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