Network Flow Model Research Articles

Customised bus route design with passenger-to-station assignment optimisation

As an emerging and innovative public transportation mode, the customised bus (CB) has drawn widespread attention. Existing studies of the CB mainly focus on issues regarding the bus station location, route design, timetabling, and fare setting, but rarely consider the passenger to bus station assignment problem which can significantly influence passengers’ benefit and the buses’ operating scheme. Thus, this study focuses on the customised bus routing problem with passenger-to-station assignment (CBRP-PSA) aiming to simultaneously minimise passengers’ CB service access cost and the bus route cost. A time-discretized multi-commodity network flow model is developed to jointly determine the CB routes, timetables, and passenger-to-station assignment by allowing split loads and mixed loads. Through the dualization, the developed model is decomposed into two solvable sub-problems, and a Lagrangian-based heuristic solution algorithm is proposed. The model and algorithm are implemented in illustrative, medium-scale, and large-scale transportation networks to demonstrate their effectiveness under different scenarios.

Reliability Estimation for Stochastic Flow Networks With Dependent Arcs

The creation and the destruction processes (CPs and DPs) are the basis of many efficient Monte Carlo methods for estimating the unreliability of highly reliable networks on both, the static and the stochastic flow network models, for the case of independent components. Some of these methods are based on the splitting variance reduction techniques. Due to the splitting basic mechanism, they operate over CP. Here, we propose a splitting-based Monte Carlo method, using the Marshall–Olkin copula for the case of nonindependent components. This proposal operates on the DP, because the Marshall–Olkin copula model over networks is quite related—and somehow similar—to DP, which is unusual but here necessary. Before addressing the proposal, the article presents a review of the methods based on CP and DP. At the end, a comparative experimental analysis shows the efficiency of the proposed approach.

Channel Network Modeling of Flow and Transport in Fractured Rock at the Äspö HRL: Data‐Worth Analysis for Model Development, Calibration and Prediction

AbstractPerformance assessment of nuclear waste disposal in deep crystalline bedrock demands a thorough understanding of the related flow and transport processes. Uncertainties may arise both from the selection of the conceptual model as well as the estimation of the related model parameters. Discrete fracture network (DFN) models are widely used for such modeling while channel network models (CNM) provide an alternative representation, the latter focusing on the fact that flow and transport in deep fractured media often are dominated by a small number of long preferential flow paths. This study applies the principle of channel networks, implemented in the Pychan3d simulator, to analyze the hydraulic and tracer transport behavior in a 450‐m‐deep fractured granite system at the Äspö Hard Rock Laboratory in Sweden, where extensive site characterization data, including hydraulic and tracer test data are available. Semi‐automated calibration of channel conductances to field characterization data (flow rates, drawdowns, and tracer recoveries) is performed using PEST algorithm. It was observed that an optimal CNM connectivity map for channel conductance calibration can only be developed by jointly fitting flow rates, drawdowns and tracer mass recovery values. Results from data‐calibrated CNM when compared to a corresponding calibrated DFN model shows that the CNM calibrates and adapts better than a DFN model with uniform fracture surfaces. This comparative study shows the differences and uncertainties between two models as well as examines the implications of using them for long term model predictions.

Numerical analysis of pumped two-phase loop: Characterization of steady-state performance

With growing heat dissipation from advanced electronics, two-phase cooling promises effective and unmatched cooling. A pumped two-phase loop (P2PL) can acquire high power and heat flux from the electronics (heat source) and transport and dissipate it to a heat sink with small total thermal resistance at negligible pumping power consumption because of highly effective phase change (boiling and condensation) heat transfer. Owing to many advantages, in recent years, extensive research efforts have been dedicated to understanding fundamental mechanisms of heat and mass transfer in phase change heat exchangers (evaporators or condensers) at a component level. However, there is little work done for an entire two-phase cooling system as a closed loop which is essential to study the system performance characteristics and the contributions/interactions of each component to the system performance. A comprehensive thermal–hydraulic flow network model was developed to study the system performance characteristics. The pressure variation of the P2PL was calculated by considering the compressibility of the vapor volume in the P2PL to account for the effect of the amount of vapor in the system. The numerical results on the thermal and hydraulic performance characteristics of the P2PL for various operating and design parameters – evaporator heat load, mass flow rate, heat sink temperature, and microchannel dimensions – are discussed. It was found that the numerical results match well with the measured steady-state temperature and pressure profiles of the P2PL. The study also highlights the trade-off between the total system thermal resistance reduction and the increased pressure drop (pumping power) with an increase in mass flow rate. It was also found that the microchannels with smaller hydraulic diameters had significant heat transfer enhancement in the evaporator but poor system performance.

