Urban Transpor XIII: Urban Transpor and he Environmen in he 21s Cenury 347 Urban public ranspor opimizaion by bus ways: a neural nework-based mehodology M. Migliore & M. Caalano Deparmen of Transporaion Engineering, Palermo Universiy, Ialy Absrac This paper describes an approach for planning he inroducion of bus lanes ino he urban road nework, which has been applied o he urban area of Palermo. The proposed modelling ool adops a muli-agen objecive funcion expressing he rade-off beween he ineress of diverse sakeholders: he generalized ranspor cos for car drivers and he ravel ime for public ranspor users. The reacion of car raffic o a cerain planning scenario has been simulaed by he DUE assignmen echnique and he posiive impac of he modal shif on he objecive funcion has been ackled by aaching a suiable weigh o he ime saving for bus passengers. The rise in he bus ravel speed, owing o he bus lane soluion, has been prediced for a se of urban roads by a neural nework, so as o ake ino accoun many quaniaive and qualiaive road aribues. The opimal locaion paern of bus ways has been searched by a greedy heurisic ha hrough a sep-by-sep sraegy builds he problem soluion by keeping, a each sage, he bes alernaive. Keywords: urban public ranspor, bus way design, welfare funcion opimizaion, neural nework, greedy heurisic. 1 Inroducion Bus lanes represen an effecive ool for buses o bypass he congesion a criical secions of he urban road nework, especially during rush hours. Furhermore, hey consis in a ranspor policy acion ha can be easily implemened. In deail, bus lanes imply he following advanages: A rise in he bus ravel speed, generally speaking, from 10 Km/h o 13-15 Km/h. The puncualiy of he public ranspor service. WIT Transacions on The Buil Environmen, Vol 96, www.wipress.com, ISSN 1743-3509 (on-line) doi:10.2495/ut070331
348 Urban Transpor XIII: Urban Transpor and he Environmen in he 21s Cenury Comfor and safey improvemens, hanks o he reducion in acceleraions and deceleraions (sop and go driving). A decrease in he environmenal impac and energy consumpions. 2 The mobiliy sysem of Palermo The General Urban Transpor Plan of Palermo esimaes he inernal movemens a 960000 ravellers per day; he 81% of such mobiliy demand uses he car, whereas he residual par chooses he public ranspor, which highlighs a criical siuaion for Palermo, since, generally speaking, wih reference o he public ranspor share, saisics show a 18%-30% range in he case of small/mediumsized owns and values higher han 50% in he big own case. Moreover, he average ravel speed on he urban road nework is 18 km/h, while, inside he cenre, he ravel speed can be over he 7 km/h level, during rush hours. Oher alarming daa regard he number of accidens per annum wihin he urban area of Palermo ha comes o abou 2000. In order o reverse his rend, he local adminisraors have recenly launched he Inegraed Plan of Transpor, for a more effecive public ranspor sysem, which suggess he bus lane sysem enhancemen (Palermo Ciy Council [1]). 3 Problem definiion and model framework The research aciviy presened has consised in developing a quaniaive mehodology for planning he inroducion of bus ways ino he urban road nework. The resuling approach has been applied o Palermo ciy: he presen bus lane sysem has been compared wih he model-based one. In paricular, o idenify he sudy area wihin Palermo and o selec he roads for he bus lane design model, he auhors have considered parameers concerning he public ranspor level of service, number of lines and frequency, and geomeric parameers such as he road widh. The considered planning problem has been solved using an objecive funcion represening he rade-off beween he ineress of privae ranspor users and public ranspor ones: ( C, T T ) O. F. = f, (1) car where, C car : rise in he ranspor moneary cos for car users; T car : rise in he ravel ime for car users; T bus : reducion in he ransi ime for bus users. The choice behaviour of car drivers has been simulaed hrough he DUE assignmen mehod (Cascea [2]). car bus WIT Transacions on The Buil Environmen, Vol 96, www.wipress.com, ISSN 1743-3509 (on-line)
