Bottleneck Model Research Articles

Modularity beyond perception: Evidence from the PRP paradigm.

The Dimension Action (DA) model asserts that the visual system is modular, and that each task involves multiple-response mechanisms rather than a unitary-response selection mechanism. The model has been supported by evidence from single-task interference paradigms. We use the psychological refractory period paradigm and show that dual-task performance can also be explained by the DA model. In 6 experiments we contrasted predictions from the DA model with predictions from the Response Selection Bottleneck (RSB; Pashler, 1994) model asserting that dual-task limitations are due to a unitary-response selection mechanism. Task 1 in all experiments was a tone discrimination task. In Experiments 1 to 3, Task 2 was a variation of either the Stroop or the flanker tasks. Experiments 4 to 6 manipulated response selection directly. The results showed that response selection effects can be underadditive in some conditions and additive in others depending on the modular nature of the response effect. Together, the results support the existence of an underlying modular architecture as proposed by the DA model and pose serious difficulties for the RSB model.

On the relation between the mean and variance of delay in dynamic queues with random capacity and demand

This paper investigates the distribution of delays during a repeatedly occurring demand peak in a congested facility with random capacity and demand, such as an airport or an urban road. Congestion is described in the form of a dynamic queue using the Vickrey bottleneck model and assuming Nash equilibrium in arrival times. The paper shows that the expected delay and the variance of delay vary differently over time during the peak and must hence be considered separately. The paper gives some characterization of how the expected delay and the variance of delay are related, which explain the looping phenomenon that has now been observed a number of times. Empirical illustration is provided.

Late backward effects in the refractory period paradigm: effects of Task 2 execution on Task 1 performance

The central bottleneck model assumes that in the psychological refractory paradigm, Task 1 performance is independent of Task 2 demands. Previous studies, however, have reported backward crosstalk effects of motor demands in Task 2 on Task 1 performance. These effects have been attributed to interference at the central level. The present study aimed to isolate more directly potential backward effects at the motor level. Therefore, in three experiments, movement distance in Task 2 was manipulated using a guided ballistic movement. The results showed that movement distance in Task 2 affected reaction time as well as response duration in Task 1. It is argued that the backward effect observed in this study is due to response coupling at motor rather than central levels.

Linear complementarity formulation for single bottleneck model with heterogeneous commuters

This paper formulates the dynamic equilibrium conditions for a single bottleneck model with heterogeneous commuters as a linear complementarity problem. This novel formulation offers a formal framework for the rigorous study and solution of a single bottleneck model with general heterogeneity parameter assumptions, enabling the adoption of well established complementarity theory and methods to analyze the model, and providing a significant contribution to the existing literature that either lacks a rigorous formulation or solves the problem under a limited set of heterogeneity parameter assumptions. The paper presents theoretical proofs for solution existence and uniqueness, and numerical results and insights for different heterogeneity assumptions.

Elastic Bottleneck Equilibrium Model for Rail Transit Passengers at Rush Hours

As the traditional bottleneck models are failed to be fully utilized in the rail transit equilibrium at rush hours, the paper proposes the elastic bottleneck concepts which can reflect the trip character in each station, and develops a bottleneck equilibrium traffic flow model. First, with extending the definition of congestion risk cost, a more reasonable travel cost model for different stations at different time is developed at rush hours. Then, the peak hours computing equation is formulated to investigate the characteristics of rush hours. Considering the elastic features of different stations, the elastic bottleneck equilibrium model at the rush hours is developed. Finally, after model solution, the similarity between the model result and land value of space diminishing is analyzed comparatively, which is used to demonstrate the rationality of the proposed elastic bottlenecks model.

Sequential Markov coalescent algorithms for population models with demographic structure

We analyse sequential Markov coalescent algorithms for populations with demographic structure: for a bottleneck model, a population-divergence model, and for a two-island model with migration. The sequential Markov coalescent method is an approximation to the coalescent suggested by McVean and Cardin, and by Marjoram and Wall. Within this algorithm we compute, for two individuals randomly sampled from the population, the correlation between times to the most recent common ancestor and the linkage probability corresponding to two different loci with recombination rate R between them. These quantities characterise the linkage between the two loci in question. We find that the sequential Markov coalescent method approximates the coalescent well in general in models with demographic structure. An exception is the case where individuals are sampled from populations separated by reduced gene flow. In this situation, the correlations may be significantly underestimated. We explain why this is the case.

