The increase of complex information results in the need of computer processing, and for the better utilization of computer systems and for fast and remote teleprocessing, it is naturally stressed to construct computer network systems. This research involves two topics. One is the design and implementation of NOVA-CYBER Communication System(NCCS) which is a two mode computer to computer communication system, and the other is the statistical modeling and computations for minimal line cost network topology of Korean Computer Network(KCN) model. NCCS has two modes-Batch mode and interactive model. Batch mode communication is performed by the characteristics of emulator of NCCS, and interactive mode communication is done by message relay function of NCCS. The preprocessor and postprocessor reside in disk and main communication processor is in a resident proportion of operating system. KCN is a multidrop line organized terminal oriented computer network. KCN model is divided into 8 submodels according to the priority schemes and the line organizations, half duplex line and full duplex line. For each submodels, the statistical values of response time are computed using single channel-single station queuing theories. The iterative algorithm to find the minimal line cost network topology of multidrop computer network is presented. Lastly a various experimentations, computations, and their results are discussed.