FIRST-DERIVATIVE AND 2ND-DERIVATIVE ESTIMATORS FOR CYCLIC CLOSED-QUEUING NETWORKS

We consider a cyclic closed-queueing network with arbitrary service ti me distributions and derive first- and second-derivative estimators of some finite horizon performance metrics with respect to a parameter o f any one of the service distributions. Our approach is based on obser ving a single sample path of this system and evaluating first- and sec ond-order effects on departure times as a result of the parameter pert urbation. We then define an estimator as a conditional expectation ove r appropriate observable quantities, using smoothed perturbation analy sis techniques, This process recovers the first-derivative estimator a long the way and gives new insights into event order change phenomena which are of higher order, Despite the complexity of the analysis, the final algorithms we obtain are relatively simple, Further, we show th at our estimators are unbiased and include some numerical examples, We also show the use of our estimators in obtaining approximations of th e entire system response surface as a function of system parameters.