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The role of switching in reducing the number of electronic ports in WDM networks
 IEEE J. Select. Areas Commun
, 2004
"... Abstract—We consider the role of switching in minimizing the number of electronic ports [e.g., synchronous optical network (SONET) add/drop multiplexers] in an optical network that carries subwavelength traffic. Providing nodes with the ability to switch traffic between wavelengths, such as through ..."
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Abstract—We consider the role of switching in minimizing the number of electronic ports [e.g., synchronous optical network (SONET) add/drop multiplexers] in an optical network that carries subwavelength traffic. Providing nodes with the ability to switch traffic between wavelengths, such as through the use of SONET crossconnects, can reduce the required number of electronic ports. We show that only limited switching ability is needed for significant reductions in the number of ports. First, we consider architectures where certain “hub ” nodes can switch traffic between wavelengths and other nodes have no switching capability. For such architectures, we provide a lower bound on the number of electronic ports that is a function of the number of hub nodes. We show that our lower bound is relatively tight by providing routing and grooming algorithms that nearly achieve the bound. For uniform traffic, we show that the number of electronic ports is nearly minimized when the number of hub nodes used is equal to the number of wavelengths of traffic generated by each node. Next, we consider architectures where the switching ability is distributed throughout the network. Such architectures are shown to require a similar number of ports as the hub architectures, but with a significantly smaller “switching cost. ” We give an algorithm for designing such architectures and characterize a class of topologies, where the minimum number of ports is used. Finally, we provide a general upper bound on the amount of switching required in the network. For uniform traffic, our bound shows that as the size of the network increases, each traffic stream must be switched at most once in order to achieve the minimum port count. Index Terms—Optical networks, synchronous optical network (SONET), traffic grooming. I.
Approximating the Traffic Grooming Problem in Tree and Star Networks ⋆ (Extended Abstract)
"... Abstract. We consider the problem of grooming paths in alloptical networks with tree topology so as to minimize the switching cost, measured by the total number of used ADMs. We first present efficient approximation algorithms with approximation factor of 2ln(δ · g)+o(ln(δ · g)) for any fixed node ..."
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Abstract. We consider the problem of grooming paths in alloptical networks with tree topology so as to minimize the switching cost, measured by the total number of used ADMs. We first present efficient approximation algorithms with approximation factor of 2ln(δ · g)+o(ln(δ · g)) for any fixed node degree bound δ and grooming factor g, and2lng + o(ln g) in unbounded degree directed trees, respectively. In the attempt of extending our results to general undirected trees we completely characterize the complexity of the problem in star networks by providing polynomial time optimal algorithms for g ≤ 2 and proving the intractability of the problem for any fixed g>2. While for general topologies the problem was known to be NPhard g not constant, the complexity for fixed values of g was still an open question.
Optimal OnLine Colorings for Minimizing the Number of ADMs in Optical Networks (Extended Abstract)
"... Abstract. We consider the problem of minimizing the number of ADMs in optical networks. All previous theoretical studies of this problem dealt with the offline case, where all the lightpaths are given in advance. In a reallife situation, the requests (lightpaths) arrive at the network online, and ..."
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Abstract. We consider the problem of minimizing the number of ADMs in optical networks. All previous theoretical studies of this problem dealt with the offline case, where all the lightpaths are given in advance. In a reallife situation, the requests (lightpaths) arrive at the network online, and we have to assign them wavelengths so as to minimize the switching cost. This study is thus of great importance in the theory of optical networks. We present an online algorithm for the problem, and show its competitive ratio to be 7. We show that this result is best possible 4 in general. Moreover, we show that even for the ring topology network there is no online algorithm with competitive ratio better than 7 4.We show that on path topology the competitive ratio of the algorithm is 3. This is optimal for this topology. The lower bound on ring topology 2 does not hold when the ring is of bounded size. We analyze the triangle topology and show a tight bound of 5 for it. The analyzes of the upper 3 bounds, as well as those for the lower bounds, are all using a variety of proof techniques, which are of interest by their own, and which might prove helpful in future research on the topic.
Game Theoretical Issues in Optical Networks
"... In this paper we focus on the problem in optical networks in which selfish or noncooperative users can configure their communications so as to minimize the cost paid for the service. Such a cost depends on the personal configuration and on the one of the other users. During a series of time steps, ..."