Refuse-derived fuel-3 production simulation using network flow modeling: Predicting the uncertainty in quality standards

Municipal solid waste management requires intelligent and integrated decision-making to achieve sustainable waste treatment processes. In particular, a waste treatment system that transforms municipal solid wastes into a commodity called refuse-derived fuel (RDF) is being researched as a promising waste to energy solution. This waste processing faces limitations in maintaining consistent production and quality control standards of RDF. In this context, a network flow modeling technique is used to design a stochastic discrete-event simulation model for the production in a general material recovery facility (MRF) to evaluate its performance. The developed model supports revisions in the strategic, tactical, and operational decision levels and is integrated with varied uncertainties like probability distributions of in-feed waste compositions, moisture content, and calorific value of individual waste components, affecting the energy performance of a MRF. The model provides improvements to operating conditions and enables prediction for quality standards of RDF, enabling the waste management authority to meet their outlined quality specification for the final product. The validation of the model is conducted in a way, where the quality measures of the final product collected from an MRF are compared with the estimated values those from the simulation. The comparison reveals that precision in results from the developed model, in all performed tests is consistent with actual observed results, inferring the developed simulation model as a viable tool for estimating quality measures for RDF. The foundations of the model are based of assumptions like emphasis on general representation but not physical properties of MRF, only selected sets of uncertainties are studied, and variations in the operating conditions can affect estimated quality of RDF.

Representation of Fully Three‐Dimensional Interfacial Curvature in Pore‐Network Models

AbstractQuasi two‐dimensional approximations of interfacial curvature, present in current network models of multiphase flow in porous media, are extended to three dimensions. The new expressions for threshold capillary pressure are validated and calibrated using high‐resolution direct numerical simulations on synthetic geometries. The effects of pore‐space expansion and sagittal interface curvature on displacement are quantified, and are shown to be a key step in improving the physical accuracy of network models. Finally, the calibrated network model is used to obtain predictions for relative permeability and capillary pressure in a water‐wet Bentheimer sandstone. The predictions are compared to experimental measurements, revealing that the inclusion of three‐dimensional interfacial curvature leads to more accurate predictions.

On the complexity and modeling of the electric vehicle sharing problem

We introduce the electric vehicle sharing problem (EVSP), a problem that arises from the planning and operation of electric car-sharing systems with one-way rental of vehicles. The problem aims at finding the maximum total daily rental time in which customers’ demands are assigned to the existing fleet. In addition, either all the customer’s demands are completely fulfilled or the customer does not use the system at all. We show that the EVSP is NP-hard, and we provide four mixed-integer linear programming formulations based on space–time network flow models, along with some theoretical results. We perform a comprehensive computational study of the behavior of the proposed formulations using two benchmark sets, one of which is based on real-world data from an electric car-sharing system located in Fortaleza, Brazil. The results show that our best formulation is effective in solving instances where each customer has only one demand. In general, we were able to optimally solve at least 55% of the instances within the time limit of one hour.

