Equal Travel Time Research Articles

COVID-19 Interventions in an informal settlement: A spatial analysis of accessibility in Kibera, Kenya

This paper introduces a methodology to explore pedestrian accessibility in informal settlements. This methodology is applied to pandemic intervention sites in Nairobi's Kibera area for 3.5 months (14 April to 31 July 2020) during the COVID-19 pandemic. Freely available transportation network data and open-source GIS software are utilised. Isochrones, areas of equal travel time, are calculated to assess pedestrian accessibility (walk times) from 30,231 Kibera structures to 138 COVID-19 stationary intervention sites. These sites aid in virus control, resource distribution, and COVID-related medical support. Travel times are determined considering different terrain slopes. Unequal access to intervention sites is observed due to indirect routes. Shortest walks (up to 21.5 min) are to handwashing and food distribution points, while longer walks (up to 61.5 min) are to interventions with fewer sites or localised clustering, such as baby product distribution. This simple accessibility analysis helps identify service gaps during crises, aiding planning authorities and communities. Our methodology offers insight into travel patterns in slums and has wider applicability to assess the relationships between transport infrastructure provision and resilience in informal settlements.

A unified model for the fairness mechanism‐based coordinated vehicle route guidance

AbstractCoordinated vehicle route guidance is recognized as an effective way to alleviate the Braess' paradox that new congestion is generated since numerous vehicles obey the same guidance from Google Maps. In conventional route games, decision‐makers are assumed to be completely rational (maximized utility is taken as an optimization objective). However, behavioral research finds that not only the expected profit is pursued, but also the fairness psychology is concerned by decision‐makers in game theory. In existing studies, the fairness concern of players is widely accepted in supply chains. Inspired by the fairness psychology of supply chain members, the vehicle fairness coefficient is originally proposed in this paper. Moreover, a unified fairness mechanism of the routing game is built to perfect the existing theoretical framework of route games. Specifically, the formulated vehicle fairness coefficient is incorporated into the payoff functions of a perfectly rational‐based routing game, which makes the single‐objective problem to be multiple. Compared with the current completely rational‐based route games, this improvement allows vehicles to focus not only on travel time but also on route schemes' fairness. The consideration of vehicle fairness concern leads the original symmetric payoff matrix of the route game to be asymmetric. Since the existing solving theorems are not necessarily valid for the asymmetrical multi‐player game, a matched reinforcement learning algorithm is adopted to solve this new game. An experimental study shows that the averaged fairness coefficient is increased from 0.798 to 1.00 on the basis of the equal travel time due to the working of the designed fairness mechanism.

Marchenko imaging based on self-adaptive traveltime updating

Marchenko imaging obtains the subsurface reflectors using one-way Green’s functions, which are retrieved by solving the Marchenko equation. This method generates an image that is free of spurious artifacts due to internal multiples. The Marchenko imaging method is a target-oriented technique; thus, it can image a user specified area. In the traditional Marchenko method, an accurate velocity model is critical for estimating direct waves from imaging points to the surface. An error in the velocity model results in the inaccurate estimation of direct waves. In turn, this leads to errors in computation of one-way Green’s functions, which then affects the final Marchenko images. To solve this problem, in this paper, we propose a self-adaptive traveltime updating technique based on the principle of equal traveltime to improve the Marchenko imaging method. The proposed method calculates the time shift of direct waves caused by the error in the velocity model, and corrects the wrong direct wave according to the time shift and reconstructs the correct Green’s functions. The proposed method improves the results of imaging using an inaccurate velocity model. By comparing the results from traditional Marchenko and the new method using synthetic data experiments, we demonstrated that the adaptive traveltime updating Marchenko imaging method could restore the image of geological structures to their true positions.

多中心与单中心区域内城市的交通供给效率 —— 基于等时间交通圈的对比研究及规划政策刍议

多中心与单中心区域内城市的交通供给效率 —— 基于等时间交通圈的对比研究及规划政策刍议

Converting mixed pedestrian flows into equivalent commuters using standard pedestrian equivalent factors

This paper develops the concept of standard pedestrian equivalent (SPE) factors for converting a mixed pedestrian flow into an equivalent commuter flow. After a comprehensive review of passenger car equivalent (PCE) methodologies, the equal total travel time method is utilised for SPE estimation. A micro-simulation approach is employed for the formulation of the total travel time–flow relationship. Field data collected on walking speed distributions for commuters and older adults in Australia are used as model inputs. An independent samples t-test confirms the significant difference between walking speeds of commuters and older adults. For this paper, a unidirectional flow on flat walkways is initially considered and evaluated across proportions of older people, different flows and different walkway widths. The introduction of older adults significantly increases total travel time especially under congested conditions. Results of this investigation can be used for evaluation or design of pedestrian facilities experiencing similar flow conditions.

