reviewed paper Public transport travel time simulation Tomáš CHLEBNICAN, Jiří CTYROKY, Marek ZDERADICKA

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1 reviewed paper Public tranport travel time imulation Tomáš CHLEBNICAN, Jiří CTYROKY, Marek ZDERADICKA (Mgr. Jiří ČTYROKÝ, Útvar rozvoje hl. m. Prahy, Vyšehradká 57, Prague, 18 00, (Ing. Marek ZDĚRADIČKA, Útvar rozvoje hl. m. Prahy, Vyšehradká 57, Prague, 18 00, (ing. Tomáš CHLEBNIČAN, CHAPS pol. r.o., Bráfova 1617/1, Brno, , 1 INTRODUCTION Information on reliable time baed travel ditance within the urban area i of increaing importance for management of today citie truggling with congeted traffic and limited opportunitie for reduction of traffic demand. The public tranport promotion i for many European citie the only way to tackle the ituation. The quality of public tranport (PT) i cloely connected with the real time acceibility of the area by public tranport mean. Generally oberved indicator of quality of the PT ytem i Total Travel Time defined a total time pent on journey form any place to the final PT top including walking from origin to the nearet PT top and average travel time pent on travelling with PT ytem. Both determine attractivene of the PT ervice on a local or global level. A a upport tool for town and tranport planning activitie City Development Authority of Prague ue analyi baed on modelling of the time acceibility in both level. Thee analye provide town planner more realitic information about time acceibility of particular area a an aement tool of them for both urban development and development of the public tranport ytem. Pic 1: Cae tudy revealed need of footbridge over the motorway in order to improve acceibility of metro tation and local hopping centre. At the ame time there i clearly howed difference between theoretical iochrone (circle) and due to GIS imulated cloe-to-real walking ditance (line). On the local (micro) level Walking acce time from the ite to the nearet public tranport top coming out of real footpath i being evaluated baed on GIS technologie. Thi level help to reveal barrier in the area and to optimie location of top and tation. Other output are catchment area or o called PT top ervice area. Thi output i ued for comparion of calculated cloe-to-reality walking acceibility with theoretical concentric ring iochrone that are traditionally ued for decription ervice area of PT top without taking into account the towncape. Beide it, planner and PT manager put their focu on time acceibility of the city centre, uually (due to the highet concentration of workplace) or to other point of interet in a global, let u ay citywide view. The indicator i Average travel time and how u the quality of the PT ervice from the time point of view. REAL CORP 008 Proceeding / Tagungband ISBN: (CD-ROM); ISBN: (Print) Vienna, May Editor: Manfred SCHRENK, Vaily V. POPOVICH, Dirk ENGELKE, Pietro ELISEI 359

