Motivated by experience gained during the validation of a recent Approximate Mean Value Analysis (AMVA) model of modern shared memory architectures, this paper re-examines the "standard" AMVA approximation for non-exponential FCFS queues. We find that this approximation is often inaccurate for FCFS queues with high service time variability. For such queues, we propose and evaluate: (1) AMVA estimates of the mean residual service time at an arrival instant that are much more accurate than the

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... ndard AMVA estimate, (2) a new AMVA technique that provides a much more accurate estimate of mean center residence time than the standard AMVA estimate, and (3) a new AMVA technique for computing the mean residence time at a "downstream" queue which has a more bursty arrival process than is assumed in the standard AMVA equations. Together, these new techniques increase the range of applications to which AMVA may be fruitfully applied, so that for example, the memory system architecture of shared memory systems with complex modern processors can 'be analyzed with these computationally efficient methods.