Andrea Rah, Chrs Van Houe, Judh Y.T. Wang, and Mahas Ehrgo APPLYING BI-OBJECTIVE SHORTEST PATH METHODS TO MODEL CYCLE ROUTE-CHOICE Andrea Rah 1, Chrs Van Houe 2, Judh Y. T. Wang 3, and Mahas Ehrgo 4 The Unversy of Auckland Prvae Bag 92019, Auckland, New Zealand ABSTRACT I s wdely acknowledged ha cyclss choose her roue dfferenly o drvers of rvae vehcles. Commuer drvers ofen have only one objecve for her roue-choce, o reduce her generalsed ravel cos, whch s a combned moneary value reresenng he combned ravel me and vehcle oerang cos. Commuer cyclss, on he oher hand, usually have mulle objecves when choosng her roue: he ravel me and he suably of a roue for cyclng. Some of he facors ha characerse he suably, or aracveness of a roue nclude he safey (.e. raffc volumes, raffc seeds, resence of bcycle lanes) and wheher he erran s fla or hlly. Ths aer summarses a sudy on he roue-choce behavour of commuer cyclss usng bobjecve shores ah (BSP) mehods. The wo objecves consdered are ravel me and he aracveness of a roue. A mehod s develoed o quanfy he aracveness of a roue for cyclss and o denfy fas and aracve roues. Raher han deermnng a sngle roue for a cycls, we deermne a choce se of omal alernave roues (effcen roues) from whch a cycls selecs one accordng o her ersonal reference (accordng o her valuaon of ravel me versus oher ah crera summarsed as aracveness). Ths mehod s hen mlemened n a case sudy n Auckland. Ths sudy rovdes a sarng on for he raffc assgnmen of cyclss, and wh furher research, he b-objecve shores ah model develoed can be aled o creae a comlee ravel demand model for cycle rs. Keywords: B-objecve shores ah mehods, cycle roue-choce, raffc assgnmen 1 INTRODUCTION In ransor lannng, cycle rs are convenonally combned wh walkng rs under he erm 'acve modes'. Acve modes are wdely acknowledged o be effcen oons for commung rs, as hey have no vehcle emssons, do no conrbue o raffc queues, ose lle rsk o oher road users and ncrease he healh of he oulaon. In fac, hyscal acvy s consdered o be one of he 'bes value' mehods of mrovng ublc healh (Morrs, 1994). Dese he benefs, exercse, such as cyclng, ends o be romoed o he ublc as a lesure acvy, raher han as a ransor alernave (Oglve e al., 2004). One reason for hs s ha cyclng can be erceved as a dangerous underakng, esecally n Auckland. Hgh raffc volumes, narrow roads and a lack of cycle ahs are jus a few of he obsacles ha cyclss mus face. One Brsh sudy (Lngwood, 2004) concludes ha cyclng canno be romoed as a ransor alernave, unl he journeys can be underaken n a safe, cyclefrendly envronmen. In order o acheve Auckland Cy Councl s vson of ncreasng he 1 Corresondng auhor; Dearmen of Engneerng Scence, he Unversy of Auckland. Emal address: a.rah@auckland.ac.nz 2 Dearmen of Cvl and Envronmenal Engneerng, he Unversy of Auckland 3 The Energy Cenre, The Unversy of Auckland Busness School. 4 Dearmen of Engneerng Scence, he Unversy of Auckland -1-
Andrea Rah, Chrs Van Houe, Judh Y.T. Wang, and Mahas Ehrgo rooron of cycle rs (Auckland Cy Councl, 1998), he mos oular roues of cyclss need o be denfed. Thus, n order o ncrease cycle rs, a cycls's safey mus be mroved. Provdng cyclesecfc nfrasrucure, such as a bcycle lane or ah, s he mos obvous means of achevng hs (Dll and Carr, 2003). However, wh lmed fundng avalable for hese facles, her lacemen whn a road nework s very moran. In order o do so, we wll need o be able o non secons of he road nework wh he hghes cycls volumes. From here, hese areas can be argeed o become more cyclng-frendly, and cyclng o work can hen be more effecvely romoed as a feasble alernave o commung by car. In a convenonal four-sage ransor lannng model, roue-choce s modelled n he fnal sage, raffc assgnmen. Traffc assgnmen s erformed for rvae vehcle and ublc ransor rs n order o deermne he lnk volumes n erms of vehcular flow and aronage on ublc ransor servces. Cycle