This paper analyzes the problem of modeling the collisions in a wireless network supporting multi-packet communication by spatial reuse. Typically, in a multi-packet scenario, the result of a transmission attempt is established using two main approaches: one, more idealized but suitable for theoretical analyses, based on the success probability or on the threshold on the number of sustainable communications, and another one, more realistic, relying on the signal-to-interference ratio (SIR) experienced by the receiving node. The two approaches may lead to considerably different results, since the number of allowed communications is often estimated neglecting many physical aspects. This study investigates this issue by presenting a mathematical model, validated by simulations, which relates the number of active communications with the statistic of the SIR. Moving from the developed framework, this paper discusses how some assumptions usually adopted for analyzing multi-packet networks exploiting spatial reuse may be revised in presence of a more detailed characterization of the spatial domain.
