This paper studies the decentralized output-feedback control of large-scale systems defined over a directed connected graph with communication delay and random missing measurements. The nodes in the graph represent the subsystems, and the edges represent the communication connection. The information travels across an edge in the graph and suffers from one step communication delay. For saving the storage space, the information delayed more than D step times is discarded. In addition, to model the system in a more practical case, we assume that the observation for the subsystem output suffers random missing. Under this new information pattern, the optimal output-feedback control problem is non-convex, what is worse, the separation principle fails. This implies that the optimal control problem with the information pattern introduced above is difficult to solve. In this paper, a new decentralized control scheme is proposed. In particular, a new estimator structure and a new controller structure are constructed, and the gains of the estimator and the controller are designed simultaneously. An optimality condition with respect to the gains is established. Based on the optimality condition, an iterative algorithm is exploited to design the gains numerically. It is shown that the exploited algorithm converges to Nash optimum. Finally, the proposed theoretical results are illustrated by a physical system which is a heavy duty vehicles platoon. (C) 2018 Elsevier Ltd. All rights reserved.