rs are no modelled a all n hs sage. In racce, walk and cycle rs are ofen reresened as one acve mode r marx deermned n he hrd sage, modal sl, whch wll be u asde only for reference. As raffc assgnmen s ofen no erformed for cycle rs (e.g. n Auckland), wll no be ossble o erform an economc evaluaon for cycle nework mrovemen n he convenonal way as wha s normally carred ou for road mrovemen rojecs. As a sarng on, we wll need o model cyclss roue-choce behavour. Ths roue-choce model can hen become he buldng block for he develomen of a cycls raffc assgnmen model, from whch we wll be able o deermne he lnk volumes on a cycle nework. The urose of hs sudy s o develo a roue-choce model for cyclss wh a b-objecve shores ah mehod. The model develoed s aled o a case sudy n New Zealand. We analyse Auckland's commung rs n he mornng eak erod, beween a reresenave orgn and desnaon n he Auckland Cy regon. 2 LITERATURE REVIEW Before a road nework can be analysed for s suably for cyclss, a dealed undersandng of he needs of cyclss s requred. The urose of hs leraure revew s o analyse he facors ha affec cycle roue-choce, fnd an emrcal mehod o quanfy he qualave facors, and consder mehods ha analyse hese facors a he same me, so ha he bes roues for cyclss can be found. 2.1 Roue-Choce Behavour of Cyclss In order o undersand he roue-choce behavour of commuer cyclss, he facors ha nfluence her choces mus be undersood. Numerous sudes oulne and model hese facors, and s unanmously denfed ha ravel me s he mos moran nfluence for he roue-choce decson (Dll and Carr, 2003, Snson and Bha, 2003, Aulman-Hall e al., 1997). Thus, when analysng he roue-choce facors, ravel me can be searaed from all he oher ones. However, here are numerous oher facors ha affec roue-choce. Some of hese facors are subjecve (such as cos, hyscal fness and valuaon of me) and canno be quanavely assessed (FHWA U.S. Dearmen of Transoraon, 1992). Oher facors such as moor raffc volume, resence of cycle facles and oograhy are objecve, so can be evaluaed n a roue-choce sudy. In hs sudy, hese objecve facors are aggregaed no he erm aracveness ; a generc erm ha descrbes how suable (.e. safe and comforable) a road s for cyclss whou resumng a valuaon ha of course deends on each ndvdual cycls. -2-
Andrea Rah, Chrs Van Houe, Judh Y.T. Wang, and Mahas Ehrgo 2.2 Mehods o Quanfy Roue-Choce Facors For aracveness o be consdered as one of he facors, s crucal o fnd a sysemac way of evaluang how suable a roue s for cyclss. A Land Transor Safey Auhory (2004) reor suggess erformng a Bcycle Level of Servce (BLOS) assessmen o evaluae how suable a roue s for cyclss. Three man BLOS mehods have been denfed n he leraure. Two sudes n he Uned Saes (Harkey e al., 1998), (Florda Dearmen of Transoraon, 2002) came u wh echncally sound BLOS mehods, bu hey do no consder some facors ha are moran o Auckland s cyclss, such as road graden. A sudy n he Uned Kngdom (Insue of Hghways and Transoraon, 1998) develoed a comrehensve assessmen mehod ha evaluaes a roue s aracveness agans more facors han he oher wo mehods. I s desgned o mnmse subjecve facors, and o consder cycle rs n her enrey, raher han focussng only on each ndvdual lnk. 2.3 Consderng Two Objecves Smulaneously For modellng uroses, he facors nfluencng cycls roue-choce can be smlfed no wo caegores: Roue-level, such as ravel me; and Lnk-level, such as aracveness, safey and comfor. Convenonal raffc assgnmen mehodologes are based on he assumon ha all drvers have one sngle objecve. However, a roblem arses when modellng cyclss, as her decson s based on more han one objecve. Therefore, a b-objecve roue-choce model, based on he wo caegores oulned above, s more arorae o model cyclss rouechoce decsons. BSP echnques can analyse wo ndeenden facors a he same me (Rah and Ehrgo, 2009). 3 NETWORK CODING Before cycle roue-choce can be modelled n erms of he wo objecves, he ravel me and he aracveness of a roue, Auckland s road nework n he raffc assgnmen model has o be modfed. Ths secon dscusses how a cycle nework s coded for he sudy area. The sudy area for hs research s defned as a reresenave r beween wo zones n he Auckland regon (he shaded regons A and B n Fgure 1 below), wh all he ossble roues beween he gven orgn and desnaon beng assessed. B A Fgure 1: Zone Plan of Auckland Regon n he Auckland Regonal Transor Plannng Model (Source: Auckland Regonal Councl) -3-
