46 research outputs found

    Distributed Failure Restoration for Asynchronous Transfer Mode (ATM) Tactical Communication Networks

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    Asynchronous Transfer Mode (A TM) is an attractive choice for future military communication systems because it can provide high throughput and support multi-service applications. Furthermore its use is consistent with the 'off the shelf technology policy that is currently operated by the Defence Engineering Research Agency of Great Britain. However, A TM has been developed as a civil standard and is designed to operate in network infrastructures with very low failure rates. In contrast, tactical networks are much less reliable. Indeed tactical networks operate on the premise that failures, particularly node failures, are expected. Hence, efficient, automatic failure restoration schemes are essential if an A TM based tactical network is to remain operational. The main objective of this research is the proposal and verification of one or more new restoration algorithms that meet the specific requirements of tactical networks. The aspects of ATM networks that influence restoration algorithms' implementation are discussed. In particular, the features of A TM networks such as the concept of Virtual Paths Virtual Channels and OAM (Operation And Maintenance) mechanisms that facilitate implementation of efficient restoration techniques. The unique characteristics of tactical networks and their impact on restoration are also presented. A significant part of the research was the study and evaluation of existing approaches to failure restoration in civil networks. A critical analysis of the suitability of these approaches to the tactical environment shows no one restoration algorithm fully meets the requirements of tactical networks. Consequently, two restoration algorithms for tactical A TM networks, DRA-TN (Dynamic Restoration Algorithm for Tactical Networks) and PPR-TN (Pre-planned Restoration Algorithm for Tactical Networks), are proposed and described in detail. Since the primary concern of restoration in tactical networks is the recovery of high priority connections the proposed algorithms attempt to restore high-priority connections by disrupting low-priority calls. Also, a number of additional mechanisms are proposed to reduce the use of bandwidth, which is a scarce resource in tactical networks. It is next argued that software simulation is the most appropriate method to prove the consistency of the proposed algorithms, assess their performance and test them on different network topologies as well as traffic and failure conditions. For this reason a simulation software package was designed and built specifically to model the proposed restoration algorithms. The design of the package is presented in detail and the most important implementation issues are discussed. The proposed restoration algorithms are modelled on three network topologies under various traffic loads, and their performance compared against the performance of known algorithms proposed for civil networks. It is shown that DRA-TN and PPR-TN provide better restoration of higher priority traffic. Furthermore, as the traffic load increases the relative performance of the DRA-TN and PPR-TN algorithms increases. The DRA-TN and PPR-TN algorithms are also compared and their advantages and disadvantages noted. Also, recommendations are given about the applicability of the proposed algorithms, and some practical implementation issues are discussed. The number of problems that need further study are briefly described.Defence Engineering Research Agency of Great Britai

    Fault Tolerant Rerouting in Broadband Multiclass Networks

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    Modern broadband integrated service digital networks (B-ISDN) must handle multiclass traffic with diverse quality of service (QOS) requirements. The main purpose of our research is to design call rerouting mechanisms which provide rapid restoration of network services in case of link failures. We suggest two approaches: Virtual circuit (VC) and virtual path (VP) reroutings. The first approach is more reactive while the latter is more proactive. The applicability conditions for the first approach include the availability of a layered network structure similar to VC/VP architecture which is widely accepted in asynchronous transfer mode (ATM) networks. Another applicability condition is the extent of network failure: VP level restoration is designed for single link failures - the most common in the telecommunication networks. On the other hand, in case of less predictable multiple link failures, VC-level rerouting is appropriate. These two rerouting approaches vary in the amount of time required to carry them out. Though both schemes are designed to work in real time, VP-level rerouting tends to be faster and can be performed in an on-line mode using pre-computed paths. VC- level rerouting requires real-time computation of routes which may result in a noticeable impact on some services. On the other hand, VP-level rerouting requires a substantial amount of off- line computation to design the VP layout and the backup routes.In this dissertation we propose a new model and associated algorithms to solve a VC-rerouting problem in real time. This model takes advantage of the distributed network data and computational resources by decomposing the problem at an early stage and then performing the computations in a decentralized mode.In order to solve the fault tolerant VP layout problem, we formulate a bi-criteria optimization model reflecting the tradeoff between throughput and certain QOS requirements. The model involves a piece-wise linear approximation to the capacity allocation rule for variable bit rate connections statistically multiplexed over a VP.Both models are formulated as integer programs. The solution method developed employ relaxation and aggregation of variables, feasible solution heuristics and valid inequalities. The results of the computational experiments presented indicate that the methods developed are efficient and produce accurate solutions

