Aggregated Binary Logit Modal-Split Model Calibration: An Evaluation for Istanbul

Transcription

1 Aggregated Binary Logit Modal-Split Model Calibration: An Evaluation for Istanbul H. B. Celikoglu a,1 and M. Akad a,2 a Technical University of Istanbul Dept. of Transportation, Faculty of Civil Engineering, Maslak, 34469, Istanbul, Turkey Abstract: This study examines the possibilities of obtaining better modal-split models for each trip purpose in Istanbul Metropolitan Area by calibrating the binary logit modal-split models at the appropriate aggregation level with the appropriate variables. The modal-split for the year 22 is then studied by using the valid models with current data. The applications of the calibrated modal-split models are presented. The modal-split model is calibrated by taking the interzonal trip matrices used for Istanbul Master Plan Transport Study (1997), and splitting them between private, public and service transport modes. By means of the intersectoral data obtained by the aggregation process; a single variable logit model with the generalized trip cost variable and a multivariable logit model with the trip cost and the trip time variables are calibrated for each trip purpose to determine the valid models. Key Words: Transportation planning, modal split, logit model 1 hbcelikoglu@ins.itu.edu.tr 2 muratakad@ins.itu.edu.tr

2 1 Introduction In this study, aggregated logit model calibration, which gives an opportunity to estimate the modal split of urban trips in Istanbul to different modes of transport, is examined. First, in order to obtain models with a good level of estimation power for different trip purposes, it is necessary to determine the level of aggregation of relevant variables for the logit model calibration and to determine the appropriate variables. After this was realised, modal split of trips to different transport modes were examined with the obtained valid models. 2 Logit Modal-Split Model Calibration for Istanbul The modal split model determines the rates trips, which were estimated by the trip distribution model, will be distributed among different transport modes. In this study, the logit model is calibrated in order to make the distribution of trips to private cars, public transit and service vehicle modes. The purpose-based matrices used for model calibration are the ones that were used for the Istanbul Transportation Master Plan in The trip costs, trip times and generalised trip costs that are used in calibrations in order to obtain valid models of to trips according to purposes, are also calculated according to the 1996 values. Calibration data for the model were aggregated based on two different sectors of size 7 and 2. With help of inter-sectoral data obtained by aggregation, the single-variable logit model based on the generalised cost variable and the two-variable binary logit model based on trip cost and trip time, were calibrated. Thus, valid model has been sought according to different trip purposes. Trips that constitute data in the logit model for other work and home-based trips are evaluated as trips made by users with opportunities of utilising private cars. It is obvious that individuals that do not have the opportunity to use private cars tend to use public transport. Thus, evaluating these two types of trips would result in obtaining wrong models. Therefore, in the logit modal split model, calibrated for the other work and homebased trip purpose, trips of those having the opportunity to utilise private cars are evaluated. School trips are deduced from total trips because they contain a very low amount of private car utilisation (9%). The remaining school trips are divided into two, either service vehicles or public transport. The logit model was calibrated accordingly. For the trips with other purposes, service vehicle utilisation is negligible (5.5%). So, these trips were also deduced from total trips. The remaining trips, of which the rate of private car utilisation opportunity is unknown, are divided into two, the ones using private cars and public transportation. The model was calibrated accordingly.

