Prospect of Technology for Public Transit Planning using Smart Card Data

Transcription

1 Prospect of Technology for Public Transit Planning using Smart Card Data Inmook Lee 1 and Suk-mun Oh and Jae Hong Min Department of Railway Policy & Strategy, Korea Railroad Research Institute, Woram-dong, Uiwang-si, Gyeonggi-do, Republic of Korea Abstract The smart card system has been applied for all subway and bus in Seoul metropolitan area since In Seoul area public transport more than 90% of passengers use smart cards to pay fare. The boarding and alighting information from the smart cards enable to calculate the OD (origin - destination) and total travel distance of each transit passenger. The smart card system of Seoul is operated as one system integrating metro and buses. Therefore, passenger's overall travel information (trip chain) is available linking each individual trip OD data of modes and lines. The smart card system also enables to obtain the information of detailed (very specific) individual transit usage and operation. In other words, a large amount of very specific public transit data for public transport planning and operations has been established. This paper proposes the method to derive transit information from the smart card data and arranged valid data for transportation planning and operation. Especially, the concept of Real OD (trip chain) database based on multi-modal trip chains is presented. The technical prospect of demand analysis, service performance assessment, multimodal transit assignment, and optimization was presented. In addition, several conceptual models of transit performance indices and transit assignment are proposed. Transit passenger and OD information based on the smart card is not estimated data derived from surveys but actual performance data. So, the information is much more realistic and detailed than existing methods. Preliminary feasibility test and verification are possible at the simulator using assignment and optimization models based on Real OD (trip chains). This will contribute to encourage rail project investment and passenger services. Keywords: Smart card, Trip chain, Transit information, Transit OD, Transit assignment 1. Introduction The Seoul city public transport overall reform policy - trunk/branch lines, route restructuring, fare rate system etc. - was implemented in Accordingly, unified distance scale fare, central bus lane, trunk/branch line system have improved existing public transport system dramatically. Especially, unified distance scale fare system eliminates the additional transfer fare and is proportional to the total travel distance regardless of modes ( subway, bus) and lines. To implement this fare system, the smart card system has been applied for all subway and bus in Seoul and the suburbs of Seoul. The boarding and alighting information from the smart cards made it possible to calculate the total travel distance of each transit passenger. The initial purpose to apply the smart card system is to operate economically and use conveniently with electronic payment system. However, the smart card system also made it possible to obtain the information of detailed (very specific) individual transit usage and operation. In other words, a large amount of very specific public transit data for public transport planning and operations has been established. Now the smart card system covers the Seoul metropolitan area (50% of Korea's population reside), and long-term government policy of the integrated smart card according to the national level, the so-called 'one card all pass' is expected to be built into the system. This paper presents the transit information using the smart card system data achieved conceptually: deriving data, establishing database, the possibility and ways of utilize to improve public transport services (scheduling, route adjustments, etc.) and transportation operations. And this paper introduces the progress and direction of R&D project Development of NxTIS to Implement Railway Oriented Public Transportation Framework of Korea Railroad Research Institute. NxTIS means Next Generation Public Transport Information System. This paper is a part of this R&D project and NxTIS 1 address: mook79@krri.re.kr. 1