Oscillations of the process described by the telegraph equation for a system consisting of two segments with different densities and elasticities

If the impedances of the two segments of the rod are not equal, then the contact point of these two seg� ments generates a series of reflected and passing waves, which are hard to completely describe. However, the task becomes much easier when the densities, the elas� ticity coefficients, and the lengths of these two seg� ments are chosen so that the segments have equal travel times. In this paper, we present explicit analytic expressions for the solutions of the discontinuous tele� graph equation arising in this case.

A mixed problem describing oscillations of a rod consisting of several segments with equal wave travel times

A mixed problem describing oscillations of a rod consisting of several segments with equal wave travel times

Which rainfall spatial information for flash flood response modelling? A numerical investigation based on data from the Carpathian range, Romania

Summary This paper aims to clarify the dependence existing between spatial rainfall organisation, basin morphology and runoff response. This is obtained by applying a spatial rainfall metric which describes the spatial rainfall organisation in terms of concentration and dispersion statistics as a function of the flow travel time measured along the river network. The metric is based on the observation that runoff routing through branched channel networks imposes an effective averaging of spatial rainfall excess at equal travel time, in spite of the inherent spatial variability. High resolution radar rainfall fields and a distributed hydrologic model are employed to examine how effective are these statistics in describing the degree of spatial rainfall organisation which is important for runoff modelling, and in quantifying the effects of neglecting the spatial rainfall variability on flood modelling. The investigation focuses on three extreme flash flood events occurred on the Carpathian range (Romania) in the period 2005–2007. The size of the study catchments ranges between 36 and 167 km2. The analysis reported here shows that neglecting the spatial rainfall variability results in a considerable loss of simulation Nash–Sutcliffe (NS) efficiency in almost 30% of the cases (NS less than 0.8), with NS less than 0.6 in one of the cases. This provides a significant documentation of the influence of the spatial rainfall variability on runoff modelling for catchment size less than 160 km2. Moreover, it is shown that these rainfall statistics, used in combination, are able to isolate and describe the features of rainfall spatial organisation which have significant impact on runoff simulation. An alternative rainfall spatial variability index, which is computed irrespective of flow travel time structure, provides a comparatively poor description of the influence of neglecting rainfall spatial variability on flood modelling. Overall, this implies that rainfall organisation measured along the river network by using the travel time coordinate may be a significant property of rainfall spatial variability when considering flood response modelling.

Realizing Wardrop equilibria with real-time traffic information

A Wardrop equilibrium for multiple routes from the same origin to the same destination requires equal travel time on each path used. With the advent of real-time traffic data regarding travel times on alternative routes, it becomes important to analyze how best to use the information provided to drivers. In particular, can a Wardrop equilibrium, which is a desired state, be realized? Simulations using a realistic traffic model (the three-phase model) on a two-route example are presented to answer this question. One route (the main line) is a two-lane highway with a stalled vehicle in the right lane and the other route is a low-speed bypass. For a critical incoming flow of vehicles, a phase transition between free flow and congested flow near the stalled vehicle is observed, making this a challenging example. In the first scenario, drivers choose routes selfishly on the basis of current travel times. The result is strong oscillations in travel time because of the inherent delay in the information provided. The second scenario involves a hypothetical control system that limits the number of vehicles on the main line to prevent the free-flow to congested-flow phase transition by diverting sufficient flow to the bypass. The resulting steady state is neither a Wardrop equilibrium nor a system optimum, but an intermediate state in which the main-line travel time is less than on the bypass but the average for all vehicles is close to a minimum. In a third scenario, anticipation is used as a driver-advice system to provide a fair indicator of which route to take. Prediction is based on real-time data comparing the number of vehicles on the main line at the time a vehicle leaves the origin to the actual travel time when it reaches the destination. Steady states that approximate Wardrop equilibria, or at least as close to them as can be expected, are obtained. This approach is also applied to an example with a low-speed boundary condition imposed at the destination in place of a stalled vehicle. The steady state flow approaches a Wardrop equilibrium because there is no abrupt change in travel time due to a phase transition.

