Determination model of optimal operating length for modern tram Y.H. LI & K.M. CHEN &Y. LI & Y.Q. CHENG

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1 5th Internatonal Conference on Cvl, Archtectural and Hydraulc Engneerng (ICCAHE 2016) Determnaton model of optmal operatng length for modern tram Y.H. LI & K.M. CHEN &Y. LI & Y.Q. CHENG School of Hghway, Chang an Unversty, X an, Shaanx, Chna KEYWORD: Modern tram, Net-operaton separaton, Optmal operatng length ABSTRACT: Wth consderaton of operatng speed, road condtons, economc benefts, and forecast passenger volume, an optmzaton method was proposed to determne the optmal length of modern tram lne. Based on the prncples of net-operaton separaton, theoptmal operatng length of tram s determned accordng to tram road characterstcs, and the model was verfed by an example. Analyss result showed that the optmal length for modern tram lnes are between 15m and 25m under normal ntenstes of passenger flow, whch was nversely proportonal to the optmal length of tram lne. INTRODUCTION Modern tram s functonal smlar to Bus Rapd Transt(BRT) (CJJ/T ). They are belong to mddle-low transt modes between regular transt and subway. Tram manly lad on the cty road surface, and operatng mxed wth other vehcle transportaton. Compared wth BRT, the tram system s more complex, hgher cost, and the tram tran s consttute of 2-7 modules(lu Xmng et al. 2013). Wth the development of urbanzaton, the tram have a further mprovement for traffc volume. So the tram has very broad applcablty, nclude:1. Supplementary of metropoltan where lac of ralway transt; provdng densty and connecton capabltes;2. Dstrbuton of external groups nsde bg ctes;3. Man transt system n medum and small ctes;4. For specal purposes, such as toursm lne(zhang Zdong. 2013).The ordnary modern tram s shown as Fgure 1. Fgure 1. The ordnary tram The man dfference of tram and urban ral transt s that the tram s separated n net and operaton. Dfferent operaton lnes can be determned on dfferent passenger demand, dfferent road envronment, dfferent urban development level n one tram networ.these characterstcs above determne the need to confrm the optmal operatng lengths,mae sure the ratonalty of operatonal management, economc, supply and demand, whch provde useful references for future plannng, desgn, and operaton(zhang Zdong et al. 2013). Chen(2009) studed the relatonshp between passenger dstrbutng centers and urban ral transt networ,put forward a new method to calculate urban ral transt networ scale based on the connectvty between passenger dstrbutng centers(chen Kuan-mn et al. 2009). Luo(2010) dscussed the optmal method of urban ral transt lne length from the economc pont of vew, and the relatonshp between length and constructon costs, vehcle purchasng costs, operatng and mantenance costs, the savng value of travel tme and the tcet ncome of urban ral transt (LUO Xao-qang et al. 2009). Wang(2011) researched the reasonable economc length of the regonal ral transt lne The authors - Publshed by Atlants Press 747

2 from economc pont of vew(wang Shao-nan et al. 2011). Gong(2012) consdered the nfluence of speed, effcency and benefts of urban ral transt lnes, nterval of statons and passenger traffc densty on urban ral transt lnes length,establshed a model wth the maxmum value of the relatve net benefts(gong Qan et al. 2012). For the moment, many ctes have planned and constructed the modern tram.generally speang, the problem of optmal length of urban tal transt s stll n the research, and optmal operatng length for modern tram has not yet been studed. In order to meet the dverstes of domestc ral transportaton,and provde properly suggestons for tram plannng, t s urgently need to quantfy the analytcal technques to gude the tram route plannng, desgn and operatng length. FEATURES OF MODERN TRAM 1. Operatng on the road, the techncal parameters are between bus and subway. 2. Pea hour traffc volume could reach passengers. 3. Maxmum speed s 70m/h, the average operatng speed s 15-25m/h n urban area,and 30m/h n suburban area(lu Xmng et al. 2013). 4. Smaller radus curve s permssble n tram plannng, adaptve to tough road condtons. 5. Separated n operatng networ and lne networ. 6. Tram s flexble n module so t can adapt to the future elastc development of new cty.7. Tram can be desgned as tangent lne outsde the bg cty, bacbone of small cty, connectons for areas surround the end of subway lne. 8. Influenced by operatng speed, boundary condtons, road condtons, the operatng length can not be very long. 9. Consder the sgnal prorty at ntersectons n order to promote the operatng effcency(shen Jng-yan. 2008). FACTORS OF TRAM OPERATING LENGTH For ralway, the man factors nfluence the route plannng are natural condtons, the geologcal condtons, power supply, ventlaton, sgnal, depot, envronment, hertage conservaton, constructon cost, fnancal. In the process of tram plannng, we should consder the followng questons : Urban agglomeraton plannng, Urban plannng, Networ plannng, land propertes, ndustry and professons, transportaton development, populaton dstrbuton, demand analyss. Compared wth the general urban subway, tram has ts own unque character. From the perspectve of operaton, the tram belong to the upgradng mode of bus. Compared wth the subway and lght ralway, the tram operatng separated wth networ. Its operatng lne s based on passengers volume, land use, mportant nodes, and plannng dfferent operatng lne n the same networ. Compared wth subway, tram s more vulnerable effected by road traffc, ntersectons and other external factors(jin Feng. 2008). Because of the above characterstcs of the tram, determned the research of optmal operatng length for tram s more complex than subway. Thus, total constructon costs, passenger flow, the tme value of benefts are mportant consderatons(l Ta-hu. 2008). DETERMINATION MODEL OF OPTIMAL OPERATING LENGTH Transt volume ntensty Transt volume ntensty of subway s an mportant ndex for ral traffc operatonal effcency. On the one hand, modern tram play an mportant role n the publc transt systems, the tram lne should be desgned n the man traffc corrdors, and connectng mportant passenger dstrbuton pont, major transport hub, the cty's man resdental and commercal group,then provde good servces for commuter passenger ; On the other hand, volume ntensty also reflects the basc relatonshp between supply and demand of tram system, and t reflects the operatonal effcency drectly (Chen Kuanmn et al. 2011). 748

