Percolation-theoretic bounds on the cache size of nodes in mobile opportunistic networks

The node buffer size has a large influence on the performance of Mobile Opportunistic Networks (MONs). This is mainly because each node should temporarily cache packets to deal with the intermittently connected links. In this paper, we study fundamental bounds on node buffer size below which the network system can not achieve the expected performance such as the transmission delay and packet delivery ratio. Given the condition that each link has the same probability p to be active in the next time slot when the link is inactive and q to be inactive when the link is active, there exists a critical value p (c) from a percolation perspective. If p > p (c), the network is in the supercritical case, where we found that there is an achievable upper bound on the buffer size of nodes, independent of the inactive probability q. When p < p (c), the network is in the subcritical case, and there exists a closed-form solution for buffer occupation, which is independent of the size of the network.