Grooming Ratio Research Articles

Optimal Groomings with Grooming Ratios Six and Seven

Grooming uniform all-to-all traffic in optical (SONET) rings with grooming ratio C requires the determination of a decomposition of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The determination of optimal C-groomings has been considered for , and completely solved for . For , it has been shown that the lower bound for the drop cost of an optimal C-grooming can be attained for almost all orders with 5 exceptions and 308 possible exceptions. For , there are infinitely many unsettled orders; especially the case is far from complete. In this paper, we show that the lower bound for the drop cost of a 6-grooming can be attained for almost all orders by reducing the 308 possible exceptions to 3, and that the lower bound for the drop cost of a 7-grooming can be attained for almost all orders with seven exceptions and 16 possible exceptions. Moreover, for the unsettled orders, we give upper bounds for the minimum drop costs.

A Complete Solution to Spectrum Problem for Five‐Vertex Graphs with Application to Traffic Grooming in Optical Networks

AbstractA G‐design of order n is a decomposition of the complete graph on n vertices into edge‐disjoint subgraphs isomorphic to G. Grooming uniform all‐to‐all traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph on n vertices into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The existence spectrum problem of G‐designs for five‐vertex graphs is a long standing problem posed by Bermond, Huang, Rosa and Sotteau in 1980, which is closely related to traffic groomings in optical networks. Although considerable progress has been made over the past 30 years, the existence problems for such G‐designs and their related traffic groomings in optical networks are far from complete. In this paper, we first give a complete solution to this spectrum problem for five‐vertex graphs by eliminating all the undetermined possible exceptions. Then, we determine almost completely the minimum drop cost of 8‐groomings for all orders n by reducing the 37 possible exceptions to 8. Finally, we show the minimum possible drop cost of 9‐groomings for all orders n is realizable with 14 exceptions and 12 possible exceptions.

Optical grooming with grooming ratio nine

Grooming uniform all-to-all traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The minimum drop cost is determined for grooming ratio 9. Previously this bound was shown to be met when n ≡ 0 ( mod 9 ) with two exceptions and eleven additional possible exceptions for n , and also when n ≡ 1 ( mod 9 ) with one exception and one possible exception for n . In this paper it is shown that the bound is met for all n ≡ 2 , 5 , 8 ( mod 9 ) with four exceptions for n ∈ { 8 , 11 , 14 , 17 } and one possible exception for n = 20 . Using this result, it is further shown that when n ≡ 3 , 4 , 6 , 7 ( mod 9 ) and n is sufficiently large, the bound is also met.

Optical grooming with grooming ratio eight

Grooming uniform all-to-all traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The minimum possible drop cost is determined for grooming ratio 8, and this cost is shown to be realized with six exceptions, and 37 possible exceptions, the largest being 105.

Minimizing SONET ADMs in Unidirectional WDM Rings with Grooming Ratio Seven

In order to reduce the number of add-drop multiplexers (ADMs) in SONET/WDM networks using wavelength add-drop multiplexing, certain graph decompositions can be used to form a “grooming” that specifies the assignment of traffic to wavelengths. When traffic among nodes is all-to-all and uniform, the drop cost of such a decomposition is the sum, over all graphs in the decomposition, of the number of vertices of nonzero degree in the graph. The number of ADMs required is this drop cost. The existence of such decompositions with minimum cost, when every pair of sites employs no more than $\frac{1}{7}$ of the wavelength capacity, is determined within an additive constant. Indeed when the number n of sites satisfies $n \equiv 1$ (mod 3) and $n \neq 19$, the determination is exact; when $n \equiv 0$ (mod 3), $n \not\equiv 18$ (mod 24), and n is large enough, the determination is also exact; and when $n \equiv 2$ (mod 3) and n is large enough, the gap between the cost of the best construction and the cost of the lower bound is independent of n and does not exceed 4.

APPROXIMATIONS FOR ALL-TO-ALL UNIFORM TRAFFIC GROOMING ON UNIDIRECTIONAL RINGS

Traffic grooming in a WDM network consists of assigning to each request (lightpath) a wavelength with the constraint that a given wavelength can carry at most C requests or equivalently a request uses 1/C of the bandwidth. C is known as the grooming ratio. A request (lightpath) needs two SONET add-drop multiplexers (ADMs) at each end node; using grooming, different requests can share the same ADM. The so called traffic grooming problem consists of minimizing the total number of ADMs to be used (in order to reduce the overall cost of the network). Here we consider the traffic grooming problem in WDM unidirectional rings which has been recently shown to be APX-hard and for which no constant approximations are known. We furthermore suppose an all to all uniform unitary traffic. This problem has been optimally solved for specific values of the grooming ratio, namely C = 2, 3, 4, 5, 6. In this paper we present various simple constructions for the grooming problem providing approximation of the total number of ADMs with a small constant ratio. For that we use the fact that the problem corresponds to a partition of the edges of the complete graph into subgraphs, where each subgraph has at most C edges and where the total number of vertices has to be minimized.

