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.

翻译：长期流动是将交通网络等各种应用中产生的流动动态纳入流动动态的自然方式。本文介绍了确定性流体排队模式的自然变体,即用户力求在预定期限之前在到达目的地后尽量减少成本;我们确定纳什流动的存在和结构,并充分说明这一模式的无政府状态价格。无政府状态价格衡量平衡质量和最佳流动质量的比例,我们用两种不同的自然性能衡量来评估质量:一个特定期限的吞吐量和一定流量的抽出量。虽然这两种无政府状态的价格一般可以不受限制,但我们为平行道路网络的重要亚类提供了紧凑的界限。奇怪的是,两种绩效衡量方法在这里产生不同的结果。