Simulation vs Numerical Convolution — The Study of a Discrepancy

In this note, predictions for an M/D/1 queue with alternating high (>1) and low traffic intensities are derived using elementary deterministic and queueing theoretic methods. These are compared with results available from a simulation study. Good agreement between the two sets of results is found except for one discrepancy which an exact analysis by numerical convolution failed to resolve and for which a tentative explanation is given.