Topological Design Optimization of a Yottabit-Per-Second Lattice Network Jules R

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 22, NO. 9, NOVEMBER 2004 1613 Topological Design Optimization of a Yottabit-Per-Second Lattice Network Jules R. Dégila, Student Member, IEEE, and Brunilde Sansò, Member, IEEE Abstract—This paper deals with the topological design of a yottabit-per-second @I yotta a 10PRA multidimensional network. The YottaWeb is a recently proposed architecture based upon agile optical cores that provides fully meshed connectivity with direct optical paths between edge nodes that are electronically controlled. In order to arrange the edge nodes around the agile cores (ACs) into a suitable and efficient YottaWeb, one proposal is to create a multidimensional lattice structure of ACs. The problem of designing such a structure is highly combinatorial. In this paper, we present the problem, that we call nodal arrangement problem, and we propose a meta-search procedure based on Tabu and VNS to solve it. The performance of the algorithm is gauged using a set of randomly generated networks with different distribution of traffic. Index Terms—Agile optical core, lattice structure, meta-search, Fig. 1. Fundamental concept of the AC. next-generation Internet, nodal arrangement problem (NAP), optical internet, PetaWeb, tabu search, variable neighborhood de- scent, YottaWeb. I. INTRODUCTION O KEEP UP with the progression of the current In- T ternet, new proposals led by the next-generation Internet (NGI) initiative [1], supported by Defense Advanced Research Projects Agency (DARPA), have been considered. They con- sist of the development of protocols, standards and testbed networks. One such development is an architecture called the PetaWeb [2]–[5]. The PetaWeb scales to a total capacity of several petabits per second (Pb/s), three orders of magnitude higher than the external capacity of the current global Internet. The concept of the PetaWeb is based on the development of an Fig. 2. General optimization model of the YottaWeb. agile optical core (using the wavelength-division multiplexed (WDM) fibers and optical cross-connectors (OXCs) [5]) that sketched in [6] is to use the agile cores (ACs) from the PetaWeb can provide a high-capacity interconnexion between a transport as building blocks for an expanding network. Hence, the network edge nodes. It also allows to overcome the problems involved network design problem implies the need for the with the current Internet by providing a direct high-capacity efficient use of the AC’s enabling technology. One important interconnection between the edge nodes (see Fig. 1). The parameter to reach the required efficiency, is the choice of a PetaWeb architecture is intended to accommodate thousands of good topology which could allow tremendous growth of the such high-capacity edge nodes distributed nationwide. global capacity and a low number of hops between edge nodes. Based on the motivation that a global high-capacity network, Fig. 2 illustrates the optimization challenge involved in the such as the Internet, could contain millions of high-capacity design of the YottaWeb: it consists in deciding which edges edge nodes. Beshai et al. proposed an architecture that could nodes (ENs) should be connected to which AC. Such a solu- reach an external capacity in the order of yottabit-per-section can be embedded into a virtual conceptual frame. onds, called the YottaWeb [6]. The main idea of the YottaWeb One such virtual frame is a lattice structure, proposed by Beshai et al. [6] for the YottaWeb. The structure is built on Manuscript received February 26, 2003; revised January 26, 2004. This work the basis of the number of ACs attached to the same edge nodes was supported in part by a Collaborative Research and Development (CRD) Grant between Nortel Networks and the National Sciences and Engineering Re- and on the number of edge nodes that are connected to the search Council of Canada. same AC. Thus, an important and highly combinatorial problem The authors are with the GERAD and the Department of Electrical Engi- that gives rise in this context is the nodal arrangement problem neering, École Polytechnique de Montréal, Montréal, QC H3C 3A7, Canada (e-mail: [email protected]; [email protected]). (NAP), which defines which edge nodes should be connected Digital Object Identifier 10.1109/JSAC.2004.829642 together in the conceptual lattice structure. 