2 will be implemented in the actual system in 3 years. This paper is organized as follows. Chapter 2 presents the smart card data structure analysis, transit information database building. Chapter 3 introduces and suggests the ways to analyze transit performance and demand using the smart card data. Chapter 4 introduces the direction of developing models and indices of transit service and performance. Chapter 5 presents the prospect of multimodal transit assignment and future prospects. Chapter 6 presents conclusions and future prospects. 2. Transit information database based on the Smart card (1) Advantage and value of the smart card transit information The smart card data is very high values as the reliability and utilization, since the detailed smart card data is generated by over 90% people of the Seoul Metropolitan Area continuously. Also, without a field study, the data is accumulated automatically. Park & Kim (2006) addressed that there are seven kinds of benefits using the smart card system as transit information. Table 1 shows the benefits. Table1. The benefits using the smart card system as transit information (Park & Kim 2006) Accuracy Low cost Wide range Time reduce Usability Scalability Safe survey Accurate and reliable data Reduce the cost of survey dramatically Able to obtain data for all time slots and wide areas Real time DB building and time reduce Increase data usability to analyze travel Huge data and data scalability No accident to field survey (actually no field survey) The smart card data includes a variety of information, and depending on the analysis process of this data, the utilization value may be more or less. Validate the existing OD: The current transportation surveys depend on sample surveys - vehicle license plate survey, roadside interview survey, site visiting survey, cordon line survey. However, the smart card data has a complete survey data for all transit. In addition, it s very easy to obtain some special data, such as in-vehicle persons. Transit service system establish: The current demand forecasting is based on historical data more than a year ago. However, the smart card data is up-to-date achieved data at least a month ago. The data is not a forecasted data but a actual data. Using the smart card data, transit demand can be analyzed and the schedule can be optimized. Transportation policy before-and-after assessment: Researchers may develop transit assignment, and schedule optimization models with the smart card data. These models may be utilized to pre-assess projects, such as new railroad construction. (2) Basic data from the smart card system The smart card data includes these items regardless of region and operator. Table2. Smart card data items Data Items Items details Smart card ID Each smart card s ID (passenger ID) Departure date and time Departure time of a current vehicle (train) Each passenger s travel ID Transaction ID (Even if a passenger transfers to another modes or lines, transaction ID is same within a trip chain.) Mode code Current mode s ID (bus, subway) Number of transfers Number of transfers is a trip chain Line ID Current line s ID (line number) Operator ID Subway or bus s operator(company) ID Vehicle ID Current boarding vehicle s ID Passenger class Passenger class ID (general, student, aged, handicapped etc.) 2

3 Boarding time Boarded or transferred time (sec. units) Stop ID boarded Stop(or station) s ID of boarded or transferred Alighting time Alighted time (sec. units) Stop ID alighted Stop(or station) s ID of alighted Number of a party Number of passengers that belongs the card (generally 1) Boarding fare Basic fare Alighting fare Additional fare charged proportional to total distance Travel distance Total distance traveled (the sum of each trips) Date and time Travel date and time Each smart card has a unique ID in a separate, because, a passenger's travel information can be detected as a set of stops and stations. With these set of stops and stations, passengers travel routes are also able to be calculated. Depending on the type of the smart card, some smart cards include the privacy. According to the privacy agreement, privacy information is excluded for this research. (3) Trip chain and Real OD generation Transaction ID is to form a trip chain by linking each segment trips of various modes and lines. Transaction ID enables to generate trip chains from each segment trips. Figure1. Concept of trip chain For example, it's available that "One passenger takes line X of mode M from origin A, and transfer to line Y of mode at the place of B, and arrive at the place of C." The origin and destination correspond to stops or stations that passengers visited, so can get precise O-D data compared to the existing transportation planning zone - generally, region area. Stops or stations are approximate passenger's actual (real) OD. In this sense, in this study, it referred to public transport 'Real-OD'. With a database of aggregate each passenger's smart card data, precise transit use and service information is available. Bagchi & White ( 2005) introduced the potential and utilization of the smart card data for transit behavior analysis. However, the data they used had limitation that does not record each trip length. In Seoul area, the public transport fare is adjusted by the travel distance. To measure the distance on vehicle, passengers contact their cards to the card reader on the vehicle (or station) at their getting on and off. This means the limitation described by Bagchi & White ( 2005) can be solved. Travel distance data is available in smart card system. Because Real OD enable transit demand by stops or stations, each stop and station can be used as small units of transportation zone in theory. Even if there is some difference by each analysis method, transit information by Real OD enables very detailed zone analysis by a block or a intersection. In addition, transit zone can be enlarged gradually by aggregating small zones. (4) Real OD database building The key point of Real OD database is to build the entire passenger trip chain data from segment smart card data. In this paper, In this paper, Real OD database was built from all segment trips of 3

