First and second derivative estimators for closed Jackson-like queueing networks using perturbation analysis techniques

摘要

Considers a closed Jackson-like queueing network with arbitrary service time distributions and derives an unbiased second derivative estimator of the throughput over N customers served at some node with respect to a parameter of the service distribution at that node. The authors' approach gives new insights to the type of sample path information needed to condition on for higher-order derivative estimation. Despite the complexity of the analysis, the final algorithm obtained is relatively simple. The authors' estimators can be used in conjunction with other techniques to obtain rational approximations of the entire throughput response surface as a function of system parameters.