A pollution-free ultra-weak FOSLS discretization of the Helmholtz equation

We consider an ultra-weak first order system discretization of the Helmholtz equation. By employing the optimal test norm, the `ideal' method yields the best approximation to the pair of the Helmholtz solution and its scaled gradient w.r.t.~the norm on $L_2(\Omega)\times L_2(\Omega)^d$ from the selected finite element trial space. On convex polygons, the `practical', implementable method is shown to be pollution-free when the polynomial degree of the finite element test space grows proportionally with $\log \kappa$. Numerical results also on other domains show a much better accuracy than for the Galerkin method

Least squares solvers for ill-posed PDEs that are conditionally stable

This paper is concerned with the design and analysis of least squares solvers for ill-posed PDEs that are conditionally stable. The norms and the regularization term used in the least squares functional are determined by the ingredients of the conditional stability assumption. We are then able to establish a general error bound that, in view of the conditional stability assumption, is qualitatively the best possible, without assuming consistent data. The price for these advantages is to handle dual norms which reduces to verifying suitable inf-sup stability. This, in turn, is done by constructing appropriate Fortin projectors for all sample scenarios. The theoretical findings are illustrated by numerical experiments

Investigating the role of preference variation in the perceptions of railway passengers in Great Britain

This study explores the factors associated with passenger satisfaction on the UK railways. To uncover taste variation, the data was segmented into three homogeneous groups of passengers through a latent class ordered logit model, whereby the class allocation was based on observed personal and trip characteristics. The findings suggest that there is significant variation in the impact of service attributes on overall satisfaction across the segments, ‘class a’, ‘class b’ and ‘class c’. Class a (15% of the sample) consists of moderately dissatisfied to highly dissatisfied passengers, for whom ‘punctuality/reliability’ is most impactful on overall satisfaction. Respondents in this class are much more likely to experience adverse service conditions such as delays or crowding conditions. Class b (32% of the sample) consists of passenger who are quite critical and moderately satisfied, for whom ‘hedonic’ factors such as ‘upkeep and repair of the train’ and ‘seat comfort’ were most impactful. Finally, class c (53% of the sample) consists of passengers that are generally satisfied, and for whom the ‘value for money of the ticket price’ is most impactful on overall satisfaction. Interestingly, for both ‘class b’ and ‘class c’, ‘punctuality/reliability’ plays a more limited role in determining overall satisfaction compared to ‘class a’. This suggests that the role of ‘punctuality/reliability’ in determining overall satisfaction is more complex than presented in the literature thus far. Finally, unobserved taste variation plays an important role in the model, as the class allocation is not always easily linked to observed groups in the data. This paper thus highlights the importance of accounting for unobserved and systematic sources of heterogeneity in the data and could provide useful insights for analysts, policy makers and practitioners, to provide more targeted strategies to improve passenger satisfaction

The impact of train and station types on perceived rail service quality

This paper aims to highlight the impact of train and station types in the evaluation of service quality, whilst taking account of a range of relevant trip and socio-demographic factors. It applies a partial constrained proportional odds model (an extension of ordered logit model) to data extracted from the 32nd wave of the National Rail Passenger Survey (NRPS) held in spring 2015, which comprises around 30,000 trip-level observations of passenger satisfaction of rail services across Great Britain. The results indicate that the impact of train types on service quality is significant. Thus, for type of train services the modelling results indicate that high speed rail, long distance, inter urban rail and especially open access operators are more likely to lead to satisfied customers compared to commuter and rural railway services. For stations, users of the smallest station category are more likely to be satisfied than those of larger category stations, but other station types do not significantly impact satisfaction. Next, delays have a significant negative impact on satisfaction levels. Considering passenger segments, respondents in the oldest age category are more likely to be satisfied compared to respondents in the youngest age category and commuters are less likely to be satisfied compared to respondents on a business or leisure trip. Overall these results show how TOCs (Train Operating Companies) might best focus their efforts on improving passenger satisfaction according to train type, station type, and trip stage and/or user segment

Robust UAV Mission Planning

Unmanned Areal Vehicles (UAVs) can provide significant contributions to information gathering in military missions. UAVs can be used to capture both full motion video and still imagery of specific target locations within the area of interest. In order to improve the effectiveness of a reconnaissance mission, it is important to visit the largest number of interesting target locations possible, taking into consideration operational constraints related to fuel usage between target locations, weather conditions and endurance of the UAV. We model this planning problem as the well-known orienteering problem, which is a generalization of the traveling salesman problem. Given the uncertainty in the military operational environment, robust planning solutions are required. As such, our model takes into account uncertainty in the fuel usage between targets (for instance due to weather conditions) as well as uncertainty in the importance of visiting specific target locations. We report results using different uncertainty sets that specify the degree of uncertainty against which any feasible solution will be protected. We also compare the probability that a solution is feasible for the robust solution on one hand and the solution found with average fuel usage and expected value of information on the other. In doing so, we show how the sustainability of a UAV mission can be significantly improved

Analysing bus passengers' satisfaction in Dhaka using discrete choice models

The bus transport system in Dhaka is unsafe, unreliable and inefficient, and struggles to cope with the day-to-day mobility of its massive population. Consequently, measuring the performance of bus service quality (SQ) from the customers’ perspective is fundamental in planning a sustainable bus transport system for Dhaka, and in developing the associated policies and regulations. Although there are some studies addressing the performance of the public transport systems in Bangladesh, little research considers how SQ attributes affect passengers’ satisfaction. The purpose of this paper is to examine a relationship between bus SQ and its influencing factors in Dhaka. Using a customer satisfaction survey with a sample size of 955, discrete choice models (e.g. multinomial logit and mixed logit) have been developed. The results indicate that the inhabitants, as expected, are dissatisfied with their bus services (less than 10% rated SQ as either excellent/good) and service attributes such as comfort level and driver skills were found to be the most important contributors towards the poor and very poor perceptions of SQ. Other influencing factors are punctuality, safety, entry and exit processes, waiting time and vehicle condition. One surprising finding was that the multinomial logit model provides better goodness-of-fit for the sample data relative to the mixed logit model implying that bus users in Dhaka may represent a homogeneous group as they do have access to other modes. Findings from this study can be utilised to develop policies and regulations to improve bus transport in Dhaka