This article presents the problem of quickest descent, or the Brachistochrone curve, that may be solved by the calculus of variations and the Euler-Lagrange equation. The cycloid is the quickest curve and also has the property of isochronism by which Huygens improved on Galileo’s pendulum. AMS Subject Classification: 34A02, 00A09, 97A20

A dynamic network consists of a graph with capacities and transit times on its edges. The quickest transshipment problem is defined by a dynamic network with several sources and sinks; each source has a specified supply and each sink has a specified demand. The problem is to send exactly the right amount of flow out of each source and into each sink in the minimum overall time. Variations of th...

In recent years, catastrophic disasters by massive earthquakes are increasing in the world, and disaster management is required more than ever. In the case of disasters such as tsunami from which the slight delay of evacuation deprives of life. In this article, we formalize the emergency evacuation planning model for the evacuation from tsunami etc. based on the idea of the universally quickest...

Given a network with capacities and transit times on the arcs, the quickest flow problem asks for a “flow over time” that satisfies given demands within minimal time. In the setting of flows over time, flow on arcs may vary over time and the transit time of an arc is the time it takes for flow to travel through this arc. In most real-world applications (such as, e.g., road traffic, communicatio...

In the classical problem of quickest change detection, a decision maker observes a sequence of random variables. At some point in time, the distribution of the random variables changes abruptly. The objective is to detect this change in distribution with minimum possible delay, subject to a constraint on the false alarm rate. In many applications of quickest change detection, e.g., where the ch...