In this paper we investigate the traversal time of a file across N communication links (or edges) subject to stochastic changes in the sending rate of each link. Each link's sending rate is modeled by a finite-state Markov process. Two cases, one where links evolve independently of one another (N mutually independent Markov processes), and the second where their behaviors are dependent (these N Markov processes are not mutually independent) are considered. A particular instance where the above is encountered is in ad hoc delay/tolerant networks where edges are subject to intermittent unavailability.