Validating the passenger traffic model for Copenhagen

Transcription

1 Transportation (2006) 33: Ó Springer 2006 DOI /s Validating the passenger traffic model for Copenhagen GORAN VUK 1, * & CHRISTIAN OVERGAARD HANSEN 2 1 Danish Transport Research Institute, Knuth-Winterfeldts Alle, Bygning 116 Vest, 2800, Lyngby, Denmark; 2 Centre for Traffic and Transport, Technical University of Denmark, Bygning 115, 2800, Lyngby, Denmark (*Author for correspondence, gv@dtf.dk) Key words: assignment modelling, demand traffic modelling, metro system, model validation Abstract. The paper presents a comprehensive validation procedure for the passenger traffic model for Copenhagen based on external data from the Danish national travel survey and traffic counts. The model was validated for the years , with 2004 being of particular interest because the Copenhagen Metro became operational in autumn We observed that forecasts from the demand sub-models agree well with the data from the 2000 national travel survey, with the mode choice forecasts in particular being a good match with the observed modal split. The results of the 2000 car assignment model matched the observed traffic better than those of the transit assignment model. With respect to the metro forecasts, the model over-predicts metro passenger flows by %. The wide range of findings from the project resulted in two actions. First, a project was started in January 2005 to upgrade the model s base trip matrices. Second, a dialog between researchers and the Ministry of Transport has been initiated to discuss the need to upgrade the Copenhagen model, e.g. a switching to an activity-based paradigm and improving assignment procedures. 1. Introduction Model validation is a method of ensuring that the model replicates the observed conditions and produces reasonable forecasting results. The literature in the field of model validation in general reveals that no well-established framework exists while research into the validation of demand and assignment models for transit modes is alarmingly poor (Barton-Aschman Associates and Cambridge Systematics 1997). The travel demand part of the traffic model for Copenhagen, the Orestad Traffic Model (OTM), is a state-of-practice nested logit model in which the generation, distribution and mode choice sub-models are connected via logsums. The OTM forecasts tours for an average workday undertaken by car, bus, train, metro, bicycle and walk. The tours are converted into day trips before the assignment procedure. The OTM was estimated and calibrated for the year 2000, when the Copenhagen Metro was still under construction, and

2 372 the model s metro forecasts were therefore the main preoccupation of city planners and local politicians at the time. On the other hand, the model accuracy for personal car traffic was the main concern of the Danish Road Directorate. As a result, the OTM s objectives relate to private cars and transit modes, while the slow modes are of secondary importance, mainly due to poor counts. The OTM is an operative traffic model for Copenhagen often used for generating year forecasts. The prime objective of the paper is to list and apply a range of available tools for model validation, according equal weight to the demand and assignment elements of the model. These tools enabled us to identify the accuracy and weaknesses of the model, which should be included as input to model updates. The OTM is calibrated to its base 1992 year. Model validation has been designed to include all steps of the model in a dynamic approach not restricted to the base year only. The paper reports primarily on the validation for 2000, but 2003 and 2004 are also used to validate the forecasting capability and sensitivity of the model. We also try to point out that, data permitting, the validation design should focus on model objectives and the potential uses of the model such as forecasting passengers in transit, which is particularly important in a country like Denmark where car taxation is extremely high. Our hypothesis is that acceptance of a model depends on factors such as model type, objectives and year of validation (base year, forecast or backcast). The validation criteria can therefore not be exactly formulated and the validation results should be presented and discussed in a framework of policy requirements and experiences. External data from the Danish national traffic survey were used to validate the passenger demand model. The transit assignment results for separate modes and geographical areas were validated on the basis of well-known existing statistical tools such as %RMSE and GEH statistics. A similar validation was conducted for cars as well, where efforts were made to validate the model forecasts for the peak traffic. Section 2 contains a short review of the OTM. Sections 3 and 4 are dedicated to the validation of the demand and assignment models, respectively, of the OTM for 2000, while Section 5 deals with the model validation for period the Conclusions are summarised in Section Model structure 2.1. Model analysis area The OTM covers the Greater Copenhagen area with 1.7 million inhabitants. Figure 1 illustrates the part of Copenhagen in the catchment area of the

3 373 Figure 1. The road, rail and metro networks in the city area covered by the metro s alignment. metro. It shows the road network in white, the rail network in grey, and the metro network in black. A motorway runs across southern Amager (thick black line in the bottom of the figure), extending east towards Malmo, Sweden, and south towards south Sjælland. Metro line 1 (M1) runs to a new town, Ørestad in west Amager, while metro line 2 (M2) runs to Lergravsparken in east Amager. The two lines meet on the Amager side of the harbour corridor (a sea channel between the islands of Sjælland and Amager delimited by the Knippelsbro and Langebro bridges), just before Knippelsbro bridge where the metro goes underground towards the island of Sjælland. The analysis area is split into 601 internal zones while the surrounding area is defined by 17 port zones. The OTM network includes some 13,000 nodes, of which 10,000 are bus nodes, 150 are train nodes, while there are 2,850 road nodes. Apart from that, the transit network includes 1,200 lines, while the road network includes 4,100 road links Passenger demand model The OTM predicts traffic demand for an average workday, omitting weekend traffic. The model s nested logit structure uses revealed preference (RP) and stated preference (SP) data in which the sub-models are connected via

