Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph

Abstract

Abstract. Traffic grooming is a major issue in optical networks. It refers to grouping low rate signals into higher speed streams, in order to reduce the equipment cost. In SONET WDM networks, this cost is mostly given by the number of electronic terminations, namely Add-Drop Multiplexers (ADMs for short). We consider the unidirectional ring topology with a generic grooming factor C, and in this case, in graph-theoretical terms, the traffic grooming problem consists in partitioning the edges of a request graph into subgraphs with at most C edges, while minimizing the total number of vertices of the decomposition.We consider the case when the request graph has bounded degree Δ, and our aim is to design a network (namely, place the ADMs at each node) being able to support any request graph with maximum degree at most Δ. The existing theoretical models in the literature are much more rigid, and do not allow such adaptability. We formalize the problem, and we solve the cases Δ = 2 (for all values of C) and Δ = 3 (except the case C = 4). We also provide lower and upper bounds for the general case.

Drop Cost and Wavelength Optimal Two-Period Grooming with Ratio 4

“…Some articles consider variable (dynamic) traffic, such as finding a solution which works for the maximum traffic demand [7,30] or for all request graphs with a given maximum degree [23], but all keep a fixed grooming factor. In [13] an interesting variation of the traffic grooming problem, grooming for two-period optical networks, has been introduced in order to capture some dynamic nature of the traffic.…”

Graph Partitioning and Traffic Grooming with Bounded Degree Request Graph

“…The cases where ∆ = 2 and the cases ∆ = 3, C = 4 were solved in [12]. In this article we establish the value of M (C, ∆) for the following cases: when ∆ = 3 and C = 4 (answering a conjecture of [12], c.f. Section 3), when ∆ ≥ 4 is even for any C (c.f.…”

“…We would like to place, for each value of the grooming factor C, a minimum number of ADMs at each node in such a way that they could support any traffic pattern where each node is the end-node of at most ∆ requests. This model was recently introduced in [12], and it is interesting because the network can support dynamic traffic without replacement of the ADMs. The problem can be formulated as a graph partition problem as follows: ∆-Degree-Bounded Traffic Grooming in Unidirectional Rings Input: Three integers n (size of the ring), C (grooming factor), and ∆ (maximum degree).…”

An efficient algorithm for solving traffic grooming problems in optical networks

“…In [14], a multi-level decomposition method is introduced to address the multi-layered routing and multi-rate connection characteristics of traffic grooming. In [11], the objective is to design a ring network that is able to satisfy any request graph with maximum degree at most δ. The cases of δ = 2 and δ = 3 were solved by graph decomposition.…”