Mobile ad hoc networks are characterized by having nodes that are cooperative and communicate without any kind of infrastructure. The mobility and multihop capability of these networks lead the network topology to change rapidly and unpredictably; this aspect must be incorporated in effective models to describe the dynamics of multihop paths.When modeling the duration of multihop paths, a great part of the literature assumes that the links of multihop paths behave independently. This simplifies the modeling and reduces the complexity of computations. However, each link shares a common node with each of its neighbor links, turning the independent link assumption generally not valid. In this chapter, we use a piecewise deterministic Markov model that characterizes the random behaviour of a multihop path not assuming independent links. We obtain the mean path duration of multihop paths and compare the results for the used model with the ones obtained by assuming independent links. Numerical results illustrate that independent link approximation results underestimate the mean path duration, with the most significant differences being observed with low node mobility and higher path durations.

CEMAT - Center for Computational and Stochastic Mathematics