4 374 the measure of accessibility (logsums). The model includes four segments: the business (BS), commuter (HW), education (HE) and leisure (PR) segments and four travel modes: car, public transport, bicycle and walk. The BS segment is trip based while the other three are tour based. In the OTM, a tour is defined as the sequence of a simple trip from home to destination and a simple return trip from destination to home. Input data to the demand model are zone data and files of level of service (LOS). The zone data describe the distribution of the population, jobs, education places, shopping places, car ownership and parking costs in the 601 zones. Zone-to-zone travel times and travel costs for each available mode are represented in the LOS files. These files are produced in the car and transit assignment models, and hence the LOS variables are exogenous to the demand model. The distribution model is conditional on the generation model, and the mode choice model is conditional on the distribution model (the three models previously described as demand sub-models). Based on a number of traffic surveys at the end of the 1980s and the beginning of the 1990s in the Greater Copenhagen area, 1992 travel matrices for walk, bicycle, car and public transport modes were built. They are 24-hour tour matrices, which have been continuously improved in a number of traffic planning projects. The OTM consistently uses base 1992 observed matrices being the model s base year -- in a pivot point procedure throughout the demand model as the last step of the sub-models in order to usefully exploit the available data sources. For instance, the procedure is used in the generation model as follows. The number of tours for both the forecasting year and the base 1992 year for each zone are calculated first (so-called synthetic matrices). The forecasted generated tours by zone are then calculated as the ratio of the synthetic matrices multiplied by the observed zone tours from the base year tour matrix. Sixteen matrices of one day s travel (four journey purposes by four travel modes) are produced after the execution of the mode choice model. They are then split into three time-of-day matrices, namely matrices for the morning peak period (7 a.m.--9 a.m.), afternoon peak period (3 p.m.--5 p.m.) and outof-peak period (rest of the day) based on the observed time split existing in the base 1992 matrices. The HW, HE and PR tour matrices are simultaneously converted into trip matrices. The midpoint of a trip defines time of day. A detailed description of the OTM s passenger demand model structure is given in Jovicic and Hansen (2003) Assignment models The OTM includes assignment models for all four modes, where walk and bicycle trips are assigned by an all-or-nothing procedure based on travel

5 times. In larger planning projects and long-term forecasts, the scenario is built by creating a pseudo equilibrium situation where the demand and assignment models are run in a number of iterations by a manually operated feedback loop, typically in three iterations. A probit-based stochastic user equilibrium model is used in the car assignment model, applying the principles developed by Daganzo and Sheffi (1977) and Sheffi and Powell (1982). In the OTM, the travel resistance at a link level, U a, is given by: U a ¼ðb 1 þ nþ1 a þ b 2 t o;a þ b 3 t d;a þ e a where l a is travel costs of link a, t o,a is free travel time, t d,a is delay, and b is a parameter. n represents variation of the cost coefficient while e a represents variation at link level. Delay is calculated as the difference between travel time and free flow time. In the OTM, e a follows the gamma distribution since it is reproductive in mean and variance (just like the normal distribution) but has the advantage of being non-negative, i.e. it results in non-negative link costs (see Nielsen et al. 2002, for more details). In the transit assignment model, trips are categorised by transit mode (bus, train and metro) and route. It is a simple assignment procedure based on a frequency-aggregated network using the following route costs V r : V r ¼ a a t a;r þ a w t w;r þ a v t v;r þ a t t t;r where t a,r is access/egress time using route r, t w,r is waiting time at first boarding, t v,r is in-vehicle time, and t t,r is transfer time. Waiting times are calculated as half the headway aggregated across different but similar routes for the same origin-destination zone pairs. To allow for the time it takes for travellers to adapt to timetables, waiting time at first boarding is maximised to 6.5 minutes in the model. The parameters in the car and transit assignment models are estimated using SP data. The transit assignment procedure starts by selecting the applicable routes between each pair of zones. Extensive calibrations based on 1992 data suggested that only the two best routes according to minimum values of formula (2) should be used, otherwise inferior and non-used routes would enter the assignment. In the second phase of the transit assignment procedure, the probability of using route r2{1, 2} is calculated by the Kirchhoff s formula where k=2 (as found in the model calibration): P r ¼ P 2 i¼1 V k r V k i 375 ð1þ ð2þ ð3þ

