Stochastic analysis for fluid queueing systems

The existing literature on network and queuing analysis has a tendency to move as quickly as possible away from the flow equations to a description of the problem in terms of probabilities, leaving behind the sample path description. In this paper we formulate and solve a number of general questions in this area using sample path methods as an important part of the process. Relying, as it does, on the theory of stochastic differential equations, this approach brings to bear a heretofore ignored but quite effective problem solving methodology. It also serves to bring the subject of controlling queues in closer contact with other branches of automatic control