A stabilizing benders decomposition method for the accessibility-oriented charging station location problem

Electric vehicles are a promising selection to deal with climate change and energy crises. However, the development of electric vehicles is impeded by various barriers including shortened driving range, lack of charging facilities, and long recharging periods. Setting additional charging facilities is essential to construct an efficient charging network. Previous studies neglected accessibility-oriented indicators to locate charging stations. This study locates charging stations by maximizing the space-time-electricity accessibility of electric vehicle travelers. For the accessibility-oriented charging station location problem, we formulate a multi-commodity network flow model in the space-time-electricity network. Then, we reformulate this model into a two-stage integer program and develop a Benders decomposition method with stabilizing techniques. At each iteration, a relaxed Benders master problem (RMP) and a set of dual routing subproblems (DSPs) are solved. The RMP provides an ascending lower bound and a feasible charging station location scheme. These DSPs generate a set of Benders optimality cuts for RMP and a feasible solution to update the upper bound. All instances in three transportation networks are solved optimally, showing that the stabilizing techniques can significantly improve the performance of the standard Benders decomposition method.

A Network Flow Model for Operational Planning in an Underground Gold Mine

In underground mines, the problem of efficiently scheduling and allocating weekly operations has a major impact on the long-term productivity of the mine. The problem of selecting the optimal locations for operations in an underground gold mine is a complex task. It is not solved by simply selecting the levels with the richest grade because the transportation network for ore in an underground mine has a diverse set of capacity constraints that can frustrate immediate mining of all the richest levels. To solve this scheduling difficulty, we formulated a new mixed-integer network flow model of the problem of weekly allocating mining operations in an underground goldmine such that the total gold mined (in ounces) was maximized subject transportation capacity constraints. The model was applied an underground gold mine in Red Lake, Ontario, Canada. The results were compared to those of a two greedy heuristic models that were designed to represent the decision-making heuristics that are currently used at the mine. It was found that the new model yielded solutions that improved upon the two greedy heuristics by 14.7% and 6.0%, respectively. The results of this research illustrate that the development of this optimization model can support decisions to improve a gold mine’s productivity.

Information dissemination dynamics through Vehicle-to-Vehicle communication built upon traffic flow dynamics over roadway networks

This research is dedicated to developing a discrete mathematical simulation framework to track information dissemination dynamics via Vehicle-to-Vehicle (V2V) communication factoring traffic flow dynamics, traffic intersection operation settings, and traffic intersection geometrical design over a road traffic network. Specifically, we develop information network flow models (INFMs), including IFNM-a and IFNM-r, respectively for tracking information wavefront spreading dynamics at arterial intersections and at highway-ramp intersections. Next, by integrating IFNMs with the information and traffic coupled cell transmission model (IT-CTM) model developed by Du et al. [16] for capturing the information front propagation dynamics on a road segment, we establish a discrete mathematical simulation framework (IFNM-CTM) to track the information front spreading dynamics over a road network at discrete time stamps. Furthermore, by combining the IFNM-CTM framework and the deep search algorithms, this study tracks the information coverage dynamics and investigates its correlation to traffic congestion evolution over a traffic network at discrete time stamps. Our experiments built upon Sioux Falls city network indicate that the IFNM-CTM is able to track the information front spreading, including location and coverage, accurately with the mean absolute error (MAE) less than 6% and 5%, respectively. More importantly, our studies found a strong correlation existing between information front spreading dynamics and traffic congestion evolution over the network. Specifically, a mild congestion condition (i.e., LOS C and D) provides the best traffic condition to sustain information spreading as compared to sparse (i.e., LOS A or B) and heavily congested (i.e., LOS E or F) traffic conditions since neither of them can sustain stable and constant wireless communication due to the limited transmission range of DSRC and interference issues.

Parameterization of a channel network model for groundwater flow in crystalline rock using geological and hydraulic test data

Groundwater flow in sparsely fractured crystalline rocks is highly channelized due to the existing complex hydrogeological heterogeneity in fracture networks. The impacts of multiscale hydraulic heterogeneity on channelized flow in a block of fractured rock under the unidirectional flow condition are investigated by three-dimensional (3D) discrete fracture network (DFN) modeling. A channel network (CN) model generated from DFN is used to model the channelized groundwater flow in fractured crystalline rock. An approach for parameterizing the channel conductance is proposed which uses information from the hydrogeological characterization data. The results show that the network scale hydrogeological heterogeneity dominates the distribution variability of flowrates. The proposed parameterization approach for the channel conductance is effective and robust. Based on the available hydrogeological characterization data, it is possible to compensate for the neglected heterogeneity in the CN model by enhancing the variability of assigned channel conductance. The findings from this work are useful for model simplification from 3D DFN to CN, and for overcoming the difficulty in the parameterization of CN models in applications.