3 2.1 Applied Model Two different methods were used for the model calibration. In the first of these, modal usage in inter-zonal trips is related with the trip cost and trip time variables by using multi-variable linear regression method. With the binary logit model, P O, which is the possibility of an individual using private car between zones i and j, can be calculated as in Equation 1 [2]. P O = 1 (1) O O { 1+ exp[ λ ( C C ) + ( T T ) + δ ) where, P O : Private car utilisation rate between zones i and j C, C O : Inter-zonal costs for public transport and private car trips between zones i and j T, T O : Inter-zonal trip times for public transport and private car trips between zones i and j λ : Calibration coefficient δ : Coefficient of public transport type While making evaluations according to trip cost and trip time variables, no time value data is input into the transport model. In the equation obtained as a result of linear regression, the ratio of the coefficient of trip time difference variable to the coefficient of trip cost difference variable gives the value of time. According to the binary logit model, P, which is the possibility of the usage of public transport type between zones i and j can be calculated as in Equation 2. P = 1 P (2) O The other used for the logit model calibration is realised by relating the utilisation of transport modes in inter-zonal trips with the generalised cost variable by a single-variable linear regression method. With the binary logit model, P O, which is the possibility of an individual s usage of private car between zones i and j can be calculated as in Equation 3. P O = 1 (3) O { 1 + exp[ λ( GC + δ GC ) where, P O : Rate of private car usage between zones i and j GC, GC O : Inter-zonal generalised costs for public transport and private car trips between zones i and j λ : Calibration coefficient δ: Coefficient of public transport type In order to make an evaluation according to the generalised cost variable, value of time is also input into the transport model along with generalised costs. In the models used for school trips, service vehicles are included in the calibration instead of private cars. Therefore, statements representing private cars are acquiring the values of service vehicles.

4 2.2 Data Aggregation Number of inter-zonal trips, trip costs, trip times and generalised trip costs, which are the basic data for the model calibration, are aggregated into sectors of size 2 and 7, in order to determine the most appropriate level of aggregation. The zones aggregated in 2 sectors can be seen in Figure 4.1 and the ones aggregated in 7 sectors can be seen in Figure 4.2. Zonal data used in the study were aggregated by uniting the relevant zones. 29 of the 33 counties of Istanbul were originally divided homogeneously to obtain zones appropriate for planning and giving usable data in the sense of land use and socio-economic features. These zones were then grouped to acquire bigger sectors; by paying attention to bring neighbouring zones that show similar social, economical and physical characteristics together. Another criterion taken into consideration while aggregating zones is the distribution of urban transport network. 2.3 Information on Calibrated Model Variables Inter-Regional Trip Costs In this study, inter-zonal trip costs were calculated at desired aggregation levels by including the characteristics and values of urban transport modes and relating them with inter-zonal trip matrices. For the transport model used, transport networks for all of the urban transport modes in Istanbul were defined. Sector-based private car and public transport tip costs were calculate desperately, according to the zones through which the defined road networks pass. These costs, which were included in the model as input data, were evaluated as an independent variable from trip times in the model calibration. Therefore, trip costs that will supply data for the multiple regression made according to trip time and trip cost variables were included in the model as average data by using trip type, trip distance and trip fare values. In order to obtain the valid model, logit model calibration was made according to the values of year Inter-Regional Trip Times Another set of data for the two-variable modal split model calibration; trip time variable values were obtained by using the trip distribution model, which is the second phase of the four-phased transport model. The values serving as a base for the calibration were included in the model as the same with that of 1996 Transportation Master Plan values; however, they show differences in different aggregation levels. Average trip times for the sectors obtained by uniting the zones, were estimated by dividing the values acquired from the model by the number of zones in the sector. Trip times obtained from the model at two different aggregation levels of 2 and 7, were examined in the sub-titles according to the transport mode Generalised Cost (GC) and Value of Time (VOT) for Calibrations Along with the calibration of the modal split model with the two-variable regression by using the inter-zonal trip costs and trip times, another calibration was made by applying a single-

