No abstract

A bs t r ac tBehavior characteristics of alternate routing schemes under homogeneous traffic in fully connected nonhierarchical networks have been investigated in the past. The fundamental behavioral characteristic of these networks has been shown t o be that of a fold catastro he. In this paper, we investigate the behavioral as ects wien the traffic intensity towards a node is much higger when compared with the t r d c intensity towards other nodes. We call the high intensity traffic the concentrated trafic. In relation to the traffic intensity corresponding to the fold point under homogeneous traffic, the concentrated t r d c intensity may be much higher while the intensity of traffic other than the concentrated one is mudl lower. For the behavioral characterization of the node under concentrated traffic, the tool of analysis employed in this paper is the same as that employed in the earlier behavioral analyses under uniform traffic: formulating the flow balance function, then obtaining the potential function from the flow balance function and finally finding the degeneracy of the potential function based on tlie results from catastrophe theory. The model presented in this paper is only for the node under the concentrated traffic. The analysis, though based on the average values of traffic parameters, yields satisfactory results when compared with the results obtained from siinulation when the number of trunks per link is large.

Structural relation between load and blocking probability of an alternate routing scheme employed in a fully connected homogeneous non-hierarchical network is already known. In this paper, we inspect the structural aspects of such a scheme when blocked messages make retrial, and when different alternate routing strategies are employed so as to overcome congestion. The model employed for analysis is based on the p o w approximation. It is found that retrials push the stable equilibrium state away from the zero blocking state, thereby aggravating congestion. The alternate routing stmtegies 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.