Urban Transpor XIII: Urban Transpor and he Environmen in he 21s Cenury 349 The effec of bus ways on he bus ravel speed has been evaluaed by a neural nework (Bishop [3]), allowing for several road aribues. The auhors have also considered he posiive impac of he modal shif on he local communiy welfare by assigning a suiable weigh o he ime saving for bus passengers. The opimal se of bus ways has been deermined hrough ieraions of a greedy algorihm (Tadei and Della Croce [4]). 4 Soluion process 4.1 The inpu for he bus lane design model To se he poenial sies for bus lanes, he auhors have seleced hose roads respecing he following crieria: one regarding he widh of he road secion for buses; anoher one consising in he frequency of he public ranspor service. In Table 1, he reader can analyze a marix reporing he differen ranspor policy acions ha he auhors propose for various combinaions of he aforesaid crieria. Table 1: Transpor policy acions based on he public ranspor level of service and road parameers. Crieria Public ranspor Widh of he road secion Transpor policy acion frequency, F for buses, L * (meers) (buses per hour) F 21 L 5 Bus lane F 21 L < 5 Closed o raffic zone 12 F < 21 L 5 The bus lane soluion is o be weighed 12 F < 21 L < 5 No acion F < 12 No acion * I excludes he space for car parking. 4.2 The esimaion of he objecive funcion s componens As saed before, he opimal bus lane sysem for Palermo has been searched adoping he following muli-agen objecive funcion: ( C, T T ) O. F. = f, (2) car car bus WIT Transacions on The Buil Environmen, Vol 96, www.wipress.com, ISSN 1743-3509 (on-line)
350 Urban Transpor XIII: Urban Transpor and he Environmen in he 21s Cenury In deail: T bus = C car = [ euros per car - km cars - km] ; T car = [ euros per car - hour cars - hour] ; [ euros per bus passenger - hour bus passengers - hour] where, cars-km: variaion of he cars-km variable owing o he inroducion of bus ways. Such quaniy refers o he number of privae vehicles moving on he nework and he disances covered by hemselves. cars-hour: variaion of he cars-hour variable arising from a cerain bus lane paern. This variable measures he ransi ime spen by privae vehicles. bus passengers-hour: variaion of he passengers-hour variable arising from a cerain bus lane paern. This variable measures he ransi ime spen by bus users. 4.2.1 The deerminaion of bus passengers-hour To compue bus passengers-hour, wo elemens need o be evaluaed: he public ranspor ravel speed for he roads under analysis (namely, he poenial locaions for bus ways) and, for each of hese ones, he number of he public ranspor cusomers. In paricular, o predic he public ranspor ravel speed, he auhors have adoped a neural nework, whose archiecure is he mulilayer percepron one (Bishop, [3]). In deail, a hree layer srucure has been used: Inpu layer: wih a number of neurons equal o he one of he variables observed for a generic road secion. I ransfers inpu daa o he processing layer hrough linear mahemaical funcions. Hidden layer: he compuing core of he neural nework wih a number of neurons deermined by he pruning approach. I employs he anh ransfer funcion. Oupu layer: wih a neuron for esimaing he bus ravel speed. Such an arificial inelligence ool processes empirical daa regarding he following quaniaive and qualiaive road aribues: bus way availabiliy (Y/N); number of bus sops; number of juncions wih raffic lighs; number of side roads; number of pedesrian crossings; possibiliy of parking wih he line of march (Y/N); ransgression of he parking rules (Y/N); presence of shops (Y/N); raffic flow/road capaciy (La Franca e al [5]). On he basis of he above-lised variables, he urban roads under analysis have been subdivided ino homogeneous secions. Moreover, he aforesaid empirical road daa have been normalized, o be processed by he neural nework as dimensionless and comparable inpus. In order o calculae he number of bus passengers, he origin-desinaion marix represening he public ranspor demand of Palermo during he peak hour of a working day (2002) has been assigned o he corresponding graph by he. WIT Transacions on The Buil Environmen, Vol 96, www.wipress.com, ISSN 1743-3509 (on-line)
