The team has developed three complementary approaches, that present different strengths and weaknesses and might be applicable in different junction configurations or traffic conditions:

1. A continuous-variable, discrete-time optimisation approach for de- termining the fraction of green time to give to each arm of a junc- tion during the next traffic light cycle, in order to minimise total weighted squared vehicle waiting times, with more weight on buses than on cars.

2. A piece-wise linear ordinary differential equation model of queue length dynamics on a junction arm, based on flux of vehicles into and out of that arm.

3. Adiscrete-variable,discrete-timeMarkovDecisionProcessapproach. The state of the system is comprised of vehicle queue lengths and the junction’s current stage. The action is to stay in the current stage or move to the next stage. An optimal policy minimises long run expected discounted weighted delay.

A simple standalone affordable dead-reckoning system is needed, but it is inherently difficult to determine the diver’s movements. The system needs to be very cheap, so that price is not a barrier to its deployment. The system needs to be small.

The Study Group investigated the possibility of such a system making use of cheaply available accelerometer, gyroscope and magnetic field sensors, similar to those included in many modern smart phones.

The Study Group captured data using an Android device strapped to a skateboard to simulate the type of movements a diver might make underwater. Different modes of movement were evident from filtered versions of the sensor outputs, so indicating that a pedometry based solution ought to be feasible. The Study Group then formulated and investigated the feasibility of a generic dead-reckoning system. Although sensors provide more data than is strictly necessary, significant errors arise from imperfect calibration and from noise for which the Study Group derived estimates of the resulting drift in position over time. The accuracy of practical numerical integration schemes in the context of rotating frames was investigated, and a Kalman filter was used to reduce error in the orientation data by combining accelerometer and gyroscopic data.

Note: there are three separate reports contained within the uploaded .pdf file.

By analysing model outputs and actual data, we found that the model does not satisfy any of our proposed “validation” criteria and have therefore suggested a series of possible ways forward for the model development team. We have provided visualisation tools in both Matlab and R, which will be of use in analysing subsequent model versions. We have also provided a series of statistical indicators of model quality. Lastly, and perhaps most importantly, we have described in detail what can be done if additional information were to be made available, for instance further runs of the model or extra data from the operations centre.

modeled by a damped spring. One step further we also allow for pitch, a swinging motion around a horizontal axis perpendicular to the ship. It is recommended to investigate the way waves may directly drive this mode and to determine the amount of energy that flows along this path towards the roll mode. Since at sea waves are a superposition of waves with different wavelengths, we also pay attention to the properties of such a type of forcing containing stochastic elements. It is recommended that as a measure for the

occurrence of large deflections of the roll angle one should take the expected time for which a given large deflection may occur instead of the mean amplitude of the deflection.

mine probabilities on pre-impact car velocities, given the evidence from the crash scene. A disadvantage of this method is that it requires a prior distribution on the velocities of the cars involved in the crash. We suggest a different approach, that of statistical significance testing, which can be carried out without a prior. We explain this method, and apply it to a toy model. Finally, a sensitivity analysis is performed on a simple two-car collision model.

We non-dimensionalize the models and thereby remove a number of parameters,

so that, due to a scaling symmetry, only the rudder (or thruster) angle remains as a free parameter.

Using ‘degree theory’, we show that a slight modification of the model pos-

sesses at least one steady state for each angle and find certain constraints on the possible steady state configuration. We show that straight motion is unstable for the Hamburg test case and use numerical continuation and bifurcation software to compute a number of curves of states together with their stability, and the corresponding radii of the ship motion. In particular, straight forward motion can be stabilised by increasing the rudder size parameter, and the smallest possible radius is ∼ 119 m.

These analyses illustrate methods and tools from dynamical systems theory that can be used to analyse a model without simulation. Compared with simulations, the numerical bifurcation analysis is much less time consuming. We have implemented the model in MATLAB and the bifurcation software AUTO.

In this paper we focus on the allocation process to determine the settings for each thruster that results in the minimal total power and thus fuel consumption. The mathematical formulation of this situation leads to a nonlinear optimization problem with equality and inequality constraints, which can be solved by applying Lagrange multipliers.

We give three approaches: first of all, the full problem was solved using the MATLAB fmincon routine with the solution from the linearised problem as a starting point. This implementation, with robust handling of the situations where the thrusters are overloaded, lead to promising results: an average reduction in fuel consumption of approximately two percent. However, further analysis proved useful. A second approach changes the set of variables and so reduces the number of equations. The third and last approach solves the Lagrange equations with an iterative method on the linearized Lagrange problem.

