In this paper a method of classifying and enumurating a feasible system states of a series of finite queue having exponential distribution has been described. In this paper we investigate the queueing situation when service times are assumed to be exponential and no specific assumption is made concerning the arrival pattern other than that successive interarrival times are independent and identically distributed. The method utilizes matrix multiplication to combine subsystems or to add extra stations to an existing system Storing the classified states of an L-station system the an L-dimensional array.