Real-time transit network modelling for improved arrival time predictions
IASC-NZSA 2017

University of Auckland

Approx. real-time positions for all of Auckland!

Part 1

Motivation

What's wrong with the current system?

Currently, it works like this …

  1. Bus arrives at a stop, delay is recorded
  2. ETA = scheduled arrival time + delay
  3. Repeat for all stops until it reaches yours …
stop3 stop4

ETAs for a person waiting at the 7:40 stop:

  • Initial expected waiting time: 10 minutes
  • Actual waiting time: 16 minutes

Part 2

Proposed predictive framework

  1. Improved vehicle state model (speed)
  2. Network state model (road travel times)
  3. Predict arrival times using vehicle + network states

1. Bus model: particle filter

  • Flexibility: asymmetry, multimodality
  • Intuitive likelihood: distance between two points
  • Transition function: explicitly model bus behaviour
  • Computationally demanding

1. Bus model: particle filter

$ X_k = \begin{bmatrix} d_k \\ v_k \end{bmatrix} $ $ = f(X_{k-1}) $

$ Y_k $ $ = \begin{bmatrix} \phi_k \\ \lambda_k \end{bmatrix} $ $ = h(X_k) $

$ Y_k | X_k^{(i)}, \Sigma \sim \mathrm{Binormal}(h(X_k^{(i)}), \Sigma) $

$ w_i = \frac{\ell(X_k^{(i)} | Y_k, \Sigma)}{\sum_j \ell(X_k^{(j)} | Y_k, \Sigma)} $

1. Bus model: particle filter

All we need to do is …

  • Model all buses in Auckland (1000+ at peak hour)
  • In real-time, target is 30 seconds or faster

  • Goodbye R, hello C++

2. Network Model

  • Road segment = stretch of road between two intersections
  • Independent of route
  • Network state parameters:
    $\tau_\ell$ = travel time along segment $\ell$
    $\xi_\ell$ = variance of travel time along segment $\ell$
  • Data = estimated travel time of buses along segment
  • Implemented using Kalman filter

2. Network Model

  1. Model all buses in real time
  2. Update network state as buses traverse segments

3: Arrival time prediction

  • ETA = sum road segment travel times
  • Calculate ETA for each particle
    Simulate travel times, stop/traffic light wait times, etc
  • ETA distribution incorporates remaining uncertainty
  • Prediction intervals to communicate to commuters
    e.g., 10-16 minutes vs. 12 minutes
  • Future Work: journey planning?

Questions?

Thank You