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A variety of optical networking technologies and architectures have been developed and examined over the past decades. Up to date, however, only a few of them led to commercial adoption and revenue generation. According to Ramaswami (2006), Erbium doped fiber amplifiers (EDFAs), reconfigurable optical add-drop multiplexers (ROADMs), wavelength cross-connects (WXCs), and tunable lasers are good examples of devices successfully deployed in today's optical networks. In contrast, other technologies and techniques such as wavelength conversion, optical code division multiple access (OCDMA), optical packet switching (OPS), and optical burst switching (OBS) face significant challenges toward widespread deployment.
Crucial to the commercial success of any proposed networking technology and architecture is not only its performance evaluation by means of analysis or simulation but also a thorough feasibility study of its practical aspects. Toward this end, proof-of-concept demonstrators, testbeds, and field trials play a key role.
In this part, we provide an up-to-date survey of testbed activities on the latest switching techniques proposed for next-generation optical networks. A number of different optical switching techniques have been studied over the last few years. In our survey, we outline current testbed activities of the following major optical switching techniques: generalized multiprotocol label switching (GMPLS), waveband switching (WBS), photonic slot routing (PSR), optical flowswitching (OFS), optical burst switching (OBS), and optical packet switching (OPS), which were explained at length in previous chapters. We note that our survey is targeted to networks rather than stand-alone components and devices. Furthermore, we note that regional overviews of optical networking testbeds in Europe and China were recently reported in Fabianek (2006) and Lin and Wu (2006), respectively.
We have seen in Chapter 5 that generalized multiprotocol label switching (GMPLS) networks are able to support various switching granularities, covering fiber, waveband, wavelength, and subwavelength switching. To realize GMPLS networks, the underlying network nodes need to support multiple switching granularities rather than only one. Hence, ordinary optical cross-connects (OXCs) that perform only wavelength switching, such as the one shown in Fig. 1.5, must be upgraded in order to support multiple switching granularities, leading to so-called multigranularity optical cross-connects (MG-OXCs). Compared to ordinary OXCs, MG-OXCs hold great promise to reduce the complexity and costs of OXCs significantly by switching fibers and wavebands as an entity without demultiplexing the arriving WDM comb signal into its individual wavelengths, giving rise to waveband switching (WBS).
Recently, WBS has been receiving considerable attention for its practical importance in reducing the size and complexity of photonic and optical cross-connects. Due to the rapid development and worldwide deployment of dense wavelength division multiplexing (DWDM) technologies, current fibers are able to carry hundreds of wavelengths. Using ordinary wavelength-switching cross-connects would require a large number of ports. WBS comes into play here with the promise to reduce the port count, control complexity, and reduce the cost of photonic and optical cross-connects. The rationale behind WBS is to group several wavelengths together as a waveband and switch the waveband optically using a single input and a single output port instead of multiple input/output ports, one for each of the individual wavelengths of the waveband. As a result, the size of ordinary cross-connects that traditionally switch at the wavelength granularity can be reduced, including the associated control complexity and cost (Cao et al., 2003b).
Optical fiber is commonly recognized as an excellent transmission medium owing to its advantageous properties, such as low attenuation, huge bandwidth, and immunity against electromagnetic interference. Because of their unique properties, optical fibers have been widely deployed to realize high-speed links that may carry either a single wavelength channel or multiple wavelength channels by means of wavelength division multiplexing (WDM). The advent of Erbium doped fiber amplifiers was key to the commercial adoption of WDM links in today's network infrastructure. WDM links offer unprecedented amounts of capacity in a cost-effective manner and are clearly one of the major success stories of optical fiber communications.
Since their initial deployment as high-capacity links, optical WDM fiber links turned out to offer additional benefits apart from high-speed transmission. Most notably, the simple yet very effective concept of optical bypassing enabled network designers to let in-transit traffic remain in the optical domain without undergoing optical-electrical-optical conversion at intermediate network nodes. As a result, intermediate nodes can be optically bypassed and costly optical-electrical-optical conversions can be avoided, which typically represent one of the largest expenditures in optical fiber networks in terms of power consumption, footprint, port count, and processing overhead. More important, optical bypassing gave rise to so-called all-optical networks in which optical signals stay in the optical domain all the way from source node to destination node.
