The Probability of Encounters of Nomadic Lévy Walk on Unit Disk Graphs

Random walks, including the Nomadic Lévy Walk, play a crucial role in various computer science domains such as networking, distributed systems, and optimization. The Nomadic Lévy Walk, a variant of the Homesick Lévy Walk, holds promise as a potential candidate for message ferry routing schemes. This approach combines the homing behavior characteristic of the Homesick Lévy Walk with the base relocation strategy employed in Lévy walks. In Delay-Tolerant Network (DTN) routing, encounter probability is a critical factor. In this paper, we present simulation results that highlight the impact of base relocation in the Nomadic Lévy Walk on encounter probability. Additionally, we conduct thorough comparisons of encounter probabilities using unit-disk graphs with varying diameters to further investigate the efficacy of the Nomadic Lévy Walk approach.