An integrated method for resolving the seismic complex near‐surface problem

ABSTRACTWe describe an integrated method for solving the complex near‐surface problem in land seismic imaging. This solution is based on an imaging approach and is obtained without deriving a complex near‐surface velocity model. We start by obtaining from the data the kinematics of the one‐way focusing operators (i.e. time‐reversed Green's functions) that describe propagation between the acquisition surface and a chosen datum reflector using the common‐focus‐point technology. The conventional statics solutions obtained from prior information about the near surface are integrated in the initial estimates of the focusing operators. The focusing operators are updated iteratively until the imaging principle of equal traveltime is fulfilled for each subsurface gridpoint of the datum reflector. Therefore, the seismic data is left intact without any application of time shifts, which makes this method an uncommitted statics solution. The focusing operators can be used directly for wave‐equation redatuming to the respective reflector or for prestack imaging if determined for multiple reflecting boundaries. The underlying velocity model is determined by tomographic inversion of the focusing operators while also integrating any hard prior information (e.g. well information). This velocity model can be used to perform prestack depth imaging or to calculate the depth of the new datum level. We demonstrate this approach on 2D seismic data acquired in Saudi Arabia in an area characterized by rugged topography and complex near‐surface geology.

HOW INDIVIDUALS LEARN TO TAKE TURNS: EMERGENCE OF ALTERNATING COOPERATION IN A CONGESTION GAME AND THE PRISONER'S DILEMMA

In many social dilemmas, individuals tend to generate a situation with low payoffs instead of a system optimum ("tragedy of the commons"). Is the routing of traffic a similar problem? In order to address this question, we present experimental results on humans playing a route choice game in a computer laboratory, which allow one to study decision behavior in repeated games beyond the Prisoner's Dilemma. We will focus on whether individuals manage to find a cooperative and fair solution compatible with the system-optimal road usage. We find that individuals tend towards a user equilibrium with equal travel times in the beginning. However, after many iterations, they often establish a coherent oscillatory behavior, as taking turns performs better than applying pure or mixed strategies. The resulting behavior is fair and compatible with system-optimal road usage. In spite of the complex dynamics leading to coordinated oscillations, we have identified mathematical relationships quantifying the observed transition process. Our main experimental discoveries for 2- and 4-person games can be explained with a novel reinforcement learning model for an arbitrary number of persons, which is based on past experience and trial-and-error behavior. Gains in the average payoff seem to be an important driving force for the innovation of time-dependent response patterns, i.e. the evolution of more complex strategies. Our findings are relevant for decision support systems and routing in traffic or data networks.

Planar area location/layout problem in the presence of generalized congested regions with the rectilinear distance metric

This paper considers the problem of placing a single rectangular Generalized Congested Region (GCR) of given area but unknown dimensions in the presence of other rectangular GCRs, where the edges of the rectangles are parallel to the travel axes. GCRs are closed and bounded regions in ℛ2 in which facility location is prohibited but through travel is allowed at an additional cost per unit distance. An interactive model is considered in which there is interaction not only between the Input/Output (I/O) point of the new GCR and the I/O points (of the existing GCRs) but between the existing I/O points themselves. Two versions of the problem are considered when: (i) the I/O point of the new GCR is located on its boundary but its exact location has to be determined; and (ii) the I/O point is located inside the new GCR at its centroid. The feasible region is divided into cells obtained by drawing a grid. We analyze the problem based on whether or not the new GCR's placement intersects gridlines. When the new GCR does not intersect gridlines, we prove that the optimal location can be drawn from a finite set of candidate points. However, when the new GCR intersects gridlines, we split the feasible region by equal travel-time partitions such that the flows through gridlines can be uniquely classified as: (i) travel through; or (ii) left bypass; or (iii) right bypass. The solution methodologies for all cases are shown to be polynomially bounded in the number of GCRs.

