## Automatic OD-matrix Estimation Based on Counting and Weighing Trains

### Authors

O Anker Nielsen, Technical University of Denmark, Department of Transport, DK; B Friis Nielsen, Technical University of Denmark, Department of Mathematical Modelling; B Brun, R Dyhr Frederiksen, Rapidis Ltd, DK

### Description

The paper present a new methodology that uses the information from weighing trains combined with a small sample of counting trains to estimate OD-trip matrices on a daily basis.

### Abstract

Origin Destination (OD) matrices are often estimated based on expensive travel surveys. An example is the annual Danish train passenger post card survey, which is carried out a Thursday in November with the cost of 0.5 million Euro. Additional manual counts have to be collected at cross sections in time and space to estimate the annual passenger flows.

An alternative data source is counting trains with either infrared equipment (beams) or automatic video camera passenger detection systems. This is also an expensive data source, e.g. 0.5 million Euro for 8 trains in Copenhagen.

Most modern trains measure the weight of the trains compared to an empty base situation to calibrate the brakes. The Copenhagen S-trains collects this data in the train computer, which is connected to a central server. The Company got the idea to use this information for OD matrix estimation.

The paper first analyses the quality of the data. Manual counts were compared with the counting equipment. Entering and exiting passengers must equal from the start to the end station. It was shown, that the variance of the observations was approximately equal to manual counts. However, the beams had the tendency to have a larger variance per passenger at stations with many entering or exiting passenger, which introduced a systematic error along a given train run. Errors also accumulated along train runs (the volume in a given train is the sum of entering minus exiting passengers). When counts were balanced to fit along a certain train run, this meant that the average absolute error is somewhat larger in the middle of the run.

The weighing trains measure the passenger weight. The small sample of counting trains is used to estimate the weight per passenger. This may vary over the year (people wear more cloth in the wintertime) and geographically (different socio-groups and trip purposes). By comparing manual and automatic counts with the weights it was possible to evaluate the stability of passenger weights. In operation, the automatic counting trains is used to estimate the average weight per passenger in a given time-period along a given rail line. The data analyses revealed that passenger estimations based on weighing trains had a higher variance than the counting trains. However, there was no systematic bias, and the variance was independent on the passenger volumes.

The train data collection system thus consists of about 6% counting trains that are used to estimate boarding and aligning patterns as well as weight per passenger, and a 100% sample of weighing trains. The observations and their variance are fed into the Multiple Path Matrix Estimation Method (MPME, Nielsen, 1998). This methods tries 1) to fit matrices assigned to the network as good as possible to the counts (by minimising the weighted square deviations) at the same time as 2) trying to change a base matrix as little as possible (also by minimising the weighted square deviations). If the counts are consistent, then the first deviation 1) will become zero. MPME uses stochastic user equilibrium traffic assignment model, where the counts along routes are used to estimate the matrix according to the likelihood that the route is used.

A simulation method was used for validation. Here a base matrix was assumed. This was simulated to have seasonal, weekly and daily variation. Hence a ?true? year was simulated. For each day, the simulated true matrix was assigned onto the network. The weighing information was simulated according to the known uncertainty distribution of the weighing system, and a sample of the 6% counting trains was simulated as well. Then MPME was run for each day, and this was repeated for a number of years for different base matrices (ranging from the true November matrix to a uniform matrix). As a comparison, the same simulation approach was used to evaluate the existing system.

The tests showed that the error of the annual passenger estimates based on the new approach was reduced from about 3% to about 0.01%. A further benefit is that the new system estimate daily matrices segmented into 10 min. segments. This provide information on weekly and seasonal variation of passenger flows, that can be used for the overall planning of the train system, for the daily allocation of train coaches (i.e. to vary the length of the trains according to the passenger flows), and to improve the time-tables (e.g. Friday, the weekends and the evenings, where the old survey did not provide valid data on the passenger flows).

#### Publisher

Association for European Transport