5 variable regression with generalised cost values. In the transport model used in the study, it is assumed that users make their preferences about the transport modes according to the generalised costs of trips. 2.4 Logit Model Calibration upon Trip Purposes In the study, by using the logit model, urban trips according to four main trip purposes were distributed with the help of 1996 household surveys. In conjunction with the aim of the study, calibration was made with two different methods at two different aggregation levels. Characteristics of trips forming the basic data for the model calibration are explained in the trip purpose sub-titles Home Based Work (HBW) Trips Calibration of work trips was made by subtracting the service vehicle trips from total trips and then evaluating the ones with opportunity to use cars in the remainder. According to the calibrated model probability of choosing private car in 2 sectors according to trip cost and trip time is, (4) O { 1+ exp[ (.129( C C ) +.8( T T ).735) Probability of choosing private car in 2 sectors according to generalised cost is, (5) { 1 + exp[.36 ( GC GC ) ) Probability of choosing private car in 7 sectors according to trip cost and trip time is, (6) O { 1+ exp[ (.137( C C ) +.9( T T ) 1.121) Probability of choosing private car in 7 sectors according to generalised cost is, (7) { 1 + exp[.191 ( GC GC ) ) Home Based Other (HBO) Trips Discretion of data used for the calibration of modal split model of home-based other trips, and the calibration method of the model is same as that of work trips. Modal split of home-based other trips is made by subtracting the service vehicle trips from total trips and evaluating the ones with opportunity to use car within the remainder. Probability of choosing private car in 2 sectors according to trip cost and trip time is, (8) O { 1+ exp[ (.158( C C ).1( T T ) )

6 Probability of choosing private car in 2 sectors according to generalised cost is, (9) { 1 + exp[.124 ( GC GC ) ) Probability of choosing private car in 7 sectors according to trip cost and trip time is, (1) O { 1 + exp[ (.182( C C ) +.19( T T ).13) Probability of choosing private car in 7 sectors according to generalised cost is, (11) { 1 + exp[.67 ( GC GC ) ) Home Based School (HBS) Trips Unlike the previous applications for Istanbul, for this trip purpose, logit model was calibrated by using the service vehicle and public transport trip data to determine modal split. According to data from year 1996, most of the school trips are made by service vehicles; rate of private car usage is low (9%). Private car trips are thus excluded from other transport mode trips. In order to determine the modal split between the remaining service vehicle and public transit trips, the binary logit modal split model was calibrated as in the other trip purposes. Probability of choosing service vehicle in 2 sectors according to trip cost and trip time is, P S 1 (12) S { 1 + exp[ (.31( C C ).5( T T ).1389) = S Probability of choosing service vehicle in 2 sectors according to generalised cost is, P S 1 (13) { 1 + exp[.86 ( GC GC ) 27.43) = S Probability of choosing service vehicle in 7 sectors according to trip cost and trip time is, P S 1 (14) S { 1 + exp[ (.417( C C ).98( T T ).9395) = S Probability of choosing service vehicle in 7 sectors according to generalised cost is, P S 1 (15) { 1 + exp[.177 ( GC GC ) ) = S

7 2.4.4 Non Home Based (NHB) Trips Since service vehicle usage is insignificantly low (5.5%), these trips are deduced from the other-purpose trip matrix. According to data from year 1996, because it is not possible to know the places that individuals who make the other non-home-based trips live, these individuals possibility of utilising cars could not be determined. Therefore, a binary logit model calibration was made in order to make the differentiation between private car usage and public transit modes for all of the other-purpose trips. Probability of choosing private car in 2 sectors according to trip cost and trip time is, (16) O { 1 + exp[ (.425( C C ).185( T T ).633) Probability of choosing private car in 2 sectors according to generalised cost is, (17) { 1 + exp[ ( GC GC ).849) Probability of choosing private car in 7 sectors according to trip cost and trip time is, (18) O { 1+ exp[ (.58( C C ) +.39( T T ) +.2) Probability of choosing private car in 7 sectors according to generalised cost (19) { 1 + exp[.493 ( GC GC ) +.629) 3 Forecasts of Modal-Split in the year 22 Calculation of trip costs for the year 22, which is one of the aims of this study and which is going to be evaluated at the stage of distribution of trips to transport modes according to the new cost values with the help of the valid model, is made for each transport mode. To make a modal split according to the new values, it is necessary to bring the new values to be input into post-calibration valid models to the prices of year Therefore, the new trip costs and generalised costs are brought to the prices of 1996 by using the ratio between USD values of 22 and Model Variables at Modal Split Inter-Regional Trip Times Inter-zonal trip times for private car and service vehicle trips are taken into the evaluation as the same with the 1996 values used in the calibration [3]. Public transport trip times on the

