Mobile sensor intrusion detection under any shape of curve

As mobile sensors have been applied to intrusion detection, their performance has been studied. One of the limitations of the studies undertaken is that the only cases considered are those in which the fields of interest are of a specific shape, such as a circle or the perimeter of a circle. As a result of that limitation, none of the conclusions from those studies are general enough to deal with general cases that do not depend on the shapes of the fields of interest. In this paper, we study the performance of a robot group consisting of one or multiple robots that are applied to intrusion detection; in this case, the field of interest is a loop of any shape. We build a stochastic model that is based on the velocity of robots, their mobility pattern, and the number of robots involved, and that analyzes the detection quality of multiple robots or a single robot that moves along the loop. The mode of intrusion events is as follows: each of the intrusions arrives at a random point in the loop; after arriving, it stays at that point for a random length of time before disappearing. In our model, all the robots are set to periodically move along the loop at a constant speed while they are detecting. In the case of multiple robots, each robot has the same velocity as each other. Based on the number of robots involved, we derive both the general expression for intrusion loss probability and the average time required for the robot(s) to make the first capture of intrusions. Finally, we evaluate the detection quality of the robot(s).