One of the aims of this research is to investigate the accuracy of predicted arrival times of buses provided by the Real-Time Tracking System (RTTS) currently being implemented in Christchurch. Surveys have shown an increase in bus patronage since its installation and the idea of improving bus services by providing accurate estimations to bus users is gradually rising in the government's priority list. This study will analyse the prediction errors of real-time information data collected manually from selected bus stops. Actual arrival times along with predicted times of arrival displayed at bus stops are gathered and compared. Comparisons between different routes and different directions for the Christchurch system are also studied. Real-time predictions are found to be reasonably accurate except for a few spots which can be rectified with improvements in the management system. Another purpose of this research is to improve an existing model for investigating bus bunching. Newell and Potts had done some research on the maintenance of a bus schedule in the 1960's and derived a formula to calculate bus departure times at each stop along the route, with or without delay to bus 1 occurring at stop 1. However, the model will break down once a bus is able to overtake the bus in front. This research tries to incorporate the overtaking feature into the existing model by setting up a numerical model in the Excel spreadsheet. Departure times are more realistic than those found using the formula derived by Newell and Potts. However, the extended model has its limitations. When buses deviate further and further away from schedule, it will eventually result in more than a pair of buses being bunched together. The extended model will fail because it is unable to cope with more than one pair of buses joining in a bunch. Therefore, more research should be done on this topic.