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To facilitate the dissemination of a time-critical information in a vehicular ad hoc network (VANET), immediate network connectivity is needed. In other words, a time-critical message from a source should be able to propagate and reach all of the vehicles on the road segment without any delay due to the unavailability of the vehicles to forward the message. Clearly, this requires the road segment to have a certain number of vehicles equipped with communication devices. It is the task of a system designer to determine the minimum number of vehicles (i.e., the minimum penetration) necessary to form a connected network as well as the critical transmission range required to provide such connectivity. In this paper, we present an analytical framework for determining the connectivity requirements in distributing the traffic information in a self-organizing vehicular network. One- and two-way street scenarios are considered. In addition to the conventional perspective on connectivity, where the characteristics of the wireless channel are often neglected, our analysis offers a new view by taking important physical-layer parameters, such as fading, propagation path loss, transmit power, and transmission data rate, into consideration.