Realization factors and perturbation analysis of open queueing networks

The perturbation analysis of open queuing networks is discussed. The concept of realization probability is extended to realization factors for open networks. A set of linear equations is derived for realization factors. It is shown that the perturbation analysis estimate of the sensitivity of a performance measure with respect to a mean service rate (or a mean interarrival rate) converges with probability one to the sensitivity of the steady-state performance measure, which simply equals the expected value of the realization factor. The results provide an analytical method of calculating performance sensitivity and form a theoretical foundation for perturbation analysis of open networks