Spatio-temporal modelling and prediction of bus travel time using a higher-order traffic flow model

Abstract

Accurate bus travel time prediction in real-time is challenging, as numerous factors such as fluctuating travel demand, incidents, signals, bus stops, dwell times, and seasonal variations can affect travel time, a spatio-temporal variable. Literature that considered the spatio-temporal evolution of bus travel time adopting traffic flow theory-based models investigated one-equation models (also widely known as first-order model) predominantly while the two-equation models (commonly known as higher-order models) have not been sufficiently explored due to their complex structure, parameters to calibrate, hardship in obtaining the data, and difficulty in discretizing and solving. Motivated by this, the present study explores the suitability of higher order traffic flow models for the prediction of bus travel time. This study adopted a well-known two-equation model ‘Aw-Rascle model‘ (Aw and Rascle, 2000), which addressed most of the limitations of the previous models, and discretized using a Finite volume method to preserve the conservational properties of Partial Differential Equations (PDE). As Global Positioning System (GPS) is a widespread data source for transit systems, the identified model was rewritten in terms of speed by adopting a suitable pressure function. The discretized model was represented in the state-state-space form and integrated with a filtering technique using appropriate inputs, to facilitate real-time implementation. The performance of the proposed methodology was evaluated and compared with a first order model (Lighthill Whittam Richards (LWR) model) based approach to understand the efficacy of the higher-order models in travel time prediction. The prediction accuracy in terms of Mean Absolute Percentage Error (MAPE) was around 14% for the proposed methodology with an absolute deviation of around +/-1.2 min, which was better than the existing LWR model-based prediction method. The developed real-time prediction methodology is a promising one to be integrated with Advanced Public Transportation Systems (APTS) applications.