2 Public tranport travel time imulation CALCULATION OF THE AVERAGE TRAVEL TIME The key output of the analyi i Average travel time. Thi time index i compoed from Average waiting time and Average connection time. Calculation of Average waiting time Tc on each top for ervice of PT i come from connection that run within the pre-elected period of a day (e.g. morning peak from 7:00 until 9:00) with the provio that there were ought two connection at leat. Fehler! E it nicht möglich, durch die Bearbeitung von Feldfunktionen Objekte zu ertellen. (fig 1), where t1 departure time of the firt connection tn departure time of the lat connection n number of connection Average connection time T i defined a um of connection time T 1,, 3 (time that i pent on the board of the public tranport mean and on tranfer between them) divided by number of connection. T = T 1,,... n n (fig. ), where T 1,..n connection time of the 1 t, nd up to n th connection n number of connection Average travel time T p i the um of Average waiting time Tc and Average connection time T. T = T + T (fig. 3) P C S 3 AVERAGE TRAVEL TIME APPLICATION (ATTA) Traditionally, data about average travel time were collected and counted manually (uing Excel table), the data for thi calculation wa acquired from common journey planner available on the Internet. Thi approach i naturally very time-conuming, it variability and flexibility i low and regular update complicated. In order to facilitate thi aement, City Development Authority of Prague in collaboration with company CHAPS pol.r.o. that ha been authorized by the Minitry of Tranport of the Czech Republic to run The National Information Sytem of the public line paenger tranport timetable, developed the application for automatic tatitical analye of time table information. The project i called Average Travel Time Application (ATTA). The reult of ATTA evaluation are combined with the GIS baed walking ditance evaluation output, giving u complex and very cloe to real information. What more the ATTA work with regularly upgraded real timetable of the Prague Integrated Tranport (PID). 4 PHILOSOPHY OF THE ATTA Average Travel Time Application work in following tep. Firt, origin or more origin and detination or detination along with period of the day are defined. On thi bai poible PT connection are earched and comparion and election of trategie and equent calculation of average travel time i then provided. The data ource are timetable of Prague Integrated Tranport (PID), providing the real data and chedule of all integrated tranport mean (metro, tramway, bu line, uburban bu line and train, ) that are incorporated into the metropolitan paenger tranport ytem. The ame databae erve a the data ource for for the Journey Planner for public (available on the Internet). Connection earch engine for ATTA ha been derived form the Journey Planner web application. The crucial iue that wa conidered during the development of the ATTA wa how to et up the eeking trategy of the application in order to get output cloe-to-real behaving of paenger. Application work with two different trategie to earch connection from the origin/origin to the detination/detination: Strategy 1 there are concerned all poible connection with very variou route in the meaning of time, frequency and number of tranfer (e.g. much longer non-tranfer connection with low frequency v. horter connection with tranfer and higher frequency). Thi trategy cover all poibilitie but ome of them were evaluated a unlikely for everyday ue during the teting operation. It affect the reult of calculation ignificantly a well (large diperion of ought connection time that are average out). 360 REAL CORP 008: Mobility Node a Innovation Hub Verkehrknoten al Innovation- und Wiendrehcheiben

3 Tomáš Chlebnican, Jiří Ctyroky, Marek Zderadicka Strategy - there are preferred connection with higher frequency of operation with ame or imilar tranfer point and tranport mean. Reult are more homogenou and they were evaluated a more acceptable for calculation. On the other hand there are cut off all other poibilitie of travelling. Pic : Strategy 1 ue red and green type of connection while trategy ue only green type of connection Both trategie have it advantage and diadvantage. In order to avoid the biaed reult the application ue comparion method and define the preferable reult. The trategy where the longet earched connection time i horter (out of both trategie) i taken into account. Beide thi there are poibilitie of manual etting election. Thank to cooperation with Prague Integrated Tranport Coordinator (ROPID) we are able to imulate alo planned line of PT for which ROPID i able to create fictitiou timetable with the view of comparing change and aement of the time acceibility. 5 WALK DISTANCE CALCULATION Image of near-real acceibility of the area by the PT may be improved coniderably by taking the walking ditance to the PT top into conideration. The goal i, uually, to calculate the iochrone to the nearet top within the area taking into account the layout of pedetrian route network (footpath) or, in the wider concept, all walkable urface within the area. Along with thi calculation, boundarie of PT top ervice area are alo defined. The nearet top calculation can be provided by everal GIS baed method according to the elected data model. Due to the relative implicity of input data preparation and good calculation performance the grid model analyi ha been choen. The principle of the calculation i baed on the creation of grid model of footpath a the input matrix. The matrix cell value domain conit normally of two value 0 (non-walkable area) and 1 (footpath). The more complex model may, however, take into account alo the urface and lope characteritic influencing the walking peed. If the additive vertical or horizontal factor are to be taken into calculation, new eparate grid mut be ued. It i important to enure all top mut lie on the footpath. The calculation of walking ditance i baed on imple Euclidean ditance and hortet cumulative path cot ditance. The principle of cot ditance i calculation of cot (i.e. meaurable time, ditance, fuel, etc.) which mut be pent for one-unit move on the urface. In cae of normal rectangular grid it two cae have to be taken into conideration. The cot of vertical or horizontal move acro the grid from cell A to B i decribed by the formula: C a + C C = b (fig.4), where C a... cot of move on cell A, C b... cot of move on cell B The cot of diagonal move i repreented by the different expreion: ( C a + Cb) C = (fig.5), where C a... cot of move on cell A, REAL CORP 008 Proceeding / Tagungband Vienna, May ISBN: (CD-ROM); ISBN: (Print) Editor: Manfred SCHRENK, Vaily V. POPOVICH, Dirk ENGELKE, Pietro ELISEI 361

