The TT-PET collaboration is developing an MRI-compatible small animal PET scanner in which the sensitive element is a monolithic silicon pixel ASIC targeting 30 ps RMS time resolution. The photon-detection technique is based on a stack of alternating layers of high-Z photon converter and 100 $mathrm{mu m}$ silicon sensors, to produce a scanner with 0.5 $mathrm{times}$ 0.5 $mathrm{times}$ 0.2 $mathrm{mm^{3}}$ granularity for precise depth-of-interaction measurement. In this paper we present the results of simulation studies for the expected data rate, time-of-flight and spatial resolution, as well as the performance of image reconstruction with and without the use of timing information.