This paper analyzes the use of variable speed limits to optimize travel time reliability for commuters. The investigation focuses on a traffic corridor with a bottleneck subject to the capacity drop phenomenon. The optimization criterion is a linear combination of the expected value and standard deviation of average travel time, with traffic flow dynamics following the kinematic wave model (Lighthill, 1955; Richards, 1956). We develop two complementary models to optimally set variable speed limits: In the first model, daily peak traffic demand is conceptualized as a stochastic variable, and the resulting model is solved through a three-stage optimization algorithm. The second model is based on deterministic demand, instead modeling bottleneck capacity as a stochastic process using a stochastic differential equation (SDE). The practical applicability of both approaches is demonstrated through numerical examples with empirically calibrated data.