CAPACITY ASSIGNMENT FOR CIRCUIT-SWITCHED REFERENCE NETWORKS WITH NONHIERARCHICAL ROUTING

Capacity assignment (CA) implies the minimization of network cost subject to several constraints, such as traffic demands, end-to-end Grade of Services (GOS) and the non negativity conservation of flows. Real asymmetric networks may be described by several statistical moments of different orders. Thus a reference network may be characterized by the mean distance between a given set of fully intermeshed nodes, the mean traffic offered per demand pair, and the mean GOS for all end-to-end blockings. At first, we present an exact theoretical solution of the CA-problem for symmetric circuit- switched networks. We start with the formulation of the end-to-end blockinges with nonhierarchical two-link path alternate routing for reversible and nonreversible scheme, respectively. Next, we derive the Kuhn-Tucker conditions for the CA-problem. The corresponding solution is verified to be unique and stable. Then, we proceed to approximate the relevant optimal parameters, such as die economic high link blocking, the optimal size of routing sequences and the minimum link size, by using least-square fitting. The results form new rules of thumb for a wide range of traffic demand and GOS and may thus be used to support the initial dimensioning of asymmetric nonhierarchical networks. Finally an approximation for asymmetric networks is proposed and verified, which is based on an appropriate CA decomposition and relevant traffic parameters of both the symmetric reference and its asymmetric extension.