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Effective data broadcasting is essential in vehicular networks not only for road-safety message dissemination but also to aid routing and cooperative driving applications through periodic beaconing and to spread network initialization advertisements that are mandatory to support infotainment applications. Broadcast data are neither acknowledged nor retransmitted in case of failure, which raises the possibility of frame loss due to channel errors and collisions with multiple simultaneous broadcasts. This paper aims at modeling periodic broadcasting on the control channel of IEEE Std. 802.11p vehicular networks with multichannel architecture. Unlike previous related work, the proposed novel analytical approach accounts for mutual influence among nodes, frequent periodic updates of broadcasted data, standard network advertisement procedures, and 802.11p prioritized channel access with multichannel-related phenomena under various link quality conditions.