All-optical networks were quickly embraced by both academia and industry, and the research and development of novel architectures, techniques, mechanisms, algorithms, and protocols in the arena of all-optical network design took off immediately worldwide.
The IEEE standard 802.17 Resilient Packet Ring (RPR) aims at combining SONET/SDH's carrier-class functionalities of high availability, reliability, and profitable TDM service (voice) support with Ethernet's high bandwidth utilization, low equipment cost, and simplicity (Davik et al., 2004; Yuan et al., 2004; Spadaro et al., 2004). RPR is a ring-based architecture consisting of two counter directional optical fiber rings with up to 255 nodes. Similar to SONET/SDH, RPR is able to provide fast recovery from a single link or node failure within 50 ms, and carry legacy TDM traffic with a high level of quality of service (QoS). Similar to Ethernet, RPR provides advantages of low equipment cost and simplicity and exhibits an improved bandwidth utilization due to statistical multiplexing. The bandwidth utilization is further increased by means of spatial reuse. In RPR, packets are removed from the ring by the corresponding destination node (destination stripping). The destination stripping enables nodes in different ring segments to transmit simultaneously, resulting in spatial reuse of bandwidth and an increased bandwidth utilization. Furthermore, RPR provides fairness, as opposed to today's Ethernet, and allows the full ring bandwidth to be utilized under normal (failure-free) operation conditions, as opposed to today's SONET/SDH rings where 50% of the available bandwidth is reserved for protection. Current RPR networks are single-channel systems (i.e., each fiber ring carries a single wavelength channel) and are expected to be primarily deployed in metro edge and metro core areas.
In the following sections, we explain RPR in greater detail, paying particular attention to its architecture, access control, fairness control, and protection.
Optical burst switching (OBS) is one of the recently proposed optical switching techniques which probably received the greatest deal of attention (Chen et al., 2004). OBS may be viewed as a switching technique that combines the merits of optical circuit switching (OCS) and optical packet switching (OPS) while avoiding their respective shortcomings. The switching granularity at the burst rather than wavelength level allows for statistical multiplexing in OBS, which is not possible in OCS, while requiring a lower control overhead than OPS. More precisely, in OCS, the entire bandwidth of each lightpath is dedicated to one pair of source and destination nodes and unused bandwidth cannot be reclaimed by other nodes ready to send data. Thus, OCS does not allow for statistical multiplexing. On the other hand, in OCS networks no OEO conversion is needed at intermediate nodes. As a result, OCS networks provide all-optical circuits that are transparent in terms of bit rate, modulation scheme, and protocol. OCS is well suited for large data transmissions whose long connection holding time on the order of a few minutes, hours, days, weeks, or even months justify the involved twoway reservation overhead for setting up or releasing a lightpath, which may take a few hundred milliseconds. Since many applications require only subwavelength bandwidth and/or involve bursts that last only a few seconds or less, the coarse wavelength switching granularity of OCS becomes increasingly inefficient and impractical. Unlike OCS, OPS is able to provide a significant statistical multiplexing gain due to the fact that bandwidth is not dedicated to a single connection but may be shared by multiple data flows.
We survey several quantitative problems on infinite words relatedto repetitions, recurrence, and palindromes, for which the Fibonacciword often exhibits extremal behaviour.
In recent decades, qualitative approaches to probabilistic uncertainty have received more and more attention. We propose a characterisation of partial preference orders through a uniform axiomatic treatment of a variety of qualitative uncertainty notions. To this end, we prove a representation result that connects qualitative notions of partial uncertainty to their numerical counterparts. We describe an executable specification, in the declarative framework of Answer Set Programming, that constitutes the core engine for qualitative management of uncertainty. Some basic reasoning tasks are also identified.
2006 was a special year for both mathematical logic and computer science, as it celebrated Gödel's centenary. Although Gödel's work was mainly concerned with mathematics and metamathematics, the crucial role it had in the foundation of modern theoretical computer science is undeniable: for instance, one only has to remember Gödel's contributions to the birth of recursion theory as well as his part in the debate in the nineteen thirties on the subject of the Church Thesis.
