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

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