A closed queuing network that consists of M nodes was studied, and in contrast to an open network, there is a constant population of K customers in the network with no external source or sink. Each node i is a first in first out queue, where the service time is drawn independently. That is, the service time is exponentially distributed with service rates ? ? ii n ? and a customer departing from queue i chooses j next with probability j iq , . The Gordon and Newel theorem with the arrival properties of a closed network were used to analyze the Mean values for the number of customers, sojourn time, waiting times and the algorithm for solving the mean value for closed networks were then derived with series of application considered.