6 Demand model validation for the year Generation model The generation model in the OTM was estimated on the basis of a sample of 12,821 respondents from the 1997, 1998 and 1999 national travel surveys, from the sub-sample for the Greater Copenhagen area. The number of HW, HE, PR and BS tours/trips made by each respondent per day was observed, including if no trips were made. The model was then calibrated against the observed 1992 tour/trip matrices. The OTM forecasts 3.55 trips per person per workday for the year 2000, half a trip more than observed in the Danish national travel survey 2000 (Danish Transport Research Institute 2003) in the sub-sample for the Greater Copenhagen area (GCA). Table 1 compares the trip rates observed in the 2000 national travel survey and those forecasted by the model for an average workday, split between three travel purposes: home-work/education, homeleisure and business. The model s home-work and home-education travel purposes had to be combined into one segment because the available travel behaviour data do not distinguish between these travel purposes. The table shows that the disagreement between the totals is entirely explained by the difference in trip rates for home-work/education trips. The later work has showed that the 2000 national travel survey underestimates the trip rate for this travel purpose Distribution model In the OTM, the choice of destination depends on zone attractiveness, distance and logsums from the mode choice model (Jovicic & Hansen 2003). According to the national survey, residents of Copenhagen travelled 29 km per workday in The model forecast for person-km by travel mode reveals a very good overlap with the observed mode for person-km, as shown in Table 2. Table 1. Trip rates from the Danish national traffic survey and the model forecasts by travel purposes on an average workday in 2000, in number of trips per person per workday. National traffic survey, 2000 OTM Home-work/education trips Home-leisure trips Business trips Total trips per person per day

7 377 Table 2. Person-km from the Danish national traffic survey and the model forecasts for four travel modes on an average workday in 2000, in km. National traffic survey, 2000 OTM Private car Transit modes Bicycle Walking Total person-km per day Dividing the total person-km (presented in Table 2) by the person trip rate (presented in Table 1), we observe that the average observed trip length in 2000 was 9.4 km while the modelled trip length was only 8.2 km. Using a pivot point procedure, we see that the trip pattern in the OTM is strongly influenced by the 1992 trip matrices, which were estimated by matrix estimation procedures based on traffic counts (e.g. Nielsen 1997). Compared with the 2000 national survey, it seems that these procedures tend to split long trips into two or more sub-trips, thus resulting in higher trip rates and shorter trips. It is also possible that the survey respondents tended to forget short trips. For instance, in the survey, a work-shopping-home trip chain may be categorised as one long trip from work to home, whereas in the 1992 matrices it is split into two trips. In the AKTA 1 project, 280 car drivers reported that home-work trips by car are 13.6 km long on average. In the OTM, the forecasted total average car driving distance for home-work and home-education purposes is 11.3 km. Again, this supports the conclusion that the applied matrix estimation procedures may tend to produce too many short trips Mode choice model The model forecast for modal shares for the year 2000 harmonises well with the shares observed in the national travel behaviour survey for the same year, as shown in Table 3. The predicted and observed shares are particularly comparable for transit and car modes, for which the OTM includes numerous travel time components. In all, forty different values of time (VOT) were estimated in the OTM s mode choice model (a full discussion of the obtained values is provided in Jovicic & Hansen 2003). It is probably reasonable to state that the OTM overestimates the modal share for walking at the expense of cycling. The trade-off between these two modes has never been investigated in the across-mode SP experiments. Therefore, in the model, many of the modal shares for walking and bicycling

8 378 Table 3. Modal shares from the Danish national traffic survey and the model forecasts for four travel modes on an average working day in National traffic survey, 2000 (%) OTM (%) Private car Transit modes Bicycle Walking Total modal shares were explained by their alternative specific constants. Also, the 1992 matrices used in the pivot point procedure for walking and bicycle trips were inaccurate (particularly in suburban and rural areas) due to few existing counts for these two modes Demand elasticities The model has been tested for changes in demand when travel costs and travel times for car and transit modes change. Table 4 shows the calculated direct and cross-trip elasticities aggregated across the home-work, home-education and leisure travel purpose segments. Note that the values below do not take the business segment into account because this segment shows almost no change in demand for tested changes in travel supply. It should also be noted that the elasticities in the table do not include the feedback effects from the assignment model caused by network changes, e.g. an increase in car travel time is directly coded into the demand model utilities. Changes in travel cost and travel time resulted in much higher direct elasticities for transit modes than for private cars. This is most likely due to differences in income between these two groups of travellers, as transit travellers tend to have lower incomes than car users. The sensitivity analysis also showed that the direct car elasticity for driving time is higher than for driving costs, while the opposite is true for transit modes. Copenhagen car drivers are Table 4. Demand model trip elasticities, aggregated across travel purpose segments. Car Walking Bicycle Transit Car driving costs increased ) Car driving time increased ) Transit fare increased )0.35 Transit time increased )0.30

