The aim of this study is to investigate the solution algorithm for solving the
problem of determining reliable shortest paths in road networks with stochastic travel
times. The availability of reliable shortest paths enables travelers, in the face of travel
time uncertainty, to plan their trips with a pre-specified on-time arrival probability. In
this study, the reliable shortest path between origin and destination nodes is determined
using a multiple-criteria shortest path approach when link travel times follow
normal distributions. The dominance conditions involved in such problems are
established, thereby reducing the number of generated non-dominated paths during
the search processes. Two solution algorithms, multi-criteria label-setting and A*
algorithms, are proposed and their complexities analyzed. Computational results
using large scale networks are presented. Numerical examples using data from a
real-world advanced traveller information system is also given to illustrate the
applicability of the solution algorithms in practice.