First and second derivative estimators of a closed queuing network throughput using perturbation analysis techniques

A serial closed queueing network with arbitrary service time distributions is considered and a second served at some node with respect to a parameter of the service distribution at that node is derived. The authors' approach recovers the first derivative estimator along the way. Despite the complexity of the analysis, the final algorithm is relatively simple. It is shown that the authors' estimators are unbiased. Strong consistency is proved for a special case. A numerical example is included. The authors contend that their estimators can be used in conjunction with other techniques to obtain approximations of the entire throughput response surface as a function of system parameters