Optimal stochastic flow control in a high speed virtual circuit

The author addresses the problem of flow control in a high-speed network. The network is modeled as a single virtual circuit consisting of several queues in tandem. Traffic from other queues is modeled as cross-traffic that reduces the available capacity at each queue. A fluid-flow model of the virtual circuit is employed, where the cross-traffic at each queue is a random process consisting of a Markov sequence of values, with shifts in value occurring at points of time described by a pure birth process. Shifts in cross-traffic are assumed to occur only occasionally, so that the control can be considered in the context of a single shift occurring at time zero. The problem of finding the network access control that minimizes the expected delay due to backlogs is shown to be an isoperimetric problem, and the form of the solution is found. Under the additional assumption that shifts in cross-traffic at a queue take on a sequence of independent values, the solution of the Euler equation is shown to have a very simple form. The results are illustrated with a numerical example