Search results for: path constraints

Authors: Essa Abrahim Abdulgader Saleem, Thien-My Dao

Abstract:

The main objective of this paper is to optimize series-parallel system reliability using Genetic Algorithm (GA) and statistical analysis; considering system reliability constraints which involve the redundant numbers of selected components, total cost, and total weight. To perform this work, firstly the mathematical model which maximizes system reliability subject to maximum system cost and maximum system weight constraints is presented; secondly, a statistical analysis is used to optimize GA parameters, and thirdly GA is used to optimize series-parallel systems reliability. The objective is to determine the strategy choosing the redundancy level for each subsystem to maximize the overall system reliability subject to total cost and total weight constraints. Finally, the series-parallel system case study reliability optimization results are showed, and comparisons with the other previous results are presented to demonstrate the performance of our GA.

Keywords: Genetic algorithm, optimization, reliability, statistical analysis.

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Authors: N. A. H. Aizam, V. Uvaraja

Abstract:

The agenda of showing the scheduled time for performing certain tasks is known as timetabling. It is widely used in many departments such as transportation, education, and production. Some difficulties arise to ensure all tasks happen in the time and place allocated. Therefore, many researchers invented various programming models to solve the scheduling problems from several fields. However, the studies in developing the general integer programming model for many timetabling problems are still questionable. Meanwhile, this thesis describes about creating a general model which solves different types of timetabling problems by considering the basic constraints. Initially, the common basic constraints from five different fields are selected and analyzed. A general basic integer programming model was created and then verified by using the medium set of data obtained randomly which is much similar to realistic data. The mathematical software, AIMMS with CPLEX as a solver has been used to solve the model. The model obtained is significant in solving many timetabling problems easily since it is modifiable to all types of scheduling problems which have same basic constraints.

Keywords: AIMMS mathematical software, integer linear programming, scheduling problems, timetabling.

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Authors: Ramya Dorai, M. Rajaram

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A Mobile Adhoc Network (MANET) is a collection of mobile nodes that communicate with each other with wireless links and without pre-existing communication infrastructure. Routing is an important issue which impacts network performance. As MANETs lack central administration and prior organization, their security concerns are different from those of conventional networks. Wireless links make MANETs susceptible to attacks. This study proposes a new trust mechanism to mitigate wormhole attack in MANETs. Different optimization techniques find available optimal path from source to destination. This study extends trust and reputation to an improved link quality and channel utilization based Adhoc Ondemand Multipath Distance Vector (AOMDV). Differential Evolution (DE) is used for optimization.

Keywords: Mobile Adhoc Network (MANET), Adhoc Ondemand Multi-Path Distance Vector (AOMDV), Trust and Reputation, Differential Evolution (DE), Link Quality, Channel Utilization.

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Authors: Gao Xian-Zhong, Hou Zhong-xi, Guo Zheng, Liu Jian-xia

Abstract:

Gliding during night without electric power is an efficient method to enhance endurance performance of solar aircrafts. The properties of maximum gliding endurance path are studied in this paper. The problem is formulated as an optimization problem about maximum endurance can be sustained by certain potential energy storage with dynamic equations and aerodynamic parameter constrains. The optimal gliding path is generated based on gauss pseudo-spectral method. In order to analyse relationship between altitude, velocity of solar UAVs and its endurance performance, the lift coefficient in interval of [0.4, 1.2] and flight envelopes between 0~30km are investigated. Results show that broad range of lift coefficient can improve solar aircrafts- long endurance performance, and it is possible for a solar aircraft to achieve the aim of long endurance during whole night just by potential energy storage.

Keywords: Solar UAVs, Gliding Endurance, gauss pseudo-spectral method, optimization problem

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Authors: José Maria A. Pangilinan, Gerrit K. Janssens

Abstract:

This paper presents an overview of the multiobjective shortest path problem (MSPP) and a review of essential and recent issues regarding the methods to its solution. The paper further explores a multiobjective evolutionary algorithm as applied to the MSPP and describes its behavior in terms of diversity of solutions, computational complexity, and optimality of solutions. Results show that the evolutionary algorithm can find diverse solutions to the MSPP in polynomial time (based on several network instances) and can be an alternative when other methods are trapped by the tractability problem.

