Stochastic optimization in computing multiple headways for a single bus line

We consider the problem of computing multiple headways for a single bus line to maximize the expected daily profit. The stochastic bus-line model assumes that (1) the passenger arrivals follow a Poisson process with possible reneging; (2) the number of alighting passengers at each stop follows a binomial distribution; and (3) the bus travel time follows a Weibull distribution. The objective function-the expected daily profit, defined as the ticket revenue minus the operating and customer waiting costs-is discontinuous at changes in the bus frequency. For this stochastic optimization problem, we propose a retrospective optimization algorithm that can handle both homogeneous and nonhomogeneous Poisson arrivals. Simulation results are discussed.