4 trunk line buses, branch line buses, and subways, so a Real OD database user is able to analyze transit OD and route. Raw data processing to build the Real OD database follows these principles; (1) make sets of segment data by same smart card ID and Transaction ID, (2) sort in transfer order within same transaction, (3) generate a unit of Real OD data as Table3, (4)build database of Real OD data. Table3. A unit of Real OD data - Smart card ID - Boarded stop (or station) ID where the transfer order is 0. (the first boarding) - Alighted stop (or station) ID when the transfer order is max. (the last boarding) - Number of passengers that belongs the card (generally 1) - Sum of each segment trip distance within a same transaction ID - Sum of each segment trip time within a same transaction ID - Sum of each segment trip fare within a same transaction ID - Number of transfers - Sum of each time took for transfer (within a trip chain) Summing data is calculated by the sum of each segment smart card attribute value. The sum of time took for transfer can be calculated by the sum of time gap between alighted time and next boarded time by time order. For example, assume that the alighted time of 1 st segment trip is 09:10, and the boarded time of 2 nd segment trip is 09:20, and the alighted time of 2 nd segment trip is 09:50, and the boarded time of 3 rd segment trip is 10:05. In this case, the sum of time took for transfer is totally 25 minutes summing 10 minutes and 15 minutes. This formula can be expressed as follows. n is the number of transfer. If n=0, it means the 1 st segment. TA(n) is alighted time of nth segment trip, and TR(n) is boarded time of nth segment trip within a transaction. m is the total number of transfer. Trip chain data is very helpful to analyze transit information and estimate the demand. Spatial analysis and transit project assessment can be performed with geographical data and tools. With the Real OD database, transit assignment models can be developed. In addition, the schedules optimized to the real demand also are derived. Further algorithm research, however, is needed. Especially, the Real OD data is a kind of actual data, not estimated data. It s very powerful to calibrate coefficients of each models-demand estimation, transit assignment, and schedule optimization. 3. Analysis on transit statistics, behavior, and demand (1) Basic transportation indices Park & Kim (2006) presented the indices from the smart card data in terms of transportation planning and engineering as following Table4. Table4. Transportation indices derived from the smart card data (Park & Kim 2006) Class Index Calculation Passengers by the stop (station) Boarding and alighting passengers by the stop (station) Passengers by the mode and the line Boarding and alighting passengers by the mode and the line Transportation Passengers by the passenger class Boarding and alighting passengers by the passenger class elements Avg. passenger per a vehicle Total boarding passengers per total vehicles Avg. passengers in vehicle by the vehicle Sum of in-vehicle passengers in the section, divided by the number of sections Avg. travel time per a passenger Avg. gap between boarding time and alighting time Avg. distance per a passenger Avg. route distance between boarding stop and alighting stop 4

5 Fare Transfer Volume (Passengers) Avg. number of trips per a passenger Avg. travel time by the mode Congestion in vehicle Avg. fare per a passenger Total income by the vehicle Total income by the line Avg. number of transfer Avg. transfer time Avg. transfer cost Passenger by the OD pair Total number of trips divided by total passengers Sum of all passengers travel time divided by the number of passengers * Calculate for each mode Current in-vehicle passengers + boarding passengers - alighting passengers Total fare charged divided by total passengers Total fare of a vehicle s passengers Total fare of a line s passengers The number of all trips divided by total passengers Transfer time: the time gap of previous alighting and current boarding Transfer cost: additional fare for transfer Sum of all passengers through all modes from one stop(origin) to another stop(destination) In addition, by comparing the planned timetable with driving record, the rate of delay can be calculated. The mode share can be derived by a mode s total passenger-km divided by all mode s total passenger-km within the time slot and the OD. In OD analysis, In OD analysis, basic analysis of the above table, as well as valid routes of certain OD, average transfer time by the route, comparison with the road network path, railroad share by the route, passenger assignment rate by the route, are available in Real OD. Generally each index might be analyzed by the time slot, the region, the passenger class, and the mode. Data fusion analysis is also available among the indices. Besides, the research on the data fusion of transit data and highway traffic data is needed. (2) Advanced transit demand analysis This paper propose the DTM(disaggregate transport market) concept as a kind of transportation market. DTM presents disaggregated (detailed) market to serve various services with several classifications. Figure2 shows DTM classifications. Figure2. DTM classifications Passenger class is divided into general, student, disabled person, the aged matching to the smart card classification. It s to analyze the trip/travel pattern by the passenger class and to suggest appropriate service strategies for each class. Spatial scope is the Seoul metropolitan area(about 12,000 km2 ). According to the scope s area regional markets have two categories; gu/dong(administrative district) and stop(or station). Seoul city is composed of 25 gu s, and each gu is composed of about 20 dong s. Generally transportation demand is analyzed using ADT(avg. daily traffic), but time slot analysis is too poor. Using the smart card data in order to compensate the existing demand analysis, transit market can be analyzed by the peak/non-peak, weekdays/weekend, and month/season. They are very helpful to establish specific policies and plans. 5

