Service Reliability and Optimal Running Time Schedules

To improve reliability, transit routes have time points at which early vehicles are held. Holding reduces waiting time and the amount of time passengers have to budget for a trip. However, it also reduces operating speed and thus increases passenger riding time and, potentially, operating cost. A new approach is presented for quantifying the user costs associated with unreliability. User cost has three components: excess waiting time, potential travel time or buffer time (related to budgeted travel time), and mean riding time, of which the first two are reliability impacts. For long headway service, these costs can be determined from 2-percentile departure times, 95-percentile arrival times, and mean arrival and departure times at stops. With a simple route operations model on a hypothetical route, impacts of scheduling with different numbers of time points and with different levels of running time and cycle time supplements are explored, and optimal running time schedules are determined. For a typical case, the optimal time point schedule offers net benefits equivalent to 4.5 min of riding time per passenger compared with operation without time point control. Optimal route running times are roughly mean plus one standard deviation of uncontrolled running time, and optimal cycle time is roughly mean plus two to three standard deviations of uncontrolled route running time. Surprisingly, it was found that in an optimal schedule, inserting slack at time points does not increase cycle time, because slack time inserted en route simply substitutes for slack time needed in layover.