Discrete time stability analysis of an explicit rate algorithm for the ABR service

The study pursues a discrete stability analysis of a control algorithm for the available bit rate (ABR) service, denoted proportional rate and queue control algorithm (PRQCA), applied on an ATM system using FCFS scheduled switch buffers for the ABR traffic. The analysis establishes a stability condition for the control parameters of the PRQCA by using a control theoretic approach to the feedback control. The discrete model enables an implicit relation between the control parameters and the sample rate of the system, which is not possible in a continuous time model. Furthermore, for cases with different feedback delays, a mean value approximation, denoted effective delay, is introduced to replace the individual feedback delays in the analysis. A relation is derived to set the additive increase rate parameter (AIR) to avoid initial oscillations during low rates of backward resource management (RM) cells without affecting the dynamics during sufficient RM cell rates. An enhancement of the algorithm used to estimate the fair share rate (CCR averaging), is introduced to enable a mix of connections with and without rate constraints in the system while the reference values for both the rate and the queue length are still met.