Predicting the arrival time of buses

In recent years, vehicle tracking technologies (GPS) have advanced along with communication technologies (internet, mobile apps) to the point where public transport users can see the real-time location of their buses on a map through their phones. However, the information on estimated arrival time (ETA) are still undependable. In place of statistically-founded predictive models that have been used historically, ETAs are often calculated based solely on the vehicle’s current delay, as is the case here in Auckland. These predictions assume that the timetables are accurate (they often are not), and that the delays will not be affected by traffic conditions (they often are). Thus, the predictions are frequently inaccurate and ultimately unreliable.

Modelling network status using real-time data

We have been working on a predictive modeling framework that uses real-time vehicle locations to estimate network state (i.e., bus speeds along roads within the network), which is then used to generate ETAs that reflect current traffic conditions. This involves three stages:

• a vehicle model that uses vehicle location data, freely available via Auckland Transport’s public API, to estimate the vehicle’s state: how far (in meters) it has traveled along the route, its speed, and travel times along the way.
• a network state model that takes the estimated travel times of all vehicles, irrespective of route, and models the current average travel time of transit vehicles traveling along each road in the network; and
• an arrival time prediction model that combines the estimated vehicle state from (1) with estimated travel times from (2) to predict the arrival time at all upcoming stops, taking into account uncertainty due to traffic lights and intermediate stops. (see Figure 1)