts vrton on OD trps; Tble 3 dsplys vrton on the number of households. These lns, ODs, nd zones re of the most nterest nd concern n the re. Note tht lthough theoretclly ths tertve lgorthm s not gurnteed to converge, t dd rther qucly n ths test. After the successful run usng bse yer dt, the tertve pproch ws ppled to smulte potentl outcome of lnd development decsons. A proposed development of resdentl subdvson long mor rod US60 ws used for llustrton purposes. The ddtonl housng wll cuse the resdentl lnd use frcton of ths zone (TAZ #36 n Fg. 1) to ncrese from 36.4% to 46.4%. Ths new frcton ws plugged nto the household dstrbuton model long wth the bse yer trvel tme mtrx to estmte the future household dstrbuton. The terton process contnued between lnd use nd trnsportton models untl the convergence crter were met. One should note tht the employment dstrbuton ws exogenously determned n ths modelng frmewor. Future employment dstrbuton could be estmted externlly ccordng to regonl development nd locl plnnng gols. Ln Tble 1 Selected model output (ln flow) Ln flow (thrd terton) Tble 2 Selected model output (OD trps) Ln flow (second terton) Chnge between two tertons (%) L L L L L L L L L L L L L L L L L L L L Orgnton Destnton OD trps (thrd terton) OD trps (second terton) Chnge between two tertons (%) Z74 Z Z75 Z Z72 Z Z73 Z Z36 Z Z56 Z Z65 Z Z64 Z Z76 Z Z73 Z Z78 Z Z64 Z Z62 Z Z75 Z Z76 Z Z56 Z Z72 Z Z76 Z Z73 Z Z56 Z Z37 Z Z36 Z

7 166 Mewu AN et l. / An tertve pproch to n ntegrted lnd use nd trnsportton plnnng tool for Convergence ws gn reched fter three tertons. Resonble outputs were produced by the tertve procedure. The number of households n ths TAZ ncresed from to due to the development. The subdvson development s surrounded by two mor estwest rods. One s US60, nd the other s Huntertown rod. The vehcle trps generted by the new development re dstrbuted to US60 est to Lexngton, US60 west to Frnfort nd Verslles, Huntertown est to Lexngton, Huntertown west to Frnfort nd Verslles. Detled nlyss on pe hour trffc pttern ndcted tht the ddtonl 260 households do not pper to hve sgnfcnt mpct on the congeston level of the networ becuse the networ s not congested n the future n ths study re. It genertes dly trffc of whch 53 vehcle trps re dstrbuted to US60 est ncresng the rod segment s V/C rto from 0.76 to 0.77; 451 vehcle trps re llocted to US60 west rsng the rod segment s V/C rto from 0.68 to 0.70; 730 vehcle trps re dstrbuted to Huntertown est ncresng ts V/C rto from 0.27 to 0.33; 393 vehcle trps re llocted to Huntertown west rsng ts V/C rto from 0.33 to Tble 3 Selected model output (number of households) Zone Household (thrd terton) Household (second terton) Chnge between two tertons (%) Conclusons In ths pper, n ntegrted lnd use nd trnsportton modelng frmewor s ntroduced. The frmewor contns lnd use model n lner form nd trnsportton model n the form of combned trp dstrbuton nd ssgnment problem. The models run lterntvely nd use the output of ech other n the prevous round s nput. Ths feedbc process stops when convergence crter re met. A complete cse study s provded to llustrte ts pplcton potentl. The models re clbrted usng bse yer dt nd cn be used to estmte future scenros. Although the convergence of ths tertve procedure s not gurnteed n theory, the cse study does show quc convergence