Both　the　risk　of　concentration　phenomenon　for　the　navigation　system　and　the　risk　of　encountering　unacceptable　delay　are　reduced　by　guiding　risk-averse　drivers　along　reliable　paths　while　avoiding　high-risk　links　as　far　as　possible.　A　constrained　dynamic　A*　algorithm　is　proposed　to　search　for　a　reliable　path　subject　to　a　trip　duration　constraint　in　a　time-dependent　road　network.　The　efficiency　of　the　dynamic　A*　search　is　increased　by　taking　advantage　of　information　computed　off-line.　The　algorithms　proposed　are　implemented,　and　their　computational　performance　is　analyzed　in　simulation.