Mobile Agent Rendezvous on a Probabilistic Edge Evolving Ring

Rendezvous problem, which requires all mobile agents to gather on a single vertex, is one of the crucial methods for mobile agent systems. In previous studies on the rendezvous problem, mobile agents move on a static environment where the network topology does not change during the execution. However, in dynamic networks such as wireless mobile ad-hoc networks, the network continuously changes because of movements of vertices and interference of wireless signal. In this paper, we investigate the rendezvous problem in dynamic environment which is modeled by a probabilistic edge evolving graph. A probabilistic edge evolving graph is a sequence of sub graphs of an original graph G where each edge of G is contained in each sub graph probabilistically. We present a rendezvous algorithm for an evolving graph whose original graph is a ring, and its expected rendezvous time until two agents gather on a vertex. The analysis results show the impact of the initial directions to which agents start to move and the consistency of local port numbering during the execution on the expected rendezvous time.