Regenerative simulation of response times in networks of queues: statistical efficiency

Abstract

This paper deals with the statistical efficiency of estimation methods for "passage times" in closed, multiclass networks of queues with priorities. Informally, a passage time is the time for a job to traverse a portion of the network. Such quantities are important in computer and communication system models, and in this context, quantities other than mean values are of interest. We consider here the efficiencies of the "marked job method" for passage time simulation (based on the tracking of a distinguished job) and the "decomposition method" in which observed passage times for all of the jobs enter in the construction of point and interval estimates. We show that the decomposition method is superior in that, for simulations of equal length, it produces tighter confidence intervals. We also calculate theoretical values for variance constants entering into central limit theorems used to obtain confidence intervals for mean passage times. These results provide a means of quantifying the relative efficiency of the decomposition method.