A stochastic model is introduced that accurately models the message delay in mobile ad hoc networks where nodes relay messages and the networks are sparsely populated. The model has only two input parameters: the number of nodes and the parameter of an exponential distribution which describes the time until two random mobiles come within communication range of one another. Closed-form expressions are obtained for the Laplace-Stieltjes transform of the message delay, defined as the time needed to transfer a message between a source and a destination. From this we derive both a closed-form expression and an asymptotic approximation (as a function of the number of nodes) of the expected message delay. As an additional result, the probability distribution function is obtained for the number of copies of the message at the time the message is delivered. These calculations are carried out for two protocols: the two-hop multicopy and the unrestricted multicopy protocols. It is shown that despite its simplicity, the model accurately predicts the message delay for both relay strategies for a number of mobility models (the random waypoint, random direction and the random walker mobility models).

A generic stochastic model with only two input parameters is introduced to evaluate the message delay in mobile ad hoc networks (MANETs) where nodes may relay messages. The Laplace-Stieltjes transform (LST) of the message delay is obtained for two protocols: the two-hop and the unrestricted multicopy protocol. From these results we deduce the expected message delays. It is shown that, despite its simplicity, the model accurately predicts the message delay under both relay strategies for a number of mobility models (the random waypoint, random direction and the random walker mobility models).

Mobile ad hoc networks are characterized by a lack of a fixed infrastructure and by node mobility. In these networks data transfer can be improved by using mobile nodes as relay nodes. As a result, transmission power and the movement pattern of the nodes have a key impact on the performance. In this work we focus on the impact of node mobility through the analysis of a simple one-dimensional ad hoc network topology. Nodes move in adjacent segments with reflecting boundaries according to Brownian motions. Communications (or relays) between nodes can occur only when they are within transmission range of each other. We determine the expected time to relay a message and compute the probability density function of relaying locations. We also provide an approximation formula for the expected relay time between any pair of mobiles.

We consider a mobile ad hoc network consisting of three types of nodes: source, destination, and relay nodes. All the nodes are moving over a bounded region with possibly different mobility patterns. We introduce and study the notion of relay throughput, i.e. the maximum rate at which a node can relay data from the source to the destination. Our findings include the results that the relay throughput depends on the node mobility pattern only via its (stationary) node position distribution and that a node mobility pattern that results in a uniform steady-state distribution for all nodes achieves the lowest relay throughput. Random Waypoint and Random Direction mobility models in both one and in two dimensions are studied and approximate simple expressions for the relay throughput are provided. Finally, the behavior of the relay buffer occupancy is examined for the one-dimensional Random Walk, and an explicit form of its mean value is provided in the heavy-traffic case.This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the Proceedings IEEE Infocom.