Strong stochastic stability for dynamic source routing

Node movement in a Mobile Ad-Hoc Network (MANET) simulation is defined by the mobility model. To ensure reliable simulation results, many research papers have investigated the stability (or instability) of popular mobility models. In general, these works have been concerned with the following question: Will time-averaged measurements of "mobility model events" converge? For example, will average node speed or position converge as simulation time increases? These works, however, do not address stability questions at different network layers. In this paper, we study the following problem: When is the output of a network protocol stable? Network protocols are complex distributed systems, which may (or may not) preserve the stability of the mobility model. We study a basic version of the popular Dynamic Source Routing (DSR) protocol and show that if a pointwise ergodic theorem (a generalized strong law of large numbers) holds for the mobility model, then it also holds for the output of DSR; that is, time averaged measurements made at the network layer will converge almost everywhere. This, the first stability result for a network layer protocol, opens up a new area of research.