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28
On survivable routing of mesh topologies in IPoverWDM networks
 in Proc. IEEE INFOCOM 2005
, 2005
"... Abstract — Failure restoration at the IP layer in IPoverWDM networks requires to map the IP topology on the WDM topology in such a way that a failure at the WDM layer leaves the IP topology connected. Such a mapping is called survivable. Finding a survivable mapping is known to be NPcomplete, mak ..."
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Cited by 22 (3 self)
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Abstract — Failure restoration at the IP layer in IPoverWDM networks requires to map the IP topology on the WDM topology in such a way that a failure at the WDM layer leaves the IP topology connected. Such a mapping is called survivable. Finding a survivable mapping is known to be NPcomplete, making it impossible in practice to assess the existence or absence of such a mapping for large networks. (i) We first introduce a new concept of piecewise survivability, which makes the problem much easier in practice (although still NPcomplete), and allows us to formally prove that a given survivable mapping does or does not exist. (ii) Secondly, we show how to trace the vulnerable areas in the topology, and how to strengthen them to enable a survivable mapping. (iii) Thirdly, we give an efficient and scalable algorithm that finds a survivable mapping. In contrast to the heuristics proposed in the literature to date, our algorithm exhibits a number of provable properties (e.g., it guarantees the piecewise survivability) that are crucial for (i) and (ii). Index Terms — Optical communication, wavelength division multiplexing, survivability, graph theory I.
Bounds on fiber minimization in optical networks with fixed fiber capacity
 In INFOCOM 2005. 24th Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings IEEE
, 2005
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Traffic Grooming in WDM Ring Networks with the MinMax Objective
 Eds): NETWORKING 2004, LNCS
, 2004
"... We consider the problem of traffic grooming in WDM ring networks. Previous studies have focused on minimizing aggregate representations of the network cost. In this work, we consider a MinMax objective, in which it is desirable to minimize the cost at the node where this cost is maximum. Such an ob ..."
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Cited by 7 (1 self)
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We consider the problem of traffic grooming in WDM ring networks. Previous studies have focused on minimizing aggregate representations of the network cost. In this work, we consider a MinMax objective, in which it is desirable to minimize the cost at the node where this cost is maximum. Such an objective is of practical value when dimensioning a network for unknown future traffic demands and/or for dynamic traffic scenarios. We prove that traffic grooming with the MinMax objective is NPComplete even when wavelength assignment is not an issue. We also present a new polynomialtime algorithm for MinMax traffic grooming. Experiments with a wide range of problem instances demonstrate that our algorithm produces solutions which are always close to the optimal and/or the lower bound, and which scale well to large network sizes, large number of wavelengths, and high loads.
Traffic Grooming in Star Networks
 In Proceedings of the First Traffic Grooming Workshop
, 2004
"... We study the traffic grooming problem on WDM networks with the physical topology of a star. In star networks, several nodes are connected to a single hub directly through a bidirectional optical fiber, but are not connected to each other. Previous studies concentrated on the objective of minimizing ..."
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Cited by 6 (4 self)
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We study the traffic grooming problem on WDM networks with the physical topology of a star. In star networks, several nodes are connected to a single hub directly through a bidirectional optical fiber, but are not connected to each other. Previous studies concentrated on the objective of minimizing the total amount of electronic switching. However, in order to lower the network cost, we consider the objective of minimizing the number of line terminating equipment (LTE), which is the dominant cost among optical devices. We first present new complexity results for this problem. The goal of minimizing LTE cost can be embodied in two alternative objective functions, the total number of LTE or the number of LTE at the node with the greatest such number (MinMax). We provide heuristic algorithms for both objectives, and we present numerical results to demonstrate the effectiveness of our algorithms. One of our main contributions is to show that for star networks, it is usually possible to obtain nearoptimal values for both objectives simultaneously, and our heuristics can obtain such solutions. The most consistently useful solutions for both objectives can be obtained by addressing the MinMax objective as primary.
Traffic Grooming in WDM Ring Networks to Minimize the Maximum Electronic Port Cost
, 2003
"... We consider the problem of traffic grooming in WDM ring networks. Traffic grooming is a variant of the wellknown logical topology design problem, and is concerned with the development of techniques for combining low speed traffic components onto high speed channels in order to minimize network cost ..."
