Structural stability aspects of alternate routing in non-hierarchical networks under reservation

A behavioral characterization of nonhierarchical alternate routing schemes in which a certain number of trunks are reserved for direct routed traffic is presented. It is found that the fundamental behavioral characteristic of the schemes with trunk reservation control is the same as that of the schemes without reservation. A sufficient condition, which can be utilized to find the minimum number of trunks to be reserved for direct routed traffic so as to avoid the instability, obtained. Although the sufficient condition allows absolute stability of the system from the point of view of catastrophe theory, the designer may select a lower number of trunks to be reserved, provided that the stable equilibrium states remain close to each other. A performance index for comparing various levels of reservations among themselves is proposed