Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation

We consider a linear stochastic fluid network under Markov modulation, with a focus on the probability that the joint storage level attains a value in a rare set at a given point in time. The main objective is to develop efficient importance sampling algorithms with provable performance guarantees. For linear stochastic fluid networks without modulation, we prove that the number of runs needed (so as to obtain an estimate with a given precision) increases polynomially (whereas the probability under consideration decays essentially exponentially); for networks operating in the slow modulation regime, our algorithm is asymptotically efficient. Our techniques are in the tradition of the rare-event simulation procedures that were developed for the sample-mean of i.i.d. one-dimensional light-tailed random variables, and intensively use the idea of exponential twisting. In passing, we also point out how to set up a recursion to evaluate the (transient and stationary) moments of the joint storage level in Markov-modulated linear stochastic fluid networks

Electron injection in dye sensitised solar cells

In this thesis, the dynamics and quantum yields of electron injection occurring in liquid and solid state dye sensitised solar cells (DSSCs) based on titanium dioxide (TiO2) anodes sensitised with Ru – polypyridyl or organic dyes have been measured. The electron injection process is investigated through both experimental and modelling studies. A transient emission technique based on time correlated single photon counting (TCSPC) has been developed to measure the kinetics and yields of injection occurring in both films and devices. Other processes occurring in the device are probed using a range of experimental techniques, including transient absorption spectroscopy and transient photovoltage. Initially the principles of the TCSPC measurement technique are introduced and the procedure for measuring the injection in samples is outlined. Comparison of appropriate control sample measurements, which show transient emission decay dynamics in the absence of electron injection, with the TiO2 sample traces enables the quantification of injection occurring in each experimental sample. TCSPC emission decays associated with each sample are then fitted using stretch exponential functions constrained by two degrees of freedom. This TCSPC technique for measuring electron injection dynamics is validated by showing agreement with previously published kinetics for an analogous system as measured by a well established ultrafast transient absorption technique. The fits to the TCSPC decay dynamics are also shown to be accurately replicated by Monte Carlo integrations based on a previously published model of the active dye / TiO2 interface in the DSSCs. The technique is extended to probing DSSCs employing a range of different sensitisers and measuring the kinetics under different operating conditions occurring within the DSSCs where injection is found to only depend strongly on the concentration of potential determining additives. The first results chapter describes the TCSPC technique and gives examples of the data analysis procedures associated with each transient emission decay measurement. The agreement between injection kinetics measured using TCSPC with those measured using ultrafast transient absorption technique is highlighted. The model of 5 the active dye / TiO2 DSSC interface is introduced and Monte Carlo integrations based on this physical model are shown to agree well with the experimental data. The second results chapter extends the measurement of injection kinetics to different Ru – polypyridyl based sensitisers. Injection kinetics are measured for a structure – function dye series and the observed variations in the kinetics and yields are explained with reference to the dye / TiO2 interface. The measurements are extended to completely solid state DSSCs and successful fitting of the TCSPC data with integrations based on the physical model show dispersive injection kinetics observed in solid state DSSCs are controlled by the same parameters as the liquid cells. The third chapter looks at a variety of factors which may affect injection in complete, operating DSSCs. The factors addressed include presence of the commonly used iodide / triiodide redox couple, residual effects of acid versus base film synthesis procedures, effect of increasing the Fermi level in the DSSC and changing the concentration of potential determining ions in the redox electrolyte. The major controlling factor is found to be the concentration of the potential determining, commonly used tert – butyl pyridine device additive and implications of this on DSSC performance are discussed. The last chapter compares device parameters for DSSCs based on successful organic sensitiser with DSSCs based on the commonly used Ru – polypyridyl N719. Features which control the performance of organic dyes in general are outlined and the reduced performance of DSSCs employing these dyes is explained

A Tandem Fluid Network with L\'evy Input in Heavy Traffic

In this paper we study the stationary workload distribution of a fluid tandem queue in heavy traffic. We consider different types of L\'evy input, covering compound Poisson, $\alpha$-stable L\'evy motion (with $1<\alpha<2$), and Brownian motion. In our analysis we separately deal with L\'evy input processes with increments that have finite and infinite variance. A distinguishing feature of this paper is that we do not only consider the usual heavy-traffic regime, in which the load at one of the nodes goes to unity, but also a regime in which we simultaneously let the load of both servers tend to one, which, as it turns out, leads to entirely different heavy-traffic asymptotics. Numerical experiments indicate that under specific conditions the resulting simultaneous heavy-traffic approximation significantly outperforms the usual heavy-traffic approximation

Information exchange and future plans of Slovenian cattle farmers under EU policies

After accession to EU, farmers in the new-member states have to adjust to the EU agricultural policies and market. In Slovenia an analysis is made of the farm development plans and information exchange under quota and CAP. Three research questions were addressed: what information is received and how; how does the farmer prefer to receive information and what kind; how to make decisions to react to the new EU policies concerning farm management and future plans. These questions were linked to the base variables, being the farm and farmers’ characteristics. As tool a questionnaire was distributed to dairy farmers. 1114 questionnaires, 22% of the distributed ones have been returned anonymously, implying that 11% of the dairy farmers’ population is part of the analysis. It appeared that the research sample of farmers used represents the more future oriented farmers. As main factors describing the farm and farmers’ characteristics were found farm size, age and number of other activities than dairy. Results show that nearly all farmers did receive information about some specific aspects of the quota system. Communication channels dealing with this administrative info and also with farm management advice are divers, but frequency of direct contact with advisors may be less than predicted. Results also indicate a very significant demand for info about strategic planning, farm management aspects and EU premium programs, especially about CAP general policies and milk premiums, and a considerable activity in farm planning. About 40% of farmers choose for keeping the farm business the same and 50% intend to develop the farm further.CAP, Slovenian cattle farmers, information, decisions, future plans, Community/Rural/Urban Development, Q18,

Networks of ⋅/G/∞\cdot/G/\infty Server Queues with Shot-Noise-Driven Arrival Intensities

We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by shot noise. A shot-noise rate emerges as a natural model, if the arrival rate tends to display sudden increases (or: shots) at random epochs, after which the rate is inclined to revert to lower values. Exponential decay of the shot noise is assumed, so that the queueing systems are amenable for analysis. In particular, we perform transient analysis on the number of customers in the queue jointly with the value of the driving shot-noise process. Additionally, we derive heavy-traffic asymptotics for the number of customers in the system by using a linear scaling of the shot intensity. First we focus on a one dimensional setting in which there is a single infinite-server queue, which we then extend to a network setting