Methods for Human Demographic Inference Using Haplotype Patterns From Genomewide Single-Nucleotide Polymorphism Data

We propose a novel approximate-likelihood method to fit demographic models to human genomewide single-nucleotide polymorphism (SNP) data. We divide the genome into windows of constant genetic map width and then tabulate the number of distinct haplotypes and the frequency of the most common haplotype for each window. We summarize the data by the genomewide joint distribution of these two statistics-termed the HCN statistic. Coalescent simulations are used to generate the expected HCN statistic for different demographic parameters. The HCN statistic provides additional information for disentangling complex demography beyond statistics based on single-SNP frequencies. Application of our method to simulated data shows it can reliably infer parameters from growth and bottleneck models, even in the presence of recombination hotspots when properly modeled. We also examined how practical problems with genomewide data sets, such as errors in the genetic map, haplotype phase uncertainty, and SNP ascertainment bias, affect our method. Several modifications of our method served to make it robust to these problems. We have applied our method to data collected by Perlegen Sciences and find evidence for a severe population size reduction in northwestern Europe starting 32,500-47,500 years ago.

Pricing the major US hub airports

Implementing congestion pricing at 27 major US airports would reduce delays by 13 passenger-years and 1000 aircraft-hours every day, saving 3–5 million dollars daily. Chicago and Atlanta would save about 1000 dollars per aircraft. Airport revenues would increase about 11 million dollars daily. A bottleneck model with stochastic queues estimates substantial welfare gains whether or not airlines internalize self-imposed delays. Erroneously imposing fees from the non-internalizing specification on internalizing airlines, however, would be a costly mistake. The model calculates equilibrium traffic rates, queuing delays, layover times, connection times, and congestion fee schedules by minute of the day.

Rare-event probability estimation with conditional Monte Carlo

Estimation of rare-event probabilities in high-dimensional settings via importance sampling is a difficult problem due to the degeneracy of the likelihood ratio. In fact, it is generally recommended that Monte Carlo estimators involving likelihood ratios should not be used in such settings. In view of this, we develop efficient algorithms based on conditional Monte Carlo to estimate rare-event probabilities in situations where the degeneracy problem is expected to be severe. By utilizing an asymptotic description of how the rare event occurs, we derive algorithms that involve generating random variables only from the nominal distributions, thus avoiding any likelihood ratio. We consider two settings that occur frequently in applied probability: systems involving bottleneck elements and models involving heavy-tailed random variables. We first consider the problem of estimating ℙ(X 1+⋅⋅⋅+X n >γ), where X 1,…,X n are independent but not identically distributed (ind) heavy-tailed random variables. Guided by insights obtained from this model, we then study a variety of more general settings. Specifically, we consider a complex bridge network and a generalization of the widely popular normal copula model used in managing portfolio credit risk, both of which involve hundreds of random variables. We show that the same conditioning idea, guided by an asymptotic description of the way in which the rare event happens, can be used to derive estimators that outperform existing ones.

The analysis of service station allocation in the hospital based on bottleneck model

The service station allocation, which directly decides the service level and operational cost, is very important to a hospital. It is necessary for the decision makers to evaluate and optimise the service systems. The structured process to solve service station allocation problems was depicted explicitly. Taking a hospital system as an example to illustrate the whole process, the major process includes constructing the GERT model of the system by process analysis, getting an initial solution through constantly identifying the bottleneck in the system and then eliminating them, evaluating the service level of the systems and identifying object that needs improvement, then optimising them constantly by simulation analysis, eventually a satisfying solution is achieved.

Modeling Departure Time Choice under Stochastic Networks Involved in Network Design

Different travel cost functions for modeling travelers’ departure time and route choice behavior under uncertainty are investigated; then the principal equivalency of the mean-variance and scheduling approaches in modeling departure time choice is proven analytically. Based on the equivalency, a general cost function is formulated for modeling travelers’ departure time and route choice behavior under uncertainty and applied to an analysis of the departure patterns under uncertainty and a reliability-based dynamic network design problem. The analytical investigation of the departure pattern considering travel time reliability in the individual's travel cost function is presented as an extension of Vickrey's deterministic bottleneck model toward stochastic capacities. The departure pattern is significantly different from that without reliability: travelers depart earlier to reduce travel time variability. This finding (corroborated by simulations) motivated the network design approach including travel time reliability in departure time and route choice behavior. A discrete dynamic network design problem is formulated subject to a reliability-based dynamic user equilibrium, with the cost function derived from the equivalency analysis among different cost functions. Total network costs–the costs of total travel (including travel time reliability) and construction–are minimized. The network design problem consists of optimally allocating link capacities by determining the optimal numbers of lanes for a subset or a full set of links of a potential network. A genetic algorithm with some intelligence is adopted to solve the discrete optimization problem. Use of a small hypothetical network indicates that different network designs may lead to diverse departure distributions among different origin-destination (O-D) pairs over time, directly affecting travel costs. Relatively dissimilar departure patterns among different O-D pairs over time give lower travel costs.

