Bug triaging is a critical task in any software development project. It entails triagers going over a list of open bugs, deciding whether each is required to be addressed, and, if so, which developer should fix it. However, the manual bug assignment in issue tracking systems (ITS) offers only a limited solution and might easily fail when triagers must handle a large number of bug reports. During the automated assignment, there are multiple sources of uncertainties in the ITS, which should be addressed meticulously. In this study, we develop a Markov decision process (MDP) model for an online bug triage task. In addition to an optimization-based myopic technique, we provide an ADP-based bug triage solution, called ADPTriage, which has the ability to reflect the downstream uncertainty in the bug arrivals and developers' timetables. Specifically, without placing any limits on the underlying stochastic process, this technique enables real-time decision-making on bug assignments while taking into consideration developers' expertise, bug type, and bug fixing time. Our result shows a significant improvement over the myopic approach in terms of assignment accuracy and fixing time. We also demonstrate the empirical convergence of the model and conduct sensitivity analysis with various model parameters. Accordingly, this work constitutes a significant step forward in addressing the uncertainty in bug triage solutions