In the preceding chapters, we witnessed that optical fiber is widely used as the transmission medium of choice in wide, metropolitan, access, and local area (wired) networks. Passive optical networks (PONs) might be viewed as the final frontier of optical wired networks where they interface with a number of wireless access technologies. One interesting approach to integrate optical fiber networks and wireless networks are so-called radio-over-fiber (RoF) networks. In RoF networks, radiofrequencies (RFs) are carried over optical fiber links to support a variety of wireless applications. In this chapter, we describe some recently investigated RoF network architectures and their support of various wireless applications. After reviewing the use of optical fiber links for building distributed antenna systems in fiber-optic microcellular radio networks, we elaborate on the various types of RoF networks and their integration with fiber to the home (FTTH), WDM PON, and rail track networks.

Fiber-optic microcellular radio

Distributed antenna system

To increase frequency reuse and thereby support a growing number of mobile users in cellular radio networks, cells may be subdivided into smaller units referred to as microcells. The introduction of microcells not only copes with the increasing bandwidth demands of mobile users but also reduces the power consumption and size of handset devices. Instead of using a base station antenna with high-power radiation, a distributed antenna system connected to the base station via optical fibers was proposed in Chu and Gans (1991).

Future broadband optical access networks not only have to unleash the economic potential and societal benefit by opening up the first/last mile bandwidth bottleneck between bandwidth-hungry end users and high-speed backbone networks but they also must enable the support of a wide range of new and emerging services and applications (e.g., triple play, video on demand, video conferencing, peer-to-peer [P2P] audio/video file sharing, multichannel high-definition television [HDTV], multimedia/multiparty online gaming, telemedicine, telecommuting, and surveillance) to get back on the road to prosperity. Due to their longevity, low attenuation, and huge bandwidth, asynchronous transfer mode (ATM) or Ethernet-based passive optical networks (PONs) are already widely deployed in today's operational access networks (e.g., fiber-to-the-premises [FTTP] and fiber-to-the-home [FTTH] networks) (Abrams et al., 2005). Typically, these PONs are time division multiplexing (TDM) single-channel systems, where the fiber infrastructure carries a single upstream wavelength channel and a single downstream wavelength channel. To support the aforementioned emerging services and applications in a costeffective and future-proof manner and to unleash the full potential of FTTX networks, PONs need to evolve by addressing the following three tasks (Shinohara, 2005):

1. Cost Reduction: Cost is key in access networks due to the small number of costsharing subscribers compared to that of metro and wide area networks. Devices and components that can be mass produced and widely applied to different types of equipment and situations must be developed. Importantly, installation costs which largely contribute to the overall costs must be reduced. A promising example for cutting installation costs is NTT's envisioned do-it-yourself (DIY) installation which deploys a user-friendly hole-assisted fiber which exhibits negligible loss increase and sufficient reliability, even when it is bent at right angles, clinched, or knotted, and can be produced economically.

2. […]

Optical fiber provides an unprecedented bandwidth potential that is far in excess of any other known transmission medium. A single strand of fiber offers a total bandwidth of 25 000 GHz. To put this potential into perspective, it is worthwhile to note that the total bandwidth of radio on Earth is not more than 25 GHz (Green, 1996). Apart from its enormous bandwidth, optical fiber provides additional advantages such as low attenuation loss (Payne and Stern, 1986). Optical networks aim at exploiting the unique properties of fiber in an efficient and cost-effective manner.

Optical point-to-point links

The huge bandwidth potential of optical fiber has been long recognized. Optical fiber has been widely deployed to build high-speed optical networks using fiber links to interconnect geographically distributed network nodes. Optical networks have come a long way. In the early 1980s, optical fiber was primarily used to build and study point-to-point transmission systems (Hill, 1990).As shown in Fig. 1.1(a), an optical point-to-point link provides an optical single-hop connection between two nodes without any (electrical) intermediate node in between. Optical point-to-point links may be viewed as the beginning of optical networks. Optical point-to-point links may be used to interconnect two different sites for data transmission and reception. At the transmitting side, the electrical data is converted into an optical signal (EO conversion) and subsequently sent on the optical fiber. At the receiving side, the arriving optical signal is converted back into the electrical domain (OE conversion) for electronic processing and storage.

Current Ethernet passive optical networks (EPONs) are single-channel systems; that is, the fiber infrastructure carries a single downstream wavelength channel and a single upstream wavelength channel, which are typically separated by means of coarse wavelength division multiplexing (CWDM). In the upstream direction (from subscriber to network), the wavelength channel bandwidth is shared by the EPON nodes by means of time division multiplexing (TDM). In doing so, only one common type of single-channel transceiver is used network wide, resulting in simplified network operation and maintenance. At present, single-channel TDM EPONs appear to be an attractive solution to provide more bandwidth in a cost-effective manner.

