There are still some important unanswered questions about the detailed particle acceleration and escape occurring during quiescent epochs. As a result, the particle distribution that is adopted in the blazar quiescent spectral model has numerous unconstrained shapes. To help remedy this problem, we introduce an analytical particle transport model to reproduce the quiescent broadband spectral energy distribution of blazars. In this model, the exact electron distribution is solved from a generalized transport equation that contains the terms describing the first-order and second-order Fermi acceleration, the escape of particles due to both advection and spatial diffusion, and energy losses due to synchrotron emission and inverse-Compton scattering of an assumed soft photon field. We suggest that advection is a significant escape mechanism in blazar jets. We find that in our model, the advection process tends to harden the particle distribution, which enhances the high-energy components of the resulting synchrotron and synchrotron self-Compton spectra from the jets. Our model is able to roughly reproduce the observed spectra of the extreme BL Lac object 1ES 0414+009 with reasonable assumptions about the physical parameters.