Numerical and artificial neural network modelling of magnetorheological radiative hybrid nanofluid flow with Joule heating effects

In the current investigation, the radiative hybrid nanofluid flow through microchannel (HNF-MC) is investigated with the mathematical computational software MATHEMATICA with an innovative employment of intelligent computing solver based on Levenberg-Marquardt backpropagation neural networks (LMBNN). The effects of viscous dissipation, magnetohydrodynamics and velocity slip are considered. The heat transfer phenomenon is studied under the considerations of both convection and velocity slip phenomena. The governing dimensional equations are nondimensionalized with appropriate physical quantities. The data collection for proposed LMBNN is generated through different scenarios of HNF-MC model with sundry parameters via MATHEMATICA. To predict the multi-layer perceptron (MLP) values, the artificial neural network (ANN) has been developed. To obtain the approximate solutions for HNF-MC in various scenarios and for the processes of training, testing and validation are set. Later, for assurance of accuracy of the model the results are matched with given data sets. The error (ERR) and mean square error (MSE) are analysed. According to the current investigation, ANN is the best effective and accurate, and conveniently applicable for simulating the motion of hybrid nanofluid (water-CNT based nanofluid) through the parallel microchannel. It is concluded that, the stronger magnetic field declines the velocity and temperature profiles due to Lorentz forces.

Integrated electric bus timetabling and scheduling problem

Vehicle timetabling and scheduling in a public transit system are usually performed separately, with the output of timetabling serving as the input of scheduling. An obvious drawback of this sequential planning method is that the trade-off between bus timetables and vehicle schedules may be neglected when determining solutions, which in turn results in that the obtained solutions may be inferior to those produced using an integrated framework. For example, a well-planned timetable may result in a schedule that requires a large vehicle fleet size with more operational cost, while a well-planned schedule may reduce the quality of a bus timetable by limiting the use of vehicles. In this paper, we introduce a time-space network-based framework for integrating electric bus timetabling and scheduling, with minimum and maximum headway times, depot requirements, deadheading and vehicle battery capacities considerations. The underlying time-space network is constructed with well-designed inventory arcs that represent multiple operations a bus may execute, thus decreasing the network size. Using the constructed network, we formulate the considered problem with a multi-commodity network flow model and develop a Lagrangian relaxation heuristic that consists of three phases, including generating relaxed solutions, making relaxed solutions feasible, and improving feasible solutions, to solve the integrated model. Tests on a set of instances confirm that the proposed integrated solution method can efficiently produce bus timetables and schedules with valid bounds, indicate that the integrated method can produce better solutions where the profit is increased by 5.29%–20.28%, and show how the headway times, service trip profit and operating cost settings affect the solution.

Relocating emergency service vehicles with multiple coverage and critical levels partition

A relocation strategy repositions idle emergency service (ES) vehicles to prevent some demand points from being uncovered. In this study, we consider an ES system, such as natural gas emergency services system, which involves satisfying multiple-coverage requirements of demand points. This system uses a compliance table strategy that denotes the base stations of available ES vehicles depending on the system state. As different from the relocation literature, we allow multiple vehicle assignments to stations. Additionally, we categorize the system states as critical and non-critical. We proposed a mathematical model, which maximizes the expected safely covered population to construct the compliance table. According to our results, the developed model opens fewer stations and provides better safe coverage. In order to help the dispatcher, who is mostly under pressure while making relocation decisions, we also introduced vehicle moves required for relocation into the compliance table. So the dispatcher can see the relocation plan and desired stations in the compliance table in advance. For this purpose, we present a network flow model and a heuristic approach to find the relocation plan for all emergency site cases. We performed a detailed simulation study, which also provided information about the performances of each vehicle. Accordingly, the proposed relocation strategy is significantly better regarding response time related measures.

