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We study in this paper a variation of the acclaimed CSMA random accessprotocol. We will focus on the case where back-off rates at each node ispolynomial in the size of the queue. Under a condition relating the exponent inthe polynomial rates and the geometry of the interference graph, we proveconvergence of the scaled process to a deterministic fluid limit up to the timea queue reaches $0$ on the fluid scale . We outline the difficulties arising atthat time and solve them in the case of a complete interference graph. Thispaper relies on a new method to obtain a fully coupled stochastic averagingprinciple and can hopefully lead to more result in heavy load situations.

Fluid limits for Queue-based CSMA with polynomial rates, homogenization and reflection