Opportunistic or Delay Tolerant Networks (DTNs) are envisioned to complement existing wireless technologies (cellular, WiFi). Wireless peers communicate when in contact, forming a network "on the fly", whose connectivity graph is highly dynamic and only partly connected. Because of this stringent environment, solutions to common networking problems (routing, congestion control, etc.) in this context are greedy, choosing the best solution among the locally available ones. This shared trait motivates the common treatment of such greedy algorithms for DTNs and raises some interesting questions: Do they converge? How fast are they? Yet, existing models study individual solutions. Moreover, they often assume homogeneous node mobility. The study of real world traces reveals considerable heterogeneity and non-trivial structure in human mobility. While algorithms have been proposed, accounting for this heterogeneity, their analytical tractability is still a challenge. In this paper, we propose a new model for greedy DTN algorithms, supporting the full heterogeneity of node mobility. We provide closed form solutions for crucial performance metrics (delivery probability and delay) and prove necessary and sufficient conditions for algorithm convergence. For illustration, we apply our model to the content placement problem, a variant of distributed caching. We use real and synthetic mobility traces to validate our findings and examine the impact of mobility properties in depth.
