Developmen of Urban Public Transi Nework Srucure Inegraing Muli-Class Public Transi Lines and Transfer Hubs Zhenbao Wang 1, Anyan Chen 2 1College of Civil Engineering, Hebei Universiy of Engineering Handan, Hebei, China 2Beijing Key Lab of Traffic Engineering Beijing Universiy of Technology Beijing, China Absrac Urban public ransi consiss of muliple ransi modes, such as railway, BRT, and bus. The inegraion of muli-class urban public ransi lines is very imporan o achieve a more efficien ransi sysem for he ciies ha advocae he public ransi prioriy. This paper presens an urban public ransi nework srucure for he grid ransi nework form. The urban public ransi nework srucure consiss of primary roues, feeder roues and accessorial roues, which are comprised of differen class ransi lines, and ransfer hubs are he key nodes connecing muli-class public ransi lines. Primary roues spacing, MRT sops spacing and he size of ransfer hub service zone are he key design variables. From he poins of view of he raveler, operaor and auhoriy respecively, he opimizaion objecive funcions for he key design variables are formulaed, and he numerical analysis is carried ou o find he opimal soluion. To a homogenous region, he recommended values of he key design variables are pu forward. The resul can provide he foundaion for roues planning and ransfer hubs locaion. Keywords - public ransi; nework srucure; ransfer hubs; nework opimizaion; locaion planning I. INTRODUCTION Public ransi consiss of muliple ranspor modes, such as bus, railway, axi and bus rapid ransi (BRT). Some capials of he provinces in China are offering he public ransi service, only bus mode. The curren bus lines nework has an irraional srucure: low densiy, high repeiion rae, and even some blind spos for service, which resul in he low level of service (LOS): over-crowded, he long ravel ime, he low operaing speed, he long ransfer ime beween differen bus lines, ec. Some ciies are saring o plan and consruc he mass rapid ransi (MRT) lines, aim o offer variey of public ransi service and mee he passengers differen demand. Public ransi nework conains muli-class ransi lines, and ransfer hubs are he key nodes of he public ransi nework and hey connec differen class public ransi lines. Transfer hubs also play a very imporan role o decrease he passenger ravel ime. I is very imporan and significan o organize a raional and efficien public ransi nework, and he public ransi nework srucure should be designed. Researchers from all over he world use sysemaic engineering mehods such as geneic algorihm, an-colony algorihm, opimizaion heory and graph heory o solve public ransi nework opimizaion problems. Zhao e al. [1] pu forward a mahemaical mehodology for ransi roue nework opimizaion and an inegraed simulaed annealing, abu, and greedy search algorihm are used o find he expeced global opimal resul. Fan and Machemehl [2] presened a bi-level opimizaion model for solving he Public Transporaion Nework Redesign Problem (PTNRP), and Geneic Algorihm (GA) is developed o solve his PTNRP model. Shai Jerby and Avishai Ceder [3] presened an opimal rouing design mehod for shule bus service, and he opimal model and is heurisic alernaive were compared in differen scenarios on a small real-life road nework, and he research shown ha he heurisic algorihm indeed provides good (opimal in he es case) resuls. Yu e al. [4, 5] proposes a mixed ineger opimal locaion model for urban ransi hubs, wih he objecive o minimize he demand-weighed oal ravel ime; a cluser-based hierarchical locaion model for he selecion of he proper locaions and scales of urban ransi hubs was developed wih he objecive of minimizing he demand-weighed oal ravel ime. Liu [6] akes ino accoun ha he ranspor hub has a reacion o he ranspor nework, and proposes simulaneously he opimizaion problems of ransporaion hub locaion and nework