9 379 probably not fully aware of the cost of driving, because they generally only relate the cost of driving to petrol prices. Thus, the cost-of-driving factor is less important because car drivers have a rather vague idea of the actual cost of driving, a conclusion also reached in the AKTA project. Driving time, on the other hand, was perceived more realistically and thus considered more important (an increase in congested travel time was particularly unwelcome). Transit travellers focus keenly on fare due to direct out-of-pocket costs, making their perception of travel costs fairly accurate. The following discussion of each of the four sensitivity tests (the four rows in Table 4) refers to specific trip purposes where appropriate. A 10% increase in driving costs resulted in a 1.1% decrease in the number of car trips. The education segment was strongly influenced by cost increase (elasticity of )0.63), which can be explained by the low income of travellers in this group. The commuter segment had a numerically higher elasticity ()0.096) than the leisure segment ()0.070). This is probably due to differences in car occupancy for the two travel purposes, since car occupancy for leisure trips is higher than for home-work trips. A 10% increase in driving time resulted in a 1.6% decrease in the number of car trips. Again, the education segment was strongly influenced by increase in driving time (elasticity of )0.48). In this case, the commuter and leisure segments had identical elasticities of )0.15. Students proved extremely sensitive to changes in transit fare, with a 10% increase resulting in a 13% decrease in transit trips in this segment. The sensitivities of commuters and persons travelling for leisure were )0.29 and )0.26, respectively. The average direct transit elasticity for travel costs was )0.35. A 10% increase in transit travel time led to a 5.4% drop in transit demand related to education travel. According to the OTM demand model, a 10% increase in transit travel time would lead to a 3.6% switch in commuting transit trips to other modes, while 2% of leisure transit trips would switch to other modes or not be done. The average direct transit elasticity for travel time is )0.30. An EU report on car travel elasticities, TRACE (Jong & Tegge 1998), showed some similarities with the OTM s car elasticities. The project reported that in the Netherlands, France, the UK and Sweden, the direct car elasticity for driving time was numerically higher than for driving costs. However, it seems that the OTM s elasticities in absolute terms are generally lower than the other EU countries elasticities. For instance, Swedish car travel cost elasticity was reported to be )0.14 while car travel time elasticity was )0.32. One explanation is that Danish car ownership is very low compared with many other EU countries, owing to the high taxes and duties levied on cars.

10 Assignment model validation for year Validation methods Since the assignment model is the last element of the modelling process, its output can be considered to reflect the performance of the model as a whole, and most model validation efforts have traditionally focused on generating accurate link volumes. Barton-Aschman Associates and Cambridge Systematics (1997) suggest three measurements for validating link volumes: Comparing observed and estimated volumes by screen line where a reference of 5% divergence is targeted. Comparing observed versus estimated volumes for all links with counts. To compute aggregate statistics for validating traffic assignment results, the Percent Root Mean Square of the Error (%RMSE) is proposed according to (4): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P n ðx i Obs i Þ 2 %RMSE ¼ i¼1 P 1 n n i¼1 n 1 Obs i where X i is assigned traffic and Obs i observed traffic at link i. Theoretically, the nominator in (4) consists of the standard deviation and bias, since ðx i Obs i Þ¼ððX i XÞþðX Obs i ÞÞ. The denominator is simply the average of observed values. Comparing the R 2 (Coefficient of Determination) region-wide traffic counts and estimated values. Barton-Aschman Associates and Cambridge Systematics (1997) suggest that R 2 should be greater than Additionally, a scattergram of the counts versus assigned volumes should be drawn and points lying outside a reasonable boundary of a 45 degree line are recommended for review. The UK Department of Transport (DoT) (1996) offers two methods for comparing modelled values against observations: Calculating the GEH statistic according to (5): vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uðx i Obs i Þ 2 GEH ¼ t ¼ jx i Obs i j qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðx i þobs i Þ ðx i þobs i Þ 2 2 The GEH values can be calculated either for individual links or for a screen line. It is assumed that, being a special case of the more general ð4þ ð5þ