Given the steadily increasing number of users and bandwidth-hungry applications, current single-channel TDM EPONs are likely to be upgraded in order to satisfy the growing traffic demands in the future. Clearly, one approach is to increase the line rate of TDM EPONs. Note, however, that such an approach implies that all EPON nodes need to be upgraded by replacing the installed transceivers with higher-speed transceivers, resulting in a rather costly upgrade. Alternatively, single-channel TDM EPONs may be upgraded by deploying multiplewavelength channels in the installed fiber infrastructure in the upstream and/or downstream directions, resulting in wavelength division multiplexing (WDM) EPONs. As opposed to the higher-speed TDM approach, WDM EPONs provide a cautious upgrade path in that wavelength channels can be added one at a time, each possibly operating at a different line rate. More importantly, only EPON nodes with higher traffic demands may be WDM upgraded by deploying multiple fixed-tuned and/or tunable transceivers while EPON nodes with lower traffic demands remain unaffected.

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.

In this chapter we shift our attention from the existence of certain structures in random networks, to the ability of finding such structures. More precisely, we consider the problem of navigating towards a destination, using only local knowledge of the network at each node. This question has practical relevance in a number of different settings, ranging from decentralised routing in communication networks, to information retrieval in large databases, file sharing in peer-to-peer networks, and the modelling of the interaction of people in society.

The basic consideration is that there is a fundamental difference between the existence of network paths, and their algorithmic discovery. It is quite possible, for example, that paths of a certain length exist, but that they are extremely difficult, or even impossible to find without global knowledge of the network topology. It turns out that the structure of the random network plays an important role here, as there are some classes of random graphs that facilitate the algorithmic discovery of paths, while for some other classes this becomes very difficult.

Highway discovery

To illustrate the general motivation for the topics treated in this chapter, let us start with some practical considerations. We turn back to the routing protocol described in Chapter 5 to achieve the optimal scaling of the information flow in a random network. Recall from Section 5.3 that the protocol is based on a multi-hop strategy along percolation paths that arise w.h.p. inside rectangles of size m × κ log m that partition the entire network area.

One of the motivations to study random networks on the infinite plane has been the possibility of observing sharp transitions in their behaviour. We now discuss the asymptotic behaviour of sequences of finite random networks that grow larger in size. Of course, one expects that the sharp transitions that we observe on the infinite plane are a good indication of the limiting behaviour of such sequences, and we shall see to what extent this intuition is correct and can be made rigorous.

In general, asymptotic properties of networks are of interest because real systems are of finite size and one wants to discover the correct scaling laws that govern their behaviour. This means discovering how the system is likely to behave as its size increases.

We point out that there are two equivalent scalings that produce networks of a growing number of nodes: one can either keep the area where the network is observed fixed, and increase the density of the nodes to infinity; or one can keep the density constant and increase the area of interest to infinity. Although the two cases above can describe different practical scenarios, by appropriate scaling of the distance lengths, they can be viewed as the same network realisation, so that all results given in this chapter apply to both scenarios.

Preliminaries: modes of convergence and Poisson approximation

We make frequent use of a powerful tool, the Chen–Stein method, to estimate convergence to a Poisson distribution. This method is named after work of Chen (1975) and Stein (1978) and is the subject of the monograph by Barbour, Holst and Janson (1992).

What is this book about, and who is it written for? To start with the first question, this book introduces a subject placed at the interface between mathematics, physics, and information theory of systems. In doing so, it is not intended to be a comprehensive monograph and collect all the mathematical results available in the literature, but rather pursues the more ambitious goal of laying the foundations. We have tried to give emphasis to the relevant mathematical techniques that are the essential ingredients for anybody interested in the field of random networks. Dynamic coupling, renormalisation, ergodicity and deviations from the mean, correlation inequalities, Poisson approximation, as well as some other tricks and constructions that often arise in the proofs are not only applied, but also discussed with the objective of clarifying the philosophy behind their arguments. We have also tried to make available to a larger community the main mathematical results on random networks, and to place them into a new communication theory framework, trying not to sacrifice mathematical rigour. As a result, the choice of the topics was influenced by personal taste, by the willingness to keep the flow consistent, and by the desire to present a modern, communication-theoretic view of a topic that originated some fifty years ago and that has had an incredible impact in mathematics and statistical physics since then. Sometimes this has come at the price of sacrificing the presentation of results that either did not fit well in what we thought was the ideal flow of the book, or that could be obtained using the same basic ideas, but at the expense of highly technical complications.