1. Short term forecast of travel times on the Danish highway network based on TRIM data Klaus Kaae Andersen Thomas Kaare Christensen Bo Friis Nielsen Informatics and Mathematical Modelling Technical University of Denmark Viking Workshop October 2005

2. Background/Motivation The high way network in the Copenhagen area is equipped with double induction loop detectors. From this measurement system data on each passing single vehicle (e.g. speed and length) is collected. The data is referred to as the TRIM data Travel time estimates and travel time forecasts are calculated based on the TRIM data and given to the public by means of TV, radio and the Internet The travel time estimates and forecasts are based on data on an aggregated level

3. Study objectives The study objectives are Develop statistical models with aim to identify single vehicles between induction loops from the TRIM data. Hereby, the travel time between loops can be estimated directly Estimate the variability in travel times Validate the accuracy and precision of the current methods for travel time estimation and prognosis Develop new methods as an alternative to the currently used methods

4. Outline of the presentation The Data Modelling method -Pattern recognition methods based on statistical methods, dynamical modelling EWMA Results - Percentage recognized vehicles, accuracy and precision, implementation Comparison with existing methods Future work

5. TRIM data For each passing vehicle the system measures: - Time - Speed - Length - Gap … The travel times can not be estimated directly from these data!!

6. Data We are considering a stretch of the high way network (Jægersborgvej to Hillerødmotorvejen) Data is TRIM data 1)Empirical data (measurements from TRIM) 2)Simulated data (from the program VISSIM)

7. Empirical data - Time - Speed - Length - Gap …

8. Simulated data Data from the same stretch has been generated using the micro simulation program VISSIM The simulated data match the empirical data well The advantage in using simulated data is that each passing vehicle can be identified – thus the modelling method can be validated!!

9. Induction-loop data - Time - Speed - Velocity - Gap … Loop 1 Loop 2

10. Modelling method The aim is to develop a statistical method for identification of vehicles at successive loops and hereby allow for a direct estimation of the current travel time between loops The focus is on: -Pattern recognition of non-typical vehicles (non typical in terms of vehicle lengths) -Develop a statistical measure for how well a vehicle ’match’ another vehicle -Develop a dynamical model for estimation of forecasting purposes

11. Pattern recognition The vehicles are identified from the measured lengths The identification has to be unique, thus it is not possible to match every passing vehicle: 1)Sequences of vehicles (e.g. 4 passing vehicles in a sequence) 2)Long vehicles (i.e. Big trucks)

12. Identification based on sequences Assume, that 4 vehicles are registered at loop 1 having the lengths L={L1, L2, L3, L4} Subsequently, 4 vehicles are registered at loop 2 having the lengths L’={L1’, L2’, L3’, L4’} The corresponding ‘match’ (denoted M) is calculated as:

13. Identification based on sequences If M is less than the statistical measurement precision U, the sequence is defined as a ’possible match’ For each passing sequence a possible match is searched for (within a given time window) If only one ‘possible match is found’ then this is defined a a ’unique match’ From unique matches the travel time S is calculated

14. Problems and error sources It is not possible not identify a sequence if vehicles within the sequence change lane in between loops It is not possible to identify large vehicles or sequences if the measurement error is too large A non-correct sequence may falsely be classified as a correct sequence

15. Estimation of travel time The travel time at time i, T i, is estimated using an Exponentially Weighted Moving Average (EWMA) model: is the forgetting factor andS i is the current estimated travel time from the identification of non-typical vehicles. T i-1 is the travel time at time (i-1), thus the travel time 1 time instant before

16. EWMA and time window time Estimated Travel Time Statistical Uncertainty

17. Results (simulated noise-free data) Number in sequence 234567 Correctly identified 20291603897581409269 Identified in total 32841887970611424281 % Correct 61 %84 %92 %95 %96 %

18. Results

21. Computational speed and implementation Implementation of the algorithm is simple The estimation of travel time is only necessary when there is congestion Time needed for computation is not relevant (the algorithm is very fast for given and small intervals)

22. Future work: forecasts Short term forecast Pattern recognition EWMA Historical data: Travel times, accidents, weather etc Long term forecast

23. Travel time for longer distances For longer distances it must be expected that fewer sequences can be identified Methods for interpolation and estimation of travel time for longer distances will be validated

25. Conclusion The proposed method makes it possible to identify non-typical vehicles from loop to loop Thus it is possible to estimate the travel time between loops with reasonable precision Future work includes estimating the time for longer distances and validating the method using camera data