11 gamma distribution G(k, b) withk=1/2 and b=2, the GEH statistic follows a chi-squared distribution v 2 ð1þ. For individual flows, the UK DoT requires that the GEH statistic be less than 5, corresponding to v 2 97:5% ð1þ, and for screen lines with more than five links, the GEH statistic should be less than 4, corresponding to v 2 95% ð1þ in 85% of cases. Plotting modelled values against observed values and carrying out linear regression analysis. The Coefficient of Determination R 2 of the best-fit regression line through the origin should be above 0.90 and the slope between 0.9 and The %RMSE (4) is dominated by discrepancies on high-volume links and, therefore, it seems to work best on samples of similarly sized road stretches. Since 1=2ðX i þ Obs i ÞObs i, the estimated volume X i in the GEH statistic (5) approximately follows a gamma distribution: jx i Obs i j pffiffiffiffiffiffiffiffiffi 2 G 1 Obs i 2 ; 2 )jx i Obs i j2g 1 2 ; 2 p ffiffiffiffiffiffiffiffiffi Obs i 381 However, a normal distribution of estimated link volumes is more usually assumed, and the weaknesses of GEH and %RMSE will be discussed and assessed in the validations below. The methods are applied in the model validation of transit assignment (Section 4.2), car assignment (Section 4.3), and slow mode assignment (Section 4.4). ð6þ 4.2. Validation of transit assignment The bus company in the GCA performs systematic, periodical, automatic, onboard bus counts. The Danish State Railway counts train passengers once a year, on the Tuesday in the first week of November. However, no transit data are available for passenger km and passenger hours. For the model validation, 103 bus passenger link counts and 29 train passenger link counts are available for an average workday in The distribution of bus links is as follows: 52 in the downtown area, 33 in suburban areas, and 18 in rural areas. The corresponding figures for train links are 17, 7 and 3, respectively. The hourly volumes, which were not available to this study, were approximated by dividing the daily volumes by 32 (16 daytime hours, from 6 a.m. to 10 p.m., multiplied by two directions). Table 5 shows the statistical validation of bus and train passenger assignment. For bus passengers, the poor %RMSE range from 29% to 64% is due to rather low bus passenger volumes, particularly in rural areas. The %RMSE for train passengers is much lower due to accurately estimated high traffic volumes.

12 382 Table 5. Statistical validation of assigned bus passengers in Area Bus Train Observations %RMSE GEH<5 (%) Observations %RMSE GEH<5 (%) Downtown Suburban Rural Total The GEH statistic in the table is less than 5 in 74% of the 103 bus links and does not comply with the 85% requirement, which is only achieved for links in the suburban area. The train assignment also falls short of the GEH statistic threshold. The figures in Table 5 show that the performance of the transit assignment model is unacceptable according to the boundaries set by Barton-Aschman Associates and Cambridge Systematics (1997), and the UK DoT (1996). The validation procedures are primarily developed on the basis of car traffic. Since car assignment performance is usually higher than the more complex transit assignment, it seems appropriate to reduce threshold requirements when applied in validation of transit assignment. However, we conclude that the accuracy in assigning downtown transit users is inadequate at the link level. Figure 2 plots modelled bus passenger volumes against observed values, and Table 6 shows the best fit of a linear regression through the origin. Figure 2. Assigned versus observed bus passengers.

13 383 According to these sources, the bus passenger flows on links in the downtown area are overestimated while those on links in rural areas are underestimated. The Coefficient of Determination R 2 is low in rural areas, and the line of regression is therefore not a good estimate. The same procedure as above is used for train passenger assignment in Figure 3 and Table 6. The accuracy of assigned train passengers is better than for bus passengers, although there appears to be some underestimation in downtown and suburban areas. The underestimation of train passengers in these two areas is probably due to an incorrect split between bus and train caused by the simplicity of the transit assignment procedure, e.g. comfort and timetables are not considered. Figure 3. Assigned versus observed train passengers. Table 6. Linear regression analysis through the origin based on estimated versus observed directional hourly bus passenger volume. Area Bus Train Observations Slope R 2 Observations Slope R 2 Downtown Suburban Rural Total

14 Validation of car assignment The Danish Road Directorate and the Copenhagen Municipality conduct annual vehicle traffic counts on predefined road links. To validate the car traffic model on an average workday in 2000, 395 road link statistics were used, and the estimated directional peak hour flows were compared with 178 (8--9 a.m.) and 179 (4--5 p.m.) road links automatically counted and averaged over Manual one-day counts were only used in the validation of average workday flows due to considerable uncertainty in the observed peak volumes. In Figure 4, the modelled daily volumes are plotted against observed values illustrated with reasonable boundaries. Since the best fit of a linear regression through the origin results in a slope of 0.99 and R 2 =0.95, the guidelines for slope and Coefficient of Determination recommended in Section 4.1 are met, indicating no apparent over- or underestimation. In Figure 5, a similar procedure has been used to illustrate directional peak hour flows (8--9 a.m. bullet and 4--5 p.m. cross). The model underestimates the large morning and afternoon peak hour volumes resulting in a best-fit regression slope of 0.83 (R 2 =0.87). The low peak shares in the observed pivot point matrices of 1992, indicating a proportionately higher increase of commuters on motorways over the period , may explain why the model does not meet the requirements of Section 4.1. Another likely explanation is a faster decline in car occupancy in long-distance commuter traffic relative to other travel purposes. Figure 4. Assigned versus observed daily car traffic volume.