6 Analysis based on trip chain and DTM becomes the basis of unified transit management including optimized transfer and schedule. Figure3 and Table5, Table6 is the result example of DTM analysis. Figure3 is a passenger distribution by the time slot and the ages. Table5 and Table6 is a passenger statistics by the region(dong) and the weekdays/weekend. Figure3. Passenger distribution by the time slot and the ages (weekday) Table5. Passenger statistics by the dong on weekend (Oct. 31) Passengers Resion boarded Passengers alighted 1 Jongno1,2,3,4ga-dong, Jongno-gu 119, , ,074 2 Sinchon-dong, Seodaemun-gu 130, , ,504 3 Yeoksam1-dong, Gangnam-gu 104, , ,692 4 Yeongdeungpo2-dong, Yeongdeungpo-gu Sum 119, , ,614 5 Hoehyeon-dong, Jung-gu 99, , ,363 6 Bangbae2-dong, Seocho-gu 93, , ,962 7 Seogyo-dong, Mapo-gu 83, , ,373 8 Banpo4-dong, Seocho-gu 89, , ,896 9 Jamsil3-dong, Songpa-gu 91, , , Myeong-dong, Jung-gu 83, , ,747 Table6. Passenger statistics by the dong on weekday (Oct. 26) Passengers Resion boarded Passengers alighted 1 Jongno1,2,3,4ga-dong, Jongno-gu 181, , ,442 2 Yeoksam1-dong, Gangnam-gu 141, , ,800 3 Sinchon-dong, Seodaemun-gu 199, , ,883 4 Hoehyeon-dong, Jung-gu 134, , ,534 5 Bangbae2-dong, Seocho-gu 116, , ,347 6 Yeongdeungpo2-dong, Yeongdeungpo-gu Sum 145, , ,112 7 Myeong-dong, Jung-gu 108, , ,981 8 Jamsil3-dong, Songpa-gu 112, , ,963 9 Seogyo-dong, Mapo-gu 103, , , Yeoui-dong, Yeongdeungpo-gu 94, , ,300 Analyzing passenger distribution by time slot (Fifure3), the peak can be found at 8 am and 6 pm. 6

7 That s ordinary peak hour pattern. Otherwise, in case of the old (over 65 years), the peak hour is between 10 and 11 am, and travel rate after 6 pm is much lower than the general. DTM classifications (time, region, mode, passenger class) from smart card data enable to analysis each specific market and to establish transportation plans suitable for their markets. 4. Direction of developing models and indices of transit service Shin et al (2008) presented a assessment method of transit policy and service performance using the smart card data of Seoul. They proposed service indices; basic trip elements, fare, transfer, OD passenger volume. Based on these indices, the improvement priority of transit service, transit priority signal, a model to evaluate transit service is presented. Kim (2007) presented possibility of the smart card data on transit pattern analysis, demand/capacity analysis, and service performance evaluation. Existing public transit evaluation method is somewhat qualitative techniques as interview surveys. This paper presents quantitative evaluation of transit service performance using the smart card data conceptually. The possibility of quantitative evaluation means that the quantitative indices of transit service performance can be developed. This paper proposes three conceptual index model of transit service performance. First, from a passengers point of view, an index can be expressed as a linear model by each transit mode s characteristics. The characteristics may be passengers, share rate, capacity etc. In addition, the synergies can be added as a variable of the model to explain synergy effect between modes. α, β, γ are coefficients of each characteristics I. The characteristics can be derived from the Real OD data. From operators point of view, index is closely related to the line (route). An index can be explained by how transit lines cover the major OD links. In other words, the index is related whether transit lines (routes) satisfy the demand. The index is expressed as the ratio of major transit lines route length to major demand links total length. The demand includes passenger cars as well as transit, so additional demand data is needed to complete the analysis. If the routes are duplicated, it s considered same line. However, duplicated routes α, β are coefficients. Each L is the route length excluding duplicated routes, and D is total length of major demand links. Actually, headway should be considered to solve the problem of duplicated routes. The duplicated lines mean that headway is improved (shortened) ironically. The follow-up research is need to consider headway or other related characteristics. From another point of view, an index can be explained by spatio-temporal range. That s related to maximum reaching distance in certain hours or minutes. The index is expressed as the total length of segments inside the maximum reaching boundary in certain hours or minutes. 7

