A multi-commodity discrete/continuum model for a traffic equilibrium system

We consider a city with several highly compact central business districts (CBDs). The commuters’ origins are continuously dispersed. The travel demand to each CBD, which is considered to be a distinct commodity of traffic movements, is dependent on the total travel cost to that CBD. The transportation system is divided into two layers: major freeways and a dense network of surface streets. Whereas the major freeway network is modelled according to the conventional discrete-network approach, the dense surface streets are approximated as a continuum. Travellers to each CBD can either travel within the continuum (surface streets) and then transfer to the discrete network (freeways) at an interchange (ramp) before moving to the CBD on the discrete network, or they can travel directly to the CBD within the continuum. Specific travel cost-flow relationships for the two layers of transportation facilities are considered. We develop a traffic equilibrium model for this discrete/continuum transportation system in which, for each origin–destination pair, no traveller can reduce his or her individual travel cost by unilaterally changing routes. The problem is formulated as a simultaneous optimisation programme with two sub-problems. One sub-problem is a traffic assignment problem from the interchanges to the CBD in the discrete network, and the other is a traffic assignment problem within a continuum system with multiple centres (i.e. the interchange points and the CBDs). A Newtonian algorithm based on sensitivity analyses of the two sub-problems is proposed to solve the resultant simultaneous optimisation programme. A numerical example is given to demonstrate the effectiveness of the proposed method.postprin

Modelling the mode choice behaviour of visitors to Expo 2010

The purpose of the present study was to obtain a better understanding of the mode choice behaviour of visitors to Expo 2010 Shanghai and the effectiveness of various traffic management policies to reduce private transport use. Due to the possible range of survey respondents, a two-stage gradual stated preference survey method was used. Based on a large-scale stated preference survey conducted among tourists in an airport, a train station and highway service stations in Shanghai, three versions of a mixed logit model for local and out-of-town visitors were developed. The results suggest that local visitors were more sensitive to travel cost than total travel time, whereas out-of-town visitors were particularly concerned about total travel time. A scenario analysis reveals that establishing a restricted traffic zone, adjusting parking rates and providing priority lanes for Expo buses had different effects on trip mode choice. These policies should thus be implemented in combination to achieve the aim of reducing private transport use to less than 10%. An additional finding is that the Expo shuttle bus is a more attractive public transport mode than the subway among Expo visitors.published_or_final_versio

Continuum modeling approach to the spatial analysis of air quality and housing location choice

Today, air pollution is a great issue, and the transport sector is an important emission source. In this study, we present an integrated land use, transport, and environment model in which transport-related pollutants are assumed to influence people's housing location choices, and a continuum modeling approach is applied. The pollutants generated by the transport sector are dispersed by the wind and they affect air quality. The air quality changes people's housing choices, which in turn changes their travel behavior. We assume that the road users are continuously distributed over the city, that the road network is relatively dense, and that this network can be approximated as a continuum. The total demand is categorized into several classes, and the modeled region contains several subdistricts. People who live in different subdistricts or who belong to different classes of commuters are assumed to have different perceptions of travel time, air quality, and the housing provision–demand relationship. The finite element method and the Newton–Raphson algorithm are adopted to solve this problem, and a numerical valuation is given to illustrate the effectiveness and efficiency of the proposed model.postprin

Reformulating the Hoogendoorn-Bovy predictive dynamic user-optimal model in continuum space with anisotropic condition

Hoogendoorn and Bovy (2004) developed an approach for a pedestrian user-optimal dynamic assignment in continuous time and space. Although their model was proposed for pedestrian traffic, it can also be applied to urban cities. The model is very general, and consists of a conservation law (CL) and a Hamilton–Jacobi–Bellman (HJB) equation that contains a minimum value problem. However, only an isotropic application example was given in their paper. We claim that the HJB equation is difficult to compute numerically in an anisotropic case. To overcome this, we reformulate their model for a dense urban city that is arbitrary in shape and has multiple central business districts (CBDs). In our model, the minimum value problem is only used in the CL portion, and the HJB equation reduces to a Hamilton–Jacobi (HJ) equation for easier computation. The dynamic path equilibrium of our model is proven in a different way from theirs, and a numerical algorithm is also provided to solve the model. Finally, we show two numerical examples under the anisotropic case and compare the results with those of the isotropic case.postprin

A Partition-Based Random Search Method for Multimodal Optimization

Practical optimization problems are often too complex to be formulated exactly. Knowing multiple good alternatives can help decision-makers easily switch solutions when needed, such as when faced with unforeseen constraints. A multimodal optimization task aims to find multiple global optima as well as high-quality local optima of an optimization problem. Evolutionary algorithms with niching techniques are commonly used for such problems, where a rough estimate of the optima number is required to determine the population size. In this paper, a partition-based random search method is proposed, in which the entire feasible domain is partitioned into smaller and smaller subregions iteratively. Promising regions are partitioned faster than unpromising regions, thus, promising areas will be exploited earlier than unpromising areas. All promising areas are exploited in parallel, which allows multiple good solutions to be found in a single run. The proposed method does not require prior knowledge about the optima number and it is not sensitive to the distance parameter. By cooperating with local search to refine the obtained solutions, the proposed method demonstrates good performance in many benchmark functions with multiple global optima. In addition, in problems with numerous local optima, high-quality local optima are captured earlier than low-quality local optima

Revisiting Jiang's dynamic continuum model for urban cities

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A predictive continuum dynamic user-optimal model for a polycentric urban city

A predictive continuum dynamic user-optimal model is extended to investigate the traffic equilibrium problem for a polycentric urban city with multiple central business districts (CBDs). The road network within the city is assumed to be dense and can be viewed as a continuum in which travellers can choose their routes in a two-dimensional space. Travellers are assumed to choose their route to minimise the actual total cost to the destination (i.e. the CBD). The model consists of two parts: the conservation law part and the Hamilton–Jacobi part. The finite volume method is used to solve each part on unstructured meshes. Because the two parts are closely interconnected and have different initial times, solving the model can be treated as a fixed-point problem, which is solved using a self-adaptive method of successive averages. Numerical experiments for an urban city with two CBDs are presented to demonstrate the effectiveness of the model and the numerical algorithm.postprin

Maximum Angle of Stability of a Wet Granular Pile

Anyone who has built a sandcastle recognizes that the addition of liquid to granular materials increases their stability. However, measurements of this increased stability often conflict with theory and with each other [1-7]. A friction-based Mohr-Coulomb model has been developed [3,8]. However, it distinguishes between granular friction and inter-particle friction, and uses the former without providing a physical mechanism. Albert, {\em et al.} [2] analyzed the geometric stability of grains on a pile's surface. The frictionless model for dry particles is in excellent agreement with experiment. But, their model for wet grains overestimates stability and predicts no dependence on system size. Using the frictionless model and performing stability analysis within the pile, we reproduce the dependence of the stability angle on system size, particle size, and surface tension observed in our experiments. Additionally, we account for past discrepancies in experimental reports by showing that sidewalls can significantly increase the stability of granular material.Comment: 4 pages, 4 figure

Differential-phase-shift quantum key distribution using heralded narrow-band single photons

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