Motor limitation in dual-task processing with different effectors

According to the extended bottleneck model, dual-task interference does not arise only from a central bottleneck but also from processing limitations at the motor stage. Evidence for this assumption has previously been found only for same-effector tasks but not for different-effector tasks. In order to examine the existence of motor interference with different effectors, we used the psychological refractory period paradigm and employed response sequences of different length in Task 1 (R1 sequence length). Experiment 1 incorporated vocal response sequences in Task 1 and a manual response in Task 2. In Experiment 2, the assignment of the effectors to the two tasks was reversed. In both experiments, the long R1 sequence prolonged reaction time for Task 2 (RT2), and this effect was reduced with decreasing temporal overlap of the two tasks. Thus, the present experiments demonstrate motor interference between different-effector tasks. This interference may be due to on-line programming or to central response monitoring.

Atomistic congestion tolls at concentrated airports? Seeking a unified view in the internalization debate

The goal of this paper is to bring some unity to the theoretical side of the debate on internalization of airport congestion by showing that all the literature's theoretical results can be derived within one simple and unified framework. The analysis starts by replicating the results of Brueckner [Brueckner, J.K., 2002. Airport congestion when carriers have market power. American Economic Review 92, 1357–1375], who showed that, because airlines behaving in Cournot fashion internalize congestion, they should be charged low congestion tolls. The analysis then validates the findings of Daniel [Daniel, J.I., 1995. Congestion pricing and capacity of large hub airports: A bottleneck model with stochastic queues. Econometrica 63, 327–370], who argued that larger atomistic tolls are required in a model where a Stackelberg leader interacts with competitive fringe airlines. However, it is shown that this result only holds approximately when the carriers' outputs are imperfect substitutes.

Response grouping in the psychological refractory period (PRP) paradigm: Models and contamination effects

Response grouping is a ubiquitous phenomenon in psychological refractory period (PRP) tasks, yet it hampers the analysis of dual-task performance. To account for response grouping, we developed several extended versions of the standard bottleneck model, each of which incorporates a possible grouping mechanism into this model. Computer simulations were used to assess how the predictions of the standard model would change with each grouping mechanism. One set of simulations investigated the basic effects of grouping on the means and intercorrelation of the reaction times in the two tasks, as well as the percentage of trials with short interresponse times ( IRTs). A second set of simulations examined whether response grouping would invalidate the use of PRP paradigms for localizing experimental effects. Finally, we investigated whether the post-hoc elimination of trials with short IRTs removes the contaminating effects of response grouping.

BRAESS'S PARADOXES IN DYNAMIC TRAFFIC ASSIGNMENT WITH SIMULTANEOUS DEPARTURE TIME AND ROUTE CHOICES

In this paper, we investigate some new dynamic phenomena of Braess's paradox in transportation networks when both the departure time and route choices are considered simultaneously. The classical Wardropian user equilibrium principle is used to characterize route choice behavior, and the traditional bottleneck models with deterministic queues are employed to describe user's departure time choice behavior. New Braess's paradoxes with dynamic user response have been found in respect to the point queue and physical queue assumptions, and the mechanisms of such paradoxes are analyzed in details. Furthermore, it is shown in a numerical example that a paradox may occur in network when physical queue assumption is made, but the paradox may not be found in network if the point queue assumption is adopted in the proposed dynamic traffic assignment model. Due to the significant difference between point queue and physical queue assumptions, spatial dimension of queues has to be considered carefully in dynamic traffic assignment models. Finally, some traffic management measures are suggested and examined to resolve the potential paradoxes, such as link closing, ramp metering, dynamic road pricing, lane partitioning, and adaptive traffic control etc.