3 Operatng speed The modern tram operaton s affected by road condtons sgnfcantly, the most mportant factor s ntersecton sgnal control and traffc management. The relatonshp between tram operatng speed v R and ntersecton sgnal control modes s showed n Table 1. Table 1. Characterstcs and applcablty of dfferent sgnal control modes Item Influence on the transverse vehcles The average travel speed (m / h) Realzaton Dffculty Scope of applcaton Complete sgnal prorty Greater delay Part sgnal prorty Some delay No sgnal prorty No specfc delay Very complcated Transverse road wth low traffc volume and lower road grade n ntersecton Complcated Tram lne ntersect wth trun road and most of secondary road,most of branch road Easy Intersecton of lne and trun road, transverse road s close to saturaton, mxng road rghts As tram s operatng on road, and belong to open ral system. The entrance on both sdes of street, entrance of commercal facltes would affect the operatng speed of tram. The tram located on dfferent road lane has dfferent speed reducton whch can be determned by Table 2(Chen Kuanmn et al. 2011). Table 2. Characterstcs and applcablty of dfferent sgnal control modes Layout form of tram mddle n the road sdes of the road Operatng speed reducton Operatng speed Ralway staton parng tme manly determned by passengers amount of on and off, especally the tme of passengers to get on and off. Tram parng tme could be calculated as followed equaton : ( PON + POFF) ton/ OFF (1) t P = nmd Where P ON,P OFF = The on and off volume of passengers n respectve statons, determned by passengers flow forecast. t ON/OFF = The average tme requred for each passenger gettng on or off (unt: seconds). Based on nvestgaton, tang 0.6s. n = Number of operatng tram per hour. m = Number of tran marshallng. Tram marshallng number based on the passenger demand forecasts, usually tae 2-7 module. d = Number of each module unlateral doors, under normal crcumstances, each module unlateral door s

4 Constructon costs Tram s belongng to low-mddle volume mode n transt system, so the constructon costs s hgher than the cost of general bus and BRT. The average cost of tram lnes (ncludng constructon, nstallaton costs and vehcle purchase costs) s mllon yuan / m, whch the vehcle purchase costs accounted for 30% -35%, and cost about mllon yuan / column. Compared wth the same passengers capacty le BRT, the tram s undoubtedly an expensve nvestment. The overall cost of tram can be calculated as follows: C = cl ' (2) Where C = the total constructon costs of the tram lne; c' s constructon costs per unt length; L s the length of the tram lne. Operaton and mantenance costs The operaton and mantenance costs of urban ralway s hgher n the operatng perod. Consderng the mantenance costs of tram-depot and other ancllary facltes have less relatonshp wth length, so they wll not be consdered. Therefore, the costs of operaton and mantenance are consst of tram lnes and statons. In general, the unt length operaton and mantenance costs can be regarded as proportonal to passengers volume was, and staton mantenance costs was proportonal to the number of statons. After comprehensve analyss,the tram operaton and mantenance costs are smlar wth subway mantenance costs, and can be determned wth the followng formula: Φ = cl (3) Where c = the (th) year average mantenance costs per unt length,the value s ( ) 10 7 yuan/m Savng value of travel tme The savng value of travel tme can be regarded as the dfference between tram average travel tme and bus. The relatve average travel savng tme s : t = tb tr (4) Where t = s the average travel tme of tram n the -th year (hour/one unt passenger). R The average travel tme ncludng three parts, among these are travel tme, tram parng tme, walng tme of the start and the end of tram lne,whch can be calculated as follows: lr 2DR 2DR tr = + ts + (5) vr vw l = the average transport dstance n the -th year, whch can be determned by passenger Where R flow forecast; v =the average operatng speed of tram; R to trp destnaton, based on the average publc transt servce radus,and the value s 0.5m; S D = the walng dstance from tram staton R t = tram parng tme ; v w = average walng speed, tang 3.5m / h. t B s the average travel tme of bus n the -th year (hour/one unt passenger), can be calculated accordng to the followng formula: lr 2DB 2DB tb = + (6) vb vw Where D = dstance from arrval place to bus staton, tang 0.5 m; B v = average operatng B speed of bus, accordng to the actual transportaton nvestgaton. Tcet ncome General urban ral transt calculate tcet fare by dstance, therefore, tram tcet ncome may also vewed as a functon of the travel dstance, the tram tcet ncome can be calculated as follows: f = f0 + fl (7) R Where f = the startng fares of tram ; f = the ncreasng fares by each travel dstance unt 0 from the startng fares (yuan/m). 750

