The problem of the optimal flow control of a G/G/l queue at equilibrium is investigated by approximating the general (G-type) distributions by a maximum entropy model with known first two moments. 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. Furthermore, 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 distributional form of the interarrival and service patterns and a conjecture on performance bounds is made.