Andrea Rah, Chrs Van Houe, Judh Y.T. Wang, and Mahas Ehrgo Zone A reresens a resdenal zone n Pon Chevaler, and zone B corresonds o a commercal zone n Auckland s Cenral Busness Dsrc. A r from zone A o B reresens a ycal r for a cycls s mornng commue n Auckland. The cycle nework s obaned by modfyng he road nework modelled n he Auckland Regonal Transor (ART) Plannng Model, rovded by Auckland Regonal Councl (ARC). The ART model road nework consss of nodes, whch corresond o large nersecons, and lnks, ha reresen md-block secons of road. Addonal lnks are u no he nework, n locaons where only bkes are ermed, such as an off-road cycle ah. However, as oulned n Secon 2.1, cyclss end o have more objecves han drvers; hey base her roue-choce no jus on ravel me, bu numerous oher facors ha can be combned no he erm aracveness. Nex, we nroduce he wo facors, me and aracveness, ha deermne he roue-choce of cyclss. 3.1 Travel Tme Objecve 3.1.1 Lnk Travel Tme For vehcle raffc, he ravel me on each lnk s aroxmaed by a volume-delay funcon, e.g. ycally a BPR funcon (Bureau of Publc Roads, 1964) can be aled o deermne he average ravel me o raverse a lnk as a funcon of he raffc volume on hs lnk. However, hs s no alcable o cyclss, as hey do no end o wa n raffc queues, nsead assng he queue on he nsde. Therefore, a new ravel me funcon, whch s based urely on dsance, s assgned o he lnks of he road nework. The lnk dsances are derved from he Geograhc Informaon Sysems (GIS) coordnaes of he nodes and lnks n he ART model road nework. The new funcon assumes a fxed velocy for cyclss across he whole nework. In realy, graden also affecs he seed of cyclss, and herefore her ravel me. However, our model does no nclude graden n he ravel me facor. The hlls n Auckland are relavely shor n lengh, hus have a neglgble effec on cycle seed. Graden s sll a major roue-choce facor for cyclss, so we nclude as ar of he second objecve of he model, as an unaracveness facor. Ths wll be dscussed n Secon 3.2.1. 3.1.2 Inersecon Delay Tme For a commung r, ravel me no only ncludes md-block secons of road; delay a sgnalsed nersecons also makes u a consderable oron of he r. In he ART model road nework, nersecons are ycally reresened by a sngle node wh no addonal delay, as shown n Fgure 2(a). To accoun for he ncreased ravel me, he nersecons n he road nework need o be modfed. Nodes n he road nework ha corresond o large, sgnalsed nersecons are modfed wh dummy nodes and lnks, as demonsraed n Fgure 2(b). The ravel mes on hese dummy lnks reresen dreconal delays a he nersecon. A realsc delay value needs o be calculaed for he new dummy lnks. An average delay s esmaed for he sgnalsed nersecons. Assumng ha cyclss do no have o queue a raffc sgnals (.e. because of her small sze, hey can manoeuvre hrough queues and ge o he fron relavely easly), a cycls so rae for each aroach can be aroxmaed as he rooron of he sgnal cycle ha s red (red (a) (b) Fgure 2: Modfcaon of nersecon node layous. -4-