on set of resonbly strngent crter. The pplcton of the proposed lnd use model s prtculrly sutble for smller urbn res wth lmted resources. Compred to comprehensve lnd use models mplemented n lrge metropoltn res, the lnd use model ntroduced here s smpler. The model frmewor presented n the study cn serve s tool to evlute the consequences of lnd use polcy nd trnsportton nvestment decsons. References [1] S. H. Putmn, Integrted Urbn Models: Polcy Anlyss of Trnsportton nd Lnd Use, London: Pon, [2] S.H. Putmn, Results from mplementton of ntegrted trnsportton nd lnd use models n metropoltn regons, In: Networ Infrstructure nd the Urbn Envronment, New Yor: Sprnger, [3] S.H. Putmn Assoctes, Inc., Integrted trnsportton nd lnd use forecstng: senstvty tests of lterntve model systems confgurton, Wshngton D.C.: U.S. Deprtment of Trnsportton, [4] C.T. Csper, J. O Bren, M.R. Lup, et l., Applcton of TELUM by the Pes Pe, Colordo, Are Councl of Governments lessons Lerned n Colordo Sprngs, Trnsportton Reserch Record, 2009, 2119: [5] J.D Hunt, D.C. Smmonds, Theory nd pplcton of n ntegrted lnd-use nd trnsport modelng frmewor, Envronment nd Plnnng B: Plnnng nd Desgn, 1993, 20(2): [6] J.D. Hunt, Clbrtng the Nples lnd-use nd trnsport model, Envronment nd Plnnng B: Plnnng nd Desgn, 1994, 21(5): [7] J.D. Hunt, J.E. Abrhm, D. de Slv, et l., Developng nd pplyng prcel-level smulton of developer ctons n Bltmore, In: Proceedng of the 87th Annul Meetng of the Trnsportton Reserch Bord, Wshngton D.C., [8] Prsons Brncerhoff Qude & Dougls, Inc., Lnd use mpct of trnsportton: gudeboo, Wshngton D.C.: Ntonl Reserch Councl, 1998.

8 Journl of Modern Trnsportton (3): [9] J.D. Lemp, B. Zhou, K.M. Kocelmn, et l., Vsonng vs. modelng: nlyzng the lnd use-trnsportton futures of urbn regons, In: 86th Annul Meetng of the Trnsportton Reserch Bord, Wshngton D.C., [10] P. Wddle, UrbnSm: modelng urbn development for lnd use, Journl of the Amercn Plnnng Assocton, 2002, 68(3): [11] P. Wddell, J. Frnln, J. Brttng, UrbnSm: development, pplcton nd ntegrton wth the Wstch front regonl trvel model, Slt Le Cty: Wstch Front Regonl Councl, [12] P. Wddell, X.L. Lu, L.M. Wng, UrbnSm: n evolvng plnnng support system for evolvng communtes, Plnnng Support Systems for Ctes nd Regons, Cmbrdge: Lncoln Insttute for Lnd Polcy, [13] K.M. Kocelmn, Trvel behvor s functon of ccessblty, lnd use mxng, nd lnd use blnce: evdence from the Sn Frncsco by re, Trnsportton Reserch Record, 1997, 1607: [14] E.J. Mller, Lnd use trnsportton modelng, In: Trnsportton Engneerng Hndboo: Plnnng Methods nd Applctons, Flord: CRC Press LLC, [15] Y. Sheff, Urbn Trnsportton Networs: Equlbrum Anlyss wth Mthemtcl Progrmmng Methods, Englewood Clffs: Prentce-Hll, [16] D.E. Boyce, L.J. Leblnc, K.S. Chon, Networ equlbrum models of urbn locton nd trvel choces: retrospectve survey, Journl of Regonl Scence, 1988, 28(2): [17] H.C.W.L. Wllms, On the formton of trvel demnd models nd economc evluton mesures of user beneft, Envronment nd Plnnng A, 1977, 9(3): [18] Z.A. Shhrr, A. Mortez, M. Abolfzl, Combned trp dstrbuton nd ssgnment model: pplctons to cptve trps, In: 87th Annul Meetng of the Trnsportton Reserch Bord, Wshngton D.C., [19] Q. Meng, H. Yng, S.C. Wong, A combned lnd-use nd trnsportton model for wor trps, Envronment nd Plnnng B: Plnnng nd Desgn, 2000, 27(1): (Edtor: Yo ZHOU)