Novel Discrete Fracture Network Model for Multiphase Flow in Coal

Multiphase flow intensely affects the movement and accumulation of other fluids in coal and plays an essential role in predicting the permeability of coal during coalbed methane (CBM) production. Fractures have played a decisive role in the transport of CBM after hydraulic fracturing has occurred. In this study, a multiscale pore network model (PNM) was constructed on the basis of focused ion beam scanning electron microscopy (FIB-SEM) image results. Additionally, a novel discrete fracture network model, fracture–pore network model (F–PNM), was proposed to investigate the effect of fracture density, fracture developing direction, and wettability on multiphase flow. The results reveal that the permeability of F–PNM increases with the increase of the fracture density, which could be the result of the predominance of snap off. The permeability decreases as the angle between the fracture and flow direction increases; initially, the permeability decreases steeply and then it tends to remain stable; and for angles between 0° and 15°, the permeability decreased by as much as 61.8%. Moreover, the wettability of coal has limited impact on its water relative permeability; however, it has a measurable effect on gas relative permeability, which could be owing to water accumulation on the coal surface under different wettability conditions. A good wetting performance would have a negative effect on the CBM production and reduce flowback efficiency.

Development and validation of analysis code for spallation products behavior in LBE coolant system of ADS comparing with the distribution data in MEGAPIE spallation target

It is important to evaluate the inventories and the release and transport behavior of the spallation products (SPs) including polonium-210 in the Lead-Bismuth Eutectic (LBE) coolant system of Accelerator Driven System (ADS) for the safety studies of the radiological hazard both in the cases of normal operation and accident. Especially, the transport and deposition inside the coolant circulation system and the evaporation from the coolant to the cover gas are dominant mechanisms to evaluate the release and transport behavior of SPs. University of Fukui and Japan Atomic Energy Agency (JAEA) have been developing the computer analysis code TRAIL (Transport of RAdionuclides In Liquid metal systems) which predicts the time dependent behavior of SPs within the LBE coolant system of ADS for the wide range of operational events. The TRAIL code is intended to deal with the SPs transport, deposition and evaporation behavior mechanistically in consideration of a variety of the physicochemical configuration of SPs in LBE. The physicochemical configuration of the SPs is essential to evaluate the release and transport behavior because the physical and chemical properties such as the molecular weight, the density, the solubility in LBE and the vapor pressure depend on the configuration. The SPs behavior modelled in the code are based on the generalized flow network model including pipe and tank components. The flow network model is constituted from mass and energy conservation equations in consideration of the mass and energy transfer due to coolant flow effect, deposition or adsorption of SPs onto the structure surfaces, transport into the cover gas due to evaporation and radioactive decay of the radioactive SPs. The source term of both radioactive and stable SPs in the LBE coolant is given as input and the radioactive decay chain model for the radioactive SPs is implemented in the code to evaluate the effect of precursors on the SPs mobility. This paper presents the recent advancement status of the code development and the validation results comparing with the distribution data of volatile SPs in MEGAPIE spallation target.

Generalized linear‐constrained optimal power flow for distribution networks

AbstractOptimal power flow (OPF) plays an important role in the secure and economical operation of the distribution network. This paper proposes a novel generalized linear‐constrained optimal power flow (GLOPF) model for both radial and mesh distribution networks, which iteratively approaches the optimal solution to the original OPF problem. The first‐order Taylor series approximation method is applied to linearize the non‐linear and non‐convex power flow constraints for a given Taylor expansion point (TEP). In addition, the objective function of the GLOPF model is only added with an easy‐compute second‐order penalty on state variables, which is at least positive semi‐definite and guarantees the convexity of the quadratic optimization. Then a TEP‐based iterative (TEP‐I) method is proposed in the GLOPF model to construct a series of linear‐constrained convex quadratic optimizations, which avoids the complex calculation of quasi‐Hessian or Hessian matrices in traditional sequential programming methods. The converged solution to the GLOPF model is proved to satisfy the Karush–Kuhn–Tucker conditions of the original OPF problem. Furthermore, the GLOPF model at first and second iterations can be implemented as the ‘cold‐start’ and ‘warm‐start’ LOPF models, respectively. Case studies verify the super‐linear convergence and high accuracy of the proposed GLOPF model.