8 other hand, are calculated again in the model by defining the subway alternative added to the transport network Generalised Cost In this study cost of a private car trip is equal to the vehicle operating cost plus possible toll highway, toll bridge and parking fares. Vehicle operating cost is taken as fuel consumption cost. The estimated average fuel price is 1,147,889 Turkish Lira (TL)/litre. It is assumed that cars consume an average of 1 litres per kilometres in urban areas. Accordingly fuel consumption rate per car-km is calculated as 114,789 TL with 22/3/22 prices. Toll bridge fare in Istanbul is taken as 2,, TL [1]. As explained below in under the title Value of Time, value of time is found to be 38,56 TL/minute. Occupancy for private cars is taken as 1.9 individual/vehicle in the model and thus generalised cost is calculated as in equation 2. GC = *Km + (1,9*38.56)*minute (TL/ unit car) (2) Generalised cost per individual is calculated as in equation 21. GC = ( /1,9)*Km *minute (TL/ individual) (21) Generalised cost per individual in service vehicle trips is calculated by taking the kilometre values of trip per individual obtained from service vehicle usage cost estimation into consideration. It is shown in equation 22. GC = ( )*Km *minute (TL/individual) (22) Generalised costs of public transport trips are calculated by including ticket fares and value of time in the transport model Value of Time Value of time is estimated in a different manner than in the previous plans and studies for Istanbul. The total of 1,893,872 households in Istanbul is divided into groups of 1%. Then these 1-% groups are united into groups of 5%. Value of time then is determined by taking total income, monthly income of a family, monthly income of an individual, value of time for the time worked, value of time for the time that is not worked and rate of work trips into consideration. The estimated average value of time is 38,56 TL/minute/individual. 3.2 Trips Split to Modes in the Year 22 It is possible to determine the amount of change in the usage rates of transport modes when new cost values are input into the post-calibration valid models for different trip purposes. At different trip purposes and levels of aggregation, differentiation is made between trip observations of 1996 used in the model, trips distributed by models calibrated according to 1996 data and trips distributed by models calibrated according to 22 data. In order to show

9 this differentiation, two different graphs according to the level of aggregation and calibration method are given. One of them shows the relationship between observed values and the trip values obtained by the distribution of 1996 values by valid models. The other one shows the relationship between trips distributed by 1996 values and trips distributed by 22 values [1] Split HBW Trips According to the model calibrated by trip cost and trip time of 2 sectors, private car usage has increased (from 68% to 7%) compared with 22 values. According to the model calibrated by trip cost and trip time in 7 sectors, private car usage has stayed the same (67.5%). According to the 22 values, in the models calibrated on generalised cost, private car usage has decreased from 79.5% to 78.2% in 2 sectors (Figures 1 and 2). In seven sectors, private car usage has also shown decrease from 63.2% to 62.1% (Figures 3 and 4) Figure 1: Relationship of work trips by private car in 2 sectors by two-variable model with modal split by observation, 1996 and 22 values

10 Figure 2: Relationship of work trips by private car in 2 sectors by single-variable model with modal split by observation, 1996 and 22 values Figure 3: Relationship of work trips by private car in 7 sectors by two-variable model with modal split by observation, 1996 and 22 values

11 Figure 4: Relationship of work trips by private car in 7 sectors by single-variable model with modal split by observation, 1996 and 22 values Split HBO Trips According to the model calibrated by trip cost and trip time of 2 sectors, private car usage has decreased (from 73.3% to 71.7%) compared with 22 values. According to the model calibrated by trip cost and trip time in 7 sectors, private car usage has increased from 44.6% to 45%. According to the 22 values, in the models calibrated on generalised cost, private car usage has decreased from 68.8% to 63.7% in 2 sectors (Figures 5 and 6). In seven sectors, private car usage has also shown decrease from 48.8% to 44.9% (Figures 7 and 8) Figure 5: Relationship of home-based other trips by private car in 2 sectors by two-variable model with modal split by observation, 1996 and 22 values