Keywords: Multiobjective evolutionary optimization, geneticalgorithms, shortest paths.

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Authors: Gyu-Jin Shim, Seung-Moon Baek, Choon-Geun Moon, Ho-Saeng Lee, Jung-In Yoon

Abstract:

The experimental thermal performance of two heat exchangers in closed-wet cooling tower (CWCT) was investigated in this study. The test sections are heat exchangers which have multi path that is used as the entrance of cooling water and are consisting of bare-type copper tubes between 15.88mm and 19.05mm. The process fluids are the cooling water that flows from top part of heat exchanger to bottom side in the inner side of tube, and spray water that flows gravitational direction in the outer side of it. Air contacts its outer side of that as it counterflows. Heat and mass transfer coefficients and cooling capacity were calculated with variations of process fluids, multi path and different diameter tubes to figure out the performance of characteristics of CWCT. The main results were summarized as follows: The results show this experiment is reliable with values of heat and mass transfer coefficients comparing to values of correlations. Heat and mass transfer coefficients and cooling capacity of two paths are higher than these with one path using 15.88 and 19.05mm tubes. Cooling capacity per unit volume with 15.88mm tube using one and two paths are higher than 19.05mm tube due to increase of surface area per unit volume.

Keywords: Closed–Wet Cooling Tower, Cooling Capacity, Heatand Mass Transfer Coefficients.

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Authors: Tulika Bhattacharjee, A. K.Chakraborty

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Due to the deregulation of the Electric Supply Industry and the resulting emergence of electricity market, the volumes of power purchases are on the rise all over the world. In a bid to meet the customer-s demand in a reliable and yet economic manner, utilities purchase power from the energy market over and above its own production. This paper aims at developing an optimal power purchase model with two objectives viz economy and environment ,taking various functional operating constraints such as branch flow limits, load bus voltage magnitudes limits, unit capacity constraints and security constraints into consideration.The price of purchased power being an uncertain variable is modeled using fuzzy logic. DEMO (Differential Evolution For Multi-objective Optimization) is used to obtain the pareto-optimal solution set of the multi-objective problem formulated. Fuzzy set theory has been employed to extract the best compromise non-dominated solution. The results obtained on IEEE 30 bus system are presented and compared with that of NSGAII.

Keywords: Deregulation, Differential Evolution, Multi objective Optimization, Pareto Optimal Set, Optimal Power Flow

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Authors: T.C. Manjunath,

Abstract:

This paper features the trajectory planning design of a indigenously developed 4-Axis SCARA robot which is used for doing successful robotic manipulation task in the laboratory. Once, a trajectory is being designed and given as input to the robot, the robot's gripper tip moves along that specified trajectory. Trajectories have to be designed in the work space only. The main idea of this paper is to design a continuous path trajectory model for the indigenously developed SCARA robot arm during its maneuvering from one point to another point (during pick and place operations) in a workspace avoiding all the obstacles in its path of motion.

Keywords: SCARA, Trajectory, Planning.

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Authors: Miloš Šeda

Abstract:

Finding the shortest path between two positions is a fundamental problem in transportation, routing, and communications applications. In robot motion planning, the robot should pass around the obstacles touching none of them, i.e. the goal is to find a collision-free path from a starting to a target position. This task has many specific formulations depending on the shape of obstacles, allowable directions of movements, knowledge of the scene, etc. Research of path planning has yielded many fundamentally different approaches to its solution, mainly based on various decomposition and roadmap methods. In this paper, we show a possible use of visibility graphs in point-to-point motion planning in the Euclidean plane and an alternative approach using Voronoi diagrams that decreases the probability of collisions with obstacles. The second application area, investigated here, is focused on problems of finding minimal networks connecting a set of given points in the plane using either only straight connections between pairs of points (minimum spanning tree) or allowing the addition of auxiliary points to the set to obtain shorter spanning networks (minimum Steiner tree).