Andrea Rah, Chrs Van Houe, Judh Y.T. Wang, and Mahas Ehrgo me / sgnal cycle me). Furhermore, he average delay for soed cyclss can be reresened as half he red me (red me / 2). Mullyng he cycls so rae by he average delay for soed cyclss, gves he average delay for all he cyclss on each aroach: average delay where R 2C 2 (1) R s he red me for a gven aroach and C he oal sgnal cycle me. Ths formula s based urely on average hase mes, and accouns for he fac ha cyclss arrvng n he green erod wll no have any addonal delay. Acual raffc sgnal hasng daa s obaned from he Auckland Cy Councl s Sydney Coordnaed Adave Traffc Sysem (SCATS). For hs sudy, all of he 15 sgnalsed nersecons n he sudy area are coded o nclude dreconal lnks, hen ndvdually assessed o calculae he dreconal delays assocaed wh each lnk. 3.2 Aracveness Objecve The numerous oher facors (groued no he erm aracveness ) ha affec roue-choce need o be consdered n he second objecve assocaed wh each lnk of he cycle nework. 3.2.1 Aracveness Rang for each Lnk A sysemac mehod s requred o quanfy how aracve, or safe, a ceran secon of road s for cyclss. As dscussed earler, here are several BLOS mehods n he leraure ha can be aled o quanfy hs aracveness value. We consder he Brsh mehod menoned n Secon 2.2 of Gudelnes for Cycle Aud and Cycle Revew (Insuon of Hghways and Transoraon, 1998), whch rovdes a more exensve analyss han he ohers, o be he mos alcable mehod for Auckland Cy s raffc condons. Ths rocedure allows aracveness, a qualave measure, o be convered no a quanave value. In oal, 20 road facors are accouned for n he Cycle Revew aracveness rang sysem. Some of hese are: Moor raffc volume; Moor raffc seed; Road lane wdh; Presence of on-sree arkng; Graden of road; Percenage of heavy commercal vehcles; Provded cycle facles, such as cycle lanes or shared bus/cycle lanes; and Pavemen condon. The Cycle Revew mehod uses a scorng sysem o conver he above facors o a smle A-F score. Road characerscs daa are colleced for all of he lnks n he sudy area, hen u no he Cycle Revew model. The ouu of hs se s a score ou of 100 for each lnk, whch corresonds o a grade from A-F, as shown n Table 1. The grades A-F are convered no o a 1-6 neger value n he las column of Table 1, Table 1: Scorng sysem for he aracveness mehod. Aracveness Rang Score Ineger value A 81-100 6 B 61-80 5 C 41-60 4 D 21-40 3 E 1-20 2 F 0 1-5-
Andrea Rah, Chrs Van Houe, Judh Y.T. Wang, and Mahas Ehrgo as a quanave measure of aracveness. Therefore, each lnk n he sudy area can be assgned an aracveness value as a second arbue, whch quanfes he suably of he lnk o cyclss. Crash daa s no ncluded as a reresenaon of cycle safey. Prevous cycle crash hsory can ndcae unsafe ars of he road nework, however, here are numerous lmaons n he daa: here are many conrbung facors o a crash ha canno be modelled; and bcycle crashes are ofen unreored (Land Transor Safey Auhory, 2004). Thus, usng crash analyss daa canno be reled uon when modellng cycle safey. Ths sudy assumes ha crashes only occur due o road geomery and raffc roeres. 3.2.2 Inersecon Aracveness Rang As nersecons have been modelled o accoun for addonal ravel mes, s also requred o calculae an aracveness value for hese nersecons. There s very lle documened research ha raes nersecons for her aracveness o cyclss. The only exsng mehod s from he Uned Saes, whch raes he safey of nersecons for he bcycle hrough movemen (Lands e al., 2003). To arrve a an aracveness rang, hs mehod consders lane wdhs, crossng dsances, raffc volume; and he number of hrough lanes for a gven aroach. Each SCATS-conrolled sgnalsed nersecon n he sudy area s analysed for hese facors, and by alyng he mehod recommended by Lands e al. (2003), an A-F aracveness rang s deermned for he hrough movemens a all of hese nersecons. Ths mehod, however, s no alcable o urnng movemens. In hs sudy, we deermne he aracveness rang for urnng movemens based on he number of hrough lanes and he graden of he aroach o he nersecon. 3.2.3 Measurng he Aracveness of a Pah Unlke ravel me, he aracveness of a ah canno be reresened by he sum of he aracveness rangs of each lnk. Therefore, a mehod o conver he aracveness values of he lnks no a cumulave fgure has been develoed. The aracveness rang a ( ) along ah s gven by: a( ) a ( ) (2) where a ( ) s he aracveness score for he enre ah, a he aracveness score for he h lnk, lnk. ) ( he oal ravel me for, and he ravel me on he h 4 ANALYSIS OF MODIFIED NETWORK As dscussed earler, he convenonal aroach n raffc assgnmen assumes ha all drvers have one sngle objecve,.e. o mnmse generalsed ravel cos. A cycls, on he oher hand, wans o mnmse her ravel me as well as choose a roue of maxmal aracveness. The mos aracve roue may well be slower han he fases roue. Thus, BSP echnques are requred o model he roue-choce of cyclss. -6-