Behavioural equivalences are a means of establishing whether computing systems possess the same properties. The specific set of properties that are preserved by a specific behavioural equivalence clearly depends on how the system behaviour is observed and can usually be characterised by means of a modal logic. In this paper we consider three different approaches to the definition of behavioural equivalences – bisimulation, testing and trace – applied to three different classes of systems – non-deterministic, probabilistic and Markovian – and we survey the nine resulting modal logic characterisations, each of which stems from the Hennessy–Milner logic. We then compare the nine characterisations with respect to the logical operators, in order to emphasise the differences between the three approaches in the definition of behavioural equivalences and the regularities within each of them. In the probabilistic and Markovian cases we also address the issue of whether the probabilistic and temporal aspects should be treated in a local or global way and consequently whether the modal logic interpretation should be qualitative or quantitative.
The Symmetric Circulant Travelling Salesman Problem asks for the minimum cost tour in a symmetric circulant matrix. The computational complexity of this problem is not known – only upper and lower bounds have been determined. This paper provides a characterisation of the two-stripe case. Instances where the minimum cost of a tour is equal to either the upper or lower bound are recognised. A new construction providing a tour is proposed for the remaining instances, and this leads to a new upper bound that is closer than the previous one.
The density matrices of graphs are combinatorial laplacians normalised to have trace one (Braunstein et al. 2006b). If the vertices of a graph are arranged as an array, its density matrix carries a block structure with respect to which properties such as separability can be considered. We prove that the so-called degree-criterion, which was conjectured to be necessary and sufficient for the separability of density matrices of graphs, is equivalent to the PPT-criterion. As such, it is not sufficient for testing the separability of density matrices of graphs (we provide an explicit example). Nonetheless, we prove the sufficiency when one of the array dimensions has length two (see Wu (2006) for an alternative proof). Finally, we derive a rational upper bound on the concurrence of density matrices of graphs and show that this bound is exact for graphs on four vertices.
This paper studies the equational theory of bisimulation equivalence over the process algebra BCCSP extended with the priority operator of Baeten, Bergstra and Klop. We prove that, in the presence of an infinite set of actions, bisimulation equivalence has no finite, sound, ground-complete equational axiomatisation over that language. This negative result applies even if the syntax is extended with an arbitrary collection of auxiliary operators, and motivates the study of axiomatisations using equations with action predicates as conditions. In the presence of an infinite set of actions, it is shown that, in general, bisimulation equivalence has no finite, sound, ground-complete axiomatisation consisting of equations with action predicates as conditions over the language studied in this paper. Finally, sufficient conditions on the priority structure over actions are identified that lead to a finite, ground-complete axiomatisation of bisimulation equivalence using equations with action predicates as conditions.
We investigate cut elimination in propositional substructural logics. The problem is to decide whether a given calculus admits (reductive) cut elimination. We show that for commutative single-conclusion sequent calculi containing generalised knotted structural rules and arbitrary logical rules the problem can be decided by resolution-based methods. A general cut-elimination proof for these calculi is also provided.
This paper presents an analysis of definitions and decidability for exponential functions on various matrix algebras. The main idea is to show that, generically, the entries of the exponential (or logarithm) of a matrix are Pfaffian functions of the entries of the matrix.
Action-labelled transition systems (LTSs) have proved to be a fundamental model for describing and proving properties of concurrent systems. In this paper we introduce Multiple-Labelled Transition Systems (MLTSs) as generalisations of LTSs that enable us to deal with system features that are becoming increasingly important when considering languages and models for network-aware programming. MLTSs enable us to describe not only the actions that systems can perform but also their usage of resources and their handling (creation, revelation . . .) of names; these are essential for modelling changing evaluation environments. We also introduce MoMo, which is a logic inspired by Hennessy–Milner Logic and the μ-calculus, that enables us to consider state properties in a distributed environment and the impact of actions and movements over the different sites. MoMo operators are interpreted over MLTSs and both MLTSs and MoMo are used to provide a semantic framework to describe two basic calculi for mobile computing, namely μKlaim and the asynchronous π-calculus.