15 385 Figure 5. Assigned versus observed directional peak hour car traffic volume. In Table 7, the GEH statistic is less than 5 in 51% of the 178 road links and 40% of the 179 road links, which is unacceptable according to the required 85% threshold. The %RMSE test also shows significant divergences. Table 8 shows the GEH statistics and relative divergences for a set of 16 screen lines across the GCA. Only a small share of screen lines meet the requirements of GEH<4 and show a divergence less than 5%. The relatively poor results may primarily be explained by the poor basis of peak hour data as mentioned above. However, it should be stressed that we would expect less accurate results in forecasting year 2000 than in base year The results also reflect some of the weaknesses of %RMSE and GEH, since %RMSE is dominated by discrepancies on high-volume links (Figure 5) and GEH boundaries seem most likely achievable at low volumes. Finally, we used the GEH statistics by converting daily volumes into average directional hourly day-time flows similar to Section 4.2. This statistic implies that % of the road links in the three counties of the GCA Table 7. Statistical validation of assigned car traffic in 2000 by road link. Area Observations GEH< a.m a.m. (%) %RMSE Observations GEH<5 %RMSE 8--9 a.m p.m p.m. (%) 4--5 p.m. Central municipalities Copenhagen County Frederiksborg County Roskilde County Total

16 386 Table 8. Statistical validation of assigned car traffic in 2000 by screen line. Screen line Observations 8--9 a.m. GEH 8--9 a.m. Divergence 8--9 a.m. (%) Observations 4--5 p.m. GEH 4--5 p.m. Divergence 4--5 p.m. (%) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )12.4 achieve values below 5. Only the estimated flows in central municipalities seem not to meet the requirements. At 21% of daily flows, the %RMSE reflects some accurately estimated high traffic volumes in suburban areas (13%) and less accurate estimates in the central districts (25%) Validation of bicycle and walk assignment results The OTM s assignment model for slow modes (cycling and walking) is an allor-nothing model based on the shortest travel time. Little attention was paid to these two modes in the model estimations predominantly due to the lack of observed data. Even in the SP experiments completed under the OTM, walking and cycling are presented only in the context of across-mode experiments, i.e. no within-mode SP experiments were completed for the two modes. Table 9 shows available observed bicycle and walk trips across Knippelsbro and Langebro bridges (the harbour corridor in the city area) in 2000 compared with estimated volumes. The figures in the table show that bicycle traffic over the harbour corridor is overestimated by some 13%, where the vast majority of missing traffic is related to the Langebro bridge. The volume of observed walk traffic in the corridor is about 15% of bicycle traffic. The corridor walk traffic is largely underestimated by the OTM. This time the mismatch occurs on the Knippelsbro bridge. In total, the model overestimates the slow modes traffic in the Harbour corridor by 5%.

17 Table 9. Observed and estimated daily flows by bicycle and walk across Knippelsbro and Langebro bridges, Observed Estimated Divergence (%) Knippelsbro, bicycle 23,465 24, (2.7) Langebro, bicycle 21,912 27,040 5,128 (23.4) Bicycle, total 45,377 51,137 5,760 (12.6) Knippelsbro, walk 4,889 1,898 )2,001 ()61.2) Langebro, walk 2,164 2,034 )130 ()6.0) Walk, total 7,053 3,932 )3,121 ()44.2) Slow modes, total 52,430 55,069 2,639 (5.0) 387 The doubtful modelling of slow modes is a serious shortcoming of the OTM because bicycling, in particular, is an important mode in Copenhagen and, up to certain distances, a popular alternative to public transport modes. 5. Model validation for Non-metro modes Table 10 shows the relative change for observed versus modelled traffic for car, train, bus and bicycle modes in the GCA for the period Note that train traffic includes trips by the Copenhagen city train (S-train) and regional trains within the GCA. According to the table, the OTM forecasts are higher than the observed traffic changes for car, train and bus modes. The country s stagnant economy in this period provides a possible explanation, i.e. the GDP figures remained almost unchanged after 2000, while GDP had grown by almost 2% annually prior to this period (Danish Statistical Bureau 2004). The train and metro have experienced a long period of unreliable operations, which may also have negatively affected ridership. Finally, the observed increase in transit fares is not taken into account in the model, where the travel costs are kept constant by the scenario definitions specified by the client. Table 10. Modelled versus observed traffic changes in the period Modes Observed (%) OTM forecast (%) Car Copenhagen city train (S-train) )2 +11 Regional train Bus )21 )6 Bicycle +6 +2