Andrea Rah, Chrs Van Houe, Judh Y.T. Wang, and Mahas Ehrgo 4.1 B-objecve Shores Pah In BSP, nsead of obanng he bes soluon, he am s o generae a se of good comromse soluons. We call hose roues (or ahs) effcen. Effcen roues are hose, whose aracveness level would no mrove when ryng o mrove s ravel me by swchng o anoher roue and vce versa. An equvalen defnon calls a roue effcen f here s no oher roue ha s beer n one of he objecves, e.g. me, and a he same me no worse n he oher objecve, e.g. aracveness. Fgure 3 shows he ravel me and aracveness of dfferen ahs. In he fgure, he ravel me and aracveness of effcen ahs s marked by a do, whereas me and aracveness of all oher ahs are ndcaed by x. For every ah marked by an x, here exss a leas one effcen ah, ndcaed by a do, wh beer value n boh me and aracveness. We formalse hese conces n he followng. Le,,..., ) be a ah (or roue) conssng of he lnks wh ndces ( 1 2 n 1, 2 n. By P we denoe he se of all,..., ahs. The ah has ravel me ( ) and aracveness level a ( ). Formally, ah P s effcen f here exss no ah ' P such ha ( ') ( ) and a ( ') a( ) or ( ') ( ) and a ( ') a( ) (3) If, on he oher hand, here does exss such a ah ', we say ha ' domnaes. In order o oban all effcen ahs, he suable ah choces for cyclss, a b-objecve shores ah algorhm s used. Ths BSP algorhm s aled o fnd all effcen ahs beween he gven orgn and desnaon. Ths modelng echnque enables us o consder he wo roue-choce facors smulaneously. 4.2 Solvng he Cycls BSP roblem A b-objecve label correcng algorhm s used o solve he BSP roblem, for deals see (Rah and Ehrgo, 2009). Unforunaely, he roblem wh he orgnal objecves 1 mn : P and max a : P (4) ( ) canno be solved by hs algorhm as a basc assumon ha guaranees convergence of he algorhm s no sasfed. Ths assumon s ha he wo searae objecves ncrease n value when an addonal lnk s added o a ah. We can, however, show ha effcen soluons of (4) are always effcen soluons of he auxlary roblem (5) obaned by drong he denomnaor of a ( ) n (4). mn P and max a P. (5) : Fgure 3: BSP examle ouu: effcen ahs : -7-
Andrea Rah, Chrs Van Houe, Judh Y.T. Wang, and Mahas Ehrgo Problem (5) sasfes he assumon ha he objecve funcon values of a ah ncrease as an arc s added o. Hence he b-objecve label correcng algorhm can be used o fnd all effcen ahs whou cycle,.e. hose ahs n whch no lnk aears wce. Once all effcen soluons of (5) are obaned, hose among hem ha are also effcen for (4) are seleced, and he roblem s solved. I remans o rove ha an effcen ah of (4) s always an effcen ah of (5). In order o do so, assume he conrary,.e. here exss an effcen ah of (4) ha s no effcen for (5). Therefore, here exss a ah ', ha domnaes for (5). Then, by (3) or ' ' whch mles ha ' Therefore, a ' and and a a ' ' a a a, ' domnaes for (4), a conradcon o beng an effcen soluon of (4). 5 RESULTS Fgure 4: Resuls of he sudy he effcen ahs (Source of Aeral Ma: Auckland Cy Councl). All exsng lnks have been modfed o nclude he wo lnk arbues for cyclss. New nodes and lnks have been creaed where requred, such as along an off-road cycleway and a nersecons. Uon solvng he BSP roblem, he effcen ahs are obaned. Fgure 4 shows he effcen ahs suermosed on an aeral ma of he sudy area. I should be noed ha whle he sred ah s he shores one, mos ahs use a leas -8- Fgure 5: Tme and aracveness of effcen ahs.
