Summary: The authors [“A mathematical model of a passive star coupler for very high speed optical fiber local area network” (to appear) and “A dynamic model of a passive star coupler using slotted ALOHA protocol for optimal fiber local area network” (to appear)] initiated the development of dynamic models for optical fiber local area networks. This is a major departure from the traditional approach of communication engineers who are used to steady state analysis based on queueing network theory. In this paper, theoretical analysis of the proposed model for a passive star coupler based on the slotted ALOHA/ALOHA protocol for optical fiber local area networks is presented. The input, measured in terms of the number of user requests in each time slot, is modeled as a Poisson random process with time varying mean intensity thereby allowing time varying data traffic which closely models the real physical data flow. In contrast the traditional approach which uses a mean data traffic fails to capture the true dynamic nature of the system. Simulation and theoretical results are compared and they match well.