Due to their higher resistance, single layer graphene nanoribbons (GNRs) are not suitable for high-speed on-chip interconnect applications. Hence, we use multilayer GNRs (MLGNRs) that offer multiple conduction channels and lower resistance. However, MLGNRs turn into graphite as the number of layers increase, which reduces the mean-free path of each layer. Insertion of a dielectric between GNR layers prevents its conversion into graphite, thereby improving its mean-free path and scattering rate. In this paper, we are proposing an analytical model for the time-domain analysis of side-contact MLGNRs (SC-MLGNRs) with intermediate dielectric insertion. The proposed model computes scattering rate, mean-free path, and carrier mobility in GNRs where dielectric has been inserted between individual layers. Our analytical results for mobility and scattering rate have been verified with the existing experimental data that exhibit excellent accuracy (maximum of error 4% for mobility and 16% for scattering time). Based on our analysis, we have found that the electron mean-free path in GNRs strongly depends on surrounding dielectric environment. In that, the mean-free path increases with interlayer insertion of high-k dielectrics. Equivalent RLC parameters, delay, energy-delay product, and bandwidth density are calculated for our proposed GNR interconnects using our model. We observe that these performance metrics significantly improve due to the presence of dielectric between GNR layers. When compared with Cu interconnects, insertion of HfO₂ between GNR layers results in reduction in both propagation delay and energy-delay product by 2x for interconnect lengths of 1400 μm. In addition, zigzag SC-MLGNR interconnect with N = 10 and ε₂ = 20 gives nearly 35% higher bandwidth density than that of Cu interconnects for all interconnect lengths. In our analysis, we propose a new performance metric, bandwidth density/energy-delay product to determine t- e performance limits of our proposed interconnect structure Finally, we compare the performance of SC-MLGNR interconnect structure with copper and optical interconnects to exhibit its application in local and global interconnects.