5 Optmal model From the above dscussons, the optmal operatng length model could be consdered as the stuaton of net beneft maxmum. Tram relatvely net ncome could estmated from nvested and benefts. The ncome s manly from tram tcet ncome and passenger relatve savng tme value. The benefts s manly from tram constructon and operaton of nvestment. Tang consderaton of nvestment for the one-tme constructon of the tram, whereas tram tcets and the savng tme value of ncome wll be exst ever snce. Therefore, when calculatng the maxmum net beneft,t s based on passengers volume forecast and overall networ plan, tae consderaton of both nvestment and benefts, dscounted to the base year. The maxmum value can be expressed as the followng formula: n QR( ηt + f) Φ C max Z = + (8) (1 + γ ) 365 Where = 1 Q = the daly average passengers volume of tram n the -th year ; R QR = αl, α = the passengers volume ntensty of the networ, L= tram operatng length ; η = the tme value per unt ; γ = the dscount rate ; The meanngs of other symbols are showed above. In summary, the optmal model can be summarzed as follows: n QR( ηt + f) Φ C max Z = + (1 + γ) 365 = 1 t = tb tr ( PON + POFF) ton/ OFF tp= (9) nmd st.. lr 2DB 2DB tb = + vb vw Φ = cl C = cl ' Analyss from the above model, the optmal length of the tram can be converted to unconstraned programmng problems n the case of the relevant parameters determned and then solvng by ultmate values. Model Soluton Ths model s belong to the optmal model, and t could be solved by genetc algorthm (GA). GA s a smulaton of natural bologcal evoluton process of self-organzaton and adaptve artfcal ntellgence technology. It s based on the natural selecton and genetc theory, the process combned the bologcal evoluton whch the fttest ones survve and of random nformaton exchange mechansms wthn the group of chromosomes. Before the search, encodng the varables n some form (varable coded called chromosomes), dfferent chromosomes consttute a group. A new generaton of groups s based on the followng two steps: frst, accordng to the ftness value of the chromosome then select the approprate number of copes to be retaned; Secondly, process the selected chromosome wth recombnaton, mutaton to generate new chromosomes. The basc algorthm process s as follows(zheng Lpng et al. 2003): 1. Selects N ntal ponts randomly (descrbed as a group, each pont s called an ndvdual), 1 2 n X, X, L, X, = Calculate for each ndvdual's ftness, f( X ), = 1,2, L, N. '1 '2 ' n 1 2 n j 3. Selecton : Select X, X, L, X from X, X, L, X, and every X ( j = 1,2, L, N ) probablty of beng selected s ' 1 f( X ) j. PX ( = X X, L, X ) = j N N l= 1 l f( X ) 751

