Expressions are given for the first and second moments of the queue-length distribution of the single-server queue with constant service time and general arrival distribution. A general relationship between the moments of the queue-length and message-delay distributions holds in the particular case of a first-come-first-served queue discipline. The results for a single queue enable mean message delay to be estimated for a network of queues, with both deterministic and adaptive routing doctrines. Criteria for the rational choice of a deterministic doctrine for a given network and traffic matrix follow directly. A simulation study of a practical network supports the theoretical discussion, and reveals the message-delay distribution in greater detail. Adaptive simulation emerges as a useful tool for designing a network to carry a given traffic loading most efficiently.