8 Figure4. Transit service index (example) Each city has its own index value to measure the city s characteristic. With this index, planners are able to compare cities in terms of transit LOS, transit characteristics, etc. As a result, transportation planners or operators can make a decision of line and capacity planning. For example, there is a city that its transit LOS is low despite many transit lines. This city s transit planner is need to resolve this inefficient transit system with some appropriate solution like transit lines reshuffling. 5. Multi-modal transit assignment Real OD data make it possible measure the detailed properties of trip chains as well as simple OD information, so it's very good to develop a traffic assignment model and derive the parameters and coefficients. Real OD is also the actual performance data rather than statistical data, so the practicality of mass transit assignment models can be verified correctly. (1) Multi-modal transit network Basically, transit network consists of highway network, rail network, and transit lines. Figure5. Transit network conceptual structure Because the multi-modal transit has complex and diverse characteristics such as transfer, schedule, waiting time, fare etc, unlike road traffic, multi-modal transit network is needed to build considering these characteristics. In the optimal path search algorithm, the node-based algorithms are not available, because of violating Bellman s Principle of Optimality due to the transfer time. (Lim & Lim, 2003) This means the shortest path cannot be searched using the traditional node-based algorithms in the multi-modal transit network. Although several algorithms to solve this restriction are developed, most of these algorithms need extra extension of the transit network. The algorithms are also inefficient and take too much calculation time because of the stochastic method. The link-based algorithm, on the other hand, doesn t need extra transfer nodes and links. In addition, transfer cost can be considered using link labels without extra network extension. Therefore, the transit network of link-based algorithm is simple relatively, and the link-based algorithm distinguishes transit lines within same link. In other words, even if there are many transit lines along Wall Street, the link-based algorithm can distinguish which transit line is used to pass Wall Street - line1 s Wall Street section or line2 s Wall Street section? or etc. Link-based algorithms applied to the complex transport network, the node-based algorithm and unlike any additional transit nodes and eliminate the need for transit links, and links to cover the cost of transit transportation is available to consider, without extension, so you can reduce transportation Link-based algorithms, as well as node-based algorithm, unlike the presence of the duplication of the same routes in public transit transportation links because the search is based on the node using the route sure to clearly determine what you can. Cheon et al (2008) presented a link-based stop(station)-oriented multi-modal transit network to use smart card data. Building stop-oriented multi-modal transit network, the smart card transit data is 8

9 available. The network is automatically built just with stop (station) location and transit line information, so it s a very simple and efficient method. This paper adopted this link-based stop-oriented multimodal transit network presented by Cheon et al (2008). There are cases that multiple stops have same stop name or are able to be regarded as a stop actually. In this paper, to build the link-based stop-oriented multi-modal transit network, neighboring stops are unified as a representative stop at mid-block location using GIS tool. Figure6. Representative stop at mid-block In this study, the transit network is generated as dual-level network conceptually, in order to analysis transit passenger behavior as well as transit network. 1 st level network is transit network with line information, and is simplified network unifying transit lines and stops for transit assignment. Especially, stops and stations are unified as representative stops at mid-block or intersection locations as above. 2 nd level network is transit network without line information, and is detailed network with actual transit lines and stops. (2) Prospect of multi-modal transit assignment Figure7. Dual-level transit network The main purpose of multi-modal transit assignment is to analysis the effect of transportation projects and demand change. Transit assignment model enable assignment simulation. However, the key issue of transit model is to design appropriate model and to set coefficients. Real OD and trip chain data is very powerful base to design transit assignment model and to calibrate model s coefficients, because Real OD is actual performance data not estimated data. There are very diverse cases and huge transit data to verify assignment models. The model can describe transit passengers behavior more correctly than the models by survey data. Generally transit assignment model are the all-or-nothing model, optimal strategy model, stochastic model. Especially, stochastic model can make up the impractical conduct error what most 9

