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The FCC has set apart a frequency band with the specific goal of improving safety and efficiency of the transportation system. Its purpose is to provide wireless communications between stations on the roadside and mobile radio units located on board of vehicles. The resulting technology is known as WAVE and is currently under development as draft standard IEEE 802.1 lp. The most time- critical messages, carrying urgent safety-related information, are transmitted over the so-called control channel (CCH). WAVE devices use the EDCA MAC protocol, defined in the 2007 version of the IEEE 802.11 standard, to compete for the transmission medium. This work analyzes the performance of EDCA under the specific conditions of the CCH of a WAVE environment. The protocol is modeled using Markov chains and results related to throughput, frame-error rate, buffer occupancy and delay are obtained under different traffic-load conditions.