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This paper studies the multihop packet delivery delay in a low density vehicular ad hoc network (VANET). We address a disrupted vehicle-to-infrastructure communication scenario, where an end-to-end path is unlikely to exist between a vehicle and the nearest road side unit (RSU). We present an analytical framework, which takes into account the randomness of vehicle data traffic and the statistical variation of the disrupted communication channel. Our framework employs the effective bandwidth theory and its dual, the effective capacity concept, in order to obtain the maximum distance between RSUs that stochastically limits the worst case packet delivery delay to a certain bound (i.e., allows only an arbitrarily small fraction of the packets received by the farthest vehicle from the RSU to exceed a required delay bound). Our study also investigates the effect of the vehicle density, transmission range, and speed difference between vehicles on the end-to-end packet delivery delay. Extensive simulation results validate our analytical framework.