Robust airline schedules can be considered as flight schedules that are likely to minimize passenger delay. Airlines usually add an additional time-e.g., schedule padding-to scheduled gate-to-gate flight times to make their schedules less susceptible to variability and disruptions. There is a critical trade-off between any kind of buffer time and daily aircraft productivity. Aircraft speed control is a practical alternative to inserting idle times into schedules. In this study, block times are considered in two parts: Cruise times that are controllable and non-cruise times that are subject to uncertainty. Cruise time controllability is used together with idle time insertion to satisfy passenger connection service levels while ensuring minimum costs. To handle the nonlinearity of the cost functions, they are represented via second-order conic inequalities. The uncertainty in non-cruise times is modeled through chance constraints on passenger connection service levels, which are then expressed using second-order conic inequalities. Overall, it is shown, that a 2% increase in fuel costs cuts down 60% of idle time costs. A computational study shows that exact solutions can be obtained by commercial solvers in seconds for a single-hub schedule and in minutes for a four-hub daily schedule of a major U.S. carrier.