6 '1 '2 ' n 4. Crossover : Select two ndvduals wth the same probablty from X, X, L, X, Tae these two ndvduals wth restructurng operaton of gven probablty P c to produce two new ndvduals. Repeatng ths process untl a new group X, X, L, X fgure out. ''1 ''2 '' n 5. Mutaton : Change the value for each ndvdual based on certan mutaton rate P m randomly, and calculatng a new generaton of communty. 6. Inspect the ratonalty of stop crtera, f the crtera meet the computatonal requrements and accuracy then operaton s stopped, otherwse mae + 1 = and calculate t agan. CASE ANALYSIS XXan New Area s located between X'an and Xanyang, total plannng area s 882 square lometers, and constructon plannng area s 272 square lometers. Accordng to the overall plannng, the area wll be a "New functonal cty of X'an and eco-garden cty". Meanwhle, XXan New Area s planned n decentralzed cluster pattern dstrct. The man development dea s garden cty and green cty. Based on the actual characterstcs of XXan New Area, the New Area should frst mplement bus prorty prncple, and promote low-carbon modes of transt to strengthen lns between decentralzed groups. The publc transport development model n the New Area should be "establshng mddle-low capacty transt system ". Tram s overlayed on the road, and the road networ s bloced by the Wehe Rver, hstorcal relcs. Because of the dstrct overall plan, the networ system could bult wth hgher standard, ncludng hghways, expressways, trun roads and other road system, the red lne of trun roads n the new dstrct s approxmately 40m or more, and both sdes of the road have been planned wth green belt. In concluson, the constructon of tram s enforceable. The modern tram networ has been planned nne lnes n XXan New Area, whch contans two branch lnes. The total length of networ s 199 lometers, and 150 statons, ncludng 19 transfer statons, 15 transfer statons between ral and subway, as shown n Fgure 2. Fgure 2. Modern tram networ plannng of XXan New Area The modern tram networ plannng, techncal features, techncal specfcatons and other aspects of project mplementaton as shown n Table

7 Table 3. Modern tram technology parameters of XXan New Area Items Parameters Operatng Speed 20m/h Walng dstance from both ends 0.5m Constructon costs 90 mllon Yuan /m Tme value 10 Yuan / per capta h Tcet prce 3 Yuan Departure nterval 2-5 mn Operatng Speed of regular bus 15m/h Operaton and mantenance costs 8 mllon Yuan /m Dscount Rate 10% The traffc volume could be predcted by four-stage method, the predcton results shown n Fgure 3: Fgure 3. Modern tram traffc predctons n XXan New Area Based on the results of traffc volume forecast and other parameters, the optmal model could be solved by Genetc Algorthm whch dscussed above. Tae the parameters nto the optmal model and plot the graphc of the functon as shown n Fgure 4. The result of teraton s shown as the Fgure 5.Smlarly, the tram optmal operatng model can be obtaned under dfferent traffc ntensty as shown n Table

8 Fgure 4. The fgure of the optmal model Fgure 5. The result of teraton Table 4. Calculaton results of optmal model α (passengers /h) L(m) Accordng to the above results, a sutable operatng length of modern tram n XXan New Area s about 20m. Based on the passengers volume ntensty of dfferent lne, the optmal operatng length s between 15-25m n ths area. The tram lne networ plannng n XXan New Area conssts of 4 lnes n recent years. In consderaton of optmal length smulaton results, and based on the passenger volume secton of networ, the optmal operatng lnes could be planned as Fgure

9 Fgure 6. Modern tram operatng plannng of XXan New Area The operatng length of the networ are between m. It s n lne wth the requrements of tram optmal operatng length, but also n lne wth the demand of passenger volume predcton. CONCLUSION 1. Ths artcle s based on traffc engneerng prncples,tang operatng ncome as the objectve functon, combned wth the factors as trams operatng characterstcs, operatng speed, parng tme, constructon costs, operaton and mantenance costs, savng value of travel tme, tcet ncome, then establsh the tram optmal operatng length model. 2. The economc traffc volume of tram s passengers /hour, based on the above model, calculated the optmal operatng length of tram s 15-25m, the operatng tme s also about an hour. The optmal operatng length s nversely wth traffc ntensty. 3. Ths artcle dscussed the general factors that affect the operatng length of modern tram, but n the process of actual operaton and management, the operatng characterstcs and operatng envronment of the tram s more complcated than subway, so the optmal operatng length should be adjusted by the urban plannng, road characterstcs, passenger dstrbuton pont and such actual condtons. REFERENCES [1] Standard for classfcaton of urban publc transportaton[s]. (CJJ/T ). [2] Lu Xmng, & L Na Ratonal and Sustanable Development of Streetcars[J], Urban Transport of Chna, 11(4): [3] Zhang Zdong Streetcar System Plannng and Desgn[J], Urban Transport of Chna, 11(4): [4] CHEN Kuan-mn, & FAN Da-e, & MA Chao-qun Cal-culaton of urban ral transt networ scale based on pas-senger dstrbutng centers[j], Journal of Chang an Un-versty, 29(6): [5] LUO Xao-qang, & CHEN Kuan-mn Determned mod-els of optmal length for urban ral transt lne[j]. Journal of Traffc and Transportaton Engneerng, 10(3): [6] WANG Shao-nan, & LIANG Qng-hua Research on Economc Length of Regonal Ral Transt Lne[J].RAILWAY TRANSPORT AND ECONOMY, 33(10):1-6. [7] Gong Qan, & Gu Bao-nan Decson model of reason-able lne length for urban mass transt[j].urban Mass Transt, 011:

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