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.Nevertheless,　the　risky　travelers　prefer　to　choose　the　routes　with　the　less　average　travel　time.　©　2019,　Editorial　Department,　Journal　of　South　China　University　of　Technology.　All　right　reserved.