The problem of optimal end-to-end control of a maximum entropy flow equivalent queueing model of virtual circuit packet-switched networks with non-exponential channel transmission limes is investigated. A new Norton-maximum entropy algorithm is proposed in order to reduce the complexity of the end-to-end network and facilitate the optimization process. It is shown that the flow control mechanism maximizing the throughput, under a bounded time delay criterion, is of ‘window’ type (bang-bang control). The maximum number of packets in transit within the system (i.e. sliding window size) is derived in terms of the maximum allowed average time delay, flow equivalent parameters, and maximum input rate. Numerical results provide useful information on how critically the optimal throughput is affected by the distributional form of the channel transmission times.