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An approximation for the distribution of time delays experienced by a customer in a network of queues is presented. Approximate analytical models are necessary since exact solutions are only available for a very restricted class of networks, and are too complex computationally to be viable in practice. Approximations have so far often proved inadequate, particularly for closed networks with first come first served queueing disciplines. We also prove that the correlation between the sojourn times at successive servers on a customer's path in a closed queueing network with exponential servers is negative.