Distribution Function Of Capacity Research Articles

Directional displacement of non-aqueous fluids through spontaneous aqueous imbibition in porous structures

The concept of the spatial wettability gradient is applied to bulk porous media to passively influence directional spontaneous imbibition flow. The imbibition process in an oil-bearing medium was mathematically modeled and experimentally validated for cores with an induced wettability profile. This was modeled by defining a wettability capacity distribution function (WCD), which is incorporated into the capillary forces term in the transport equation. The performance of the model was verified via experiments varying the interfacial tension, viscosity, permeability, core size, and porous materials. Gypsum, calcite, and hydromagnesite exhibited specific displacement patterns under one-end-open and two-ends-open boundary conditions. Of these materials, calcite and gypsum showed a symmetric saturation pattern. In contrast, hydromagnesite was the only material that exhibited a directional phase displacement under a two-ends-open boundary condition. This behavior has been associated with a WCD. The mathematical model accurately predicted this behavior, reflecting that the main interacting forces have been considered.

Defining Freeway Design Capacity Based on Stochastic Observations

The estimation of capacity as a parameter to assess traffic flow performance on freeway facilities has received considerable attention in the literature. Despite the general acceptance of the stochastic notion of capacity, limited research has been conducted on how to select a single representative design value from a capacity distribution function. This paper reports the results of an empirical comparison between conventional capacity estimates and those obtained by maximizing the sustained flow index (SFI) for 19 U.S. freeway sections. The SFI is defined as the product of the traffic volume and the probability of survival at this volume. The capacity of each cross-section was estimated by analyzing the speed–flow relationship and applying methods for stochastic capacity analysis. The results show that the optimum volumes obtained by maximizing the SFI estimated in 5-minute intervals correspond well to the 15% probability of breakdown proposed in the Highway Capacity Manual 6 th Edition to estimate the capacity from field data. From these results, it was concluded that maximizing the SFI can be considered a preferred approach to estimate a single, representative value of freeway capacity.

Single-user MIMO system, Painlevé transcendents, and double scaling

In this paper, we study a particular Painlevé V (denoted PV) that arises from multi-input-multi-output wireless communication systems. Such PV appears through its intimate relation with the Hankel determinant that describes the moment generating function (MGF) of the Shannon capacity. This originates through the multiplication of the Laguerre weight or the gamma density xαe−x, x > 0, for α > −1 by (1 + x/t)λ with t > 0 a scaling parameter. Here the λ parameter “generates” the Shannon capacity; see Chen, Y. and McKay, M. R. [IEEE Trans. Inf. Theory 58, 4594–4634 (2012)]. It was found that the MGF has an integral representation as a functional of y(t) and y′(t), where y(t) satisfies the “classical form” of PV. In this paper, we consider the situation where n, the number of transmit antennas, (or the size of the random matrix), tends to infinity and the signal-to-noise ratio, P, tends to infinity such that s = 4n2/P is finite. Under such double scaling, the MGF, effectively an infinite determinant, has an integral representation in terms of a “lesser” PIII. We also consider the situations where α=k+1/2,k∈N, and α ∈ {0, 1, 2, …}, λ ∈ {1, 2, …}, linking the relevant quantity to a solution of the two-dimensional sine-Gordon equation in radial coordinates and a certain discrete Painlevé-II. From the large n asymptotic of the orthogonal polynomials, which appears naturally, we obtain the double scaled MGF for small and large s, together with the constant term in the large s expansion. With the aid of these, we derive a number of cumulants and find that the capacity distribution function is non-Gaussian.

Sustained Flow Index: Stochastic Measure of Freeway Performance

Research into the operation of traffic flow at high volumes reveals that the capacity of freeways is not a fixed number but is rather a random variable. Since traditional operational performance measures for the analysis of traffic flow on freeways typically disregard the randomness of capacity, new approaches to make use of the concept of randomness for freeway operation analysis are required. To address that need, this paper introduces a new indicator of freeway performance based solely on a stochastic approach to capacity computation. With this new indicator, the maximum reliable volume that can be carried by a freeway over prolonged time periods was derived from parameters of capacity distribution functions. The breakdown probability corresponding to the optimum volume can be used to select a single value from the capacity distribution function. To explore the empirical relationship between expected values of capacity and the optimum volumes calculated from this new computational process, flow data from several German freeway sections were analyzed. To illustrate the application potential for a sustained flow index, this paper also discusses the bases for increasing the effectiveness of ramp metering and vehicle routing management techniques.