design esablishing a wo-sep decision-making model. Lü [7, 8] pus urban ransfer hub ino five caegories and esablishes he passenger ransfer hubs locaion model for he urban cenral disric; he auhor presens ha he ransfer hub should be locaed in he poin ha serves he maximum amoun of people and jobs wihin he reasonable walking area. Oher auhors have sudied srucural ransi quesions. For example, Byrne [9], radial sysems, Wirasinghe e al. [1], corridors and Newell [11]. Daganzo [12] presens a hybrid concep and hese hybrid neworks combine a grid srucure in he ciy cener wih a hub and spoke paern in he periphery. Esrada [13] presens and ess a mehod o design high-performance ransi neworks. The mehod produces he hybrid nework concepual plans for geomeric idealizaions of a paricular ciy ha are laer adaped o he real condiions. Felix Laube has characerized he physical configuraion of ransi service in Zurich as an inegraed nework of hree componens: (a) a primary ne, a radially DOI 1.513/IJSSST.a.17.11.13 13.1 ISSN: 1473-84x online, 1473-831 prin
oriened line-haul sysem, (b) a secondary ne, a imedransfer nework, (c) a fine-grained grid of mainly ram lines ha circulae wihin dense, buil-up areas. The regional configuraion of PT service offers a reference for his research [14]. Van Nes e al. (15) discuss and analyze possible objecives using analyical models for opimizing sop spacing and line spacing in urban ransi neworks, and he resuls of hese analyical models for wo ypical ciy ypes are analyzed by comparing performance characerisics (i.e., ravel ime, operaor coss, and paronage). This paper focuses on developing an urban public ransi nework srucure ha inegraes muli-class public ransi lines and ransfer hubs. The opimizaion model for he key design variables of public ransi nework srucure is formulaed, and he saisfacory soluion of key design parameers is proposed. II. PUBLIC TRANSIT NETWORK STUCTURE Public ransi nework consiss of he lines and he nodes, he lines are composed of railway lines, BRT lines and bus lines and so on, he nodes are composed of ransfer hubs, ransfer saions and sops. Mos of ransi models usually focus on single-class ransi neworks. Excepions can be found in lieraure on airline-nework design. In hese sudies a wo-layered nework srucure is assumed, in which he higher-level nework connecs he major airpors or he hubs and he lower-level nework connecs he oher airpors wih he hubs (he spokes) [16]. The hub and spoke nework srucure offers a soluion for he muli-class public ransi nework srucure design. Passengers need differen class public ransi lines o mee he differen rip demand: he differen rip disance, speed and passenger volume. The main PT service in China is he fixed-roue bus lines. In some meropolises, such as Beijing, Shanghai and Guangzhou, he subway service is becoming he main rip mode. The BRT also is being widely applied in China, such as Beijing, Jinan, Kunming, and Hangzhou. Public ransi lines fall ino four classes: he subway lines, he BRT lines, he runk bus lines, and he shule bus lines. The design sandards for every class public ransi lines are shown in Table I. There are several nework forms for public ransi nework, such as grid, riangular, radial and radial/arc. To he grid nework form, he ideal urban public ransi nework srucure is shown in figure 1, and i comprises of differen funcional roues, ransfer hubs and ransfer hubs service zones. The urban area is divided ino some ransfer hubs service zones, and only one ransfer hub is locaed in he cener of he ransfer hubs service zone. Transfer hubs offer he ransfer service among muli-class public ransi lines, and may combine subway lines and BRT lines wih local bus services, axi. The size of ransfer hub service zone is an accepable range around he ransfer hub. The public ransi roues consis of primary roues, feeder roues and accessorial roues: Primary roues connec he ransfer hubs and ake on he funcion of ransi corridor service beween ransfer hubs service zones. Primary roues conain one or muliple class public ransi lines, such as railway lines, BRT lines and runk bus lines, and offer various and differenial ransi service for he passengers raveling beween ransfer hubs service zones. TABLE I. DESIGN STANDARD FOR EVERY CLASS PUBLIC TRANSIT LINES Operaion Deparure Sop Lines Lengh Capaciy speed inerval spacing ype (km) (passengers/h) (km/h) (min) (km) Railway lines 25~5 3~5 >15 >1. 