Grooming of Symmetric Traffic in Unidirectional SONET/WDM Rings

In SONET/WDM networks, a wavelength channel is shared by multiple low-rate traffic demands. The multiplexing is known as traffic grooming and realized by SONET add-drop multiplexers (SADM). The grooming factor is the maximum number of low-rate traffic demands that can be multiplexed in one wavelength. Since SADMs are expensive, a key optimization problem in traffic grooming is to minimize the number of SADMs. This optimization problem is challenging and NP-hard even for unidirectional SONET/WDM ring networks with symmetric unitary traffic demands. In this paper, we propose an algorithm for this NP-hard problem. For a set R of symmetric pairs of unitary traffic demands on a SONET ring with n nodes, and a grooming factor of k, our algorithm grooms R into [|R|]/k wavelengths using at most [(1 + 1/k)|R|] + [n/4] SADMs. It can be proved that there exists an instance whose optimal solution requires as many as (1 + 1/k)|R| + |R|/2k SADMs, which is very close to our upper bound. For the guaranteed performance, our algorithm achieves a better approximation ratio than previous ones. Our algorithm uses the minimum number of wavelengths that are also precious resources in optical networks. In addition, the experimental results show that our algorithm has much better practical performance than the previous algorithms in most cases.