With the popularity of smart phones and tablets, people make intensive use of these devices on public transport. The deployment of mobile relays on public transport may increase the quality of mobile services. The objective of this paper is to study the performance of cellular networks when mobile relays are deployed in public transport vehicles. We consider two modes: in the FDD mobile relay mode, the same spectrum is reused for all links while in the TDD/FDD hybrid mode, a small part of the spectrum is dedicated to the access link between the terminals inside a transport vehicle and the mobile relay. We provide a general analytical model for the two mobile relay modes by using the stochastic geometry approach. Key metrics like the CDF of the SINR and the CDF of the end-to-end rate are computed. Furthermore, the cell total average rate and the energy efficiency in different modes are evaluated. It has been found that penetration loss is a factor that determines how much gain mobile relay can bring. Numerical results show that when the ratio of vehicular UEs in the cell is 0.4 and the penetration loss is 20 dB, the FDD mobile relay mode and the TDD/FDD hybrid mobile relay mode can achieve +16.3, +29.1% cell rate gain respectively compared with the direct mode.