    QoS Restoration using a Disjoint Path Group in ATM Networks

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    Abstract A QoS restoration scheme for VP-based ATM network is proposed and its related characteristics are evaluated. The proposed scheme is a state-independent restoration scheme using a disjoint path group. A VP assignment and capacity planning problem using disjoint path group are formulated. When a failure occurs, failed working VPs are switched to protection paths with the same QoS level using a simple and fast restoration algorithm. The simulated restoration characteristics of the proposed algorithm are presented. A scheme of excess capacity assignment to protection path for dynamic traffic demands is also presented and analyzed

    Applications of satellite technology to broadband ISDN networks

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    Two satellite architectures for delivering broadband integrated services digital network (B-ISDN) service are evaluated. The first is assumed integral to an existing terrestrial network, and provides complementary services such as interconnects to remote nodes as well as high-rate multicast and broadcast service. The interconnects are at a 155 Mbs rate and are shown as being met with a nonregenerative multibeam satellite having 10-1.5 degree spots. The second satellite architecture focuses on providing private B-ISDN networks as well as acting as a gateway to the public network. This is conceived as being provided by a regenerative multibeam satellite with on-board ATM (asynchronous transfer mode) processing payload. With up to 800 Mbs offered, higher satellite EIRP is required. This is accomplished with 12-0.4 degree hopping beams, covering a total of 110 dwell positions. It is estimated the space segment capital cost for architecture one would be about 190Mwhereasthesecondarchitecturewouldbeabout190M whereas the second architecture would be about 250M. The net user cost is given for a variety of scenarios, but the cost for 155 Mbs services is shown to be about $15-22/minute for 25 percent system utilization

    Providing Survivability In Optical Wdm Mesh Networks Considering Adaptation

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    Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2007Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2007Internet kullanımının artışı ile birlikte, hızla büyüyen bant genişliği isteklerini karşılayabilecek olan optik WDM ağları, gelecekteki en uygun Internet omurgaları haline gelmiştir. Oluşabilecek herhangi bir bağlantı hatası, o bağlantı üzerinden geçen tüm ışık yollarının başarısızlığına yol açabilir. Bu yüzden, optik WDM ağları etkili hata bağışıklığı yöntemlerine ihtiyaç duymaktadır.Optik WDM ağlarındaki hata bağışıklığı problemini etkili bir şekilde giderebilmek için son günlerde bir çok yöntem sunulmuştur. Bu yöntemler arasında paylaşılan yol ile koruma yöntemi etkin kaynak kullanımı sağlayabildiğinden, en umut verici yöntemlerden biri olarak görülmektedir. Bu yöntemde yedek ışık yolları, eğer ilişkili birincil ışık yolları karşılıklı olarak farklı ise yani ortak bağ kullanmıyor iseler, dalga boyu paylaşımı yapabilemekdirler. Bu özelliğinden dolayı paylaşılan yol ile koruma yöntemi, yedek ışık yollarına daha az kaynak ayrılmasını sağlar ve diğer koruma yöntemlerinden daha iyi performans gösterir. Bu çalışmada, bir optik WDM ağına dinamik olarak gelen bağlantı isteklerine cevap verilirken, paylaşılan yol ile koruma ve yeniden yönlendirme özelliğini kullanan etkili bir yöntem geliştirilmiştir. Adaptasyon sağlayan paylaşılan yol ile koruma yöntemi olarak adlandıralan yeni yaklaşım, dinamik trafik akışında yedek yolların yol açtığı fazla kaynak tüketimini azaltmak için zaman içinde ağı yeni durumlara adapte edebilen, etkili yani daha çok isteğe cevap verilebilen bir servis sağlayabilmektedir. Bağlantıların öncelik beklentisine göre yeniden yönlendirme yapma özelliğinden dolayı servis seviyesinde anlaşma sağlayabilen bir yaklaşımdır.WDM optical networks are able to meet the rapid growth of bandwidth demands and are considered to be the most appropriate choice of future Internet backbone. However, the failure of a network component such as a fiber link can lead to the failure of all the lightpaths that traverse the failed link. Therefore, the huge bandwidth of WDM also requires efficient survivability mechanisms. Recently, new techniques have been proposed to efficiently deal with this problem in mesh networks. Among them, shared-path protection is a promising candidate because of its desirable resource efficiency, which is a result from effective backup sharing. Backup paths can share wavelength channels, when their corresponding working paths are mutually diverse. Therefore, shared-path protection can outperform other protection techniques based on the dedicated reservation of backup capacity. In this work, we focus on rerouting feature to design an efficient algorithm, called Adaptable Shared Path Protection (ASPP), for dynamic provisioning of shared-path-protected connections in optical mesh networks employing WDM. In particular, backup-channel capacity reservation in shared-protection causes too much resource consumption parallel to network load. ASPP provides the adaptation of network against dynamic traffic, and decreases blocking probability thanks to rerouting capability of paths. Also, ASPP can present SLA by providing an uninterrupted traffic flow for connection requests come with a high priority.Yüksek LisansM.Sc

