ACabrejas / IEEE_ITSC2020_WARP

Presented in IEEE ITSC2020 (Sep'20) Pre-print version and code. WARP: Wavelet Augmented Regression Profiling

Wavelet Augmented Regression Profiling (WARP): improved long-term estimation of travel time series with recurrent congestion

This repository contains the code and paper to be presented at the Intelligent Transportation Systems Conference 2020. All intellectual property here contained belongs to Alvaro Cabrejas Egea, the Centre for Complexity Science (University of Warwick), The Alan Turing Institute and IEEE.

This repository the paper "Wavelet Augmented Regression Profiling (WARP): improved long-term estimation of travel time series with recurrent congestion", accepted to 23rd IEEE International Conference on Intelligent Transport Systems (ITSC) 2020 as a pre-print, and the code that generated the results it presents for open replication purposes.

Full paper IEEE pre-print Version: Read PDF.

Full paper ArXiv pre-print Version: Read PDF.

Goals in short

Take a dense time series of motorway travel times. Perform a continuous wavelet transform. Calculate the power of each frequency-time pair and identify outliers (median+iqr), set them to the maximum threshold, while the difference with this value is taken into the Spikes series. Inverse transform both series, separating in this manner the recurrent from outstanding congestion. Use this separated series to train a forecasting algorithm with 8 weeks of data and predict the following 4. Assess the accuracy of the forecast, comparing with the published profiles and a null method.

Abstract in Full

Reliable estimates of typical travel times allow road users to forward plan journeys to minimise travel time, potentially increasing overall system efficiency. On busy highways, however, congestion events can cause large, short-term spikes in travel time. These spikes make direct forecasting of travel time using standard time series models difficult on the timescales of hours to days that are relevant to forward planning. The problem is that some such spikes are caused by unpredictable incidents and should be filtered out, whereas others are caused by recurrent peaks in demand and should be factored into estimates. Here we present the Wavelet Augmented Regression Profiling (WARP) method for long-term estimation of typical travel times. WARP linearly decomposes historical time series of travel times into two components: background and spikes. It then further separates the spikes into contributions from recurrent and residual congestion. This is achieved using a combination of wavelet transforms, spectral filtering and locally weighted regression. The background and recurrent congestion contributions are then used to estimate typical travel times with horizon of one week in an accurate and computationally inexpensive manner. We train and test WARP on the M6 and M11 motorways in the United Kingdom using 12 weeks of link level travel time data obtained from the UK's National Traffic Information Service (NTIS). In out-of-sample validation tests, WARP compares favourably to estimates produced by a simple segmentation method and to the estimates published by NTIS.

Contents

• Paper folder: Latex template with the pre-print of the IEEE version of the full. paper
• Paper_arXiv folder: Latex template with the ArXiv version of the full paper
• Code folder: Scripts used to obtain all graphs in the paper. These should be run in order.

Running the code

1. Open R and Run 01Export_Link_to_CSV.R

• Input : Clean Travel Time data
• Output:
  1. One CSV file per link containing the Travel Time
  2. Example plots of travel times

2. Open MATLAB and Run 02Separate_Background_Spikes.m

• Input : One CSV per link containing Travel Time data
• Output: Structured in a different folder per wavelet used
  1. Two CSV files per link. One containing the background and the other containing the Spikes
  2. One plot per link showing Original Travel Time and Reconstructed Series
  3. One plot per link showing the difference between Original and Reconstructed Series

3. Go back to R and run 03Profiles_calculation.R

• Input :
  1. Clean Travel Time Data
  2. Two CSV files per link. One containing the background and the other containing the Spikes
• Output:
  1. Plots for Mean Relative Absolute Error (MARE) across the times of the day in three flavors (Normal, Only Negative (Overprediction), Density Scaled)
  2. Plots for MARE or Root Mean Squared Error (RMSE) measured from quantiles 1, 95, 99, and a user defined one (default:50)
  3. Plots for the MARE as a timeseries for the 4 predicted weeks in three flavors (Normal, Only Negative (Overprediction), Density Scaled.

4. In R, run 04Plot_wavelet_decomposed.R

• Input :
  1. Clean Travel Time Data
  2. One CSV files per link containing the Background Series
• Output:
  1. Spectrogram with timeseries data for the Original Travel Time
  2. Spectrogram of Wavelet Transform with timeseries data for the Background Series (Spikes identified and removed)

5. In R, run 05Precision_measurements.R

• Input : Workspace from step 4.
• Output:
  1. MARE and RMSE error per link
  2. Average MARE and RMSE error per motorway
  3. Histogram of errors
  4. Table with % of samples following within different precision limits