The problem of optimal flow control of a general queuing network with random routing as a model of virtual circuit or datagram computer communication networks is presented by approximating the general channel transmission-time distributions by a maximum entropy model with known first-two moments. A Norton-maximum entropy algorithm is used to facilitate the optimisation process. It is shown that the flow control mechanism maximising the throughput, under a bounded time delay criterion, is of the 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. Consequently, the relationship between the maximum throughput and maximum time delay is determined. Numerical examples provide useful information on how critically the optimal throughput is affected by the random routing and the distributional form of the traffic patterns.