Performance sensitivity formulae, algorithms and estimates for closed queueing networks with exponential servers

We study the sensitivities of the performance measures in a closed queueing network with exponential service requirements and load-dependent service rates. The performance measures have two general forms: customer average and time average. We derive formulae for the elasticities of the performance measures for both averages with respect to system parameters and develop efficient algorithms for the calculation of them. The obtained formulae lead naturally to new on-line consistent estimation schemes for the elasticities; these schemes are based purely on the sample average performances, thus recursive and requiring no knowledge of the system parameters