Allocating epidemic response teams and vaccine deliveries by drone in generic network structures, according to expected prevented exposures

Stochastic rounding: implementation, error analysis and applications

Stochastic rounding (SR) randomly maps a real number x to one of the two nearest values in a finite precision number system. The probability of choosing either of these two numbers is 1 minus their relative distance to x. This rounding mode was first proposed for use in computer arithmetic in the 1950s and it is currently experiencing a resurgence of interest. If used to compute the inner product of two vectors of length n in floating-point arithmetic, it yields an error bound with constant n u with high probability, where u is the unit round-off. This is not necessarily the case for round to nearest (RN), for which the worst-case error bound has constant nu. A particular attraction of SR is that, unlike RN, it is immune to the phenomenon of stagnation, whereby a sequence of tiny updates to a relatively large quantity is lost. We survey SR by discussing its mathematical properties and probabilistic error analysis, its implementation, and its use in applications, with a focus on machine learning and the numerical solution of differential equations.

Investigation of Merge Assist Policies to Improve Safety of Drone Traffic in a Constrained Urban Airspace

Package delivery via autonomous drones is often presumed to hold commercial and societal value when applied to urban environments. However, to realise the benefits, the challenge of safely managing high traffic densities of drones in heavily constrained urban spaces needs to be addressed. This paper applies the principles of traffic segmentation and alignment to a constrained airspace in efforts to mitigate the probability of conflict. The study proposes an en-route airspace concept in which drone flights are directly guided along a one-way street network. This one-way airspace concept uses heading-altitude rules to vertically segment cruising traffic as well as transitioning flights with respect to their travel direction. However, transition flights trigger a substantial number of merging conflicts, thus negating a large part of the benefits gained from airspace structuring. In this paper, we aim to reduce the occurrence of merging conflicts and intrusions by using a delay-based and speed-based merge-assist strategy, both well-established methods from road traffic research. We apply these merge assistance strategies to the one-way airspace design and perform simulations for three traffic densities for the experiment area of Manhattan, New York. The results indicate, at most, a 9–16% decrease in total number of intrusions with the use of merge assistance. By investigating mesoscopic features of the urban street network, the data suggest that the relatively low efficacy of the merge strategies is mainly caused by insufficient space for safe manoeuvrability and the inability for the strategies to fully respond and thus resolve conflicts on short-distance streets.