In this study a hub and spoke system for medium haul travel is analysed, with particular reference to the time at which departing waves are set from the hub airport. Initially, an optimal wave time based only on the geography of the hub is considered. Subsequently, a model is developed which includes the constraints of market share and limited fleet size, and an example timetable produced. A final note is made about game theoretical aspects that might be considered in moving the work forward.

1) 1968-1971

2) 1974-1977

3) 1978-1980

4) 1980-1983

5) 1984-1986

6) 1987-1988

We divided the problem into three subtasks. The first task is to develop a load plan for a train based on the expected mix of containers. An ideal plan specifies positions on the train for various container types in a way that minimises the number of wagons required while meeting a number of packing, safety and aerodynamic constraints. The second task is truck dispatching - when a truck arrives at the terminal, where should it be sent? This problem is not straightforward because trucks arrive randomly and loading and unloading occur simultaneously, and so the ideal position for a container may not yet be available. The third task is to dispatch the stackers that transfer containers between trains and trucks in such a way that truck waiting time is minimised.

The train planning problem can be formulated as an integer programming problem, but it can also be solved using the OASIS software already owned by National Rail Corporation. Train plans can be made more flexible by using container classes rather than specific container details.

The study group suggested several truck dispatch schemes, but did not have sufficient data to evaluate the schemes.

Due to repeated unloadings of the weight on the bearing during oscillations, the bearing collar may slowly slip against the axle box wall. Although our calculations show that abrasive wear due to this slippage is negligible, the calculation raises general principles that apply to other possible wear mechanisms. If lifetime is proportional to hardness, we can estimate relative lifetimes of refurbished and new boxes. Although the resleeve material is softer than the original, the cost to lifetime ratio would favour refurbishment under this assumption.

Important unanswered questions are identified and a specific integrated program of field, laboratory, and theoretical study is suggested.

The previous paragraph describes the broad problem presented to the workshop. In what follows we organize a simple mathematical model to represent the major components of the system, and we indicate how this model may be validated (or not) by tests and, if it is successful, how it can be used in a predictive capacity.

The Painted Body Storage (PBS), which precedes Final Assembly, has 4 lanes that can be used to partially reschedule a vehicle sequence. Information on vehicle work content is available prior to arrival at the PBS, and GMHAL wants advice on using this data and the PBS to achieve a more satisfactory input to Final Assembly.

The Study Group devised three approaches.

1. Use the rules to show which short sequences are desirable and devise input and output strategies for the PBS to achieve these consistently. Choice between the strategies requires further investigation.

2. Model Final Assembly to produce an optimality criterion for vehicle sequences and use combinatorial optimization methods to optimise it over possible PBS outputs. A characterization of these outputs was derived.

3. Suggest that the initial production be suitably scheduled, which may substantially reduce the difficulties at the PBS stage.

Here, we address the issue of where to locate a new car center based on a limited dataset. A method for distilling aggregate population information down to sub-regions is developed to provide estimates that feed into the optimization algorithm.

Two measures were used in the optimization: (i) total market share and (ii) total attractiveness. Total market share optimization is found to lead to placing the center close to competitors, while total attractiveness optimization is found to lead to placing the center closer to centroid of the population.

Tucumán cuenta con 15 ingenios, en los que se procesa la totalidad de la producción de caña de azúcar de la provincia. El transporte de la caña de los distintos productores hacia los ingenios se realiza en la actualidad a partir de convenios particulares que no tienen en cuenta el rendimiento final total de la cosecha. Así, un productor puede enviar la caña de sus tierras a un ingenio distante, aún cuando en el camino los camiones que realizan el transporte pasen por delante de otros ingenios.

Este problema es sólo un aspecto de otro mayor, que tiene que ver con la eficiencia global del sistema productivo. Actualmente, durante los primeros y los últimos días de la zafra (cosecha temprana y cosecha tardía), la caña madura no es suficiente para satisfacer la demanda de los ingenios. Inversamente, en el período intermedio la cantidad de caña sobresatura la capacidad de procesamiento. Como consecuencia se produce menos azúcar de la que se podría. Teniendo esto en cuenta, la racionalización del transporte sería un primer paso en el avance hacia un sistema más eficiente.

