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We propose a novel paradigm for conflict resolution in multivehicle traffic systems, where a number of mobile agents move freely in a finite area, with each agent following a prespecified-motion profile. The key idea behind the proposed method is the tessellation of the underlying motion area in a number of cells and the treatment of these cells as resources that must be acquired by the mobile agents for the execution of their motion profiles, according to an appropriate resource allocation protocol. We capitalize upon the existing literature on the real-time management of sequential resource allocation systems (RASs) and develop such protocols that can formally guarantee the safe and live operation of the underlying traffic system, while they remain scalable with respect to the number of the moving agents. Collective past experience with the considered policies indicates that they also provide a pretty large coverage of the RAS behavioral space that characterizes its safe and live operation. Finally, we also establish that the aforementioned approach is applicable even in traffic systems where all vehicles must be in perpetual motion until their retirement.