In wireless ad hoc and sensor networks, it is the number of nodes that is large. We have shown that this type of largeness can also lead to simple and critical insights in control. In particular, we study the problem of the fundamental capacity-delay tradeoff in large mobile ad hoc networks. Note that although it is well known that mobility can improve network capacity, it remained a challenging problem as to what is the maximum capacity under a given delay constraint, and how to achieve this maximum capacity. We have developed a systematic methodology both for finding the optimal capacity-delay tradeoff and for designing the capacity-achieving scheme. Our methodology can be applied to a number of mobility models, such as the i.i.d. mobility model, the random way-point mobility model, and the Brownian motion mobility model. In each case, we have identified the limitations of existing works, obtained sharper results under more general settings, and provided new insights on the fundamental capacity-delay tradeoffs. In particular, under the i.i.d. mobility model, our study allows us to develop a scheme that can exploit mobility and achieve a provably larger per-node capacity than that of the static networks even with delay that does not grow with the number of nodes. This is the first such result of its kind in the literature. Our methodology can also be extended to incorporate additional scheduling constraints in the system, and be used to find optimal scheduling schemes in a variety of network settings.
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