In [I, 21 the present authors initiated the development of dynamic models for optical fiber local area networks. This is a major departure fro111 the traditional approach of communication engineers who are used t,o steady state analysis based on queueing network theory. Here in this paper, theoretical analysis of the proposed model for a passive star coupler based on the S1ott)ed ALOHAIALOHA prot,ocol for optical fiber local area networks is presented. The input. ~neasured in terms of t,he riumber of user requests in each t,inie slot,, is rnodelect as a Poissori random process with time varying mean intensity thereby allowing time varying data traffic which closely models the real physical data flow. In contrast the tradkional approach which uses a mean data traffic fails to capture t,he true dynamic nature of the system. Simulat,ion and theoretical results are compared and they rnatrh well.