Mildly relativistic, oblique shocks are frequently invoked as possible sites of relativistic particle acceleration and production of strongly variable, polarized multi-wavelength emission from relativistic jet sources such as blazars, via diffusive shock acceleration (DSA). In recent work, we had self-consistently coupled DSA and radiation transfer simulations in blazar jets. These one-zone models determined that the observed spectral energy distributions (SEDs) of blazars strongly constrain the nature of the hydromagnetic turbulence responsible for pitch-angle scattering. In this paper, we expand our previous work by including full time dependence and treating two emission zones, one being the site of acceleration.
This modeling is applied to a multiwavelength flare of the flat spectrum radio quasar 3C~279, fitting snap-shot SEDs and light curves. We predict spectral hysteresis patterns in various energy bands as well as cross-band time lags with optical and GeV $\gamma$-rays as well as radio and X-rays tracing each other closely with zero time lag, but radio and X-rays lagging behind the optical and $\gamma$-ray variability by several hours.