This paper focuses on inter-vehicular networks providing warning delivery service. As soon as a danger is detected, the propagation of a warning message is triggered, with the aim of guaranteeing a safety area around the point in which the danger is located. Multiple broadcast cycles can be generated so that a given lifetime of the safety area is guaranteed. The service is based on multi-hop ad hoc inter-vehicular communications with a probabilistic choice of relay nodes. The scenario we

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... r consists of high speed streets, such as highways, in which vehicles exhibit one-dimensional movements along the direction of the road. We propose some analytical models for the study of this service and derive performance indices such as the probability that a vehicle is informed, the average number of duplicate messages received by a vehicle and the average delay. Moreover, we use the models to discuss system design issues, which include the proper setting of the forwarding probability at each vehicle, so that a given probability to receive the warning can be guaranteed to all vehicles in the safety area. The analytical results are validated against simulation results. By being very accurate, the models can be instrumental to the performance evaluation and design of broadcasting techniques in inter-vehicular networks. Index Terms-Vehicular networks, broadcast, multi-hop ad hoc networks, road safety.