This paper establishes a general framework to study the impacts of real-time information on the users' routing decisions and the system cost in a stochastic time-dependent traffic network under a generalized equilibrium condition. Users are assumed to make strategic routing decisions, and the rule that maps a user's current state, including node, time, and information, to a decision on the next node to take, is defined as a routing policy. This definition allows for a wide variety of information accessibility situations, thus excluding the usually simplified assumptions, such as either no information or full information. A user's choice set contains routing policies rather than simple paths. A fixed-point problem formulation of the user equilibrium is given, and a method of successive average heuristic is designed. Computational tests are carried out in a hypothetical network, where random incidents are the source of stochasticity. System costs derived from three models with different information accessibility situations are compared. The strategic route choices lead to shorter expected travel times at equilibrium. Smaller travel time variances are obtained as a byproduct. The value of real-time information is an increasing function of the incident probability. However, it is not a monotonic function of the market penetration of information, which suggests that in designing a traveler information system or route guidance system, the information penetration needs to be chosen carefully to maximize benefits.