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This paper presents a theoretical analysis for a self-driving vehicle’s velocity as it navigates through a random environment. We study a stylized environment and vehicle mobility model capturing the essential features of a self-driving vehicle’s behavior, and leverage results from stochastic geometry to characterize the distribution of a typical vehicle’s safe driving velocity, as a function of key network parameters such as the density of objects in the environment and sensing accuracy. We then consider a setting wherein the sensing accuracy is subject to a sensing/communication rate constraint. We propose a procedure that focuses the vehicle’s sensing/communication resources and estimation efforts on the objects that affect its velocity and safety the most so as to optimize its ability to drive faster in uncertain environments. Simulation results show that the proposed methodology achieves considerable gains in the vehicle’s safe driving velocity as compared to uniform rate allocation policies.