Sin perder de vista este objetivo, la simple puesta en práctica, en el corto plazo, de un criterio optimizado de distribución representaría una mejora respecto de la situación actual. En primer lugar, disminuiría el consumo de combustible. Debe tenerse en cuenta que uno de los subproductos de la caña es el alcohol, a partir del cual se produce el bioetanol, y con el que se rebaja, por ley, un 5% de las naftas. En este sentido, la reducción del consumo de combustibles fósiles adquiere una doble importancia. Por otro lado, un mejor sistema de distribución tendría también una importante repercusión social. Los camiones que transportan la caña viajan usualmente de noche, sin luces y a muy baja velocidad y son, en consecuencia, responsables de numerosos accidentes de tránsito, puesto que no son vistos a tiempo por los automovilistas. La disminución de la cantidad de camiones recorriendo las rutas y caminos de la provincia contribuiría a reducir la cantidad de accidentes.

Finalmente, un sistema optimizado de distribución serviría, en vistas del problema general, como herramienta de diagnóstico permitiendo señalar algunos puntos por mejorar.

Podrían, por ejemplo, identificarse zonas en las que sería provechoso cambiar la plantación de una variedad de maduración tardía a una de maduración temprana, con la que proveer a los ingenios cercanos en el primer período de zafra.

In the first part of this report we determine the minimum particle size that can be removed by centrifugal separation.

The second part discusses the mechanisms for particle growth within the exhaust system in order to estimate the particle growth rate.

In section two we estimate the minimum particle diameter that can be removed by a cyclone separator is around one micron. This estimate is consistent with current applications of hydrocyclones. The particle size measurements by Perkins Technology together with our estimates from section three, suggest that the soot particles are an order of magnitude smaller than this. Although it may be possible to remove some particles less than one micron in diameter with a well designed high-speed cyclone, we do not think it will be possible to remove a substantial proportion of 100 nm or smaller particles.

The growth rate of the particles increases if the particles volume fraction or the polydispersity is increased. Therefore aggregation could be enhanced by the addition of larger particles (d > 1 µm) or water droplets (provided the water does not all vapourise) to the exhaust gas.

The various contributions to the change in temperature of the fluid can be summarised as:

(a) -5 K from the adiabatic cooling

(b) 15 K from the convection near the nozzle

(c) ΔT_s/17 from the conduction in the annulus. This depends on the average temperature of the wall of the annulus, which is unknown, but certainly between 300 and 5.50 K, corresponding to ΔT_s = 0-250 K. Hence the smallest and largest rises in temperature are 0 and 15 K respectively.

The maximal rise in temperature of the fluid is hence 25 K. A more likely estimate might be 10 K.

Some useful data, in the absence of actual heat measurements inside the fuel reservoir around the needle, would be the temperature of the wall TB. Knowledge of its spatial variation would also be of interest, since it has just been been treated as an average in this report.

In the workshop we examined models for information flow on networks that considered trade-offs between the overall network utility (or flow rate) and path diversity to ensure balanced usage of all parts of the network (and to ensure stability and robustness against local disruptions in parts of the network).

While the linear programming solution of the basic max flow problem cannot handle the current problem, the approaches primal/dual formulation for describing the constrained optimization problem can be applied to the current generation of problems, called network utility maximization (NUM) problems. In particular, primal/dual formulations have been used extensively in studies of such networks.

A key feature of the traffic-routing model we are considering is its formulation as an economic system, governed by principles of supply and demand. Considering channel capacities as a commodity of limited supply, we might suspect that a system that regulates traffic via a pricing scheme would assign prices to channels in a manner inversely proportional to their respective capacities.

Once an appropriate network optimization problem has been formulated, it remains to solve the optimization problem; this will need to be done numerically, but the process can greatly benefit from simplifications and reductions that follow from analysis of the problem. Ideally the form of the numerical solution scheme can give insight on the design of a distributed algorithm for a Transmission Control Protocol (TCP) that can be directly implemented on the network.

At the workshop we considered the optimization problems for two small prototype network topologies: the two-link network and the diamond network. These examples are small enough to be tractable during the workshop, but retain some of the key features relevant to larger networks (competing routes with different capacities from the source to the destination, and routes with overlapping channels, respectively). We have studied a gradient descent method for solving obtaining the optimal solution via the dual problem. The numerical method was implemented in MATLAB and further analysis of the dual problem and properties of the gradient method were carried out. Another thrust of the group's work was in direct simulations of information flow in these small networks via Monte Carlo simulations as a means of directly testing the efficiencies of various allocation strategies.