The influence of adverse weather conditions on probability of congestion on Dutch motorways

Weather conditions are widely acknowledged to contribute to the occurrence of congestion on motorway traffic by influencing both traffic supply and traffic demand. To the best of our knowledge, this is the first paper that explicitly integrates supply and demand effects in predicting the influence of adverse weather conditions on the probability of occurrence of congestion. Traffic demand is examined by conducting a stated adaptation experiment, in which changes in travel choices are observed under adverse weather scenarios. Based on these choices, a Panel Mixed Logit model is estimated. Supply effects are taken into account by examining the influence of precipitation on motorway capacity. Based on the Product Limit Method, capacity distribution functions are estimated for dry weather, light rain and heavy rain. With the developed model to integrate the supply and demand effects breakdown probabilities can be calculated for any given traffic demand and capacity. The results show that rainfall leads to a significant increase in the probability of traffic breakdown at bottleneck locations. Interestingly the probability of a breakdown at these bottleneck locations is predicted to be slightly higher in light rain (98.7%) than in heavy rain (95.7%) conditions, which is the result of the higher traffic demand in light rain conditions. Based on the results presented in this paper, it can be recommended to always incorporate both supply and demand effects in the predictions of motorway breakdown probabilities due to adverse weather conditions to improve the validity of the predictions.

Impact of Variable Speed Limits on Motorway Level of Service

Variable speed limits are applied on a considerable number of motorway sections. Besides the impact on road safety, variable speed limits harmonize traffic flow at high volumes and hence influence motorway capacity. The paper reports empirical findings obtained for motorway sections with different speed control conditions in Germany. The capacity of each cross section is determined by analyzing the speed-flow relationship as well as by applying methods for stochastic capacity analysis. The results show that the main effect of variable speed limits is a significantly reduced variance of the capacity distribution function. Hence, the application of variable speed limits leads to a lower risk of a traffic breakdown at moderate volumes, which significantly reduces the probability of congestion occurrence. In highway capacity guidelines, this effect can be considered by applying different thresholds of LOS E for motorway sections with and without variable speed limits.

Interference Management in Cognitive Radio Systems With Feasibility Detection

In this paper, we consider a cognitive radio system with N secondary user (SU) pairs sharing a spectrum with a pair of primary users (PUs). The SU power allocation problem is formulated as a capacity maximization problem under PU and SU quality of service (QoS) and SU peak power constraints. We show that our problem formulation is a geometric program and can be solved with convex optimization techniques. We examine the effect of PU transmissions in our formulations. Solutions for both low- and high-signal-to-interference-and-noise ratio (SINR) scenarios are provided. We show that including PU capacity in the optimization problem in some circumstances leads to increased PU performance while not significantly degrading SU capacity. In a practical wireless communication system, accurate channel state information (CSI) is not often available; hence, we formulate power allocation problems with both perfect and imperfect CSI and analyze the performance loss incurred due to imperfect CSI. Furthermore, we present a novel method of detecting and removing infeasible SU QoS constraints from the SU power allocation problem that results in considerably improved SU performance. Cumulative distribution functions of capacity for various Rayleigh fading channels are presented.

Spectrum Efficiency of Weibull Fading Channels for Various Adaptation Policies with and Without Diversity Combining

In this paper, closed-form expressions for the capacities per unit bandwidth (spectrum efficiency) of Weibull fading channels are derived and plotted for (a) Switch and Stay Combining diversity case and (b) no diversity case for adaptation policies like: (i) Optimal Power and Rate Adaptation policy, (ii) Optimal Rate Adaptation with constant transmit power policy, (iii) Channel Inversion with Fixed Rate policy, and (iv) Truncated Channel Inversion policy. In addition, spectrum efficiency expressions for asymptotic approximations, upper bounds, approximations for low and high SNR cases are derived for the cases with and without diversity. The probability density function of capacity, and the complementary cumulative distribution function of capacity are derived and plotted from the moment generating function for the cases with and without diversity. Optimal power and rate adaptation policy provides the highest capacity and optimal rate adaptation with constant transmit power policy provides the highest capacity penalty over other policies for the no diversity and SSC diversity cases. Numerical results for spectrum efficiency are plotted for all adaptation policies with and without diversity.