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In this paper we focus on the problem in optical networks in which selfish or noncooperative users can configure their communications so as to minimize the cost paid for the service. Such a cost depends on the personal configuration and on the one of the other users. During a series of time steps, at each of which only one user can move to a better configuration, a Nash equilibrium is eventually reached, that is a situation in which no user can select an improved solution and thus is interested in further modifications. In such a setting, the network provider must determine suitable payment functions covering the network costs that induce Nash equilibria with the best possible global performances. We first present results in the classical scenario in which we are interested in optimizing the optical spectrum, that is in minimizing the total number of used wavelengths. We then outline possible settings in which the approach can be eventually applied to minimize the cost of optical routing due to specific hardware components such as ADMs or filters, that are typical examples of expensive elements whose price can be shared among different lightpaths under specific constraints. I.
ADDRESSING THE GRWA PROBLEM IN WDM NETWORKS
"... The traffic Grooming, Routing and Wavelength Assignment (GRWA) problem in Wavelength Division Multiplexed networks is addressed. A new heuristic algorithm, the GRWABOU algorithm, has been developed from Tabu Search techniques. Its objective function seeks the minimization of network costs through th ..."
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The traffic Grooming, Routing and Wavelength Assignment (GRWA) problem in Wavelength Division Multiplexed networks is addressed. A new heuristic algorithm, the GRWABOU algorithm, has been developed from Tabu Search techniques. Its objective function seeks the minimization of network costs through the minimization of the number of electronic cards used in network nodes. It uses an evaluation function that, in addition to depending on the objective function, provides means to handle constraint violations in order to travel in the nonfeasible domain in a controlled way. It can be applied to ring or general mesh networks. It accepts any type of traffic demand with any type of granularity on the client side. On the transport side, it supports multiple bit rates simultaneously. Computational experiments on three different mesh networks are presented, showing the versatility of the algorithm not only for cost minimization studies but also for other types of studies concerning, as example, number of hops, wavelength capacity usage and MultiService Provisioning Platform (MSPP) port usage.
DOI 10.1007/s0045301195305 On Equilibria for ADM Minimization Games
"... Abstract In the ADM minimization problem the input is a set of arcs along a directed ring. The input arcs need to be partitioned into nonoverlapping chains and cycles so as to minimize the total number of endpoints, where a karc cycle contributes k endpoints and a karc chain contains k + 1 endpoi ..."
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Abstract In the ADM minimization problem the input is a set of arcs along a directed ring. The input arcs need to be partitioned into nonoverlapping chains and cycles so as to minimize the total number of endpoints, where a karc cycle contributes k endpoints and a karc chain contains k + 1 endpoints. We study ADM minimization problem both as noncooperative and cooperative games. In these games each arc corresponds to a player, and the players share the cost of the ADM switches. We consider two cost allocation models, a model which was considered by Flammini et al., and a new cost allocation model, which is inspired by congestion games. We compare the price of anarchy and price of stability in the two cost allocation models, as well as the strong price of anarchy and the strong price of stability.
Addressing the GRWA Problem in WDM Networks with a Tabu Search Algorithm
"... Abstract: We developed a Tabu Search algorithm that can be used to solve simultaneously the grooming, routing and wavelength assignment problems in WDM networks. This algorithm, called GRWABOU, is adequate for network cost minimization in a general context. ©2005 Optical Society of America OCIS code ..."
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Abstract: We developed a Tabu Search algorithm that can be used to solve simultaneously the grooming, routing and wavelength assignment problems in WDM networks. This algorithm, called GRWABOU, is adequate for network cost minimization in a general context. ©2005 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.4250) Networks
On Minimizing the Numbers of ADMs – Better Bounds for an Algorithm with Preprocessing ∗
"... Abstract Minimizing the number of electronic switches in optical networks is a main research topic in recent studies. In such networks we assign colors to a given set of lightpaths. Thus the lightpaths are partitioned into cycles and paths, and the switching cost is minimized when the number of path ..."
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Abstract Minimizing the number of electronic switches in optical networks is a main research topic in recent studies. In such networks we assign colors to a given set of lightpaths. Thus the lightpaths are partitioned into cycles and paths, and the switching cost is minimized when the number of paths is minimized. The problem of minimizing the switching cost is NPhard. A basic approximation algorithm for this problem eliminates cycles of size at most l and has a performance guarantee of OPT + 1 2 N(1 + ε), where OPT is the cost of an optimal solution, N is the number of lightpaths and 0 ≤ ε ≤ 1 l+2, for any given odd l. Shalom improved the analysis of this algorithm and 1 1 prove that 2l+3 ≤ ε ≤ 3. In this paper, we further reduce the gap between the lower bound and 2 (l+2) the upper bound of ε. We show that a better upper bound of ε by constructing a greater matching, i.e., ε ≤ 1 5.