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

• 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?