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This paper presents a distributed MPC scheme for the class of input-coupled linear systems implemented over wireless networks. The approach allows each agent to achieve reduced communication latency by sending less information to their neighbours. Uncertainties incurred by this delayed and incomplete information are handled by a constraint tightening procedure. Simulation examples demonstrate that for distributed systems with chain structure, our tightening method is invariant to the number of agents in the network. Moreover, we show that by a proper tuning of latency, an optimized control performance can be achieved.