Conservation equations and variance reduction in queueing simulations

We consider the efficient estimation of mean delay in queue, <italic>d</italic>, mean wait in system, <italic>w</italic>, time average number in queue, <italic>Q</italic>, and time average number in system, <italic>L</italic>, for simulated queueing systems. We prove for the <italic>GI/G/s</italic> queue that it is more efficient to estimate <italic>w, Q</italic>, and <italic>L</italic> from an estimate of <italic>d</italic> than it is to estimate them directly. This generalizes previous results for the <italic>M/G/</italic>l queue and also confirms empirical studies on other <italic>GI/G/s</italic> queues.