25~5 BRT lines >25 4~8 >15 >1. 3 Trunk bus lines 18~2 4~1 1~15.5~.8 5 Shule bus lines 15~2 4~1 <8.3~.5 3 Feeder roues deliver he ravelers from and o MRT sops or ransfer hubs. On he oher hand, feeder roues offer he ransi service wihin he ransfer hubs service zone. Feeder roues conain he shule bus lines operaing wihin he ransfer hubs service zone and he exending segmen of runk bus lines ha exend from he ransfer hub o he inside of he ransfer hubs service zone. Accessorial roues are regarded as he complemen of primary roues and ake on he service funcion of secondary ransi corridor beween ransfer hubs service zones. Accessorial roues connec he ravelers concenraion disrics and offer he nonsop ransi service for he neighboring ransfer hubs service zones. Accessorial roues comprise of runk bus lines. Legend Transfer hubs Bus erminals Figure 1. Ideal urban public ransi nework srucure. primary roues feeder roues accessorial roues Urban area Transfer hubs service zone Figure 2 shows an urban public ransi corridor ha is comprised of muli-class public ransi lines. Primary roue is comprised of he segmens of MRT line and runk bus line beween ransfer hub i and ransfer hub j. Feeder roues are comprised of he segmens of runk bus line beween bus sop k and i and beween bus sop l and i and he shule bus lines. Accessorial roue is comprised of he segmens of runk bus line beween bus sop m and n. Figure 2. Urban public ransi corridor wih muli-class lines. DOI 1.513/IJSSST.a.17.11.13 13.2 ISSN: 1473-84x online, 1473-831 prin
III. KEY DESIGN VARIABLES FOR URBAN PUBLIC TRANSIT NETWORK Figure 3 is he skech map of key design variables of urban public ransi nework, he key design variables are he primary roues spacing D l, he MRT sops spacing and he size of ransfer hub service zone D l D l. D l and D s wih differen values will resul in differen passengers ravel ime, and operaional cos. Figure 3. Illusraion of key design variables of public ransi nework srucure. The main dilemma in ransi-nework design is he conroversy beween he raveler and he operaor. Simply pu, he raveler wans o ravel a any ime and as fas as possible o his or her desinaion. This requires a nework having a high nework densiy and high frequencies. Such a nework is clearly oo expensive for an operaor, who would like o have a nework of profiable lines only. Thus, regarding he raveler, he main characerisic of a ransi nework is oal ravel ime. This ravel ime can be divided ino access ime, waiing ime, in-vehicle ime, ransfer ime, and egress ime. From he poin of view of he operaor, he main characerisics are he revenues and he operaional coss. In pracice, here is also a hird pary involved in ransi-nework design he local auhoriies. They migh op for he raveler, for insance by subsidizing ransi, or hey migh ry o find a balance beween he raveler s and operaor s ineress using he concep of social welfare [15]. On he assumpion ha he rips whose origin and desinaion is wihin he same ransfer hub service zone are compleed by aking feeder roues or accessorial roues; he rips whose origin and desinaion belong o he adjacen wo ransfer hub service zones are compleed by aking accessorial roues; he rips whose origin and desinaion are no belong o he adjacen wo ransfer hub service zones (span-mulizone rips) are compleed by aking he