In this paper a distributed model predictive control (DMPC) strategy with network-induced, bounded, time-varying, communication delays is proposed. The non-cooperative algorithm is successfully tested in simulation on a cooperative adaptive cruise control (CACC) vehicle platoon, with unidirectional communication links. Using a five vehicle platoon with a leader-following framework, the proposed DMPC strategy with variable communication delays is compared with a DMPC method with constant delays in the communication network, and the results are promising.