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Abstract: Unlimited access to a motorway network can, in overloaded conditions, cause a loss of throughput. Ramp metering, by controlling access to the motorway at onramps, can help avoid this loss of throughput. The queues that form at onramps are dependent on the metering rates chosen at the onramps, and these choices affect how the capacities of different motorway sections are shared amongst competing flows. In this paper we perform an analytical study of a fluid, or differential equation, model of a linear network topology with onramp queues. The model allows for adaptive arrivals, in the sense that the rate at which external traffic enters the queue at an onramp can depend on the current perceived delay in that queue. The model also includes a ramp metering policy which uses global onramp queue length information to determine the rate at which traffic enters the motorway from each onramp. This ramp metering policy minimizes the maximum delay over all onramps and produces equal delay times over many onramps. The paper characterizes both the dynamics and the equilibrium behavior of the system under this policy. While we consider an idealized model that leaves out many practical details, an aim of the paper is to develop analytical methods that yield interesting qualitative insights and might be adapted to more general contexts. The paper can be considered as a step in developing an analytical approach towards studying more complex network topologies and incorporating other model features.

Many of the implications of climate change for Aotearoa (New Zealand) remain unclear. To identify so-far unseen or understudied threats and opportunities related to climate change we applied a horizon-scanning process. First, we collated 171 threats and opportunities across our diverse fields of research. We then scored each item for novelty and potential impact and finally reduced the list to ten threats and ten opportunities through a prioritisation process. Within the 20 items presented in this paper, we uncover a range of climate-related costs and benefits. Unexpected opportunities evolve from economic reorganisation and changes to perspectives. The threats we highlight include the overall failure to interconnect siloed policy responses, as well as those relating to extreme events and feedbacks, as well as pressures that undermine the coherence of society. A major theme of our work is that climate change effects in Aotearoa are likely to transgress the boundaries of research disciplines, industry sectors and policy systems, emphasising the importance of developing transdisciplinary methods and approaches. We use this insight to connect potential responses to climate change with Aotearoa's culture and geography. [ABSTRACT FROM AUTHOR]

Because new learning technologies are enabling students to build and explore probability models, we believe that there is a need to determine the big enduring ideas that underpin probabilistic thinking and modeling. By uncovering the elements of the thinking modes of expert users of probability models we aim to provide a base for the setting of new and more relevant goals for probability education in the 21st century. We interviewed seven practitioners, whose professional lives are centered on probability modeling over a diverse range of fields including the development of probability theory. A thematic analysis approach produced four frameworks: (1) probability modeling approaches; (2) probabilistic thinking approaches to a problem; (3) a probability modeling cycle; and (4) core building blocks for probabilistic thinking and modeling. The main finding was that seeing structure and applying structure were important aspects of probability modeling. The implications of our findings for probability education are discussed.

A core component of informal statistical inference is the recognition that judgments based on sample data are inherently uncertain. This implies that instruction aimed at developing informal inference needs to foster basic probabilistic reasoning. In this article, we analyze and critique the now-common practice of introducing students to both "theoretical" and "experimental" probability, typically with the hope that students will come to see the latter as converging on the former as the number of observations grows. On the surface of it, this approach would seem to fit well with objectives in teaching informal inference. However, our in-depth analysis of one eighth-grader's reasoning about experimental and theoretical probabilities points to various pitfalls in this approach. We offer tentative recommendations about how some of these issues might be addressed. (Contains 15 footnotes and 2 figures.)