0733-8716/04$20.00 © 2004 IEEE 1614 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 22, NO. 9, NOVEMBER 2004 Fig. 3. Structure of PetaWeb. The object of this paper is to present a powerful metaheuristic for the solution of the NAP. The algorithm was developed after formally exploring the properties of the lattice structure for the YottaWeb, which is presented in this paper for the first time. This paper is organized as follows. In Section II, the basic ele- ments of the YottaWeb Architecture and their relationship with the PetaWeb, the lattice structure, and the NAP are described. Section III is devoted to a literature review on problems that are similar or are related to the NAP. In Section IV,the resolution algorithm, that we have called Lattice Arrangement Meta-Search Procedure (LAMP) for is presented in detail. Numerical results follow in Section V and the conclusions and recommendations Fig. 4. Parallel-planes optical core node in the PetaWeb. for further work are finally presented in Section VI. of clarity, only two ENs are considered. As explained in [5], II. YOTTAWEB TOPOLOGY AND THE an edge node is connected to a core node with one or more NODAL ARRANGEMENT PROBLEM fiber links, each link having several channels. Fig. 4 shows The enabling technology behind the YottaWeb proposal given the parallel space switches composing a core node. Incoming in [6], is the PetaWeb architecture and in particular, its high- optical signals are demultiplexed and associated to different capacity, distributed, edge controlled, optical core. Indeed, the channels. Outgoing channels associated with a given edge node configuration of the AC allows to consider one PetaWeb as a are multiplexed into a fiber link going back to the edge node. subnet of a greater network. The concept allows information delivery at the optical rate, In what follows, we present the basic configuration of the within the network, since the optical cores are bufferless without PetaWeb, and we show how it gives rise to the YottaWeb ar- connections between them. A time-locking mechanism coordi- chitecture and the virtual lattice structure. The section is con- nates the edge nodes, enabling the PetaWeb core to resemble cluded with an explanation of the NAP, its definition, and some one geographically distributed switch. From now on, to explain previous algorithms that attempted at a solution. the YottaWeb in Section II-B, we will use the term “agile core” (AC) to signify the set of high-capacity optical core nodes of a A. PetaWeb PetaWeb. This set of optical core nodes forming a PetaWeb is Fig. 3 (modified form [5]) sketches the structure of the grouped within the dotted circle of Fig. 3 and is symbolized by PetaWeb, which is a composite-star network. The PetaWeb the star at the right which represents an AC. uses a channel-switching core and a distributed control system that dynamically modifies the routing of individual channels as B. Lattice Topology of the YottaWeb the need arises. The access nodes to the core could be electronic The YottaWeb structure defines a way of efficiently con- switches in packet switching or adaptative circuit mode, with necting the edge nodes to the ACs. A schematic view is high capacity of multiple Terabits 10 per second. The portrayed in Fig. 2. In the figure, the edge nodes can be con- optical core nodes, which should be an array of parallel space nected to several ACs. The fundamental question of the design switches, provide fully meshed connectivity with direct optical is to determine which are the best links for the connection; in paths between edge nodes. The connection of the ENs to the other words, to determine which edge node should be connected optical core through the parallel space switches is depicted to which AC. Of course, the term “best” is used in reference to in Fig. 4 (similar to the one proposed in [5]). For the sake the optimization metric chosen by the designer. DÉGILA AND SANSÒ: TOPOLOGICAL DESIGN OPTIMIZATION OF A YOTTABIT-PER-SECOND LATTICE NETWORK 1615 which the edge nodes in the line are connected. From this definition of the lattice topology, we deduce some of its properties in Section II-C. C. Some Structural Properties of the Lattice Topology The lattice structure, as defined above, corresponds to a regular form. In that form, each pair of lines representing an AC are parallel or perpendicular. In addition, every AC links the same number of nodes. Those assumptions could be different in an irregular form, which is not studied in this article. In addition, let us classify the ACs following the dimensions. An example is given in Fig. 6, where the AC’s 1, 2, 3, and 4 are the ACs of the 2nd dimension as they are parallel to the axis , and the AC’s 5, 6, 7, and 8 are named the ACs of the first dimension. In general, we define by AC of the th dimension, an AC parallel to the axis . The next proposition gives the conditions of the existence of the regular lattice structure. Proposition 1: Let , , and be respectively the number of nodes, the number of ACs, the dimension of the network and the capacity of each AC. For a regular lattice structure representation, the following two equalities are satisfied. Fig. 5. YottaWeb arrangement into lattice structure.

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