Energy-efficient monitoring of the strip by identical one side directed devices

In many security systems, it is sufficient to monitor a certain territory with the same type of devices in such a way that each point of the territory falls into the coverage area of at least one device while minimizing the energy consumption of the devices. However, in some security systems, it is necessary to observe objects from a certain side. For example, to identify a person you need to see the person's face. If people walk along the corridor in one direction (for example, for passport control before boarding a plane), then it is necessary to monitor the strip with video cameras directed one way. Thus, in a simplified formulation, the problem arises of constructing the least dense coverage of a strip by identical sectors in such a way that the vertex of each sector is from a given side of the points covered by the sector. In this paper, several feasible coverage models are proposed and optimal parameters of sectors for each model are found, which allows choosing the best cover depending on the characteristics of the devices.