Genome-Wide Patterns of Nucleotide Polymorphism in Domesticated Rice

Domesticated Asian rice (Oryza sativa) is one of the oldest domesticated crop species in the world, having fed more people than any other plant in human history. We report the patterns of DNA sequence variation in rice and its wild ancestor, O. rufipogon, across 111 randomly chosen gene fragments, and use these to infer the evolutionary dynamics that led to the origins of rice. There is a genome-wide excess of high-frequency derived single nucleotide polymorphisms (SNPs) in O. sativa varieties, a pattern that has not been reported for other crop species. We developed several alternative models to explain contemporary patterns of polymorphisms in rice, including a (i) selectively neutral population bottleneck model, (ii) bottleneck plus migration model, (iii) multiple selective sweeps model, and (iv) bottleneck plus selective sweeps model. We find that a simple bottleneck model, which has been the dominant demographic model for domesticated species, cannot explain the derived nucleotide polymorphism site frequency spectrum in rice. Instead, a bottleneck model that incorporates selective sweeps, or a more complex demographic model that includes subdivision and gene flow, are more plausible explanations for patterns of variation in domesticated rice varieties. If selective sweeps are indeed the explanation for the observed nucleotide data of domesticated rice, it suggests that strong selection can leave its imprint on genome-wide polymorphism patterns, contrary to expectations that selection results only in a local signature of variation.

(When) Do hub airlines internalize their self-imposed congestion delays?

Specification tests using stochastic bottleneck models of airport congestion investigate whether dominant airlines internalize or ignore self-imposed delays at twenty-seven major US airports. Data on flight times determine the airport's landing and takeoff delays for every minute of operation during peak travel days. Dynamic congestion functions based on stochastic-queuing theory separately identify delays that aircraft experience directly, impose internally on their airline's other aircraft, or impose externally on other airlines. Specification tests largely reject internalization and fail to reject non-internalization by dominant airlines. Optimal pricing should value all time using non-dominant aircraft time values and treat all delays as external.

Convergence to Equilibrium in Dynamic Traffic Networks when Route Cost Is Decay Monotone

This paper addresses the issue of convergence to equilibrium in dynamic traffic assignment. Within-day time is considered to be a continuous variable, so that traffic flows and costs are functions of within-day time. Flow propagates along routes connecting origin-destination (OD) pairs with the demand for travel between each OD pair considered to be rigid (fixed from day to day although it can vary within day). Day-to-day time is also modelled as continuous with the day-to-day dynamical system derived naturally from the usual dynamical user equilibrium (DUE) condition. This paper focuses on the bottleneck model, which has deterministic vertical queueing at bottleneck link exits when flow exceeds capacity. A new property called decay monotonicity is introduced. The link delay (and hence link cost) function is shown to be a decay monotone function of link flow provided that the link capacity is continuously differentiable and positive. In a restricted version of the single bottleneck per route case, it is shown that link cost decay monotonicity implies route cost decay monotonicity. Decay monotonicity of the route cost function is shown to be sufficient for convergence to equilibrium of the dynamical system.

Task prioritisation in multitasking during driving: opportunity to abort a concurrent task does not insulate braking responses from dual‐task slowing

AbstractIn typical dual‐task driving studies, participants concurrently perform pairs of driving‐related and ‐unrelated tasks (e.g. vehicle braking and mental arithmetic). Requiring responses to both may implicitly equate their importance. In real‐life driving, however, the potential for collision dictates that a concurrent task should be assigned far lower priority than driving. To better reflect naturalistic driving conditions, we not only instructed participants to assign maximum priority to braking in a simulated driving task, but also encouraged them to ignore the concurrent task altogether on dual‐task trials. Despite these instructions, responses to the concurrent task often preceded braking, which suffered from dual‐task interference. We also found that redundant signals to the lead vehicle's brake lights resulted in faster braking responses and an increased likelihood that the braking response would occur first. The results are consistent with the Central Bottleneck (CB) model of dual‐task interference and may help guide the design of driver‐assistance systems. Copyright © 2007 John Wiley & Sons, Ltd.

T1 difficulty and the attentional blink: Expectancy versus backward masking

According to bottleneck models of the attentional blink (AB), first-target (T1) processing difficulty should be related to AB magnitude. Tests of this prediction that have varied T1 difficulty in the context of a standard AB paradigm, however, have yielded mixed results. The present work examines two factors that may mediate the relationship between T1 difficulty and the AB: observer expectancy and backward masking of T1. In two experiments, omission of the backward mask consistently yielded the predicted relationship between T1 difficulty and the AB. In contrast, observer expectancy influenced target identification accuracy but did not mediate the relationship between T1 difficulty and the AB.