The uncertainty associated with public transport services can be partially counteracted by developing real-time models to predict downstream service conditions. In this study, a hybrid approach for predicting bus trajectories by integrating multiple predictors is proposed. The prediction model combines schedule, instantaneous and historical data. The contribution of each predictor as well as values of respective parameters is estimated by minimizing the prediction error using a linear

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... heuristic. The hybrid method was applied to five bus routes in Stockholm, Sweden, and Brisbane, Australia. The results indicate that the hybrid method consistently outperforms the timetable and delay conservation prediction method for different route layouts, passenger demands and operation practices. Model validation confirms model transferability and real-time applicability. Generating more accurate predictions can help service users adjust their travel plans and service providers to deploy proactive management and control strategies to mitigate the negative effects of service disturbances. predictions of downstream conditions facilitate the deployment of proactive management and control strategies designed to mitigate the negative effects of service disruptions. Several methods have been introduced for bus downstream trajectories prediction in the last two decades, all aiming at providing fast and more accurate travel time prediction in various prediction circumstances (e.g. prediction horizon, route characteristics, traffic condition and data availability). However, it is still contentious to choose the 'best model' being capable of delivering fast and accurate prediction over a wide range of transportation networks. Moreover, existence of such model is doubtful and unverified in the literature [4] . Hence, development of a fusion framework, in which the advantage of different models and data sources considering the targeted prediction circumstance are combined, is highly desirable. The combination process has been generally performed in two different ways: serial and parallel. In the first way, two methods are employed with a different functionality. The former is implemented to pre-process, simplify or group the input data (e.g. clustering to diminish the number of data features). The latter method then obtains predictions using the first method output [5, 6] . In a parallel way, two (or more) models are parallely implemented to sum up the advantages of each individual model [7, 8] . In this study, the second approach is considered, because the relevant data are wildly available in the appropriate format and can therefore be integrated simultaneously to improve the performance of the prediction models. This study proposes a hybrid prediction model that combines the advantages of three independent prediction methods. The hybrid model integrates prediction methods, which are based on schedule, instantaneous and historical. In the training phase, a weight for each prediction method is determined by a heuristic algorithm on the basis of its prediction error. Prediction is performed on a rolling horizon basis with each prediction projecting the remaining bus trajectory (i.e. departure time predictions for all the downstream stops). Previous work tested the feasibility of estimating parts of the prediction model using a genetic algorithm [9] and compared the performance of the model from passengers' and operators' perspective when estimated for each route separately as opposed to joint estimation [10] . This study builds up on the rolling horizon prediction approach while devising an efficient model calibration technique and performing an extended validation. The main contribution of this study is developing and implementing a methodology for integrating and estimating the contribution of different prediction models and data sources while satisfying practical requirements related to the generation of real-time information. In addition, the prediction model is calibrated and validated on the basis of data of five routes from two public transport systems, confirming method transferability. This study builds up on our previous works [9, 10] by devising a hybrid prediction model with significant advances in prediction methodology, parameter calibration and an extended validation. The remaining of this paper is organized as follows: we first review previous studies in the context of bus travel time prediction (Section 2). Then, the proposed hybrid prediction method is described in detail (Section 3). Five bus routes in two case study areas, Brisbane and Stockholm, are described (Section 4), followed by an explanation of implementation details including data processing and specifications for the optimization process (Section 5). Then, the proposed method is applied to the case study routes, and the results are benchmarked against the currently deployed prediction methods in Brisbane and Stockholm (Section 6). Finally, we conclude with an overall assessment of the proposed approach, discuss its advantages and shortcomings and outline directions for further research (Section 7). LITERATURE REVIEW Previous research in traffic predictions has developed a large range of methodologies that are often categorized into data-driven and model-driven methods. Data-driven methods are generally empirical models that statistically model the relationships between the variables. Such models can be classified into parametric and non-parametric models. Parametric methods are based on a structural pre-defined function with a number of independent variables, whereas the structure and parameters of the model are mined from data in the case of non-parametric methods. In the context of bus travel time predictions, the two most commonly used parametric models are linear regression models and time-series models. Linear regression models formulate bus travel time as a linear function of independent variables [2, 11, 12] such as distance, 2131 HYBRID SCHEME FOR REAL-TIME PREDICTION