Intelligent transportation systems have recently emerged to address the growing interest for safer, more efficient, and sustainable transportation solutions. In this direction, this paper presents distributed algorithms for control and optimization over vehicular networks. First, we formulate the autonomous vehicle platooning framework based on model-predictive-control (MPC) strategies and present its objective optimization as a cooperative quadratic cost function. Then, we propose a distributed algorithm to locally optimize this objective at every vehicle subject to data quantization over the communication network of vehicles. In contrast to most existing literature that assumes ideal communication channels, log-scale data quantization over the network is addressed in this work, which is more realistic and practical. In particular, we show by simulation that the proposed log-quantized algorithm reaches optimal convergence with less residual and optimality gap. This outperforms the existing literature considering uniform quantization which leads to a large optimality gap and residual.