This paper introduces a variable time discretization strategy for a time-dependent A^∗ shortest path algorithm. The strategy is aimed at determining the optimal memory allocation for time-dependent travel times data in order to achieve a desirable compromise between accuracy and memory usage. The proposed strategy is based on the dispersion index of the travel times/costs over the entire analysis period, as a result, producing different intervals for each link. The links with travel times that have a higher variance and a lower mean will need to have a shorter time discretization length due to greater fluctuation in travel times. The proposed strategy is implemented in the time-dependent A^∗ algorithm and tested with a numerical experiment on a Tucson, AZ, traffic network. The results show that with the same amount of computer memory usage, the proposed variable time discretization strategy achieves much higher accuracy than that of uniform time discretization.