Urban Transpor XIII: Urban Transpor and he Environmen in he 21s Cenury 351 hyperpah minimum algorihm, aking ino accoun he rise of he bus ravel speed, due o he inroducion of bus lanes (Cascea [2]). The oupu of he described bus passengers-hour esimaion process can be analyzed in Tables 2 and 3: Table 2: The neural nework-based oupu. Road name Via Noarbarolo Viale Lazio Via Basile Via Dane Via Pone di Mare Secions Lengh (km) Bus speed wihou bus lane (Km/h) Bus speed wih bus lane (Km/h) 1 0.15 6.57 14.58 2 0.25 7.07 7.57 3 0.25 6.31 7.96 4 0.2 7.88 15.06 5 0.15 6.28 13.75 1 0.25 7.00 7.10 2 0.3 6.98 10.46 3 0.24 6.31 9.77 4 0.24 6.52 8.16 1 0.70 14.12 16.37 2 0.35 15.09 15.94 3 0.50 9.84 15.99 4 0.45 11.38 15.17 1 0.3 5.94 11.77 2 0.15 5.88 9.16 3 0.4 6.08 11.09 4 0.35 7.91 8.77 1 0.27 9.22 15.94 2 0.47 7.66 15.15 3 0.38 7.55 8.89 4 0.47 7.88 13.56 4.2.2 The deerminaion of cars-km and cars-hour To appraise cars-km and cars-hour, he origin-desinaion marix represening he privae ranspor demand of Palermo during he peak period of a working day (2002) has been assigned by he DUE approach o he corresponding graph, aking ino accoun he reducion in space for car movemens, due o he inroducion of bus lanes. 4.3 Compuaional resuls This secion shows he oucomes achieved by he greedy algorihm (Tadei and Della Croce [4]) applied o deermine he opimal se of bus ways for he public ranspor sysem of Palermo. WIT Transacions on The Buil Environmen, Vol 96, www.wipress.com, ISSN 1743-3509 (on-line)
352 Urban Transpor XIII: Urban Transpor and he Environmen in he 21s Cenury Table 3: The neural nework-based oupu. Road name Corso Albero Amedeo Corso Tukory Secions Lengh (km) Bus speed wihou bus lane (km/h) Bus speed wih bus lane (km/h) 1 0.2 6.44 13.64 2 0.4 9.86 15.81 1 0.2 11.72 12.20 2 0.2 13.51 12.54 3 0.2 9.51 15.74 4 0.15 6.74 14.52 Via Goehe 1 0.35 7.54 11.16 1 0.4 7.04 15.06 Via Duca della Verdura Via Marchese di Villabianca 2 0.2 6.36 14.02 1 0.1 7.15 14.84 2 0.15 6.04 9.09 3 0.25 5.95 10.02 4 0.15 7.07 13.39 5 0.15 9.70 13.80 6 0.1 10.40 15.95 The above-menioned heurisic consrucs he bus lane design problem soluion hrough a sep-by-sep opimizaion process and he following objecive funcion: W.F. = α ( bus passengers-hour cars-hour) β cars-km (3) where, W.F.: Welfare Funcion α: value of ime (2.6 euros per passenger-hour) β: privae ranspor cos (0.1 euros per car-km) The value of ime characerizing he mobiliy sysem of Palermo can be esimaed a 2 euros/hour. Such a figure has been muliplied by 1.3, so as o ake ino accoun, on one hand, he posiive environmenal impac of a more compeiive public ranspor service and, on he oher hand, he need of urning cars-hour ino car passengers-hour; in fac, he privae ranspor occupancy facor for Palermo can be appraised a 1.3 ravellers per vehicle (Palermo Ciy Council [1]). As a consequence: W.F. = (2 euros per hour) 1.3 ( bus passengers-hour cars-hour), (0.1 euros per car-km) cars-km. (4) The opimal se of bus ways has been buil by a sequenial approach: a each sage ( = 1, 2,, N), amongs he available roads wih a criical public WIT Transacions on The Buil Environmen, Vol 96, www.wipress.com, ISSN 1743-3509 (on-line)
Urban Transpor XIII: Urban Transpor and he Environmen in he 21s Cenury 353 Table 4: The comparison beween he pre-exisen bus way nework of Palermo and he model-based one. Road name The presen bus lane sysem of Palermo The model oupu Corso Tukory Via Dane (firs secion)* - Via Dane (second and hird secions) - Via Duca Della Verdura Via Goehe - Via Liberà* Via Maqueda* Via Marchese di Villabianca - Via Noarbarolo Via Oreo* - Via Pone di Mare - Via Roma* Viale Lazio - Viale Srasburgo* Via Erneso Basile - - Corso Albero Amedeo - : wih a bus lane; -:wihou a bus lane. *: roads wih a so high bus frequency ha hey have been assigned a bus way ou of he model. ranspor frequency (lying beween 12 and 21 buses/hour; see Table 1), he algorihm idenifies he one maximizing he Welfare Funcion by he inroducion of a bus lane. In formal erms: 1. = 1 Max W. F., subjec o x = 1 2. ( ) x x 3. If maxw. F. ( x ) 0 x 4. Else x = arg maxw. F. ( x ) x 5. = + 1 6. + 1 MaxW. F. x x x j= 1 2,, -1 k hen sop j k, subjec o xk = 1 and k j x x, j = 1, WIT Transacions on The Buil Environmen, Vol 96, www.wipress.com, ISSN 1743-3509 (on-line)
