On-line sensitivity analysis of feedback controlled queueing systems with respect to buffer capacity

The paper develops a method for online estimation of performance sensitivities between the nominal system and the perturbed systems. With this method, the performance measures of the nominal system are first obtained by observing a sample path of the nominal system. Then, estimators which utilize the proportional relationship between the steady state probabilities of the nominal and perturbed systems are derived. These estimators compute the performance measures of the perturbed system from the data observed in the sample path. The performance sensitivities are determined by calculating the differences between the performance measures of the nominal and perturbed systems. Applying the proportional relationship method, the paper studies a feedback controlled queueing system. Through the proportional relationship, sensitivities of the loss probability, mean queue length, and mean delay with respect to the buffer capacity are determined. The method developed in the paper has several advantages. The method is applicable to determining performance sensitivities in queueing systems (such as the feedback controlled queueing system studied in the paper) which are not amenable to existing online sensitivity estimation methods. The method also requires less system information than existing methods and is applicable even when some system information is a priori unknown or not available in the observed data