Keywords: motion planning, spanning tree, Steiner tree, Delaunay triangulation, Voronoi diagram.

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Authors: M. Ravindra, R. Srinivasa Rao, V. Shanmukha Naga Raju

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This paper presents state estimation with Phasor Measurement Unit (PMU) allocation to obtain complete observability of network. A matrix is designed with modeling of zero injection constraints to minimize PMU allocations. State estimation algorithm is developed with optimal allocation of PMUs to find accurate states of network. The incorporation of PMU into traditional state estimation process improves accuracy and computational performance for large power systems. The nonlinearity integrated with zero injection (ZI) constraints is remodeled to linear frame to optimize number of PMUs. The problem of optimal PMU allocation is regarded with modeling of ZI constraints, PMU loss or line outage, cost factor and redundant measurements. The proposed state estimation with optimal PMU allocation has been compared with traditional state estimation process to show its importance. MATLAB programming on IEEE 14, 30, 57, and 118 bus networks is implemented out by Binary Integer Programming (BIP) method and compared with other methods to show its effectiveness.

Keywords: Observability, phasor measurement units, synchrophasors, SCADA measurements, zero injection bus.

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Authors: Yen-Chun Lin, Yen-Ting Chen, Szu-Yin Lin, Jen-Hua Wu

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This paper proposes a location-aware system for household robots which allows users to paste predefined paper tags at different locations according to users- comprehension of the house. In this system a household robot may be aware of its location and the attributes thereof by visually recognizing the tags when the robot is moving. This paper also presents a novel user interface to define a moving path of the robot, which allows users to draw the path in the air with a finger so as to generate commands for following motions.

Keywords: finger tip tracking, household robot, location awareness, tag recognition

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Authors: Bassem Fahs, Philippe Barré, Patrick Ozenne, Eric Chartier, Guillaume Hérault, Sébastien Jacquet, Sébastien Clamagirand

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We present a dual-band (Cellular & PCS) dual-path zero-IF receiver for CDMA2000 diversity, monitoring and simultaneous-GPS. The secondary path is a SAW-less diversity CDMA receiver which can be also used for advanced features like monitoring when supported with an additional external VCO. A GPS receiver is integrated with its dedicated VCO allowing simultaneous positioning during a cellular call. The circuit is implemented in a 0.25μm 40GHz-fT BiCMOS process and uses a HVQFN 56-pin package. It consumes a maximum 300mW from a 2.8V supply in dual-modes. The chip area is 12.8mm2.

Keywords: CDMA, diversity, GPS, zero-IF, SAW-less

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Authors: Sara Mohtashami, Habib Rajabi Mashhadi

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With the growth of electricity generation from gas energy gas pipeline reliability can substantially impact the electric generation. A physical disruption to pipeline or to a compressor station can interrupt the flow of gas or reduce the pressure and lead to loss of multiple gas-fired electric generators, which could dramatically reduce the supplied power and threaten the power system security. Gas pressure drops during peak loading time on pipeline system, is a common problem in network with no enough transportation capacity which limits gas transportation and causes many problem for thermal domain power systems in supplying their demand. For a feasible generation scheduling planning in networks with no sufficient gas transportation capacity, it is required to consider gas pipeline constraints in solving the optimization problem and evaluate the impacts of gas consumption in power plants on gas pipelines operating condition. This paper studies about operating of gas fired power plants in critical conditions when the demand of gas and electricity peak together. An integrated model of gas and electric model is used to consider the gas pipeline constraints in the economic dispatch problem of gas-fueled thermal generator units.

