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Communication between two neighboring nodes is the most basic operation in wireless networks. Yet very little research has focused on the local delay, defined as the mean time it takes a node to connect to its nearest neighbor. In this paper, the authors derive the local delay in Poisson networks with ALOHA and find the conditions for which the local delay is finite. It turns out that while the local delay is always finite in highly mobile networks, there is a phase transition in static networks, i.e., there is a maximum transmit probability above which the local delay is infinite.
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