Inverse-Ray Imaging of 2D Layered Structures from Seismic Reflection Data

ABSTRACTShooting angle of an inverse ray for imaging 2D multi-layered structures from reflected travel-times is derived in a closed form. By considering the normal incidence of two neighboring rays reflected at interfaces when sources are at the same locations as receivers, the traveling distance and direction of two inverse-rays are determined successively from the lowermost layer to the uppermost layer. This approach is similar to and also confirmed with the Huygens' principle that the equal travel-time along a wave front (perpendicular to the rays) is conserved. The closed-form solution of the inverse rays is further applied to image a complex structure of a ramp-flat fault with eleven layers. The results demonstrate that the inverse-ray imaging from travel-time picks of all layers is superior to that picked by a layer-stripping approach.

From the Hagedoorn imaging technique to Kirchhoff migration and inversion

The seminal 1954 paper by J.G. Hagedoorn introduced a heuristic for seismic reflector imaging. That heuristic was a construction technique – a ‘string construction’ or ‘ruler and compass’ method – for finding reflectors as an envelope of equal traveltime curves defined by events on a seismic trace. Later, Kirchhoff migration was developed. This method is based on an integral representation of the solution of the wave equation. For decades Kirchhoff migration has been one of the most popular methods for imaging seismic data. Parallel with the development of Kirchhoff wave‐equation migration has been that of Kirchhoff inversion, which has as its objectives both structural imaging and the recovery of angle‐dependent reflection coefficients. The relationship between Kirchhoff migration/inversion and Hagedoorn's constructive technique has only recently been explored. This paper addresses this relationship, presenting the mathematical structure that the Kirchhoff approach adds to Hagedoorn's constructive method and showing the relationship between the two.

A constrained parametric inversion for velocity analysis based on CFP technology

A method of velocity analysis based on the common focusing point (CFP) method is presented. The two important aspects of the method are the use of the CFP domain and the use of a new parameterization—a vertical velocity gradient to describe the lateral velocity variation within a layer. The layer velocity is defined with only two parameters: an average velocity [Formula: see text]and a vertical velocity gradient (β). Layer velocity parameterization using [Formula: see text] and β assumes that the lithology of the layer is constant and that the overburden and fluid pressure increase linearly with depth. This type of parameterization is suitable for areas with gross changes in lithology (clastic‐carbonate‐salt) and for rock in hydrostatic equilibrium. A layer‐based model is required for these areas. The salt dome data example presented belongs to this type of area, so the layer‐based model with the defined parameterization produced a very good subsurface velocity model. The method is based on the principle of equal traveltime between the focusing operator and the corresponding focus point response. The velocity estimation problem is formulated as a constrained parametric inversion process. The method of perturbation is applied where linear assumptions are made; the velocity inversion, however, is a nonlinear problem, and the model parameter updates are computed iteratively using Newton’s method. The velocity model is built by layers in a top‐down approach, which makes the problem quasi‐linear.

Using desktop GIS for the investigation of accessibility by public transport: an isochrone approach

The application of existing desktop geographical information systems (GIS) to the assessment of accessibility by public transport has been investigated. Two approaches to the measurement of accessibility aggregate accessibility measures and the space-time geography framework are described. It is suggested that isochrones (lines of equal travel time) are a natural way to combine these approaches in a GIS setting. A desktop GIS application has been developed which can automatically generate isochrones for travel by public transport. The application successfully copes with the complexity of the public transport of a large city (Glasgow), comprising bus, rail, and underground services. Journeys may include an initial walk to a public transport stop, several interchanges between services of the same or different modes, and a final walk. Options provide for plotting isochrones for journeys by bus only or train only; and for exact or approximate isochrones, the latter generated more quickly. The application is described in some detail, and assessed. Sample outputs are presented, including an example involving further processing of isochrones to produce a constrained accessibility map, which demonstrates the generality of this approach.

