ASU Scholarship Showcase

There is a need for indicators of transportation-land use system quality that are understandable to a wide range of stakeholders, and which can provide immediate feedback on the quality of interactively designed scenarios. Location-based accessibility indicators are promising candidates, but indicator values can vary strongly depending on time of day and transfer wait times. Capturing this variation increases complexity, slowing down calculations. We present new methods for rapid yet rigorous computation of accessibility metrics, allowing immediate feedback during early-stage transit planning, while being rigorous enough for final analyses. Our approach is statistical, characterizing the uncertainty and variability in accessibility metrics due to differences in departure time and headway-based scenario specification. The analysis is carried out on a detailed multi-modal network model including both public transportation and streets. Land use data are represented at high resolution. These methods have been implemented as open-source software running on commodity cloud infrastructure. Networks are constructed from standard open data sources, and scenarios are built in a map-based web interface. We conclude with a case study, describing how these methods were applied in a long-term transportation planning process for metropolitan Amsterdam.

Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub{Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to nd a subspace approximation to the full problem. Determination of the regularization, parameter for the projected problem by unbiased predictive risk estimation, generalized cross validation, and discrepancy principle techniques is investigated. It is shown that the regularized parameter obtained by the unbiased predictive risk estimator can provide a good estimate which can be used for a full problem that is moderately to severely ill-posed. A similar analysis provides the weight parameter for the weighted generalized cross validation such that the approach is also useful in these cases, and also explains why the generalized cross validation without weighting is not always useful. All results are independent of whether systems are over- or underdetermined. Numerical simulations for standard one-dimensional test problems and two- dimensional data, for both image restoration and tomographic image reconstruction, support the analysis and validate the techniques. The size of the projected problem is found using an extension of a noise revealing function for the projected problem [I. Hn etynkov a, M. Ple singer, and Z. Strako s, BIT Numer. Math., 49 (2009), pp. 669{696]. Furthermore, an iteratively reweighted regularization approach for edge preserving regularization is extended for projected systems, providing stabilization of the solutions of the projected systems and reducing dependence on the determination of the size of the projected subspace.