On the structural uniqueness of alternate routing schemes in non-hierarchical networks

The authors examine the structural relationship between load and blocking probability for a fully connected homogeneous nonhierarchical network when blocked messages cause retrial and when different alternate routing strategies are employed to overcome congestion. The model employed for analysis is based on the flow approximation. It is found that retrials push the stable equilibrium state away from the zero blocking state, thereby aggravating congestion. The alternate routing strategies accommodate the stable equilibrium state close to the zero blocking state. However, both the retrials and the alternate routing strategies do not alter the fundamental structure of the system, namely, the fold catastrophe. By solving the degenerate equation, the value of appropriate control parameters can be obtained. According to the present model, it is only under schemes with no alternate routing that the system attains stability, in the mathematical sense of the term.<<ETX>>