Dynamic Connectivity in ALOHA Ad Hoc Networks

In a wireless network the set of transmitting nodes changes frequently because of the MAC scheduler and the traffic load. Previously, connectivity in wireless n etworks was analyzed using static geometric graphs, and as we show leads to an overly constrained design criterion. The dynamic nature of the transmitting set introduces additional randomness in a wireless system that improves the connectivity, and this additional randomness is not captured by a static connectivity graph. In this paper, we consider an ad hoc network with half-duplex radios that uses multihop routing and slotted ALOHA for the MAC contention and introduce a random dynamic multi-digraph to model its connectivity. We first provide analytical results about the degree distribution o f the graph. Next, defining the path formation time as the minimum time required for a causal path to form between the source and destination on the dynamic graph, we derive the distributional properties of the connection delay using techniques from first-passage percolation and epidemic processes. We c onsider the giant component of the network formed when communication is noise-limited (by neglecting interference). Then, in the presence of interference, we prove that the delay scales linearly with t he source-destination distance on this giant component. We also provide simulation results to support the theoretical results.

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