Relationship Between Perturbation Realization Factors With Queueing Models and Markov Models

Perturbation realization factor is an important concept in perturbation analysis of both queueing systems and Markov systems. A perturbation realization factor measures the effect of a perturbation on the system performance. This concept is important for the performance sensitivity and performance optimization of these systems. Since the perturbations in queueing systems are continuous in nature and those in Markov systems are discrete, it is not straightforward to establish the relationship between these two types of fundamental concepts. This note solves this long-standing problem. We find a formula that links these two types of perturbation realization factors in Gordon-Newell and open Jackson networks together. The results enhance our understanding of perturbation analysis and lead to new research directions.