The possibility of flexibly assigning spectrum resources with channels of different sizes greatly improves the spectral efficiency of optical networks, but can also lead to unwanted spectrum fragmentation. We study this problem in a scenario where traffic demands are categorized in two types (low or high bit-rate) by assessing the performance of three allocation policies. Our first contribution consists of exact Markov chain models for these allocation policies, which allow us to numerically compute the relevant performance measures. However, these exact models do not scale to large systems, in the sense that the computations required to determine the blocking probabilities—which measure the performance of the allocation policies—become intractable. In order to address this, we first extend an approximate reduced-state Markov chain model that is available in the literature to the three considered allocation policies. These reduced-state Markov chain models allow us to tractably compute approximations of the blocking probabilities, but the accuracy of these approximations cannot be easily verified. Our main contribution then is the introduction of reduced-state imprecise Markov chain models that allow us to derive guaranteed lower and upper bounds on blocking probabilities, for the three allocation policies separately or for all possible allocation policies simultaneously.
Several authors have investigated the unfairness of blocking probabilities in semi-flexible optical networks in the two-service scenario. propose an approximate MC model for the calculation of blocking probabilities of the two types of traffic requests along a single optical link, assuming that spectrum allocation is performed randomly. This model has been refined in @cite_20 @cite_24 @cite_25 to include spectrum portions exclusively reserved for each of the two connection types. In this contribution, we generalise the original model by means of an imprecise MC, which is an MC that allows for imprecise---partially specified---transition rates. In this way, we can provide guaranteed lower and upper bounds on the performance of a wide class of spectrum allocation policies. As exemplificative cases, we consider three such cases: the random, least-filled and most-filled allocation policies. Furthermore, we also use our partially specified transition rates to provide guaranteed lower and upper bounds on the performance of spectrum allocation policy.
@cite_24 @cite_25 @cite_20
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Elastic Optical Networks (EONs) have the potential to improve the fiber spectrum utilization by allocating spectrum resources to multiple traffic requests proportionally to the amount of carried traffic. However, achieving high spectrum utilization in this elastic scenario is hindered by the resulting spectrum fragmentation. A number of studies have addressed and made attempts to mitigate spectrum fragmentation. Most of these studies are based on simulation techniques and target the overall blocking probability experienced by the offered traffic requests due to the lack of available spectrum resources. Some studies have also shown that blocking probability in EON can be uneven, i.e., high-rate circuit requests are more likely to be blocked when compared to low-rate requests due to the shortage of contiguously available spectrum resources. The contribution of this paper is to extend an existing Markov Chain (MC) model previously proposed by the authors to quantify blocking probability in a two-service elastic fiber link. The model extension accounts for a self-limited and partial sharing of the fiber spectrum to accommodate the two types of service. The MC model is used to quantify both the blocking probability and its fairness across the two types of service, documenting how the EON uneven blocking behavior can be significantly mitigated by performing partial (as opposed to full) sharing of the fiber spectrum. A resource allocation framework is presented for spectrum underlay in cognitive wireless networks. We consider both interference constraints for primary users and quality of service (QoS) constraints for secondary users. Specifically, interference from secondary users to primary users is constrained to be below a tolerable limit. Also, signal to interference plus noise ratio (SINR) of each secondary user is maintained higher than a desired level for QoS insurance. We propose admission control algorithms to be used during high network load conditions which are performed jointly with power control so that QoS requirements of all admitted secondary users are satisfied while keeping the interference to primary users below the tolerable limit. If all secondary users can be supported at minimum rates, we allow them to increase their transmission rates and share the spectrum in a fair manner. We formulate the joint power rate allocation with proportional and max-min fairness criteria as optimization problems. We show how to transform these optimization problems into a convex form so that their globally optimal solutions can be obtained. Numerical results show that the proposed admission control algorithms achieve performance very close to that of the optimal solution. Also, impacts of different system and QoS parameters on the network performance are investigated for the admission control, and rate power allocation algorithms under different fairness criteria. This paper addresses the multicast wavelength assignment (MC-WA) problem in wavelength-routed WDM networks with full light splitting and wavelength conversion capabilities. Current approaches are based on the multicast switch model that supports only split-convert (S-C) switch scheme. This scheme leads to redundant wavelength conversions for a given multicast request. In this paper, we propose a new split-convert-split (S-C-S) switch scheme capable of eliminating the redundant wavelength conversions. In order to implement this new switch scheme, we develop a new multicast switch model based on the concept of sharing of light splitters and wavelength converters. Furthermore, existing multicast wavelength assignment algorithm allows only one wavelength to carry the light signal on a fiber link, the so-called single-wavelength assignment strategy. In this paper, we explore the advantages of a new multi-wavelength assignment strategy which allows multiple available wavelengths in a link to carry the multicast signal. This will reduce the number of wavelength conversions required for the multicast request. Consequently, based on the new S-C-S multicast switch model and the new multi-wavelength assignment strategy, we generalize the existing algorithms to produce a new Multicast 'Wavelength Assignment Algorithm (MWAA) to support both the new switch model and the new wavelength assignment strategy. Compared with the existing algorithm, our new algorithm is a more general one which makes the multicast wavelength assignment more flexible, covering different switch schemes and different assignment strategies. In addition, it delivers good performance in term of minimizing the number of wavelength conversions. The improvement percentage is sensitive to the maximum out-degree value of a node, D. For a 100-node multicast tree, the improvement percentage increases from 38 at D = 3 to about 73 at D = 16. This is highly significant A generalization of the Gaussian dirty-paper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa's strategies (i.e. by a random binning scheme induced by Costa's auxiliary random variables) vanish in the limit when the interference signals are strong. In contrast, it is shown that lattice strategies ("lattice precoding") can achieve positive rates independent of the interferences, and in fact in some cases - which depend on the noise variance and power constraints - they are optimal. In particular, lattice strategies are optimal in the limit of high SNR. It is also shown that the gap between the achievable rate region and the capacity region is at most 0.167 bit. Thus, the dirty MAC is another instance of a network setup, like the Korner-Marton modulo-two sum problem, where linear coding is potentially better than random binning. Lattice transmission schemes and conditions for optimality for the asymmetric case, where there is only one interference which is known to one of the users (who serves as a "helper" to the other user), and for the "common interference" case are also derived. In the former case the gap between the helper achievable rate and its capacity is at most 0.085 bit.