    Topological Design of Multiple Virtual Private Networks UTILIZING SINK-TREE PATHS

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    With the deployment of MultiProtocol Label Switching (MPLS) over a core backbone networks, it is possible for a service provider to built Virtual Private Networks (VPNs) supporting various classes of services with QoS guarantees. Efficiently mapping the logical layout of multiple VPNs over a service provider network is a challenging traffic engineering problem. The use of sink-tree (multipoint-to-point) routing paths in a MPLS network makes the VPN design problem different from traditional design approaches where a full-mesh of point-to-point paths is often the choice. The clear benefits of using sink-tree paths are the reduction in the number of label switch paths and bandwidth savings due to larger granularities of bandwidth aggregation within the network. In this thesis, the design of multiple VPNs over a MPLS-like infrastructure network, using sink-tree routing, is formulated as a mixed integer programming problem to simultaneously find a set of VPN logical topologies and their dimensions to carry multi-service, multi-hour traffic from various customers. Such a problem formulation yields a NP-hard complexity. A heuristic path selection algorithm is proposed here to scale the VPN design problem by choosing a small-but-good candidate set of feasible sink-tree paths over which the optimal routes and capacity assignments are determined. The proposed heuristic has clearly shown to speed up the optimization process and the solution can be obtained within a reasonable time for a realistic-size network. Nevertheless, when a large number of VPNs are being layout simultaneously, a standard optimization approach has a limited scalability. Here, the heuristics termed the Minimum-Capacity Sink-Tree Assignment (MCSTA) algorithm proposed to approximate the optimal bandwidth and sink-tree route assignment for multiple VPNs within a polynomial computational time. Numerical results demonstrate the MCSTA algorithm yields a good solution within a small error and sometimes yields the exact solution. Lastly, the proposed VPN design models and solution algorithms are extended for multipoint traffic demand including multipoint-to-point and broadcasting connections