Analysis of Operational Interactions between Freeway Managed Lanes and Parallel, General Purpose Lanes

Roadway agencies face growing challenges to expand freeway capacity. Under the constraints of rising construction costs, right-of-way limitations, and environmental regulations, transportation agencies are seeking solutions for efficiently managing the demand on existing freeway facilities and for providing options for travelers. The concept of managed lanes (MLs) is an increasingly popular countermeasure that aims to make the most efficient use of freeway facilities by restricting access to one or more lanes to certain vehicle classes on a facility that is parallel to existing general purpose (GP) lanes. With different strategies for separating ML and GP lanes, this study examines the interaction between GP lanes and ML operations. It scrutinizes this interaction as a function of different separation types, the number of MLs, and operational ML strategies, including high-occupancy toll (HOT) and high-occupancy vehicle (HOV) lanes. Four freeway sites were selected to explore the effect of this interaction. The research shows that, for HOT facilities, separation type has the most significant impact on explaining the intensity of the frictional effect, as paint-separated ML facilities are readily affected by congestion in adjacent GP lanes. For HOV facilities, the frictional effect was observed by adopting a stochastic approach to capacity estimation to estimate the capacity distribution function for both GP and HOV lanes. It was determined that GP lanes had a stochastic dominance over HOV lanes under any breakdown probability. The results make the case that ML operations should not be evaluated independently of adjacent GP lanes, and these results have implications for both proposed analytical approaches and simulation-based analyses.

Capacity effects of variable speed limits on German freeways

Variable speed limits are applied on a number of heavily trafficked freeway sections in Germany. Besides the impact on road safety, variable speed limits harmonize traffic flow at high volumes and hence influence freeway capacity. The paper reports empirical findings obtained for several freeway sections with different speed control conditions in Germany. The capacity of each cross section is determined by analyzing the speed-flow relationship as well as by applying methods for stochastic capacity analysis. The results show that the main effect of variable speed limits is a significantly reduced variance of the capacity distribution function. Hence, the application of variable speed limits leads to a lower risk of a traffic breakdown at moderate volumes. In highway capacity guidelines, this effect can be considered by applying different thresholds of LOS E for freeway sections with and without variable speed limits.

Consistency of Stochastic Capacity Estimations

The randomness of capacity is a well-known feature of freeway traffic flow. For the estimation of capacity distribution functions based on empirical traffic data, different methodologies were developed and applied. The consistency of these estimation methods for different types of capacity distributions is analyzed. A macroscopic simulation model is used to assess to what extent a given capacity distribution function can be reproduced with the estimation methods. It is found that consistent capacity estimations are obtained only by applying methods based on statistical models for censored data.

Estimation of Passenger Car Equivalents Based on Capacity Variability

Passenger car equivalents are used in highway capacity analysis procedures to convert mixed traffic stream volumes into equivalent passenger car volumes. This paper presents a new empirical method for estimating passenger car equivalents for heavy vehicles on freeways. The proposed approach is based on the concept of stochastic capacities. Capacity distribution functions are estimated in passenger car units. With a determination of the equivalency factor for which the coefficient of variation of the capacity distribution function becomes minimal, passenger car equivalents for heavy vehicles can be derived. The methodology is demonstrated for a number of freeway bottlenecks. The new approach also gives insight into the extent at which the variance of prebreakdown volumes is attributable to variable percentages of heavy vehicles.

Comparison of fractional bed-material load �computation methods in sand-bed channels

This paper presents a comparison of different fractional bed-material load computation methods in sand-bed channels. These methods include the direct computation by size fraction approach of Einstein, Laursen and Toffaleti; the bed material fraction (BMF) approach using equations of Engelund and Hansen, Ackers and White, Yang, and Karim's modified BMF method; and the transport capacity fraction (TCF) approach using the transport capacity distribution functions of Karim and Kennedy, Li, and Wu and Molinas. Over 150 sets of flume and field data in the sand size range containing a total of 1007 data points are used to evaluate and compare the accuracy of these methods. Statistical analysis and graphical comparison are utilized to demonstrate the performance and variations in different methods. Overall, the Einstein method underpredicts the transport rate for finer sizes and overpredicts for the coarser sizes, while the other methods overestimate the finer fractions and underestimate the coarser fractions. The Wu and Molinas method, which was developed to account for these deficiencies, is shown to significantly improve fractional bed-material load computations. The Karim and Kennedy method is also found to be applicable. Copyright © 2000 John Wiley & Sons, Ltd.

A Direct Method for Multi-Area Reliability Evaluation

This paper describes a model developed for multiarea generation reliability evaluation. It is based on an analytic characterization of the system failure modes, when the interconnected generation is represented by a network flow model. Reliability indices are obtained as functions of each failure mode probability and expected capacity, which are calculated directly by integrating the capacity distribution function over the set that characterizes the failure mode. The dependence of generating capacity on hydrological conditions is explicitly represented. Sensitivity indices of the expected unserved demand with respect to area generation and interconnection reinforcements are also obtained. A case study with a 5-area Brazilian is presented and discussed.