We investigate the performance of a new deployment concept in cellular networks, in which on-street parked vehicles, termed Vehicular Relay Nodes (VeRN), are opportunistically activated to become a Relay Node (RN) in the cellular infrastructure, and boost the overall deployment performance. Analyzing the performance of such network, versus traditional stationary cellular deployment, is challenging, due to the dynamic nature of vehicles. We examine the gain of VeRNs for various user locations in a cellular deployment. We provide an exact analysis of the VeRN expected gain that incorporates the dynamic behavior of the parked vehicle network. We further provide a closed-form approximation of this gain. Our results show that under the wellknown WINNER-II channel model the gains are very significant (125 - 300% gain in throughput). Simulation results show that our approximation closely follows actual network performance, and the positive influence of VeRN on network capacity.