Feedback-based flow control of B-ISDN/ATM networks

We consider a system comprising of a single bottleneck switch/node that is fed by N independent Markov-modulated fluid sources. There is a fixed propagation delay incurred by the traffic between these sources and the switch. We assume that the switch sends periodic feedback in the form of a single congestion indicator bit. This feedback also incurs a fixed propagation delay in reaching the sources. Upon reaching the sources (or the access controllers associated with the sources), this congestion indicator bit is used to choose between two rates for the excess traffic, high or low, possibly depending on the state of that source. The switch employs a threshold mechanism based on its buffer level to discard excess traffic. We show that the stationary distribution of this system satisfies a set of first-order linear differential equations along with a set of split boundary conditions. We obtain an explicit solution to these using spectral decomposition. To this end we investigate the related eigenvalue problem. Based on these results we investigate the role of delayed feedback vis-a-vis various time-constants and traffic parameters associated with the system. In particular, we identify conditions under which the feedback scheme offers significant improvement over the open-loop scheme