    Esquema de controlo para redes multicast baseadas com classes

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    Doutoramento em Engenharia ElectrotécnicaThe expectations of citizens from the Information Technologies (ITs) are increasing as the ITs have become integral part of our society, serving all kinds of activities whether professional, leisure, safety-critical applications or business. Hence, the limitations of the traditional network designs to provide innovative and enhanced services and applications motivated a consensus to integrate all services over packet switching infrastructures, using the Internet Protocol, so as to leverage flexible control and economical benefits in the Next Generation Networks (NGNs). However, the Internet is not capable of treating services differently while each service has its own requirements (e.g., Quality of Service - QoS). Therefore, the need for more evolved forms of communications has driven to radical changes of architectural and layering designs which demand appropriate solutions for service admission and network resources control. This Thesis addresses QoS and network control issues, aiming to improve overall control performance in current and future networks which classify services into classes. The Thesis is divided into three parts. In the first part, we propose two resource over-reservation algorithms, a Class-based bandwidth Over-Reservation (COR) and an Enhanced COR (ECOR). The over-reservation means reserving more bandwidth than a Class of Service (CoS) needs, so the QoS reservation signalling rate is reduced. COR and ECOR allow for dynamically defining over-reservation parameters for CoSs based on network interfaces resource conditions; they aim to reduce QoS signalling and related overhead without incurring CoS starvation or waste of bandwidth. ECOR differs from COR by allowing for optimizing control overhead minimization. Further, we propose a centralized control mechanism called Advanced Centralization Architecture (ACA), that uses a single state-full Control Decision Point (CDP) which maintains a good view of its underlying network topology and the related links resource statistics on real-time basis to control the overall network. It is very important to mention that, in this Thesis, we use multicast trees as the basis for session transport, not only for group communication purposes, but mainly to pin packets of a session mapped to a tree to follow the desired tree. Our simulation results prove a drastic reduction of QoS control signalling and the related overhead without QoS violation or waste of resources. Besides, we provide a generic-purpose analytical model to assess the impact of various parameters (e.g., link capacity, session dynamics, etc.) that generally challenge resource overprovisioning control. In the second part of this Thesis, we propose a decentralization control mechanism called Advanced Class-based resource OverpRovisioning (ACOR), that aims to achieve better scalability than the ACA approach. ACOR enables multiple CDPs, distributed at network edge, to cooperate and exchange appropriate control data (e.g., trees and bandwidth usage information) such that each CDP is able to maintain a good knowledge of the network topology and the related links resource statistics on real-time basis. From scalability perspective, ACOR cooperation is selective, meaning that control information is exchanged dynamically among only the CDPs which are concerned (correlated). Moreover, the synchronization is carried out through our proposed concept of Virtual Over-Provisioned Resource (VOPR), which is a share of over-reservations of each interface to each tree that uses the interface. Thus, each CDP can process several session requests over a tree without requiring synchronization between the correlated CDPs as long as the VOPR of the tree is not exhausted. Analytical and simulation results demonstrate that aggregate over-reservation control in decentralized scenarios keep low signalling without QoS violations or waste of resources. We also introduced a control signalling protocol called ACOR Protocol (ACOR-P) to support the centralization and decentralization designs in this Thesis. Further, we propose an Extended ACOR (E-ACOR) which aggregates the VOPR of all trees that originate at the same CDP, and more session requests can be processed without synchronization when compared with ACOR. In addition, E-ACOR introduces a mechanism to efficiently track network congestion information to prevent unnecessary synchronization during congestion time when VOPRs would exhaust upon every session request. The performance evaluation through analytical and simulation results proves the superiority of E-ACOR in minimizing overall control signalling overhead while keeping all advantages of ACOR, that is, without incurring QoS violations or waste of resources. The last part of this Thesis includes the Survivable ACOR (SACOR) proposal to support stable operations of the QoS and network control mechanisms in case of failures and recoveries (e.g., of links and nodes). The performance results show flexible survivability characterized by fast convergence time and differentiation of traffic re-routing under efficient resource utilization i.e. without wasting bandwidth. In summary, the QoS and architectural control mechanisms proposed in this Thesis provide efficient and scalable support for network control key sub-systems (e.g., QoS and resource control, traffic engineering, multicasting, etc.), and thus allow for optimizing network overall control performance.