Abstract
In recent years, the problem of bus travel time prediction is becoming more important for applications such as informing passengers regarding the expected bus arrival time in order to make public transit more attractive to the urban commuters. One of the popular techniques reported for such prediction is the use of time series analysis. Most of the studies on the application of time series techniques for bus arrival time prediction used Box-Jenkins AutoRegressive Integrated Moving Average (ARIMA) models, which are presently not suited for real time implementation. This is mainly due to the necessity and dependence of ARIMA models on a time series modelling software to execute. Moreover, the ARIMA model building process is time consuming, making it difficult to use for real-time implementations. Alternatively, Exponential Smoothing (ES) methods can be used, as they are easy to understand and implement when compared to ARIMA models. The present study is an attempt in this direction, where the basic equation of ES is used, as the state equation with Kalman filtering to recursively update the travel time estimate as the new observation becomes available. The proposed algorithm of state space formulation of ES with Kalman filtering for bus travel time and arrival time prediction was field tested using 105 actual bus trips data along a particular bus route from Chennai, India. The results are promising and a comparison of the proposed algorithm with ES alone without state space formulation and Kalman filtering has also been performed. An information system based on a webpage for real-time display of bus arrival times has been designed and developed using the proposed algorithm.
Highlights
In recent years, the problem of bus travel time prediction is becoming more important for applications such as informing passengers regarding the expected bus arrival time in real time to make public transit more attractive to urban commuters
Using the best performing Exponential Smoothing (ES) combined with Kalman Filtering Technique (KFT) method, a web application was developed in the present study to inform commuters the Expected Arrival Time (ETA) at any chosen bus-stop in 5C route
Concluding Remarks The bus travel time prediction is an important component in bus arrival prediction applications such as providing accurate bus arrival time information using Variable Message Signs (VMS) or web pages in order to attract more public transit users, which help to reduce congestion on the urban roads
Summary
Jeong, Rilett 2005; Yu et al 2006, 2010a, 2010b, 2011; Seema, Alex 2009; Gurmu 2010; Mazloumi et al 2012; Raut, Goyal 2012; Lin et al 2013) and support vector machines (Yu et al 2006, 2010a, 2010b, 2011, 2014), model based approaches using Kalman filtering (Wall, Dailey 1999; Cathey, Dailey 2003; Shalaby, Farhan 2004; Vanajakshi et al 2009; Padmanaban et al 2010; Sun et al 2011; Gao et al 2013), statistical methods such as regression analysis (Patnaik et al 2004; Shalaby, Farhan 2004; Jeong, Rilett 2005; Yo et al 2009; Yu et al 2011) and time series techniques (Rajbhandari 2005; Yu et al 2010a, 2010b; Suwardo et al 2010; Chen et al 2012; Kumar, Vanajakshi 2012) and other techniques like nonparametric regression (Chang et al 2010) and k-nearest neighbours (Yu et al 2011). The studies on the application of time series technique to the problem of real time bus travel time/arrival time prediction is very limited. The proposed model does not require any specialized time series modelling software and a few lines of code in any programming language would be enough to run the recursive equations of Kalman filtering with real time data as inputs. The proposed algorithm of state space formulation of ES with Kalman filtering for bus travel time and arrival time prediction was field-tested using 105 actual bus trips data along a particular bus route from Chennai, India. The data extraction involved extracting each 100 m section travel time along the study stretch and arrival time at 21 bus stops for all the 105 trips of the five days considered
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