Estimating the Transmission Probability in Wireless Networks with Configuration Models

We propose a new methodology to estimate the probability of successful transmissions for random access scheduling in wireless networks, in particular those using Carrier Sense Multiple Access (CSMA). Instead of focusing on spatial configurations of users, we model the interference between users as a random graph. Using configuration models for random graphs, we show how the properties of the medium access mechanism are captured by some deterministic differential equations when the size of the graph gets large. Performance indicators such as the probability of connection of a given node can then be efficiently computed from these equations. We also perform simulations to illustrate the results on different types of random graphs. Even on spatial structures, these estimates get very accurate as soon as the variance of the interference is not negligible.

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