Vehicle platooning systems are often equipped with vehicle-to-vehicle (V2V) communication technologies to improve both the road efficiency and road safety by exchanging vehicle information over wireless networks to maintain relatively small inter-vehicle distance. The road safety often relies on the quality of service delivered by the V2V communication. The V2V networks are, however, subject to channel fading and often have limited communication bandwidth. The limited bandwidth inevitably compromises the road safety as the vehicular network will easily get congested if the number of vehicles joining the network increases. To address the challenges of ensuring vehicle safety under unreliable wireless network with limited bandwidth, this paper first uses a two-state Markov chain to model the channel fading in vehicular networks. Under the Markov chain model, this paper further develops a novel distributed event triggered strategies under which the vehicle platooning system achieves stochastic L ₂ string stability while ensuring an efficient use of the limited communication bandwidth. The simulation results are provided to verify the effectiveness and advantages of the proposed methods.