combinaion of primary roues and oher feeder modes, such as feeder roues, walking and bicycle, and he rips need o ransfer a he ransfer hubs or MRT sops. The rips beween MRT sop service zone Z1 and Z2 belong o he span-muli-zone rips (Figure 3). The following secions presen he opimizaion model for he key design variables from he poins of view of he raveler, operaor and auhoriy respecively for he span-muli-zone rips. A. Traveler s Objecive The oal ravel ime for span-muli-zone rip is divided ino access ime (from he origin o MRT sops or ransfer hubs), waiing ime (a he MRT sops or ransfer hubs), in-vehicle ime (aking MRT lines), egress ime(from MRT sops or ransfer hubs o he desinaion) and ime los a a ransfer hub for ransferring beween MRT lines. 1) Access ime from origin o MRT sops or ransfer hubs The main rip modes from origin o MRT sops or ransfer hubs are walking, bicycle and feeder bus. Access ime (Ta) can be defined as Ta Taw Paw Tab Pab Taf P (1) af where T aw is he average walking ravel ime access o MRT sops or ransfer hubs, T ab is he average ravel ime aking bicycle access o MRT sops or ransfer hubs, and T af is he average ravel ime aking feeder bus access o MRT sops or ransfer hubs, P aw is he walking mode spli proporion, P ab is he bicycle mode spli proporion, and P af is he feeder bus mode spli proporion. The modes spli proporion can be described using he logi mode-choice model. To simplify he problem, on he assumpion ha he ravelers whose origins are wihin he 4m radius around he ransfer hubs or MRT sops arrive o he ransfer hubs or MRT sops by walking, and oher raveler by bicycle and feeder bus. The mode spli proporion of bicycle and feeder bus is deermined according o he mode spli forecasing for he planning years. The raio of feeder bus mode o bicycle mode is p, and 1 8 Paw ( 4 4) /( ) 2 2 2 D s (2) 1 Pap Pab p 1 p (1 Pap ) Paf p 1 The average walking ime access o MRT sops or ransfer hubs is 1 T aw Daw / Vw 2 4 /1 267 (s) (3) 3 where D aw is he average walking disance access o MRT sops or ransfer hubs, and V P is he walking speed, 1.m/s; The average ravel ime aking bicycle access o MRT sops or ransfer hubs is Tab 3.6 Dab / Vb T (4) b where D ab is he average ravel disance of bicycle mode access o MRT sops or ransfer hubs, and 1 2 1 2 2128 16 16 (5) Dab 1 8 4 where V b is he average ravel speed of bicycle mode, 16km/h, and T b is he ime los during bicycle parking a he MRT sops or ransfer hubs. The average ravel ime aking feeder bus access o MRT sops or ransfer hubs is Taf 3.6 Daf / V f Twf T (6) f where D af is average ravel disance of feeder bus mode access o MRT sops or ransfer hubs, and D af=d ab, V f is he DOI 1.513/IJSSST.a.17.11.13 13.3 ISSN: 1473-84x online, 1473-831 prin
average operaion speed of feeder bus lines, T wf is he sum of walking ime and waiing ime from origin o bus sop, and T f is he ransfer ime los beween feeder bus and MRT lines. 2) Waiing ime a he ransfer hubs or MRT sops Waiing ime mainly depends on he frequency of he service; he waiing ime can be defined easily by 36 Tw f w (7) F where f w is he facor for he waiing ime, and F is he frequency of he MRT lines service. 3) in-vehicle ime of MRT lines The in-vehicle ime is deermined by he average spanmuli-zone ravel disance, he maximum speed of MRT lines and he ime los a each sop: 1 D 3.6 Ti ( Ts ) (8) v Where, D is he average ravel disance of span-mulizone rips, v is he maximum speed of MRT lines, and T s is he ime los a a ransfer hub or a MRT line sop. 4) Egress ime from he MRT sop or he ransfer hub o he desinaion To each rip mode, he egress ime from he MRT sop or he ransfer hub o he desinaion is equal o he access ime from origin o he MRT sop or he ransfer hub: Tew Taw (9) Teb Tab Tef Taf where T ew, T eb and T ef are he average walking ime, he average bicycle ravel ime and he average feeder bus ravel ime from he MRT sop or he ransfer hub o he desinaion respecively. The average egress ime from he MRT sop or he ransfer hub o he desinaion can be defined as Te Tew Pew Teb Peb Tef P (1) ef where P ew, P eb and P ef are he mode spli proporion of walking, he bicycle and he feeder bus from he MRT sop or he ransfer hub o he desinaion respecively. 