The goal of the study described is to exploit the capabilities of emerging lightwave technology and the fact that the IEEE 802.6 MAN is a linear network, to construct near optimal linear multihop lightwave networks. Heuristic algorithms are proposed for constructing photonic implementations of near optimal distributed queue dual bus (DQDB) structures. Two sets of heuristic optimization algorithms are formulated. The first set is concerned with minimizing the maximum flow in any link in the network, while the second set of heuristics is aimed at minimizing the network-wide mean packet delay. Important properties of these algorithms are analyzed and their performance is demonstrated with several representative numerical examples.