À medida que as Tecnologias de Informação (TIs) se tornaram parte integrante da nossa sociedade, a expectativa dos cidadãos relativamente ao uso desses serviços também demonstrou um aumento, seja no âmbito das atividades profissionais, de lazer, aplicações de segurança crítica ou negócios. Portanto, as limitações dos projetos de rede tradicionais quanto ao fornecimento de serviços inovadores e aplicações avançadas motivaram um consenso quanto à integração de todos os serviços e infra-estruturas de comutação de pacotes, utilizando o IP, de modo a extrair benefícios económicos e um controlo mais flexível nas Redes de Nova Geração (RNG). Entretanto, tendo em vista que a Internet não apresenta capacidade de diferenciação de serviços, e sabendo que cada serviço apresenta as suas necessidades próprias, como por exemplo, a Qualidade de Serviço - QoS, a necessidade de formas mais evoluídas de comunicação tem-se tornado cada vez mais visível, levando a mudanças radicais na arquitectura das redes, que exigem soluções adequadas para a admissão de serviços e controlo de recursos de rede. Sendo assim, este trabalho aborda questões de controlo de QoS e rede com o objetivo de melhorar o desempenho do controlo de recursos total em redes atuais e futuras, através da análise dos serviços de acordo com as suas classes de serviço. Esta Tese encontra-se dividida em três partes. Na primeira parte são propostos dois algoritmos de sobre-reserva, o Class-based bandwidth Over-Reservation (COR) e uma extensão melhorada do COR denominado de Enhanced COR (ECOR). A sobre-reserva significa a reserva de uma largura de banda maior para o serviço em questão do que uma classe de serviço (CoS) necessita e, portanto, a quantidade de sinalização para reserva de recursos é reduzida. COR e ECOR consideram uma definição dinâmica de sobre-reserva de parâmetros para CoSs com base nas condições da rede, com vista à redução da sobrecarga de sinalização em QoS sem que ocorra desperdício de largura de banda. O ECOR, por sua vez, difere do COR por permitir a otimização com minimização de controlo de overhead. Além disso, nesta Tese é proposto também um mecanismo de controlo centralizado chamado Advanced Centralization Architecture (ACA) , usando um único Ponto de Controlo de Decisão (CDP) que mantém uma visão ampla da topologia de rede e de análise dos recursos ocupados em tempo real como base de controlo para a rede global. Nesta Tese são utilizadas árvores multicast como base para o transporte de sessão, não só para fins de comunicação em grupo, mas principalmente para que os pacotes que pertençam a uma sessão que é mapeada numa determinada árvore sigam o seu caminho. Os resultados obtidos nas simulações dos mecanismos mostram uma redução significativa da sobrecarga da sinalização de controlo, sem a violação dos requisitos de QoS ou desperdício de recursos. Além disso, foi proposto um modelo analítico no sentido de avaliar o impacto provocado por diversos parâmetros (como por exemplo, a capacidade da ligação, a dinâmica das sessões, etc), no sobre-provisionamento dos recursos. Na segunda parte desta tese propôe-se um mecanismo para controlo descentralizado de recursos denominado de Advanced Class-based resource OverprRovisioning (ACOR), que permite obter uma melhor escalabilidade do que o obtido pelo ACA. O ACOR permite que os pontos de decisão e controlo da rede, os CDPs, sejam distribuídos na periferia da rede, cooperem entre si, através da troca de dados e controlo adequados (por exemplo, localização das árvores e informações sobre o uso da largura de banda), de tal forma que cada CDP seja capaz de manter um bom conhecimento da topologia da rede, bem como das suas ligações. Do ponto de vista de escalabilidade, a cooperação do ACOR é seletiva, o que significa que as informações de controlo são trocadas de forma dinâmica apenas entre os CDPs analisados. Além disso, a sincronização é feita através do conceito proposto de Recursos Virtuais Sobre-Provisionado (VOPR), que partilha as reservas de cada interface para cada árvore que usa a interface. Assim, cada CDP pode processar pedidos de sessão numa ou mais árvores, sem a necessidade de sincronização entre os CDPs correlacionados, enquanto o VOPR da árvore não estiver esgotado. Os resultados analíticos e de simulação demonstram que o controlo de sobre-reserva é agregado em cenários descentralizados, mantendo a sinalização de QoS baixa sem perda de largura de banda. Também é desenvolvido um protocolo de controlo de sinalização chamado ACOR Protocol (ACOR-P) para suportar as arquitecturas de centralização e descentralização deste trabalho. O ACOR Estendido (E-ACOR) agrega a VOPR de todas as árvores que se originam no mesmo CDP, e mais pedidos de sessão podem ser processados sem a necessidade de sincronização quando comparado com ACOR. Além disso, E-ACOR introduz um mecanismo para controlar as informações àcerca do congestionamento da rede, e impede a sincronização desnecessária durante o tempo de congestionamento quando os VOPRs esgotam consoante cada pedido de sessão. A avaliação de desempenho, através de resultados analíticos e de simulação, mostra a superioridade do E-ACOR em minimizar o controlo geral da carga da sinalização, mantendo todas as vantagens do ACOR, sem apresentar violações de QoS ou desperdício de recursos. A última parte desta Tese inclui a proposta para recuperação a falhas, o Survivability ACOR (SACOR), o qual permite ter QoS estável em caso de falhas de ligações e nós. Os resultados de desempenho analisados mostram uma capacidade flexível de sobrevivência caracterizada por um tempo de convergência rápido e diferenciação de tráfego com uma utilização eficiente dos recursos. Em resumo, os mecanismos de controlo de recursos propostos nesta Tese fornecem um suporte eficiente e escalável para controlo da rede, como também para os seus principais sub-sistemas (por exemplo, QoS, controlo de recursos, engenharia de tráfego, multicast, etc) e, assim, permitir a otimização do desempenho da rede a nível do controlo global

