We consider the problem of frequency optimization in transit systems, whose objective is to determine the time interval between subsequent buses for a set of public transportation lines. We extend an existing single level model by adding a constraint on bus capacities, while maintaining user choice on routes by means of an assignment sub-model. The resulting formulation is bilevel, and is transformed into a mixed integer linear programming formulation (MILP) that can be solved to optimality for small-sized problem instances, using standard MILP techniques. We study different variants of the same formulation to better understand the bilevel nature of the model and its application to real settings.

This paper studies the Vehicle Scheduling Problem (VSP) in the context of suburban passenger transportation. The problem consists in finding a set of sequences of trips which have to be assigned to the available fleet of buses. The complexity of this problem depends on the number of depots where the fleet is housed. The paper focuses on the resolution of Multiple Depot VSP (MDVSP) which has NP-Hard Complexity. A column generation heuristic is proposed to solve the problem, and two heuristic algorithms are used to provide a set of initial columns, one of them is based on the auction algorithm for Single Depot VSP (SDVSP). The algorithms where tested with a small instance and real world one, obtaining solutions which are either optimal or have lower cost and use less buses than the best known solution for a related and more complex problem.

The RVR (recursive variance reduction) simulation technique has been used with success for the evaluation of the K-terminal reliability measure of networks where only links can fail. In this paper, we show how this technique can be adapted for computing the K-terminal residual connectedness reliability measure in the case of networks where nodes can fail. We prove that an RVR simulation of the residual connectedness reliability has a lower variance than standard Monte Carlo simulation, leading to better estimates. We study the worst-case computational complexity of the RVR method, and we discuss the influence of the node failure probability on the algorithm performance, which makes it more efficient and especially suited for very reliable networks.