This paper presents a modeling approach to linking stochastic acceleration and lane-changing behavior to travel time reliability on congested freeways. Individual driving behavior is represented by a prospect-theory-based model that takes into account uncertainty and risk evaluation in terms of gains and losses while following a lead vehicle. Given a set of stimuli (i.e., headways, relative speeds, etc.), the stochastic acceleration model generates acceleration probability distribution functions rather than deterministic acceleration values. Such distribution functions may be associated with travel time reliability through the construction of travel time distributions. In addition, lane-changing decision is represented by a stochastic hazard-based duration model that accounts for the surrounding traffic conditions (i.e., traffic density, distance to ramp, etc.). Numerical results from Monte Carlo simulations demonstrate that the proposed microscopic stochastic modeling approach produces realistic macroscopic traffic flow patterns and can be used to generate travel time distributions. With proper experimental setup and sensitivity analysis, travel time distributions may be estimated and linked to safety-based parameters.