    LOGICAL TOPOLOGY DESIGN FOR SURVIVABILITY IN IP-OVER-WDM NETWORKS

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    IP-over-WDM networks integrate Wavelength Division Multiplexing (WDM) technology with Internet Protocol (IP) and are widely regarded as the architecture for the next generation high-speed Internet. The problem of designing an IP-over-WDM network can be modeled as an embedding problem in which an IP network is embedded in a WDM network by establishing all optical paths between IP routers in the WDM network. Survivability is considered a vital requirement in such networks, which can be achieved by embedding the IP network in the WDM network in such a way that the IP network stays connected in the presence of failure or failures in the WDM network. Otherwise, some of the IP routers may not be reachable.The problem can be formulated as an Integer Linear Program (ILP), which can be solved optimally but is NP-complete. In this thesis, we have studied and proposed various efficient algorithms that can be used to make IP-over-WDM networks survivable in the presence of a single WDM link (optical fiber cable or cables) failure.First we evaluate an existing approach, named Survivable Mapping Algorithm by Ring Trimming (SMART), which provides survivability for an entire network by successively considering pieces of the network. The evaluation provides much insight into the approach, which allowed us to propose several enhancements. The modified approach with enhancements leads to better performance than the original SMART.We have also proposed a hybrid algorithm that guarantees survivability, if the IP and the WDM networks are at least 2-edge connected. The algorithm uses a combination of proactive (protection) and reactive (restoration) mechanisms to obtain a survivable embedding for any given IP network in any given WDM network.Circuits and cutsets are dual concepts. SMART approach is based on circuits. The question then arises whether there exists a dual methodology based on cutsets. We investigate this question and provide much needed insight. We provide a unified algorithmic framework based on circuits and cutsets. We also provide new methodologies based on cutsets and give a new proof of correctnessof SMART. We also develop a method based on incidence sets that are a special case of cutsets. Noting that for some IP networks a survivable embedding may not exist, the option of adding new IP links is pursued. Comparative evaluations of all the algorithms through extensive simulations are also given in this dissertation

    Survivable Logical Topology Mapping under Multiple Constraints in IP-over-WDM Networks

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    The survivable logical topology mapping problem in an IP-over-WDM network deals with the cascading effect of link failures from the bottom (physical) layer to the upper (logical) layer. Multiple logical links may get disconnected due to a single physical link failure, which may cause the disconnection of the logical network. Here we study survivability issues in IP-over-WDM networks with respect to various criteria.We first give an overview of the two major lines of pioneering works for the survivable design problem. Though theoretically elegant, the first approach which uses Integer Linear Programming (ILP) formulations suffers from the drawback of scalability. The second approach, the structural approach, utilizes the concept of duality between circuits and cutsets in a graph and is based on an algorithmic framework called Survivable Mapping Algorithm by Ring Trimming (SMART). Several SMART-based algorithms have been proposed in the literature.In order to generate the survivable routing, the SMART-based algorithms require the existence of disjoint lightpaths for certain groups of logical links in the physical topology, which might not always exist. Therefore, we propose in Chapter 4 an approach to augment the logical topology with new logical links to guarantee survivability. We first identify a logical topology that admits a survivable mapping against one physical link failure. We then generalize these results to achieve augmentation of a given logical topology to survive multiple physical link failures.We propose in Chapter 5 a generalized version of SMART-based algorithms and introduce the concept of robustness of an algorithm which captures the ability of the algorithm to provide survivability against multiple physical link failures. We demonstrate that even when a SMART-based algorithm cannot be guaranteed to provide survivability against multiple physical link failures, its robustness could be very high.Most previous works on the survivable logical topology design problem in IP-over-WDM networks did not consider physical capacities and logical demands. In Chapter 6, we study this problem taking into account logical link demands and physical link capacities. We define weak survivability and strong survivability in capacitated IP-over-WDM networks. Two-stage Mixed-Integer Linear Programming (MILP) formulations and heuristics to solve the survivable design problems are proposed. Based on the 2-stage MILP framework, we also propose several extensions to the weakly survivable design problem, considering several performance criteria. Noting that for some logical networks a survivable mapping may not exist, which prohibits us from applying the 2-stage MILP approach, our first extension is to augment the logical network using an MILP formulation to guarantee the existence of a survivable routing. We then propose approaches to balance the logical demands satisfying absolute or ratio-weighted fairness. Finally we show how to formulate the survivable logical topology design problem as an MILP for the multiple failure case.We conclude with an outline of two promising new directions of research
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