In this paper we study the synchronization problem that exists in the linear lightwave network (LLN), a recently proposed fiber-optic architecture. The currently proposed solution prevents efficient implementation of time division multiple access (TDMA) schemes for sharing the common broadcast medium. The problem is typical of passive optical networks with a tree physical topology. In this paper we propose to overcome the synchronization problem in LLN by properly selecting the routing of the optical signals. The proposed scheme provides efficient utilization of the multiaccess channel with relatively low synchronization complexity.