A key issue in solving the difficult bus-bunching problem' is being able to have reliable information about the location of the buses in the network. Most advanced public transport systems have buses with GPS devices, but the problem remains of how to send reliable information from the buses to the control unit, particularly when the density of buses is low, but there are high communications reliability requirements. As a solution, we study locating roadside units (RSUs) along the route. The buses, together with the RSUs, form a linear vehicular ad-hoc network (VANET). The RSUs are deployed so to maximize the probability of a vehicle communicating with an RSU in at most two hops. Previous studies on RSU location never took into account two hops, a conceptually different type of network. Rather, they consider that a vehicle is able to communicate only directly to an RSU (one hop), which is a well-known Maximum Covering Problem, in which one of the parties is always immobile, similar to a mobile phone network. Oppositely, our method solves the problem in which two of the intervening parties are mobile and communicate with each other, not possible to solve as a Maximum Covering Problem. We estimate the probability of a vehicle accessing successfully an RSU either directly or through the relay of another vehicle. This probability is later embedded in an integer programming formulation that optimizes the RSU locations for maximum communications likelihood.
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