Performance modeling and optimization of networks of bridged LANs

An internetwork of LANs is modeled as a graph with LAN segments as edges and transparent bridges and repeaters as nodes. The graph model leads to a simple expression for the effective load on an arbitrary LAN segment, which takes into account the overhead traffic due to the learning mechanism of the transparent bridges. Simplifying assumptions for the operation of the MAC layer protocol lead to a simple expression for the average end-to-end delay in terms of the effective loads on the LAN segments. The problem of optimally locating bridges and repeaters on the nodes in order to minimize the average delay is then studied. It is shown that this problem is equivalent to the set partitioning problem, which is NP-complete, but for which good algorithms exist to solve large problems. The related problem of minimizing cost subject to a constraint on average end-to-end delay is also discussed. Finally, the problem of locating bridges and repeaters on a linear topology, as typically found in an office building with a large number of floors, is studied. This special case gives rise to an O(L²) algorithm, where L is the number of floors.