Through assuming the route-free flow travel time as the lower bound of route travel time，the travel time budget model with truncated normal distribution was proposed． And the model was compared with the travel time budget model with general normal distribution． In the multi-class user stochastic network，travelers were assumed to be heterogeneous with respect to their desired on-time arrival probabilities． Then the reliability-based multi-class stochastic user equilibrium model was developed，its equivalent variational inequality formulation was given． The results show that the budget time of travelers under truncated normal distribution is larger than that under general normal distribution． In this case，the risk aversion levels of travelers are context-based adaptive． In addition，the results also demonstrate that the punctual travelers tend to choose the routes with the better reliability． Neverthe- less，the risky travelers prefer to choose the routes with the less average travel time．