Stability and performance analysis of rate-based feedback flow controlled ATM networks

Motivated by ABR class of service in ATM networks, we study a continuous time queueing system with a feedback control of the arrival rate of some of the sources. The feedback about the queue length or the total workload is provided at regular intervals (variations on it, especially the traffic management specification TM 4.0, are also considered). The propagation delays can be nonnegligible. For a general class of feedback algorithms, we obtain the stability of the system in the presence of one or more bottleneck nodes in the virtual circuit. Our system is general enough that it can be useful to study feedback control in other network protocols. We also obtain rates of convergence to the stationary distributions and finiteness of moments. For the single bottleneck case, we provide algorithms to compute the stationary distributions and the moments of the sojourn times in different sets of states. We also show analytically (by showing continuity of stationary distributions and moments) that for small propagation delays, we can provide feedback algorithms which have higher mean throughput, lower probability of overflow and lower delay jitter than any open loop policy. Finally these results are supplemented by some computational results.