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Cited by 6 (3 self)
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We consider the problem of traffic grooming in WDM ring networks. Traffic grooming is a variant of the wellknown logical topology design problem, and is concerned with the development of techniques for combining low speed traffic components onto high speed channels in order to minimize network cost. Previous studies have focused on aggregate representations of the network cost. In this work, we consider a MinMax objective, in which it is desirable to minimize the cost at the node where this cost is maximum. Such an objective is of high practical value when dimensioning a network for unknown future traffic demands and/or for dynamic traffic scenarios. We present new theoretical results which demonstrate that traffic grooming with the MinMax objective is NPComplete even when wavelength assignment is not an issue. We also present a new polynomialtime traffic grooming algorithm for minimizing the maximum electronic port cost in both uni and bidirectional rings. We evaluate our algorithm through experiments with a wide range of problem instances, by varying the network size, number of wavelengths, traffic load, and traffic pattern. Our results indicate that our algorithm produces solutions which are always close to the optimal and/or the lower bound, and which scale well to large network sizes, large number of wavelengths, and high loads. We also demonstrate that, despite its focus on minimizing the maximum cost, our algorithm also performs well in terms of the aggregate electronic port cost over all ring nodes.
Scheduling algorithms for throughput maximization in data networks
 Ph.D. thesis, MIT
, 2007
"... This thesis considers the performance implications of throughput optimal scheduling in physically and computationally constrained data networks. We study optical networks, packet switches, and wireless networks, each of which has an assortment of features and constraints that challenge the design de ..."
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Cited by 4 (2 self)
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This thesis considers the performance implications of throughput optimal scheduling in physically and computationally constrained data networks. We study optical networks, packet switches, and wireless networks, each of which has an assortment of features and constraints that challenge the design decisions of network architects. In this work, each of these network settings are subsumed under a canonical model and scheduling framework. Tools of queueing analysis are used to evaluate network throughput properties, and demonstrate throughput optimality of scheduling and routing algorithms under stochastic traffic. Techniques of graph theory are used to study network topologies having desirable throughput properties. Combinatorial algorithms are proposed for efficient resource allocation. In the optical network setting, the key enabling technology is wavelength division multiplexing (WDM), which allows each optical fiber link to simultaneously carry a large number of independent data streams at high rate. To take advantage of this high data processing potential, engineers and physicists have developed numerous technologies, including wavelength converters, optical switches, and tunable transceivers. While the functionality pro
On the multicast capacity of unidirectional and bidirectional packetswitched WDM ring networks
 Supplement on Optical Communications and Networking
, 2007
"... Abstract — In this paper we examine the relationship between the effective capacity (stability limit) of unidirectional and bidirectional packetswitched wavelength division multiplexing (WDM) ring networks for multicast traffic. We consider both bidirectional rings with one packet copy transmission ..."
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Cited by 4 (3 self)
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Abstract — In this paper we examine the relationship between the effective capacity (stability limit) of unidirectional and bidirectional packetswitched wavelength division multiplexing (WDM) ring networks for multicast traffic. We consider both bidirectional rings with one packet copy transmission per wavelength channel and two packet copy transmissions. We first prove bounds for the ratio of the multicast capacity of the bidirectional ring to the multicast capacity of the unidirectional ring. Specifically, we show that this ratio is at least two for two copy transmission in the bidirectional ring, and at most two for one copy transmission. We derive closed form expressions of the multicast capacity ratios for networks with a large number of nodes and from these expressions show that the ratios tend to two for a large number of multicast destinations. We demonstrate that for the bidirectional ring with two copy transmission the ratio becomes as large as 2.276. We also find that in the bidirectional ring, the capacity gain with two copy transmission over one copy transmission reaches 30.4%. Index Terms — Destination stripping, multicast, ring network, spatial wavelength reuse, throughput capacity, wavelength division multiplexing. I.