4 Public tranport travel time imulation C b... cot of move on cell B The cumulative cot path from ource cell to detination i then calculated a the minimal um of all poible cot path : C CP = min( CAB ) (fig. 6), where C CP... total cot of move from ource to detination C AB... cot of move between two neighbouring cell on the path The total cot path depend, however, on the grid reolution. Final cot um mut be multiplied by the value of grid reolution in ditance unit if the cot grid reolution doe not equal to the ditance unit. For the purpoe of walking ditance modelling in Prague 1m grid reolution i being ued. The value may be interpreted a the real geographic ditance or time ditance in econd a the peed 1 m/ well correpond with average walking peed (3.6 km/h). Thi implification may be, however, ued only if no terrain factor are taken into conideration. 6 TERRAIN FACTORS Pic 3: Cot ditance to top on the walking network Calculation of cot path a decribed above i provide very acceptable reult when the modelled area i flat-haped and/or if the reult hould be figured out in the ditance unit only. In cae of rugged topography the vertical factor influence the real cot ditance in two way. Firt, the real ditance on the loped link i bigger than the ditance on the horizontal footprint of the link (urface factor), econd the difficulty of moving on the terrain varie with the lope and the move direction (vertical factor). The difficulty i then reflected on the moving peed, fuel conumption and related factor. If the urface and vertical factor are taken into calculation, the total cot algorithm from move from cell A to B i then extended: C = D VF C (fig. 7), where C... the cot from move from cell A to B, D... the urface ditance, VF... the vertical factor, C... the horizontal cot according to the fig. 1 or repectively Surface ditance D i calculated a the actual ground ditance between cell A and B. The ditance calculation i baed on definition of right triangle with the one ide ha the length equal to the grid reolution and econd ide length i the difference between height (Z value) of the cell A and height of the cell B. The third ide (the urface ditance) i then calculated uing the Pythagorean theorem: D = R + ( Za Zb) (fig. 8), where 36 REAL CORP 008: Mobility Node a Innovation Hub Verkehrknoten al Innovation- und Wiendrehcheiben

5 Tomáš Chlebnican, Jiří Ctyroky, Marek Zderadicka D... the urface ditance, R... the grid reolution, Z a, Z b... the height of cell A or B repectively The poitive or negative influence of the lope on the move depend very much on the unit ued for cot meaurement and mode of tranport. There can be defined everal function for the decription of the dependence of the move cot on the terrain lope. The detail reearch on the bet fit function ha not been undertaken o far, thu, the baic invere linear function for the walk ditance calculation i ued for practical purpoe. The figure that influence the moving cot dependently on the actual moving angle from cell A to B i called the vertical factor: 1 VF = (fig. 8), where 1 + VRMA SM VF... the vertical factor, VRMA... the vertical relative moving angle from cell A to B, SM... the lope modifier variable The value of SM influence the teepne of the vertical factor curve, for the calculation purpoe i et to 1/45 (45 lope i the limit for common walking in both up and down direction). fig. 10: vertical factor function curve Pic 4: Demontration of terrain factor influence (from left): a) 5 minute iochrone without terrain factor calculation, b) after urface ditance implementation, c) after urface and vertical factor downhill move direction, d) after urface and vertical factor uphill move direction 7 PT STOPS SERVICE AREAS So far, we have dicued the way how to calculate the walking ditance cot (time) from top along the pedetrian network. Now we will try to match the reult from the time-table analyi and the walking ditance analyi. The tak i to find for each cell on the network uch combination of walking route to the top and conequent PT travel cot from thi top to the detination, where the cumulative cot for both trip i minimal. REAL CORP 008 Proceeding / Tagungband Vienna, May ISBN: (CD-ROM); ISBN: (Print) Editor: Manfred SCHRENK, Vaily V. POPOVICH, Dirk ENGELKE, Pietro ELISEI 363