For a restricted version of this problem an ILP approach has been presented in the literature. In this paper, we consider the general shunting problem and derive a greedy heuristic approach and an exact solution method based on dynamic programming. Both methods are flexible in the sense that they allow the incorporation of practical planning rules and may be extended to cover additional requirements from practice.

An optimal stopping problem that minimises the total jerk was formulated and solved. This model was extended by including a linear relationship between the brake pressure and the acceleration of the car where the coefficients are estimated by linear regression. Finally, a Kalman filter estimates the state of the car using the tone wheel.

The Study Group was asked to investigate ways of putting bounds on the accuracy of such a system, and to suggest any improvements that might be made.

The work performed in the week followed three strands:

(a) an understanding of how deviations from the camera’s calibrated position lead to errors in the train’s calculated position and velocity;

(b) development of models for the train suspension, designed to place bounds on these deviations;

and (c) the performance of the associated image processing algorithms.

For the AFTS, a movement path is specified, translated into platform coordinates and executed on the machine. During the execution, the load cell measures the forces and moments that act on the prosthetic foot. We wish to find the particular movement path of the Stewart platform that will generate the target force profile. Thus, we are interested in solving an inverse problem. The main goal of the workshop was to investigate potential solution methods for this ‘force-control’ problem, including looking into its feasibility.

It was clear early in the workshop that this problem could be handled quickly by reviewing the analysis which was done in 2000, and extending those ideas to the new problems at hand. We reviewed the required Fourier techniques to describe the harmonic problem, and statistical techniques to deal with the linear model that described how to accurately measure quantities that come from real experimental measurements. The “prime method” and “good lattice points method” were reviewed and re-analysed so we could understand (and prove) why they work so well. We then looked at extending these methods and successfully found solutions to problem 1) and 2) posed by Michelin. Matlab code was written to test and verify the algorithms developed. We have some ideas on problems 3) and 4), which are also described.

The parametric model is found to be the better approach, because although a detailed model of each type of machine must be developed, an exact measurement of the model parameters is not required, and the model requires far less data for training that the non-parametric one.

Due to these low-emission environmental requirements in California, solutions must be implemented that do not entail release of these vapors into the atmosphere. One solution requires that the vapors fill a balloon during the appropriate times. However, the size of the balloon at typical inflation rates requires a significant amount of physical space (approximately 1000-2000 liters), which may not necessarily be available at filling stations in urban areas. Veeder-Root has a patent pending for a system to compress the vapors that are released to a 10:1 ratio, store this compressed vapor in a small storage tank, and then return the vapors to the original underground fuel tank when the conditions are thermodynamically appropriate (see Figure 1 for the schematic representation of this system).

The limitation of the compressor, however, is that the compression phase must take place below the ignition temperature of the vapor. For a 10:1 compression ratio, however, the adiabatic temperature rise of a vapor would be above the ignition temperature. Mathematical modeling is necessary here to estimate the

performance of the compressor, and to suggest paths in design for improvement.

This report starts with a mathematical formulation of an ideal compressor, and uses the anticipated geometry of the compressor to state a simplified set of partial differential equations. The adiabatic case is then considered, assuming that the temporary storage tank is kept at a constant temperature. Next, the

heat transfer from the compression chamber through the compressor walls is incorporated into the model.

Finally, we consider the case near the valve wall, which is subject to the maximum temperature rise over the estimated 10,000 cycles that will be necessary for the process to occur. We find that for adiabatic conditions, there is a hot spot close to the wall where the vapor temperature can exceed the wall temperature. Lastly, we discuss the implications of our analysis, and its limitations.

The aim of this work is to derive a measure of travel time performance depending on the number of road users who are participating in the central route planner. The approach is mainly of a statistical nature.

An empirical relation from the seismology literature is used to relate earthquake magnitude, distance from the epicentre and the peak ground acceleration resulting from the seismic waves. This relation is used to estimate the likely damage at the mine site. Also, the decay scale for Rayleigh (surface) waves is calculated and the implications for the mine workings considered.

The two-dimensional scattering of shear (SH) seismic waves from the mine workings is considered. Analytical solutions relevant to various mine tunnel geometries are presented with the stress and displacement amplification, due to scattering from the mine workings, calculated and discussed.