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A mobile wireless delay-tolerant network (DTN) model is proposed andanalyzed, in which infinitely many nodes are initially placed on R^2 accordingto a uniform Poisson point process (PPP) and subsequently travel, independentlyof each other, along trajectories comprised of line segments, changing traveldirection at time instances that form a Poisson process, each time selecting anew travel direction from an arbitrary distribution; all nodes maintainconstant speed. A single information packet is traveling towards a givendirection using both wireless transmissions and sojourns on node buffers,according to a member of a broad class of possible routing rules. For thismodel, we compute the long-term averages of the speed with which the packettravels towards its destination and the rate with which the wirelesstransmission cost accumulates. Because of the complexity of the problem, weemploy two intuitive, simplifying approximations; simulations verify that theapproximation error is typically small. Our results quantify the fundamentaltrade-off that exists in mobile wireless DTNs between the packet speed and thepacket delivery cost. The framework developed here is both general andversatile, and can be used as a starting point for further investigation.

Packet Speed and Cost in Mobile Wireless Delay-Tolerant Networks