Multiobjective evolutionary approach to cost-effective traffic grooming in unidirectional SONET/WDM rings

Traffic grooming in optical networks is the process of multiplexing and demultiplexing low-speed traffic streams onto high-speed wavelengths. The research in the domain of traffic grooming mainly focuses on minimizing number of SONET add/drop multiplexers (SADMs) in SONET/WDM rings and it has been shown that they can potentially be reduced by careful assignment of low-speed traffic streams onto high-speed wavelengths. However, the cost of the network not only depends on the number of SADMs, but also the number of wavelengths and the grooming ratio. It is often the case that all of them cannot be minimized simultaneously. In this article, the problem of minimization of cost of a SONET/WDM unidirectional ring has been modeled as a multiobjective optimization problem which simultaneously minimizes the number of SADMs, the number of wavelengths, and the grooming ratio. A popular multiobjective genetic algorithm (NSGA-II) has been used as the underlying optimization tool. The resultant set of near-Pareto-optimal solutions contains a number of nondominated solutions, which the user can judge relatively and pick up the most promising one according to the problem requirements. Performance of the proposed algorithm has been demonstrated on different network topologies.

Grooming for two‐period optical networks

AbstractMinimizing the number of add‐drop multiplexers (ADMs) in a unidirectional SONET ring can be formulated as a graph decomposition problem. When traffic requirements are uniform and all‐to‐all, groomings that minimize the number of ADMs (equivalently, the drop cost) have been characterized for grooming ratio at most six. However, when two different traffic requirements are supported, these solutions do not ensure optimality. In two‐period optical networks, n vertices are required to support a grooming ratio of Ca in the first time period, while in the second time period a grooming ratio of Cb, Cb<Ca, is required for v ≤ n vertices. This allows the two‐period grooming problem to be expressed as an optimization problem on graph decompositions of Kn that embed graph decompositions of Kv for v ≤ n. Using this formulation, optimal two‐period groomings are found for small grooming ratios using techniques from the theory of graphs and designs. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008

Virtual topology reconfiguration on optical WDM networks considering traffic grooming

This paper investigates the virtual topology reconfiguration (VTR) problem of optical WDM networks by taking the traffic grooming factor into consideration. Firstly, by applying a common “divide and conquer” approach, the problem is categorized and handled as two independent sub-problems, triggering policy and the proper algorithm. Secondly, the VTR problem considering traffic grooming is formulated with new variables and constraints by a mixed-integer linear program (MILP). In order to handle the tradeoff between the advantages and disadvantages of VTR, both network resource utilization and network disruption are examined and quantified in terms of measurable parameters. A new multi-objective VTR algorithm called integrated reconfiguration (IR) algorithm is proposed to provide better overall VTR performance. Different from previous studies this newly proposed VTR algorithm combines three main factors (traffic load, traffic grooming ratio and route length of lightpaths) into one single objective and considers them all when reconfiguring. The results of simulations indicate that proposed VTR policy, periodic VTR triggering policy with IR algorithm, achieves performance improvements for overall VTR performance.

Traffic Grooming in Unidirectional Wavelength-Division Multiplexed Rings with Grooming RatioC= 6

SONET/WDM networks using wavelength add-drop multiplexing can be constructed using certain graph decompositions used to form a grooming, consisting of unions of primitive rings. The cost of such a decomposition is the sum, over all graphs in the decomposition, of the number of vertices of nonzero degree in the graph. The existence of such decompositions with minimum cost, when every pair of sites employs no more than $\frac{1}{6}$ of the wavelength capacity, is determined with a finite number of possible exceptions. Indeed, when the number N of sites satisfies $N \equiv 1 \pmod{3}$, the determination is complete, and when $N \equiv 2 \pmod{3}$, the only value left undetermined is N = 17. When $N \equiv 0 \pmod{3}$, a finite number of values of N remain, the largest being N = 2580. The techniques developed rely heavily on tools from combinatorial design theory.

Minimizing SONET ADMs in unidirectional WDM rings with grooming ratio 3

AbstractWe consider traffic grooming in WDM unidirectional rings with all‐to‐all uniform unitary traffic. We determine the minimum number of SONET/SDH add–drop multiplexers (ADMs) required when the grooming ratio is 3. In fact, using tools of design theory, we solve the equivalent edge‐partitioning problem: Find a partition of the edges of the complete graph on n vertices (Kn) into subgraphs having at most three edges and in which the total number of vertices has to be minimized. © 2003 Wiley Periodicals, Inc.

Improved Approaches for Cost-Effective Traffic Grooming in WDM Ring Networks: Uniform-Traffic Case.

To fully utilize the capabilities of a SONET/ADM network, traffic grooming is needed to multiplex a number of lower-rate traffic streams into a higher-rate stream, and vice versa. Although the capacity of a SONET ring network can be upgraded by operating it over multiple wavelengths, the corresponding network design may be costly if it employs a large number of ADMs. A cost-effective design attempts to minimize the total number of ADMs used in the network while carrying the offered traffic. We introduce and evaluate the performance characteristics of two new traffic-grooming approaches for WDM ring networks, called single-hop and multihop. Our single-hop implementation uses the simulated-annealing heuristic. After placing all the traffic on “virtual circles”, we group the circles in order to reduce the number of ADMs in the network. Our multihop implementation places an ADM at each node based on the requested traffic in the traffic-demand matrix; then, it tries to groom the wavelengths which can be groomed. We select one of the nodes to be the “hub” node which has an ADM for each wavelength. The hub node, therefore, can “bridge” traffic between all of the wavelengths. Each algorithm is specified and illustrated by a simple example. Our results demonstrate that it is beneficial to use a single-hop approach based on simulated annealing for a small grooming ratio, but for a large grooming ratio and node number, we advocate the use of the multihop approach.