  Flows over time are a natural way to incorporate flow dynamics that arise in
various applications such as traffic networks. In this paper we introduce a
natural variant of the deterministic fluid queuing model in which users aim to
minimize their costs subject to arrival at their destination before a
pre-specified deadline. We determine the existence and the structure of Nash
flows over time and fully characterize the price of anarchy for this model. The
price of anarchy measures the ratio of the quality of the equilibrium and the
quality of the optimum flow, where we evaluate the quality using two different
natural performance measures: the throughput for a given deadline and the
makespan for a given amount of flow. While it turns out that both prices of
anarchy can be unbounded in general, we provide tight bounds for the important
subclass of parallel path networks. Surprisingly, the two performance measures
yield different results here.