Pushing the limits of seismic imaging, Part II: Integration of prestack migration, velocity estimation, and AVO analysis

The author proposes an operator‐driven prestack migration scheme that is based on the synthesis of common focus‐point (CFP) gathers. Each CFP gather represents the response of a synthesized source array that aims at the illumination of one subsurface gridpoint (focus point). The involved synthesis operator is referred to as the focusing operator. If the time‐reversed focusing operator and its related focus‐point response have equal traveltimes, then the underlying macro velocity model is correct and the focus‐point response in the CFP gather is stacked by weighted addition along the common traveltime curve (CFP‐stacking), yielding the prestack migration result at the subsurface grid point under consideration. If the time‐reversed focusing operator and its related focus‐point response have different traveltimes, then the underlying macro velocity model is incorrect and the correct focusing operator can be derived from the two traveltime curves. A simple updating procedure is proposed. The total CFP migration process of synthesis, updating, and stacking is repeated for all subsurface grid points of interest, leading to the prestack migration result in one‐way image time together with a distribution of updated focusing operators. In a postprocessing step, all operator traveltime information can be used to derive a velocity model for the time‐to‐depth conversion process. Hence, in the presented “CFP technology” the author proposes to estimate the velocity model from the correct focusing operators by a global inversion process after the migration process has been carried out (“beyond depth migration”). For each subsurface grid point, the amplitudes along the pairs of updated traveltime curves provide amplitude‐versus‐offset (AVO) information. In addition, by introducing the grid‐point gather with the aid of an extension of the second focusing process, the author shows that this gather leads to the extraction of pre‐ and postcritical amplitude‐versus‐ray parameter (AVP) information at each grid point. Finally, just as a velocity model can be estimated from all grid‐point‐oriented traveltime information, a lithology model can be estimated from all grid‐point—oriented amplitude information by a postimaging global inversion process.

Visualising stochastic catchments in geographical networks

Abstract This paper presents an approach to visualising the area of the catchment for a service facility within a network which allows recognition of variability in travel time along the different road segments. By way of illustration fifteen different road conditions are modelled, for the 10 minute travel zone from the Leicester Royal Infirmary. The catchments at each state are then summed, and the resulting composite catchment is visualized as grey scale images, with zones of equal travel time appearing in similar greys. The observed pattern is of a core-periphery catchment, the core having high probabilities of being within a certain travel time, and the periphery having increasingly low probabilities. Four factors which may influence the size and shape of the zones are described. Finally, discussion centres on the shortcomings of both raster and vector data structures for completing the proposed procedure.

Psychological mechanisms and the Marginal Value Theorem: dynamics of scalar memory for travel time

Abstract. The relation between memory for travel time and foraging decisions was studied experimentally. The temporal properties of two environments with patchily distributed food were simulated in the laboratory using pigeons, Columba livia, as subjects. The two environments differed in mean travel time, while the coefficient of variation of travel time and the decelerated function relating cumulative food gain to time in the patch were held constant within and between environments. Each environment contained a uniform mixture of five travel times experienced in a random order. Two of the five travel times were common in both environments. Effects of travel time were studied by comparing prey collected per patch visit (PPV) after various travel times within each environment, and by comparing patch exploitation after equal travel times between environments. Within the environment with long mean travel time (LMT) PPV was positively correlated with the last and the penultimate travel times but not with travel times before that. The increase in PPV per second of last travel time was six times greater than the increase per second of penultimate travel time, implying very steep memory discounting. In the environment with short mean travel time (SMT), there was no correlation between PPV and previous travel times. However, comparisons between environments of visits following travel times common to both environments (thus removing the effect of the last travel time) showed that substantially more prey were taken after equal travel times in the LMT than in the SMT environment. This difference cannot be accounted for by the within-environment effect of penultimate travel time, implying that there is a different, less steeply devalued, effect of the mixture of travel times. A model of information processing based on combining Scalar Expectancy Theory with the predictions of rate maximization under the Marginal Value Theorem is presented. The model can approximate the results obtained in this and previous experiments and provides a framework for further analysis of memory mechanisms of foraging behaviour.

Synthetic acoustic seismograms by dereverberating sources

Using the dereverberated-source concept, the synthetic seismograms for stratified equal travel-time layering for source and receiver at the surface as well as for a buried receiver as in the VSP data are derived. Here the simpler acoustic representation of seismograms is treated. These results are extended to data of equal vertical delay time, τ, and horizontal ray parameter, p. Since only time domain operators are used, it is not necessary to use Fourier transforms to compute the seismic response for any depth point, or any ray parameter. In addition to extending Goupillaud’s equal travel-time layer synthetic seismogram method to a buried receiver and to the case of non-normal incidence, the use of the dereverberated-source concept intuitively illustrates the nature of the seismic impulse response for a one-dimensional earth.