Andrea Rah, Chrs Van Houe, Judh Y.T. Wang, and Mahas Ehrgo ar of he longer off-road cycleway arallel o he moorway (e.g. he black and doed ahs). The BSP ouu corresondng o he effcen ahs s shown n Fgure 5. Each of he ons on he grah reresens he oal ravel me and aracveness rang for an effcen ah. 6 DIRECTIONS FOR FUTURE RESEARCH 6.1 Calbraon and Valdaon Calbraon of he model mus be erformed, n order o reflec he sensvy of he ravellers. The Cycle Revew mehod (Insue of Hghways and Transoraon, 1998), whch has been used o quanfy he aracveness of a secon of road, s a regresson model where he coeffcens are sandardsed for Brsh cyclss. However, alhough he facors ncluded n he model are resen for every cycls, each cycls would wegh hese facors dfferenly. Where wo ces have dfferences n erran and raffc condons, he coeffcens n he regresson model wll always change. In order o calbrae he model for Auckland Cy, a full calbraon sudy s requred. Ths would nvolve seng u es roues around Auckland Cy, sendng a large samle of cyclss along hese roues, and geng hem o rae he aracveness of each secon of he roue. Sascal analyses could hen be erformed o correlae he aracveness rangs wh he road roeres. Ths would allow he coeffcens n he Cycle Revew model o be alered o reflec characerscs of Auckland s cyclss. For valdaon, daa are obaned from a 2007 Auckland Regonal Councl Cycle Survey, where he roues of cyclss around Auckland have been monored over a erod of wo weeks. The survey s mos oular roues n he sudy area are comared o he ouu from our nework model. Unforunaely, dese some encouragng nal comarsons, he samle sze of he ARC survey s far oo small o oban any meanngful correlaons. Therefore, furher valdaon of he resuls of hs sudy s requred wh a dealed survey of commuer cyclss wh bgger scale and larger samle sze. 6.2 Creaon of a Cycle Ma In order o romoe cyclng as a vable alernave o commung by car, a cycle ma could be creaed o recommend he bes roues for a cycls beween he wo zones; a roue ha s he bes comromse of ravel me and aracveness for an average commuer cycls. One ossble way s o aly an arbrary consran, such as he bes ah s he ah wh he fases ravel me, such ha he average aracveness rang s beer han a C. A cycle ma can be creaed by alyng hs mehod o all orgn-desnaon ars, whch could be dsrbued o he ublc n an effor o romoe cyclng as an alernave mode of ransor. 6.3 Travel Demand Modellng To suor ransor lannng decsons, such as evaluang nfrasrucure nvesmen oons for mrovemen of cyclng facles, esmang he execed usage of facles would be requred. In order o do so, we wll need o develo a raffc assgnmen model for cycle rs. By alyng he BSP mehod, we wll be able o fnd he effcen ahs for cyclss for each orgn-desnaon ar. Ths becomes he choce se for he cycls. Indvdual reference wll deend on he cycls. For examle, an exerenced commuer cycls mgh no worry abou he hllness or safey of he roue, and choose he roue wh he lowes ravel me. On he oher hand, a dfferen ye of cycls may value safey much hgher han an exerenced cycls, herefore choose he mos aracve, bu longes roue. Thus, furher research s requred o develo an assgnmen mehod o assgn he cyclss o her referred roue. Convenonal raffc assgnmen mehods, e.g. deermnsc raffc assgnmen model based -9-
