In this paper, we analyze the performance of multiple event-based systems that share access to the same network. Transmissions are attempted only when a local state-based scheduler generates an event, and access to the network is determined using a Carrier Sensing Multiple Access (CSMA) protocol. In general, the interactions in such a multiple access network introduce correlations between the system variables of the various loops, and the respective traffic contributions as well. Hence, analyzing the performance of this network is difficult. However, a class of state-based schedulers, introduced in the paper, permits a joint analysis of the scheduler and the Contention Resolution Mechanism (CRM). The analysis is based on a Markov model, which is validated through simulations. The resulting steady-state model makes it possible to characterize the statistics of packet arrivals in this network.