Exciton-polariton transmission in quantum dot waveguides is investigated with quantum time-evolution equations in Liouville space for exciton wave packet dynamics. The transmission efficiency of the exciton-polariton wave with the longitudinal and transverse mode transformations strongly depends on the geometric parameters (bending angle and interdot distance) of the waveguides and on configuration of an additional branch attached to the waveguide. We have numerically demonstrated that the transmission efficiency significantly improves by controlling these geometric parameters and the configuration of the branched waveguide. The optimal bending angle for efficient transmission with the longitudinal and transverse mode transformations deviates from the right angle owing to more than nearest-neighbor-site interactions through a shortcut. We have also found that existence of thermal relaxation enables to open a new transmission channel along which the exciton-polariton transmission through the Coulomb interaction is suppressed.