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The operation of digital systems are based on time slotting and it finds many applications particularly in communication networks. It is important to analyze a digital network on some digital concepts. In this paper we analyze the network buffer through discrete time queueing system in which queue is discrete in nature and it is used to analyze the performance of the communication networks buffer. Discrete time models can be used to represents such type of systems in terms of slotted time units to models any physical system. More than one state changes in discrete time models from one time unit to another. Discrete time markov chains are used to describes the behavior of the network under the specific conditions and various performance measures are evaluated such as queue length, mean waiting time and mean number in the system.