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In this paper, we investigate the performance of a cellular network using an M/G/n-GPS queue to model the network nodes. We present the performance analysis of a queuing network having multiple chains of customers, using classical queuing networks theory. We only determine the performance evaluation of elastic data transfers in cellular networks. Hence all the chains are assumed to be closed chains. The state probabilities for the closed chains are obtained using multidimensional convolution algorithm and hence the performance measures are calculated which includes sojourn time and average number of customers at all nodes.