In this paper, we present a numerical approach to the performance study of a delayed feedback system with one congested node and multiple connections. This approach consists of modeling the feedback system as a finite quasi-birth-death process. Due to the peculiar block tridiagonal nature of its generator, efficient techniques exist for its steady-state and transient solutions. Using these techniques, we examine a simple parsimonious feedback system for issues such as throughput/loss performance, fairness, and stability. Our approach has the flexibility to study the effect of several additional factors such as asynchronous feedback, two-level control, and explicit rate notification in the presence of underlying high-priority traffic. This study brings to light the tradeoffs between system performance and the complexity of the feedback scheme. Our study shows that the time scales of correlation of the feedback system have a dominant effect on its performance. These time scales are associated with the feedback delay, the durations of active/idle periods of traffic sources, and the time scales of the underlying high-priority traffic. We also examine the effect of the time scales on the convergence time for the transient queueing system.

Closed-loop input rate regulation schemes have come to play an important role in the transport of the available bit rate (ABR) traffic service category for ATM. We present a numerical approach to the performance study of a delayed feedback system with one congested node and multiple connections. This approach consists in modeling the feedback system as a finite quasi-birth-death (QBD) process. Due to the peculiar block tri-diagonal nature of its generator, efficient techniques exist for its steady-state and transient solutions. Using these techniques, we examine a simple parsimonious feedback system for issues such as throughput/loss performance, fairness and stability. Our approach has the flexibility to study the effect of several additional factors such as asynchronous feedback, two-level control and explicit rate notification in the presence of underlying high-priority traffic. This study brings to light the trade-offs between system performance and the complexity of the feedback scheme. Our study shows that the time scales of correlation of the feedback system have a dominant effect on its performance. These time scales are associated with the feedback delay, the durations of active/idle periods of traffic sources and the time scales of the underlying high-priority traffic. We also examine the effect of the time scales on the convergence time for the transient queueing system.