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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]

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. [ABSTRACT FROM AUTHOR]

It is easy to see that I f i ( I k i ) is of order HT ht if HT ht 's are light-tailed. Assume that HT ht new jobs arrive at the beginning of time slot I k i , and HT ht is an i.i.d. sequence. Denote by HT ht and let I f i ( I k i ) be such that HT ht for HT ht . [Extracted from the article]

In 1964, Kleinrock proposed a queueing discipline for a single-server queue in which customers from different classes accumulate priority as linear functions of their waiting time. At the instant that a server becomes free, it selects the waiting customer with the highest accumulated priority, provided that the queue is nonempty. He developed a recursion for calculating the expected waiting time for each class. In 2014, Stanford, Taylor, and Ziedins reconsidered this queue, which they termed the accumulating priority queue (APQ), and derived the waiting time distribution for each class. Kleinrock and Finkelstein in 1967 also studied an accumulating priority system in which customers' priorities increase as a power-law function of their waiting time. They established that it is possible to associate a particular linear APQ with such a power-law APQ, so that the expected waiting times of customers from all classes are preserved. In this paper, we extend their analysis to characterise the class of nonlinear APQs for which an equivalent linear APQ can be found, in the sense that, for identical sample paths of the arrival and service processes, the ordering of all customers is identical at all times in both the linear and nonlinear systems. [ABSTRACT FROM AUTHOR]

The article presents a study on the performance of the accumulating priority queue, also known as the time-dependent priority queue as developed by L. Kleinrock in his study of queueing systems. Topics include waiting time distributions for priority queues, the accumulation of priority as a linear function of time, the mathematical aspects of the maximum priority process, and non-preemptive priority.

We study a simple network with two parallel batch-service queues, where service at a queue commences when the batch is full and each queue is served by infinitely many servers. A stream of general arrivals observe the current state of the system on arrival and choose which queue to join to minimize their own expected transit time. We show that for each set of parameter values there exists a unique user equilibrium policy and that it possesses various monotonicity properties. User equilibrium policies for probabilistic routing are also discussed and compared with the state-dependent setting. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Consider a system of two queues in parallel, one of which is a ⋅| M|1 single-server infinite capacity queue, and the other a ⋅| G|∞ batch service queue. A stream of general arrivals choose which queue to join, after observing the current state of the system, and so as to minimize their own expected delay. We show that a unique user equilibrium (user optimal policy) exists and that it possesses various monotonicity properties, using sample path and coupling arguments. This is a very simplified model of a transportation network with a choice of private and public modes of transport. Under probabilistic routing (which is equivalent to the assumption that users have knowledge only of the mean delays on routes), the network may exhibit the Downs-Thomson paradox observed in transportation networks with expected delay increasing as the capacity of the ⋅| M|1 queue (private transport) is increased. We give examples where state-dependent routing mitigates the Downs-Thomson effect observed under probabilistic routing, and providing additional information on the state of the system to users reduces delay considerably. [ABSTRACT FROM AUTHOR]

We consider admission and routing controls for a system of N parallel tandem queues with finite buffers as N becomes large, with the aim of minimizing costs due to loss. We obtain the fluid limit as N→∞, and solve a related optimization problem. Asymptotically, for N large, the optimal cost and associated control take one of two forms, depending on the ratio between the cost of blocking an arrival at entry and discarding after service at the first queue. [ABSTRACT FROM AUTHOR]

We consider a system of parallel, finite tandem queues with loss. Each tandem queue consists of two single-server queues in series, with capacities C1 and C2 and exponential service times with rates μ1and μ2 for the first and second queues, respectively. Customers that arrive at a queue that is full are lost. Customers arriving at the system can choose which tandem queue to enter. We show that, for customers choosing a queue to maximise the probability of their reaching the destination (or minimise their individual loss probability), it will sometimes be optimal to choose queues with more customers already present and/or with greater residual service requirements (where preceding customers are further from their final destination). [ABSTRACT FROM AUTHOR]

Explores issues involved in capturing network traffic available in the Internet community. Problems that can arise in traffic measurement; Ways to tap into high-speed links; Measurement hardware; Types of analysis used; Sources of delay when fetching a Web page; Detection of voice over Internet Protocol.

Examines the Markov random field models of multicasting in tree networks in broadcasting. Analysis of a regular tree loss network supporting unicast and multicast calls; Distribution of calls in the core of a large network; Spatial variation in the multicast blocking probabilities.

Presents information on a study which examined the connection between loss networks without controls and Markov random field theory. Discussion on loss networks; Mathematical derivation of ring network; Conclusion.

We introduce a method for maximizing the run-out time for a system where the number of components available to make repairs is finite, and some of the components may be substituted for one another. The objective is to maximize the time at which the earliest run-out of any component occurs. The approach proposed here is to find the minimum time horizon such that no feasible allocation exists for a related linear programming problem. An adaptive version of this algorithm is proposed as a heuristic for the stochastic problem. [ABSTRACT FROM AUTHOR]