# Design of logical topologies for wavelength-routed optical networks

## Abstract

This paper studies the problem of designing a logical topology over a wavelength-routed all-optical network (AON) physical topology. The physical topology consists of the nodes and fiber links in the network. On an AON physical topology, we can set up lightpaths between pairs of nodes, where a lightpath represents a direct optical connection without any intermediate electronics. The set of lightpaths along with the nodes constitutes the logical topology. For a given network physical topology and traffic pattern (relative traffic distribution among the source-destination pairs), our objective is to design the logical topology and the routing algorithm on that topology so as to minimize the network congestion while constraining the average delay seen by a source-destination pair and the amount of processing required at the nodes (degree of the logical topology). We will see that ignoring the delay constraints can result in fairly convoluted logical topologies with very long delays. On the other hand, in all our examples, imposing it results in a minimal increase in congestion. While the number of wavelengths required to imbed the resulting logical topology on the physical all-optical topology is also a constraint in general, we find that in many cases of interest this number can be quite small. We formulate the combined logical topology design and routing problem described above (ignoring the constraint on the number of available wavelengths) as a mixed integer linear programming problem which we then solve for a number of cases of a six-node network. Since this programming problem is computationally intractable for larger networks, we split it into two subproblems: logical topology design, which is computationally hard and will probably require heuristic algorithms, and routing, which can be solved by a linear program. We then compare the performance of several heuristic topology design algorithms (that do take wavelength assignment constraints into account) against that of randomly generated topologies, as well as lower bounds derived in the paper.