A UNIQUENESS THEOREM FOR BUFFER ALLOCATION

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