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This thesis investigates the conflict-free routing of vehicles through a track network, a problem frequently encountered in many applications in transportation and logistics. The most common routing approach for conflictfree routing problems in various settings is a sequential one, where requests are greedily served one after the other in a quickest way without interfering with previously routed vehicles. There is a need for a better theoretical understanding as guarantees on the quality of the routings are often missing. Conflict-free vehicle routing also is of inherent interest as a sister problem of the well-studied packet routing problem. In the first part, we present new theoretical results for the case of bidirectional networks. We consider a natural basic model for conflict-free routing of a set of k vehicles. Previously, no efficient algorithm is known with a sublinear (in k) approximation guarantee and without restrictions on the graph topology. We show that the conflict-free vehicle routing problem is hard to solve to optimality even on paths. Building on a sequential routing scheme, we present an algorithm for trees with makespan bounded by O(OPT) + k. Combining this result with ideas known from packet routing, we obtain a first efficient algorithm with sublinear approximation guarantee, namely an O( √ k)-approximation. Additionally, a randomized algorithm leading to a makespan of O(polylog(k)) ·OPT + k is presented that relies on tree embedding techniques applied to a compacted version of the graph to obtain an approximation guarantee independent of the graph size. The second part is about routing in the Personal Rapid Transit (PRT) application. PRT is a public transportation mode in which small automated vehicles transport passengers on demand. Central control of the vehicles leads to interesting possibilities for optimized routings. Routing in PRT is an online problem where transit requests appear over time and where routing decisions need to be taken without knowledge of future requests. Further, the network in PRT is directed. The complexity of the routing problems together with the fact that routing algorithms for PRT essentially have to run in real-time often leads to the choice of a fast sequential scheme. The simplicity of such schemes stems from the property that a chosen route is never changed later. This is as well the main drawback of it, potentially leading to large detours.

Conflict-free Vehicle Routing with an Application to Personal Rapid Transit