18 Assignment model for the metro Phase 1 of the metro opened in October In 2003, screen line counts were conducted once a week, rotating between weekdays. In most cases, counts were located on the stretch between Nørreport and Kongens Nytorv stations (sample counts), and metro passenger estimates were computed from the sample counts. Total counts (all metro stations) of boarding passengers have only been conducted a couple of times to date owing to the high costs associated with conducting this type of count. Following an initial running-in process, the metro became fully operational in mid-january As the summer and autumn of 2003 were characterised by the opening of new metro phases and unstable operation, model validation is only possible on the basis of counts from the first months of Table 11 shows available metro passenger counts for February and March A total count was conducted on 6 February 2003 when 50,354 metro passengers were counted. On average, 55,000 metro passengers travelled on a workday in the counting period. That is 5,900 passengers fewer, or 10.7%, than the traffic flow predicted by the OTM. The general overprediction by the model was mainly caused by incorrect forecasts at Lergravsparken and Island Brygge metro stations. Lergravsparken is the terminus of the line M2, and until the second week of January 2003, headways were 12 minutes in peak periods and 16 minutes in out-of-peak periods, which is considerably worse than the pre-existing bus service frequency. After the second week of January 2003, headway improved to 6 minutes in peak periods and 8 minutes in out-of-peak periods. Thus, the disappointing metro service had a longer- term effect. The Island Brygge metro station is the station closest to the University of Copenhagen, Amager, and the model predicted that many students would shift to the metro here. This seems not to have been the case. The overprediction of metro flows is also related to the fact that the model overpredicts bus and train traffic (see Table 10). Passengers using these two modes were expected to transfer many of their trips to the metro (Vuk 2005). In 2003, the metro was extended to Vanløse station in Phase 2. In early 2004, a new interchange station was opened at Flintholm, connecting the Table 11. Metro passenger counts. February ,054 March ,795 Average workday 54,925 Number of passengers

19 389 metro to the existing S-train network and a new S-train line around Copenhagen. During the first half of 2004, the metro service continued to be rather unreliable but performance improved significantly in fall 2004, and the number of passengers rose. The metro boarding and alighting passenger counts are now automatically conducted at each station. Due to poor service performance and the gradual extension of the metro system, it is difficult to compare the observed and predicted metro passenger flows. In March 2005, the metro recorded 130,000 passengers in an average workday compared with a forecast of 198,000 passengers. The high overprediction can largely be attributed to four main factors. First, the negative transit trend in the period (Table 10) had a substantial impact on the number of metro passengers. Second, the unreliable metro service delays the process of adapting to the new system. Third, it seems that overpredictions primarily relate to phase 2 of the metro (the connection of Vanløse station to Forum station), implying an inaccurate data foundation. Fourth, the bus counts at certain links show that many bus travellers still have not switched to the metro, as predicted by the model forecasts. 6. Conclusions The paper validated the OTM, the passenger traffic model for Copenhagen, for the years The validation procedure for the year 2000 is twopronged. First, the observed travel behaviour from the 2000 national travel survey, which is external to the model, was compared with the results of the generation, distribution and modal split models. Second, the car and transit assignment forecasts were tested against the traffic counted in With respect to the validation of the demand sub-models, we conclude that a tour-based demand model structure of the OTM, in which there is logsum feedback between the sub-models, produces satisfactory results for the following two main reasons. First, the modelled 2000 trip rates, as forecast by the generation model, closely approximated observed trip rates at both national and international levels. However, the forecast trip rate for home-work/education trips was somewhat higher than the observed 2000 trip rate. Because the OTM applies a pivot point procedure in each of the sub-models, the trip pattern is strongly influenced by the base 1992 trip matrices. In conclusion, it seems that the model s pivot point procedure has a tendency to split long home-work/education trips into two or more subtrips, thus resulting in higher trip rates and shorter trips than observed. Second, the differences between the forecast and observed modal split for the year 2000 were small. While the modal shares for car and transit modes