10 deterministic models have. In stochastic assignment model, each route s utility is calculated by a utility function. And passengers are assigned to each route using stochastic method - logit model or probit model. Routes can be derived from trip chains based on Real OD. Generally, travel time, travel cost, transfer, access time, wait time, boarding/dwell time, and congestion is the key parameter of multi-modal transit assignment model. Table8. Key parameters of multi-modal transit assignment model Travel time - In-vehicle time - In-vehicle time weight - Headway (Actual / perceived) Travel cost - Fare - min.(or max.) trip cost - Value of time Transfer - Max transfers - Max transfer time - Transfer penalty Access time - Walk time - Walk weight Wait time - Wait time - Wait time weight Boarding/dwell time - Dwell time weight - Boarding penalty Congestion - Congestion - Standing rate In-vehicle time can be derived from boarding and alighting time of the smart card data. Bus s headway is derived from time difference between a passenger s current bus boarding time and other passenger s next bus boarding time at same stop and same line. Subway s headway, however, is calculated from time table, because of the time difference from the ticket (smart card) gate to the platform. Similarly, transfer time of bus to subway (or subway to bus) may not be clear due to same reason. If each station s access time data from the gate to the platform is available, the transfer time may be more accurate. One of the key utilization of the smart card is line schedule optimization based on detailed actual demand and operation performance. The multi-modal transit network including all train and bus schedules is extremely complicated. So to optimize schedule heuristic algorithms may be more efficient than mathematical solutions by full transit network. The model can t prioritize influencing factors, so the heuristic algorithms may include the prioritizing strategy. Specific algorithms and system architecture will be presented before long. The optimized schedule s effect will be verified by the simulation using the assignment model. 6. Conclusions Currently the information can be obtained just from the Seoul metropolitan area, but recently the government has a plan of nationwide transportation smart card - "One Card All Pass Project". The nationwide public transport smart card is promoting standardization. Therefore, the public transportation nationwide deployment of database - based Real OD in the near future (within 3 years) is expected to be readily available. Accordingly, these huge and valuable data are needed to be reproduced to high value information. This paper proposed the method to derive transit information from the smart card data and arranged valid data for transportation planning and operation. Especially, the concept of Real OD database based on multi-modal trip chains was presented. The technical prospect of demand analysis, service performance assessment, multi-modal transit assignment, and optimization was presented. In addition, several conceptual models of transit performance indices and transit assignment was proposed. Transit passenger and OD information based on the smart card is not estimated data derived from surveys but actual performance data. So, the information is much more realistic and detailed than existing methods. Preliminary feasibility test and verification are possible at the simulator using assignment and optimization models based on Real OD (trip chains). This will contribute to encourage rail project investment and passenger services. Although some areas for further research is still needed, such as algorithms development, variety information generating methods and processing algorithms are expected, resulting from a variety of useful ways proposed by this paper. Korea Railroad Research Institute is currently developing the next-generation transit informatnio 10

11 system (NxTIS) based on the theoretical background presented above. This system will be completed after about three years, is planning to pilot operation in NxTIS will be utilized as the transit project effect estimation system, so NxTIS may be very helpful to preliminary effect assessment of planning transit lines or reshuffling existing lines or etc. In the long term, NxTIS is expected to be the transit information data warehouse based on Real transit OD. References [1] M. Bagchi and P. R. White, Road User Charging: Theory and Practices The potential of public transport smart card data, Transport Policy, Volume 12, Issue 5, Pages , September 2005 [2] S. Cheon, A Methodology of Multimodal Public Transportation Network Building and Path Searching Using Transportation Card Data, Journal of Korean Society of Transportation, Vol.26, No.3, pp , June 2008 [3] S. Cheon, Development of a Smart Card Data-based Stochastic Transit Assignment Model on Integrated Public Transportation Networks, Seoul National University PhD Thesis, 2010 [4] S. Kim, The Estimation and Application of Origin-Destination Tables by Using Smart Card Data, Seoul Development Institute, October 2007 [5] J. Park & D. Kim, Study of potential usage of contactless smart card data for establishing public transport policy, Korea Transport Institute, November 2006 [6] J. Park, The Analysis on the Characteristics of Transit Level in Seoul Using Transit Data Card, Proceedings of the KOR-KST Conference, 57 th Conference Proceeding, pp , November 2011 [7] J. Park, The study on error, missing data and imputation of the smart card data for the transit OD construction, Journal of Korean Society of Transportation, Vol.26, pp No.2, April, 2008 [8] S. Shin, Integrated Transit Service Evaluation Methodologies Using Transportation Card Data, Seoul Development Institute, December 2007 [9] S. Shin et al, The study on error, missing data and imputation of the smart card data for the transit OD construction, Proceedings of the KOR-KST Conference, 57th Conference Proceeding, pp , November