A UNIQUENESS THEOREM FOR BUFFER ALLOCATION

The exact or numerical analysis of many queueing systems is often intractable due to the complexity and size of the state space and the lack of decomposability. A frequently used paradigm for the approximate solution involves three steps. i) Partition the system into subsystem. ii) Solve each subsystem in isolation ignoring subsystem interactions. Introduce parameters to account for the unknown effects of subsystem interactions. iii) Determine the ''correct'' parameter values by invoking some form of continuity at the subsystem interfaces. Often the parameters are a fixed point of some mapping. The existence of a fixed point is usually trivial: the uniqueness is generally not. This paper examines flow control in a packet switching network by input buffer limits. It proves the paradigm determines a unique set of parameters.