5) Transfer ime los beween MRT lines Some ravelers need o ransfer a a ransfer hub beween wo MRT lines. On he assumpion ha he maximum ransfer imes for one rip is one ime, he average ransfer ime los can be defined as T p (11) where is he ransfer ime los a a ransfer hub, p is he raio of he ravelers who need o ransfer o all ravelers. The oal subjecive ravel ime is defined: Tc ( wa Ta ww Tw Ti we Te w T ) (12) where T c is he oal weighed ravel ime, and w x is he weigh for ime elemen x, w k is he weigh for ime elemen k. From he poin of view of raveler, he objecive is minimizing weighed ravel ime: min( w T w T T w T w T ) (13) a a w w i e e B. Operaor s Objecive The operaional coss in erms of coss per uni area served are deermined by he vehicle densiy, which migh be assumed o be fixed or which migh depend on he sop spacing and line spacing [15]. Operaors wan o maximize he operaional efficiency ha is he income per cos. The objecive funcion for he operaional efficiency maximum can be formulaed: ( r rs ) P ( r rs ) P max max 11 1 c o co 1 (14) where r is he fare paid by he raveler, r s is he subsidy paid by he auhoriies per raveler, P is he number of ravelers per km 2, and c o is he operaional cos per uni lengh of MRT lines. On he oher hand, operaors wan o maximize he operaional profi ha is equal o he income minus he operaional cos. The objecive funcion for he operaional profi maximum can be formulaed: 1 max ( r rs ) P co (15) Chinese governmen doesn consiue a raional subsidy sysem, and he sandard of subsidy is very differen o he differen ciies. This paper presens he objecive funcion of operaors is o minimize he operaional cos, which can be formulaed: 1 min co (16) C. Auhoriy s Objecive Local auhoriies migh ry o find a balance beween he raveler s and he operaor s ineress. One way o do so is o deermine he ne benefi of he ransi sysem. From an economic poin of view, he concep of maximizing social welfare, defined as he sum of consumer surplus and producer surplus, would be bes. The formulaion for he consumer surplus, however, is raher complicaed [15]. Therefore, a somewha simpler approach is chosen. The objecive funcion of auhoriies is o minimize he cos associaed wih raveling can be formulaed: c Tc P 1 min co (17) 36 where c is he value of ime for rips by public ransi. D. Numerical Analysis Your goal is o simulae he usual appearance of papers in a Journal of he Academy Publisher. We are requesing ha you follow hese guidelines as closely as possible. The saisics is finished for he ciies in China wih over 3,, populaions, and he densiy of populaion is beween 11, and 14, per km 2, and he ravelers ravel 2.~2.4 imes per day. The value of ime for rips by public ransi is 6~15 Chinese Yuan per hour. An assumpion was made o reduce complexiies: he densiy of rip disribuion is homogenous. DOI 1.513/IJSSST.a.17.11.13 13.4 ISSN: 1473-84x online, 1473-831 prin
The inpu parameers values (shown in Table II) are used for he numerical analysis. TABLE II. INPUT PARAMETER VALUES FOR THE NUMERICAL ANALYSIS parameer symbol values uni Span-muli-zone ravel 6,8, D disance 1 km Walking ime access o a bus sop and waiing Twf 18 s ime Time los during bicycle parking a a MRT sop Tb 18 s of a ransfer hub Transfer ime los beween feeder bus and Tf 18 s MRT lines Walking speed VP 1 m/s Bicycle speed Vb 16 km/h Feeder bus operaional speed Vf 15 km/h Maximum operaional speed of MRT lines v 4 km/h Service frequency of MRT lines F 15 vehicles/h Facor for he waiing ime fw.5 Time los a a MRT sop Ts 3 s Raio of