Andrea Rah, Chrs Van Houe, Judh Y.T. Wang, and Mahas Ehrgo on Wardro s rncle (Wardro, 1952), wll no be drecly alcable o cycle rs snce Wardro s rncle s based on a sngle objecve assgnmen. 7 CONCLUSIONS Cyclss roue-choce s currenly no modelled n a convenonal four-sage ransor lannng model. I s well known ha cyclss behave dfferenly from drvers of moor vehcles as hey consder mulle objecves n her decsons. The convenonal way of consderng generalsed cos as he sngle objecve does no aly o cyclss. We have made a frs aem o model commuer cyclss roue-choce wh a b-objecve shores ah mehod, by classfyng facors nfluencng her decson no wo caegores, namely, ravel me and aracveness. Gven an orgn-desnaon ar, he model can be aled o denfy he roue-choce se,.e. he se of effcen ahs, based on he crera consdered. We aly he model develoed o a case sudy n Auckland. However, he mehod of assessmen for roue aracveness has o be calbraed and valdaed for Auckland before can be aled on a nework wde bass. Areas for furher research are denfed. The model develoed can be aled o creae a cycle ma for he regon o romoe he use of bcycles for commung. Moreover, wh furher research n b-objecve assgnmen mehodologes, he model can also become he buldng block of a raffc assgnmen model for cycle rs. 8 ACKNOWLEDGEMENTS The auhors would lke o hank John Daves of he Auckland Regonal Councl for rovdng he Auckland Regonal Transor Plannng Model nework daa; Mark Sevenson and Rey Ofren from he Auckland Cy Councl for rovdng he Aeral Orhomagery mas. Fnally, Tom Cager mus also be acknowledged for hs conrbuon o he research, esecally n daa collecon and resenaon of resuls. 9 REFERENCES AUCKLAND CITY COUNCIL (1998) Cyclng and Walkng Sraegy. Auckland Cy. AULTMAN-HALL, L., HALL, F. & BAETZ, B. (1997) Analyss of Bcycle Commuer Roues Usng Geograhcal Informaon Sysems: Imlcaons for Bcycle Plannng. Transoraon Research Record, 1578, 102-110. BUREAU OF PUBLIC ROADS (1964) Traffc Assgnmen Manual. IN U.S. DEPARTMENT OF COMMERCE; URBAN PLANNING DIVISION (Ed.). Washngon D.C. DILL, J. & CARR, T. (2003) Bcycle Commung and Facles n Major U.S. Ces: If You Buld Them, Commuers Wll Use Them. Transoraon Research Record, 1828, 116-123. FHWA U.S. DEPARTMENT OF TRANSPORTATION (1992) Case Sudy No. 1: Reasons Why Bcyclng and Walkng Are No Beng Used More Exensvely as Travel Modes. FLORIDA DEPARTMENT OF TRANSPORTATION (2002) Qualy / Level of Servce Handbook. Tallahassee. HARKEY, D., REINFURT, D. & KNUIMAN, M. (1998) Develomen of he Bcycle Comably Index: A Level of Servce Conce. Transoraon Research Record, 1636, 13-20. INSTITUTION OF HIGHWAYS AND TRANSPORTATION (1998) Gudelnes for Cycle Aud and Cycle Revew. LAND TRANSPORT SAFETY AUTHORITY (2004) Cycle Nework and Roue Plannng Gude. LANDIS, B., VATTIKUTI, V., OTTENBERG, R., PETRITSCH, T., GUTTENPLAN, M. & CRIDER, L. (2003) Inersecon Level of Servce for he Bcycle Through Movemen. Transoraon Research Record, 1828, 101-106. LINGWOOD, P. (2004) Promong walkng and cyclng as an alernave o usng cars: Perceon of safey s bgges obsacle BMJ, 329, 7476. MORRIS, J. N. (1994) Exercse n he revenon of coronary hear dsease: oday's bes buy n ublc healh. Med Sc Sors Exercse, 26, 807-814. OGILVIE, D., EGAN, M., HAMILTON, V. & PETTICREW, M. (2004) Promong walkng and cyclng as an alernave o usng cars: sysemac revew. BMJ, 329, 763. -10-
Andrea Rah, Chrs Van Houe, Judh Y.T. Wang, and Mahas Ehrgo RAITH, A. & EHRGOTT, M. (2009) A Comarson of Soluon Sraeges For Bobjecve Shores Pah Problems. Comuers and Oeraons Research, 1299-1331. STINSON, M. A. & BHAT, C. R. (2003) Commuer Bcycls Roue Choce: Analyss Usng a Saed Preference Survey. Transoraon Research Record, 1828, 107-115. WARDROP, J. G. (1952) Some Theorecal Asecs of Road Traffc Research. Proceedngs of he Insuon of Cvl Engneers, Par II, 1, 325-362. -11-