354 Urban Transpor XIII: Urban Transpor and he Environmen in he 21s Cenury a b Table 5: The opimal bus lane locaion a each sage of he greedy algorihm a. Greedy seps Via Noarbarolo Viale Lazio Via Basile Impac (euros) on he Welfare Funcion if a bus lane is placed in: Via Dane b Via Pone di Mare Corso A. Amedeo Via Goehe Corso Tukory Via Duca della Verdura Via Marchese di Villabianca 1 +48.48 +3.79-26.74 +39.67 +15.39-3.92 +15.77-4.67 +105.93 +57.91 2 +69.72 +25.38-1.49 +63.03 +15.66 +8.65 +16.05 +17.17 - +27.24 3 - +15.78 +3.51 +56.53 +30.87 +11.84 +19.34 +14.07 - +39.64 4 - +25.98-6.19 - +43.16-2.25 +23.05 +18.07 - +44.04 5 - +18.78-1.99 - +24.96-11.85 +14.97 +13.65 - - 6 - +22.58 +0.11 - - +9.05 +26.55 +13.77 - - 7 - +8.38-16.89 - - -6.25 - +9.97 - - 8 - +24.18-4.39 - - +5.85 - - - - 9 - - -5.29 - - -10.55 - - - - A every sep, he opimal soluion is wrien in bold face; - means ha he corresponding sree has been seleced as bes sie for a bus lane a a previous ieraion. I refers o he second secion and he hird one. WIT Transacions on The Buil Environmen, Vol 96, www.wipress.com, ISSN 1743-3509 (on-line)
Urban Transpor XIII: Urban Transpor and he Environmen in he 21s Cenury 355 7. 1 If max.. + j W F x x 0 or = N hen sop x j= 1 8. Else = + 1 j x arg maxw. F. x x x j= 1 9. Go o sep 5. where, x: vecor represening he locaion paern of bus lanes, whose generic elemen is x k belonging o he se of hose roads wih a criical public ranspor frequency (lying beween 12 and 21 buses/hour); x k :1 if road k is provided wih a bus way; 0 oherwise. As for he applicaion oupu, he reader can noice in Table 5 ha he greedy algorihm sops a he eighh ieraion, since a he ninh sep, each of he available alernaives (Via Erneso Basile and Corso Albero Amedeo) enails a negaive value of he objecive funcion. 5 Conclusions A clear proof of he described mehodology uiliy emerges from he oucome showed in Table 5. In fac, consider he Corso Albero Amedeo case (see Table 3): he public ranspor is characerized by an average demand of 440 passengers per hour and an average ravel speed of 8.15 km/h; hanks o a bus lane, he average speed level of 14.72 km/h can be gained, which means a remarkable 81% rise. Consequenly, he bus lane for Corso Albero Amedeo seems o be an opporune ool o improve he public ranspor performance; on he conrary, under an overall poin of view concerning he urban mobiliy sysem, he illusraed planning model excludes he bus way soluion for Corso Albero Amedeo. Furhermore, he comparison beween he presen bus lane sysem of he sudy area and he one resuling from he described mehodology proves ha he former ha is based on a qualiaive planning approach needs o be highly developed as i has been showed in his paper (see Table 4). References [1] Palermo Ciy Council, Final Repor Urban Transpor Plan, 2002. [2] Cascea, E., Transporaion Sysems Engineering: Theory and Mehods, Dordrech (The Neherlands): Kluwer Academic Publishers, 2001. [3] Bishop, C. M., Neural Nework for Paern Recogniion, Oxford Universiy Press, Oxford, 1995. [4] Tadei, R., Della Croce, F., Ricerca Operaiva e Oimizzazione, Esculapio, Bologna, 2001. WIT Transacions on The Buil Environmen, Vol 96, www.wipress.com, ISSN 1743-3509 (on-line)
356 Urban Transpor XIII: Urban Transpor and he Environmen in he 21s Cenury [5] La Franca, L., Migliore, M., Salvo, G., Carollo, F., The auomaic vehicle monioring o improve he urban public ranspor managemen, Proc. of he World Congress CODATU XI Towards More Aracive Urban Transporaion, Bucares, 2004. WIT Transacions on The Buil Environmen, Vol 96, www.wipress.com, ISSN 1743-3509 (on-line)