6 Public tranport travel time imulation The algorithm i baed on election of the et of PT top within pre-et proximity; for each top the total travel cot than may be calculated. On thi bai the optimal ervice top i elected. In practice, thi approach ha not been o far applied. Intead of it ervice area have been defined on the traditional tatic allocation bai a the area with the common cloet top according to the walking cot. Pic 5: PT top ervice area 8 TOTAL TRAVEL TIME After definition of ervice area the travel cot expreed a time needed for moving from the ource to the detination uing the PT in connection with walk can be ummaried. To each ervice the PT travel time of the correponding top i matched and then it i added to the walking ditance value of each cell. Pic 6: PT travel time allocated to the ervice area (iochrone 5, 15, 30, 45 and 60 minute) It i ueful to viualie the reult time on the map through iochrone, motly for the eay undertanding and good comprehenion. The iochrone can be generated from the total travel time grid value (only walking network grid cell carry the value) by interpolation. Interpolation method ued in our cae i Invere Ditance Weighted Method, taking into account 1 point neighbourhood and power for calculation of the weight of each point value. 364 REAL CORP 008: Mobility Node a Innovation Hub Verkehrknoten al Innovation- und Wiendrehcheiben

7 Tomáš Chlebnican, Jiří Ctyroky, Marek Zderadicka Pic 7: Total travel time, iochrone 5, 15, 30, 45 and 60 minute 9 CONCLUSIONS For citie with high hare of public tranport on the modal plit the public tranport acceibility i the crucial factor deeply influencing the commercial attraction of particular city area. Good knowledge of nearreal acceibility make poible to provide better city management and planning through optimiation of public tranport line routing, tuning up the timetable cenario, better location of top and alo improving the walking network within the city. The practical example clearly revealed the importance of walking ditance for the total acceibility value, a well a the important role of terrain factor for the walking ditance model. The further tudy hould be focued on the dynamic definition of the public tranport top ervice area which extent in fact varie with the change of the detination place. Alo, better undertanding of vertical factor influence to the walking cot hould be beneficiary for the further development of the model. 10 EXAMPLE Demontration of the public tranport acceibility hown in thi paper wa provided for the Prague area. The objective of evaluation wa to calculate near real-time acceibility to the city centre (Wencela Square). The detination top were Muzeum or Můtek, the better (horter) total travel time of thee two wa conidered. The time period ued for time table tatitical evaluation (ATTA) wa Monday, from 6:30 to 9:00. Walking ditance were calculated uing by ESRI ArcGIS and Spatial Analyt Extenion. The reolution of the grid wa 6790 x 4935 the cell ize i 5 meter. 11 REFERENCES: CHLEBNICAN T.: ATTA manual, CHAPS Brno, 007 COOPER Simon: Meauring Public Tranport Acceibility Level (PTAL), Tranport for London, February 003 ESRI: ArcGIS Dektop Help, ArcGIS 9., Spatial Analyt, ESRI, 006 HAYNES R., A. Lovett, G. Sünnenberg: Potential acceibility, travel time, and conumer choice: geographical variation in general medical practice regitration in Eatern England, Environment and Planning A 003, volume 35, page , MAIER K. et col.: Dopravní dotupnot území v Čeké republice, report, REPUS, Prague 006, NELSON Andy: Acceibility, tranport and travel time information, in Modelling acro geographic cale, Activity.5, 000, REAL CORP 008 Proceeding / Tagungband ISBN: (CD-ROM); ISBN: (Print) Vienna, May Editor: Manfred SCHRENK, Vaily V. POPOVICH, Dirk ENGELKE, Pietro ELISEI 365