feeder bus mode o bicycle mode p 7 Raio of he ravelers who need o ransfer o p.5 all ravelers Transfer ime los a a ransfer hub 27 s Number of ravelers per uni area P 216 ravelers/km 2 Value of ime for rips Chinese c 15 by public ransi Yuan/h Operaional cos per uni Chinese co 3 lengh of MRT lines Yuan /km Weigh for he segmen wa ww wi of ravel ime 1. we w When he span-muli-zone ravel disance is 6km and MRT sops spacing is 1,2m, he relaionship beween he objecive funcion values and he primary roues spacing is illusraed in Figure 4, which is similar o he one when he MRT sops spacing is 2,m(Figure 5). As he primary roues spacing increase, he oal weighed ravel ime increase linearly, while he operaional cos and he cos associaed wih raveling per square kilomeer decrease. There is no opimum for he objecives, bu i should be noed ha he operaional cos and he cos associaed wih raveling per square kilomeer decrease rapidly when he primary roues spacing is less han 2,m, and he wo objecive funcion values are basically changeless when he primary roues spacing is more han 3,6m. When he spanmuli-zone ravel disance is 8km or 1km, he relaionship beween he objecive funcion values and he primary roues spacing is similar o he one ha he span-muli-zone ravel disance is 6km. From he poin of view of ravelers, hey hope he less primary roues spacing, bu he governmen or invesor can suppor he large-scale MRT lines consrucion. From he poin of view of operaor and auhoriy, he cos should be limied wihin an accepable range. So, he auhor hinks ha he accepable saisfacory soluion for he primary roues spacing is beween 2,m and 3,6m. Cossper square kilomeer Operainal coss(operaors' objecive) Toal weighed ravel ime(travelers' objecive) 6 5 4 3 2 1 he primary roues spacing(m) Coss associaed wih raveling(auhoriies' objecive) Figure 4. Relaionship beween he objecive funcion values and he primary roues spacing (average ravel disance 6km and MRT sop spacing 12m). Coss per square kilomeer Operainal coss(operaors' objecive) Toal weighed ravel ime(travelers' objecive) 6 5 4 3 2 1 he primary roues spacing(m) 3 25 2 15 1 5 3 25 2 15 1 5 Travel imes(s) Coss associaed wih raveling(auhoriies' objecive) Figure 5. Relaionship beween he objecive funcion values and he primary roues spacing (average ravel disance 6km and MRT sop spacing 2m). When he span-muli-zone ravel disance is 6km and he primary roues spacing is 2,5m, he relaionship beween he objecive funcion values and he MRT sops spacing is illusraed in Figure 6. There is an opimum for he oal weighed ravel ime and he cos associaed wih raveling in he case ha he MRT sops spacing equals 1,25m, and when he primary roues spacing is 3,5m, here is an opimum in he case ha he MRT sops spacing equals 1,3m(Figure 7). Coss per square kilomeer Operainal coss(operaors' objecive) Toal weighed ravel ime(travelers' objecive) 37 32 27 22 17 12 7 MRT sops spacing(m) 224 222 22 218 216 214 212 21 28 26 24 Travel imes(s) Coss associaed wih raveling(auhoriies' objecive) Figire 6. Relaionship beween he objecive funcion values and he MRT sop spacing (average ravel disance 6km and primary roues spacing 2,5m). Travel imes(s) DOI 1.513/IJSSST.a.17.11.13 13.5 ISSN: 1473-84x online, 1473-831 prin
Coss per square kilomeer Operainal coss(operaors' objecive) Toal weighed ravel ime(travelers' objecive) 32 27 22 17 12 7 MRT sops spacing(m) Coss associaed wih raveling(auhoriies' objecive) Figure 7. Relaionship beween he objecive funcion values and he MRT sop spacing (average ravel disance 6km and primary roues spacing 3,5m). When he primary roues spacing equals 2,5m and 3,5m, he relaionship beween he opimal MRT sops spacing and average ravel disance is illusraed in Figure 8. As he average ravel disance increase, he opimal MRT sops increase linearly. he opimal MRT sop spacing (m) 17 165 16 155 15 145 14 135 13 125 12 he primary