Drive-thru-Internet is a scenario in cooperative intelligent transportation systems (C-ITSs), where a road-side unit (RSU) provides multimedia services to vehicles that pass by. Performance of the drive-thru-Internet depends on various factors, including data traffic intensity, vehicle traffic density, and radio-link quality within the coverage area of the RSU, and must be evaluated at the stage of system design in order to fulfill the quality-of-service requirements of the customers in C-ITS. In this paper, we present an analytical framework that models downlink traffic in a drive-thru-Internet scenario by means of a multidimensional Markov process: the packet arrivals in the RSU buffer constitute Poisson processes and the transmission times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we use iterative perturbation techniques to calculate the stationary distribution of the Markov chain. Our numerical results reveal that the proposed approach yields accurate estimates of various performance metrics, such as the mean queue content and the mean packet delay for a wide range of workloads. © 2019 IEEE.