Optimising pedestrian flow in a topological network using various pairwise speed-density models

A speed-density model can be utilised to efficiently flow pedestrians in a network. However, how each model measures and optimises the performance of the network is rarely reported. Thus, this paper analyses and optimises the flow in a topological network using various speed-density models. Each model was first used to obtain the optimal arrival rates to all individual networks. The optimal value of each network was then set as a flow constraint in a network flow model. The network flow model was solved to find the optimal arrival rates to the source networks. The optimal values were then used to measure their effects on the performance of each available network. The performance results of the model were then compared with that of other speed-density models. The analysis of the results can help decision-makers understand how arrival rates propagate through traffic and determine the level of the network throughputs.

Novel Method to Detect Pitfalls of Intracoronary Pressure Measurements by Pressure Waveform Analysis.

Potential pitfalls of fractional flow reserve (FFR) measurements are well-known drawbacks of invasive physiology measurement, e.g., significant drift of the distal pressure trace may lead to the misclassification of stenoses. Thus, a simultaneous waveform analysis of the pressure traces may be of help in the quality control of these measurements by online detection of such artefacts as the drift or the wedging of the catheter. In the current study, we analysed the intracoronary pressure waveform with a dedicated program. In 130 patients, 232 FFR measurements were performed and derivative pressure curves were calculated. Local amplitude around the dicrotic notch was calculated from the distal intracoronary pressure traces (δdPn/dt). A unidimensional arterial network model of blood flow was employed to simulate the intracoronary pressure traces at different flow rates. There was a strong correlation between δdPn/dt values measured during hyperaemia and FFR (r = 0.88). Diagnostic performance of distal δdPn/dt ≤ 3.52 for the prediction of FFR ≤ 0.80 was 91%. The correlation between the pressure gradient and the corresponding δdPn/dt values obtained from all measurements independently of the physiological phase was also significant (r = 0.80). During simulation, the effect of flow rate on δdPn/dt further supported the close correlation between the pressure ratios and δdPn/dt. Discordance between the FFR and the δdPn/dt can be used as an indicator of possible technical problems of FFR measurements. Hence, an online calculation of the δdPn/dt may be helpful in avoiding some pitfalls of FFR evaluation.

Via-Based Redistribution Layer Routing for InFO Packages With Irregular Pad Structures

The integrated fan-out (InFO) wafer-level chip-scale package (WLCSP) is introduced for modern system-in-package designs with larger I/O counts, higher interconnection density, and small form factors. A redistribution layer (RDL) in an InFO package is an extra metal layer for interchip connections, and RDL routing is crucial for achieving desired interchip connections. In a high-density InFO package, multiple RDLs with flexible vias are often adopted. To integrate chips of different technology nodes into one package, irregular pad structures need to be considered; however, no published RDL routing work considers flexible vias or irregular pad structures. This article formulates a new RDL routing problem with unified-assigned pad pairs on a via-based multilayer multichip InFO package with irregular pad structures and presents the first algorithm for this problem. The algorithm consists of a preprocessing stage, three routing stages, and a layout optimization stage. The preprocessing stage analyzes routing resources and potential routing congestion. The first routing stage performs layer assignment based on a weighted maximum planar subset of chords algorithm to route interchip nets concurrently. The second routing stage constructs a 3-D routing graph based on partitioned octagonal tiles to handle the irregular layout structure and applies A*-search to route remaining interchip nets. The third routing stage transforms a routing graph into a network-flow model to perform concurrent routing for chip-to-board nets by applying the minimum-cost maximum-flow algorithm. Finally, we develop an efficient linear-programming-based layout optimization algorithm to find desired solutions. Experimental results show that our router can achieve 100% routablility for all benchmarks under limited RDLs, while the previous state-of-the-art work cannot.