In Delay Tolerant Networks (DTNs), two-hop routing compromises energy versus delay more conveniently than epidemic routing. Literature provides comprehensive results on optimal routing policies for mobile nodes with homogeneous mobility, often neglecting signaling costs. Routing policies are customarily computed by means of fluid approximation techniques, which assure solutions to be optimal only when the number of nodes is infinite, while they provide a coarse approximation otherwise. This work addresses heterogeneous mobility patterns and multiple wireless transmission technologies; moreover, we explicitly consider the beaconing/signaling costs to support routing and the possibility for nodes to discard packets after a local time. We theoretically characterize the optimal policies by deriving their formal properties. Such analysis is leveraged to define two algorithmic approaches which allow to trade off optimality with computational efficiency. Theoretical bounds on the approximation guarantees of the proposed algorithms are derived. We then experimentally evaluated them in realistic scenarios of multi-class DTNs.
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