Equivalent random analysis of a buffered optical switch with general interarrival times

We propose an approximate analytic model of an optical switch with fibre delay lines and wavelength converters by employing Equivalent Random Theory. General arrival traffic is modelled by means of Gamma-distributed interarrival times. The analysis is formulated in terms of virtual traffic flows within the optical switch from which we derive expressions for burst blocking probability, fibre delay line occupancy and mean delay. Emphasis is on approximations that give good numerical efficiency so that the method can be useful for formulating dimensioning problems for large-scale networks. Numerical solution values from the proposed analysis method compare well with results from a discrete-event simulation of an optical burst switch

Modelling Pascal traffic in overflow systems

In this paper, impact of changes in parameters of offeredtraffic on the accuracy of determining the parameters of overflowtraffic in hierarchy systemswithmulti-service traffic was presented. Pascal typetrafficstreamswereoffered to the consideredsystems. The study investigated the impact of changes in the number of sources, intensity of trafficoffered by individualclasses, as well as changes in the trafficoffered by single free source. The presentedresultsarebased on determined relative errors of the values of overflowtrafficobtained in simulations and on the basis of calculations

The Variance Gamma plus plus process and applications to energy markets

The purpose of this article is to introduce a new Levy process, termed the Variance Gamma++ process, to model the dynamics of assets in illiquid markets. Such a process has the mathematical tractability of the Variance Gamma process and is obtained by applying the self-decomposability of the gamma law. Compared to the Variance Gamma model, it has an additional parameter representing the measure of the trading activity. We give a full characterization of the Variance Gamma++ process in terms of its characteristic triplet, characteristic function, and transition density. In addition, we provide efficient path simulation algorithms, both forward and backward in time. We also obtain an efficient "integral-free" explicit pricing formula for European options. These results are instrumental to apply Fourier-based option pricing and maximum likelihood techniques for the parameter estimation. Finally, we apply our model to illiquid markets, namely to the calibration of European power futures market data. We accordingly evaluate exotic derivatives using the Monte Carlo method and compare these values to those obtained using the Variance Gamma process and give an economic interpretation. Finally, we illustrate an extension to the multivariate framework.Peer reviewe

Mobile Networks

The growth in the use of mobile networks has come mainly with the third generation systems and voice traffic. With the current third generation and the arrival of the 4G, the number of mobile users in the world will exceed the number of landlines users. Audio and video streaming have had a significant increase, parallel to the requirements of bandwidth and quality of service demanded by those applications. Mobile networks require that the applications and protocols that have worked successfully in fixed networks can be used with the same level of quality in mobile scenarios. Until the third generation of mobile networks, the need to ensure reliable handovers was still an important issue. On the eve of a new generation of access networks (4G) and increased connectivity between networks of different characteristics commonly called hybrid (satellite, ad-hoc, sensors, wired, WIMAX, LAN, etc.), it is necessary to transfer mechanisms of mobility to future generations of networks. In order to achieve this, it is essential to carry out a comprehensive evaluation of the performance of current protocols and the diverse topologies to suit the new mobility conditions

Continuous-Time Markowitz's Model with Transaction Costs

A continuous-time Markowitz's mean-variance portfolio selection problem is studied in a market with one stock, one bond, and proportional transaction costs. This is a singular stochastic control problem,inherently in a finite time horizon. With a series of transformations, the problem is turned into a so-called double obstacle problem, a well studied problem in physics and partial differential equation literature, featuring two time-varying free boundaries. The two boundaries, which define the buy, sell, and no-trade regions, are proved to be smooth in time. This in turn characterizes the optimal strategy, via a Skorokhod problem, as one that tries to keep a certain adjusted bond-stock position within the no-trade region. Several features of the optimal strategy are revealed that are remarkably different from its no-transaction-cost counterpart. It is shown that there exists a critical length in time, which is dependent on the stock excess return as well as the transaction fees but independent of the investment target and the stock volatility, so that an expected terminal return may not be achievable if the planning horizon is shorter than that critical length (while in the absence of transaction costs any expected return can be reached in an arbitrary period of time). It is further demonstrated that anyone following the optimal strategy should not buy the stock beyond the point when the time to maturity is shorter than the aforementioned critical length. Moreover, the investor would be less likely to buy the stock and more likely to sell the stock when the maturity date is getting closer. These features, while consistent with the widely accepted investment wisdom, suggest that the planning horizon is an integral part of the investment opportunities.Comment: 30 pages, 1 figur

Analytic modelling and resource dimensioning of optical burst switched networks

The realisation of optical network architectures may hold the key to delivering the enormous bandwidth demands of next generation Internet applications and services. Optical Burst Switching (OBS) is a potentially cost-effective switching technique that can satisfy these demands by offering a high bit rate transport service that is bandwidth-efficient under dynamic Internet traffic loads. Although various aspects of OBS performance have been extensively investigated, there remains a need to systematically assess the cost/performance trade-offs involved in dimensioning OBS switch resources in a network. This goal is essential in enabling the future deployment of OBS but poses a significant challenge due to the complexity of obtaining tractable mathematical models applicable to OBS network optimisation. The overall aim of this thesis lies within this challenge. This thesis firstly develops a novel analytic performance model of an OBS node where burst contention is resolved by combined use of Tuneable Wavelength Converters (TWCs) and Fibre Delay Lines (FDLs) connected in an efficient share-per-node configuration. The model uses a two-moment traffic representation that gives a good trade-off between accuracy and complexity, and is suitable for extension to use in network modelling. The OBS node model is then used to derive an approximate analytic model of an OBS network of switches equipped with TWCs and FDLs, again maintaining a two-moment traffic model for each end-to-end traffic path in the network. This allows evaluation of link/route loss rates under different offered traffic characteristics, whereas most OBS network models assume only a single-moment traffic representation. In the last part of this thesis, resource dimensioning of OBS networks is performed by solving single and multi-objective optimisation problems based on the analytic network model. The optimisation objectives relate to equipment cost minimisation and throughput maximisation under end-to-end loss rate constraints. Due to non-convexity of the network performance constraint equations, a search heuristic approach has been taken using a constraint-handling genetic algorithm

Neutral Diversity in Experimental Metapopulations

New automated and high-throughput methods allow the manipulation and selection of numerous bacterial populations. In this manuscript we are interested in the neutral diversity patterns that emerge from such a setup in which many bacterial populations are grown in parallel serial transfers, in some cases with population-wide extinction and splitting events. We model bacterial growth by a birth-death process and use the theory of coalescent point processes. We show that there is a dilution factor that optimises the expected amount of neutral diversity for a given amount of cycles, and study the power law behaviour of the mutation frequency spectrum for different experimental regimes. We also explore how neutral variation diverges between two recently split populations by establishing a new formula for the expected number of shared and private mutations. Finally, we show the interest of such a setup to select a phenotype of interest that requires multiple mutations.Comment: 51 pages, 25 figure