Input buffer limiting: behavior analysis of a node throughout the range of blocking probabilities

A numerical method is suggested for estimating the performance parameters of a node with input buffer limiting, throughout the range of blocking probabilities. Congestion is attributed to the sudden increase in the effective service time when the input rate increases. This sudden increase, resulting in the thrashing of the throughput rate, can be related to changes in the shape of the potential function of the node. The methodology of deriving the potential function of the node from its gradient dynamics and dynamic flow conservation considerations is presented. Using the results from catastrophe theory, it is shown that the abrupt changes in the throughput can be expected due to the existence of a catastrophe point in the parameter space. The behavior of a node in a homogeneous network can be characterized by a fold catastrophe. The simulation results are found to agree with the results obtained by the numerical method