20 390 were almost identical in the national travel survey and the OTM, the differences were slightly greater for bicycle and walk modes. The reason is that the trade-off between these two modes has never been investigated in the walk-bicycle across-mode SP experiments. The modal shares for these two travel modes were therefore largely explained in the OTM by their alternative specific constants. The sensitivity analysis showed that car cost direct demand elasticity was considerably lower than transit fare direct elasticity, which can be explained by the difference in income between the two groups of travellers. With respect to the validation of the assignment forecasts for the year 2000, the overall conclusion was that the car assignment model performed better than the transit assignment model. The car assignment model is fairly complex in structure while the transit assignment model uses a simple simultaneous mode/route procedure. The car assignment model met the accuracy threshold values of the applied statistics with respect to 24-hour traffic. However, the analysis of directional peak hour car traffic shows greater discrepancies between the observed traffic and the modelled traffic at 16 screen lines in the analysis area, where the model underestimated observed traffic. The forecast car peak traffic in the OTM is calculated on the basis of the observed percentage shares of the peak traffic in the 1992 base matrices, which seem inaccurate and outdated. The overall performance of the transit assignment model was not entirely satisfactory, particularly for the assignment of bus trips. The statistical test concerning the correspondence of the model results with observed values showed large deviations in the downtown area. The model seems to overpredict metro passenger flows by 11% in early In March 2005, the model overpredicted metro passenger flows by 50% due to factors such as the negative transit trend in Copenhagen over the period and unreliable metro services. The efforts to validate the OTM revealed a need to update the base 1992 matrices if the pivot point procedure is to be maintained. The 1992 matrices include outdated flows and inappropriate peak shares. The validation conducted has also taught us that future modelling work should pay more attention to the importance of regularity and the period of adapting to the new travel mode in order to provide ideas for improving the transit assignment model (e.g. a time-table based assignment) and establishing a model for choice of time of day. In this area, an activity-based approach to modelling travel demand might be necessary. An update of the model s trip matrices was initiated in a project started in January 2005 while the model update itself is currently being discussed by researchers and the Danish Ministry of Transport.

21 391 We wish to stress the importance of conducting model validation, often neglected in practical model development. Validation should include three main tasks: an assessment of the coefficients used in model estimation, a test of the model system and sensitivity, and a validation of results versus observed behaviour. We recommend that the design of the validation procedure should already be addressed in the planning phase of model development and should focus on: The importance of validating all model parts and not only the assignment models, as is usually the case. According equal weight when validating the model for the base year and forecasting/backcasting years in a dynamic procedure. The importance of validating transit traffic and slow modes (bicycle and walk) relative to the objectives of urban traffic models. Resources (budget) for assembling appropriate validation data. Finally, procedures and a methodological framework for model validation need to be further developed. In the paper, we applied the usual procedure for assignment validation, including GEH and %RMSE statistics. Those tests miss some basic features such as statistical foundation and assessment of biases due to the numerical formation and they cannot, therefore, be used without supplementary validations. Note 1. AKTA ( is a research study under the EU project PROGRESS ( which is part of the EU s 5th framework programme The Growth Programme on Sustainable Mobility and Intermodality (Nielsen & Jovicic 2003). References Barton-Aschman Associates and Cambridge Systematics (1997) Model Validation and Reasonableness Checking Manual. Travel Model Improvement Program, U.S. Department of Transportation. Daganzo CF & Sheffi Y (1977). On stochastic models of traffic assignment. Transportation Science 11(3): Danish Statistical Bureau (2004) A databank available at the Danish Statistical Bureau s website ( Danish Transport Research Institute (2003) Danish National Travel Survey Summary tables. Jovicic G & Hansen CO (2003) A passenger travel demand model for Copenhagen. Transportation Research, Part A 37:

22 392 Jong GC & Tegge O (1998) TRACE, Cost of Private Road Travel and Their Effect on Demand, Including Short and Long Term Elasticities. European Commission Directorate-General for Transport. ( Nielsen OA (1997) On the distribution of the stochastic component in SUE traffic assignment models. European Transport Forum (PTRC Annual Meeting). Seminar F, Transport Planning Methods vol. II, (pp ), Uxbridge, UK. Nielsen OA, Frederiksen RD & Daly A (2002) A Stochastic Route Choice Modsel for Car Travellers in the Copenhagen Region. Networks and Spatial Economics no. 2, (pp ), Kluwer. Nielsen OA & Jovicic G (2003) Sensitivity of variable definitions in SP analyses -- An empirical study of car-users evaluation of length cost and time components. 10th International Association for Travel Behaviour Research Conference. Switzerland. Sheffi Y & Powell WB (1982).An algorithm for the equlibrium assignment problem with random link times. Networks 122: UK Department of Transport (1996) Traffic Appraisal in Urban Areas, volume 12 Section 1 of the Design Manual for Roads and bridges (DMRB v12s1). Vuk G (2005) Transport impacts of the Copenhagen metro. Journal of Transport Geography 13: About the authors Goran Vuk is a senior adviser at the Danish Transport Research Institute and a senior consultant in a traffic planning company TetraPlan A/S. A graduate civil engineer, he received PhD in travel demand modelling at the Technical University of Denmark in He has been involved in a number of major modelling projects in Denmark such as the Danish National Value of Time, the Copenhagen Metro and the Great Belt project. His current research is focused at activity based passenger demand modelling. Christian Overgaard is an Associate Professor at the Centre for Traffic and Transport, Technical University of Denmark, and Director of COH ApS. A graduate civil engineer, he received PhD at the Technical University of Denmark in 1986 followed by a post doc. study at the University of California. After working at the Danish Road Administration and Carl Bro A/S, he co-founded TetraPlan A/S in He has been responsible for a number of major modelling projects e.g. the passenger model for Copenhagen (OTM).