In this paper, we propose two path-based MAXBAND models for solving signal synchronization problems for coordinated traffic signalization systems. In the first proposed model (RM1), we relax the assumptions that the lengths of the common cycle, as well as the green splits, are fixed in the base path-based MAXBAND model. These two factors are considered as decision variables in RM1, which leads us to a generalized offset optimization problem. In the second model (RM2), we further relax the free-flow speed assumption used for estimating the link travel times in the coordinated system. Since the free-flow speed can only be reached in rare occasions, we, instead, adopt the Robertson's dispersion module for this purpose. Proposed methodologies are applied to solving a real-world application in that a pure-traffic arterial system in Chubei city, Taiwan, is analyzed for performance evaluations. Numerical results suggest significant improvements from the proposed models, compared to plans suggested by the governmental authority and the literature. From path-wise perspective, model RM1 and RM2 are nip-and-tuck alternatives. From an aggregate perspective, model RM2 has the best performance among all alternatives, with overall improvements around (Formula presented.).