Real-time transit passenger information systems are intended to improve the level of service provided by transit agencies. For example, passengers are given real-time information on the expected arrival times of buses on various routes at bus stops. These real-time systems reflect emerging applications in public transit, and methods to evaluate their benefits are limited. An evaluation method is presented that focuses on the potential benefits of bus arrival information systems to passengers waiting at bus stops. Passenger arrivals and transit bus operations are modeled as a stochastic system in which the operator uses real-time bus location data to provide bus arrival-time information that maximizes passengers' utilities. Simulation results reveal the nature of the dependence of system benefits on the type of real-time data available to the operator and the bus operations characteristics. An application to an existing bus transit system demonstrates the feasibility of the developed method and its role in assessing the value of real-time bus arrival information systems to passengers.