In this paper, we analyze the performance ofmultiple event-based systems that share access to the samenetwork. Transmissions are attempted only when a local statebasedscheduler generates an event, and access to the networkis determined using a Carrier Sensing Multiple Access (CSMA)protocol. In general, the interactions in such a multiple accessnetwork introduce correlations between the system variablesof the various loops, and the respective traffic contributionsas well. Hence, analyzing the performance of this network isdifficult. However, a class of state-based schedulers, introducedin the paper, permits a joint analysis of the scheduler andthe Contention Resolution Mechanism (CRM). The analysisis based on a Markov model, which is validated throughsimulations. The resulting steady-state model makes it possibleto characterize the statistics of packet arrivals in this network.