Abstract: We design and implement an algorithm for solving the static RWA problem based on an LPrelaxation formulation. This formulation is capable of providing integer optimal solutions despite the absence of integrality constraints for a large subset of RWA input instances. In static RWA there is no a-priori knowledge of the channels usage and the interference among them cannot be avoided once the solution has been found. To take into consideration adjacent channel interference, we extend our formulation and model the interference by a set of analytical formulas as additional constraints on RWA.

Abstract: We design and implement various algorithms for
solving the static RWA problem with the objective of minimizing
the maximum number of requested wavelengths based on LPrelaxation formulations. We present a link formulation, a path
formulation and a heuristic that breaks the problem in the two
constituent subproblems and solves them individually and
sequentially. The flow cost functions that are used in these
formulations result in providing integer optimal solutions despite
the absence of integrality constraints for a large subset of RWA
input instances, while also minimizing the total number of used
wavelengths. We present a random perturbation technique that is
shown to increase the number of instances for which we find
integer solutions, and we also present appropriate iterative fixing
and rounding methods to be used when the algorithms do not yield
integer solutions. We comment on the number of variables and
constraints these formulations require and perform extensive
simulations to compare their performance to that of a typical minmax
congestion formulation.

Abstract: We consider the offline version of the routing and
wavelength assignment (RWA) problem in transparent all-optical networks. In such networks and in the absence of regenerators, the signal quality of transmission degrades due to physical layer
impairments. We initially present an algorithm for solving the static RWA problem based on an LPrelaxation formulation that tends to yield integer solutions. To account for signal degradation due to physical impairments, we model the effects of the path length, the path hop count, and the interference among ligthpaths by imposing additional (soft) constraints on RWA. The objective of the resulting optimization problem is not only to serve the
connection requests using the available wavelengths, but also to minimize the total accumulated signal degradation on the selected lightpaths. Our simulation studies indicate that the proposed RWA algorithms select the lightpaths for the requested connections so as to avoid impairment generating sources, thus dramatically reducing the overall physical-layer blocking when compared to RWA algorithms that do not account for impairments.

Abstract: We consider the offline version of the routing and
wavelength assignment (RWA) problem in transparent all-optical
networks. In such networks and in the absence of regenerators,
the signal quality of transmission degrades due to physical layer
impairments. Because of certain physical effects, routing choices
made for one lightpath affect and are affected by the choices made
for the other lightpaths. This interference among the lightpaths
is particularly difficult to formulate in an offline algorithm since,
in this version of the problem, we start without any established
connections and the utilization of lightpaths are the variables of
the problem.We initially present an algorithm for solving the pure
(without impairments) RWA problem based on a LP-relaxation
formulation that tends to yield integer solutions. Then, we extend
this algorithm and present two impairment-aware (IA) RWA algorithms
that account for the interference among lightpaths in their
formulation. The first algorithm takes the physical layer indirectly
into account by limiting the impairment-generating sources. The
second algorithm uses noise variance-related parameters to directly
account for the most important physical impairments. The
objective of the resulting cross-layer optimization problem is not
only to serve the connections using a small number of wavelengths
(network layer objective), but also to select lightpaths that have
acceptable quality of transmission (physical layer objective).
Simulations experiments using realistic network, physical layer,
and traffic parameters indicate that the proposed algorithms can
solve real problems within acceptable time.