Stability analysis of an optical system with random delay lines lengths

A new model of an optical buffer system is considered, in which the differences $\{\Delta_n\}$ between the lengths of two adjacent fiber delay lines (FDLs) are random. This is an extension of the model considered in [1] where these differences (also referred to as granularity) are constant, i. e., $\Delta_n\equiv const$. The system is modeled by utilizing the random-walk theory and closely-related asymptotic results of the renewal theory, such as the inspection paradox and the Lorden's inequality. A stability analysis is performed based on the regenerative approach. Some numerical results are included as well, showing that the obtained conditions delimit the stability region with high accuracy.