Hierarchical Traffic Grooming in LargeScale WDM Networks
, 2005
"... The advances in fiber optics and wavelength division multiplexing (WDM) technology are viewed as the key to satisfying the datadriven bandwidth demand of today’s Internet. The mismatch of bandwidths between user needs and wavelength capacity makes it clear that some multiplexing should be done to u ..."
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Cited by 3 (2 self)
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The advances in fiber optics and wavelength division multiplexing (WDM) technology are viewed as the key to satisfying the datadriven bandwidth demand of today’s Internet. The mismatch of bandwidths between user needs and wavelength capacity makes it clear that some multiplexing should be done to use the wavelength capacity efficiently, which will result in reduction on the cost of line terminating equipment (LTE). The technique is referred to as traffic grooming. Previous studies have concentrated on different objectives, or on some special network topologies such as rings. In our study, we aim at minimizing the LTE cost to directly target on minimizing the network cost. We look into the grooming problem in elemental topologies as a starting point. First, we conduct proofs to show that traffic grooming in path, ring and star topology networks with the cost function we consider is NPComplete. We also show the same complexity results for a MinMax objective that has not been considered before, on the two elementary topologies. We then design polynomialtime heuristic algorithms for the grooming problem in rings (thus implicitly paths) and stars for networks of larger size. Experiments on various network sizes and traffic patterns
Island hopping and path colouring, with applications to WDM network design
 Proc. of ACMSIAM SODA
"... Two benefits of optical communication are (a) the possibility of using a single fiber optic cable to carry multiple signals simultaneously if each signal uses light of a distinct wavelength, and (b) the decreased latency for signals that avoid expensive opticalelectricoptical (OEO) conversions. Th ..."
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Cited by 3 (1 self)
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Two benefits of optical communication are (a) the possibility of using a single fiber optic cable to carry multiple signals simultaneously if each signal uses light of a distinct wavelength, and (b) the decreased latency for signals that avoid expensive opticalelectricoptical (OEO) conversions. This paper studies two natural graph problems that arise when trying to capitalize on these benefits. Given a supply network we must route multiple demands. We install fibers in the network, each of which may carry λ signals of different wavelengths. We decouple the general problem into the following two subproblems. Fiber minimization: We wish to light the cheapest set of fibers, le fibers for edge e, such that each demand can be routed monochromatically with at most le routes of the same wavelength using an edge e. We first generalize the work of Winkler and Zhang which gave an optimal solution for line networks. Secondly, we present a 3.55approximation for the singlesource problem. Hop minimization: In general it is not possible to interconnect all fibers incident on a node. If a signal travels between two fibers that are not connected then an OEO conversion, or hop, is necessitated. We wish to minimize the number of hops required when routing the demands subject to the constraint that at most c fibers are connected to each other at each node. For c = 2, we show an O(log 1−ǫ n)approximation hardness result that complements the O(log n)approximation algorithm due to Anshelevich and Zhang. For directed supply graphs we show an O(n 1−ǫ)approximation hardness result. However, for acyclic supply graphs we present an O ( √ n)approximation algorithm. For strongly connected digraphs, our O(n 1−ǫ)hardness continues to hold for c = 2; however, for c = 3, we give a O(log n)approximation algorithm. 1
The scalability and performance of common vector solution to generalized label continuity constraint in hybrid optical/packet networks
 IEEE GLOBECOM, Washington DC
, 2007
"... Abstract—In hybrid Optical/packet networks, wavelength and VLAN tag continuity along a Label Switched Path are two common constraints. These two types of constraints, referred to as Generalized Label Continuity Constraints, have global significance in a network; namely, the label should appear only ..."
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Cited by 2 (2 self)
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Abstract—In hybrid Optical/packet networks, wavelength and VLAN tag continuity along a Label Switched Path are two common constraints. These two types of constraints, referred to as Generalized Label Continuity Constraints, have global significance in a network; namely, the label should appear only in other link or node disjoint paths. In considering these constraints, a solution is the common vector approach, which seeks a common available label along the path determined by CSPF without label constraints. In this paper, we provide an estimation method to compute the upper bound of the blocking probability for the above approach. We also address the scalability problem of the existing traffic engineering algorithms. We then present the simulation results corroborating with our analytical model.h.