12 Figure 6: Relationship of home-based other trips by private car in 2 sectors by single-variable model with modal split by observation, 1996 and 22 values Figure 7: Relationship of home-based other trips by private car in 7 sectors by two-variable model with modal split by observation, 1996 and 22 values

13 Figure 8: Relationship of home-based other trips by private car in 7 sectors by single-variable model with modal split by observation, 1996 and 22 values Split HBS Trips According to the model calibrated by trip cost and trip time of 2 sectors, service vehicle usage has decreased (from 5% to 47%) compared with 22 values. According to the model calibrated by trip cost and trip time in 7 sectors, service vehicle usage has also decreased from 32% to 26.6%. According to the 22 values, in the models calibrated on generalised cost, service vehicle usage has decreased from 59.3% to 58.7% in 2 sectors (Figures 9 and 1). In seven sectors, service vehicle usage has also shown decrease from 29.8% to 28.4% (Figures 11 and 12) Figure 9: Relationship of school trips by service vehicle in 2 sectors by two-variable model with modal split by observation, 1996 and 22 values

14 Figure 1: Relationship of school trips by service vehicle in 2 sectors by single-variable model with modal split by observation, 1996 and 22 values Figure 11: Relationship of school trips by service vehicle in 7 sectors by two-variable model with modal split by observation, 1996 and 22 values

15 Figure 12: Relationship of school trips by service vehicle in 7 sectors by single-variable model with modal split by observation, 1996 and 22 values Split NHB Trips According to the model calibrated by trip cost and trip time of 2 sectors, private car usage has increased from 41.1% to 48.6% compared with 22 values. According to the model calibrated by trip cost and trip time in 7 sectors, private car usage has also increased from 49% to 5.8%. According to the 22 values, in the models calibrated on generalised cost, private car usage has increased from 45.4% to 48.4% in 2 sectors (Figures 13 and 14). In seven sectors, private car usage has shown decrease from 39.4% to 36.4% (Figures 15 and 16) Figure 13: Relationship of other trips in 2 sectors by two-variable model with modal split by observation, 1996 and 22 values

16 Figure 14: Relationship of other trips in 2 sectors by single-variable model with modal split by observation, 1996 and 22 values Figure 15: Relationship of other trips in 7 sectors by two-variable model with modal split by observation, 1996 and 22 values

17 Figure 16: Relationship of other trips in 7 sectors by single-variable model with modal split by observation, 1996 and 22 values 4 Conclusion The conclusions of this study can be summarised as follows. -The models calibrated at higher aggregation level give more accurate and appropriate results. -Significant results are obtained from both; the simple linear regression analysis in the presence of generalized trip cost, and the multivariable linear regression analysis in the presence of trip cost and trip time. - Generalized trip cost variable includes the value of time besides the trip cost. An average value of time is calculated based on the, GDP per capita values in the year 1996 in İstanbul. Because of including the value of time that was calculated externally, the single variable logit model produces more errors as compared to the multivariable logit model. Moreover, taking an average single value of time into consideration for different trip purposes leads to model errors during the modal splitting stage. -The multivariable binary logit model allows us to determine different values of time for each trip purpose. This model gives less error in results relatively. -The mode specific constant included in the utility function of the logit model represents the unmeasurable and the unquantifiable level of service characteristics of the public transport mode such as comfort, safety, and reliability. The absolute value of the mode specific constant obtained from the single variable logit model is considerable whereas it has a negligible value in the multivariable logit model.

18 References [1] Celikoglu H.B., 22, Logit Modal-Split Model Calibration for Istanbul, Unpublished MSc Thesis, Technical University of Istanbul, Istanbul (in Turkish) [2] Kanafani A., 1983, Transportation Demand Analysis, McGraw Hill [3] Transportation Master Plan of Istanbul, 1996, Technical University of Istanbul, Istanbul (in Turkish)