roues spacing equals 2,5m he primary roues spacing equals 3,5m 6 8 1 he average ravel disance (km) Figure 8. Relaionship beween he average ravel disance and he opimal MRT sops spacing. In order o illusrae he sensiiviy o he assumpions, he densiy of populaion has been considered varying ±15%, he resul is invariable for he opimal MRT sops spacing. So, he disribuion of populaion has no direc effec on he opimal MRT sops spacing, and he average ravel disance is he key facor for deermine he opimal MRT sops spacing. This paper presens he recommended values for he key design variables according o he differen average ravel disance (shown in able III). TABLE III. RECOMMENDED VALUES FOR THE KEY DESIGN VARIABLES Span-mulizone ravel disance (km) Primary roues spacing(m) MRT sops spacing(m) 236 234 232 23 228 226 224 222 22 218 216 Travel imes(s) Size of ransfer hub service zone (m m) 4 2 1 2 2 6 25 125 25 25 8 3 1425 3 3 1 35 16 35 35 IV. CONCLUSION The auhor presens he urban public ransi nework srucure. From he poins of view of he raveler, operaor and auhoriy respecively, he opimizaion objecive funcions for he key design variables are formulaed, and he numerical analysis is carried ou o find he opimal soluion for he key design parameers. For he given inpu parameers values, he recommended values of he key design variables are pu forward. The mehodology proposed here can be implemened in designing a muli-class urban public ransi nework srucure. The resul of he key design variables can provide he foundaion for he following roues planning and ransfer hub layou. The ransfer hub service zones are clearly marked off on he urban area, and only one ransfer hub is locaed wihin every ransfer hub service zones. Transfer hubs are regarded as he key nodes for organizing he muliclass urban public ransi nework, he differen class public ransi lines should be locaed according o he ravel demand, which will be he following research direcion. Furhermore, he auhors hink ha several key issues should be discussed in he fuure research. Some recommendaions can be saed: (1)The public ransi nework srucure is designed more suiable for a grid road nework form, and furher sudy is necessary o design a public ransi nework srucure for he radial, riangular, or circular road nework form. (2)The recommended resuls for he key design variables are concluded basing on he given inpu parameers values. For oher cases, he opimal model and he analyical process can be applied o design an urban ransi nework srucure, and he inpu parameers values are differen from he ones ha his paper refers o. (3)The locaion mehod for he railway lines, BRT lines, and bus lines need o be discussed basing on he proposed urban public ransi nework srucure. ACKNOWLEDGMENT This work was suppored in par by a gran from Naural Science Foundaion of Hebei Province(No.E214423) and Hebei Universiy of Engineering Youh Academic suppor projec. We also hank he anonymous reviewers for heir helpful feedback and suggesions. REFERENCES [1] F. Zhao., Transi Nework Opimizaion-Minimizing Transfers and Opimizing Roue Direcness wih an Inegraed Simulaed Annealing and Tabu Search Mehod, CD-ROM. Transporaion Research Board of he Naional Academies, Washingon, D.C. 25. [2] W. Fan, R. B. Machemehl., A Bi-level Opimizaion Model for he Public Transporaion Nework Redesign Problem, CD-ROM. Transporaion Research Board of he Naional Academies, Washingon, D.C. 211. [3] S. Jerby and A. Ceder., Opimal Rouing Design for Shule Bus Service, In Transporaion Research Record: Journal of he Transporaion Research Board, Washingon, D.C., No. 1971, pp. 14 22, 26. [4] J. YU., Cluser-Based Opimizaion of Urban Transi Hub Locaions Mehodology and Case Sudy in China, In Transporaion Research DOI 1.513/IJSSST.a.17.11.13 13.6 ISSN: 1473-84x online, 1473-831 prin
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