The insertion loss of fiber couplers in the two fiber rings waveguide system is studied. The peak power is the same by matching coupler strength of two couplers at the resonant area. The peak transmittance is inversely proportional to the group refractive index regardless of the two reflection values. Group delay increases at the expense of reduction of the peak transmissivity. The three rings waveguide structure manifests the subluminal properties accompanying normal dispersion by doping gain media. Group delay is analyzed in the frequency domain and the time domain, respectively. This study could be regarded as the significant theoretical foundation for applications in the field of controllable light velocity theory, sensors, filters, optical buffers and so on.