Keywords:

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Authors: Rimmy Yadav, Avtar Singh

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Ant Colony Optimization (ACO) is a promising modern approach to the unused combinatorial optimization. Here ACO is applied to finding the shortest during communication link failure. In this paper, the performances of the prim’s and ACO algorithm are made. By comparing the time complexity and program execution time as set of parameters, we demonstrate the pleasant performance of ACO in finding excellent solution to finding shortest path during communication link failure.

Keywords: Ant colony optimization, link failure, prim’s algorithm.

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Authors: Pallavi Bhogaram, Xiaolong Wu, Min He, Onyedikachi Okenwa

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A transportation network is a realization of a spatial network, describing a structure which permits either vehicular movement or flow of some commodity. Examples include road networks, railways, air routes, pipelines, and many more. The transportation network plays a vital role in maintaining the vigor of the nation’s economy. Hence, ensuring the network stays resilient all the time, especially in the face of challenges such as heavy traffic loads and large scale natural disasters, is of utmost importance. In this paper, we used the Neo4j application to develop the graph. Neo4j is the world's leading open-source, NoSQL, a native graph database that implements an ACID-compliant transactional backend to applications. The Southern California network model is developed using the Neo4j application and obtained the most critical and optimal nodes and paths in the network using centrality algorithms. The edge betweenness centrality algorithm calculates the critical or optimal paths using Yen's k-shortest paths algorithm, and the node betweenness centrality algorithm calculates the amount of influence a node has over the network. The preliminary study results confirm that the Neo4j application can be a suitable tool to study the important nodes and the critical paths for the major congested metropolitan area.

Keywords: Transportation network, critical path, connectivity reliability, network model, Neo4J application, optimal path, critical path, edge betweenness centrality index, node betweenness centrality index, Yen’s k-shortest paths.

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Authors: Sandeep P. Abhang, Girish V. Chowdhay

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This paper proposes a Wavelength Division Multiplexing (WDM) technology based Storage Area Network (SAN) for all type of Disaster recovery operation. It considers recovery when all paths failure in the network as well as the main SAN site failure also the all backup sites failure by the effect of natural disasters such as earthquakes, fires and floods, power outage, and terrorist attacks, as initially SAN were designed to work within distance limited environments[2]. Paper also presents a NEW PATH algorithm when path failure occurs. The simulation result and analysis is presented for the proposed architecture with performance consideration.

Keywords: SAN, WDM, FC, Ring, IP, network load, iSCSI, miles, disaster.

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Authors: Dilip Kumar S.M, Vijaya Kumar B.P.

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The decisions made by admission control algorithms are based on the availability of network resources viz. bandwidth, energy, memory buffers, etc., without degrading the Quality-of-Service (QoS) requirement of applications that are admitted. In this paper, we present an energy-aware admission control (EAAC) scheme which provides admission control for flows in an ad hoc network based on the knowledge of the present and future residual energy of the intermediate nodes along the routing path. The aim of EAAC is to quantify the energy that the new flow will consume so that it can be decided whether the future residual energy of the nodes along the routing path can satisfy the energy requirement. In other words, this energy-aware routing admits a new flow iff any node in the routing path does not run out of its energy during the transmission of packets. The future residual energy of a node is predicted using the Multi-layer Neural Network (MNN) model. Simulation results shows that the proposed scheme increases the network lifetime. Also the performance of the MNN model is presented.

Keywords: Ad hoc networks, admission control, energy-aware routing, Quality-of-Service, future residual energy, neural network.

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Authors: V. Narasimha Raghavan, M. Venkatesh, T. Peer Meera Labbai, Praveen Dwarakanath Prabhu

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The performance and complexity of QoS routing depends on the complex interaction between a large set of parameters. This paper investigated the scaling properties of source-directed link-state routing in large core networks. The simulation results show that the routing algorithm, network topology, and link cost function each have a significant impact on the probability of successfully routing new connections. The experiments confirm and extend the findings of other studies, and also lend new insight designing efficient quality-of-service routing policies in large networks.

Keywords: QoS, Link-State Routing, Dijkstra, Path Selection, Path Computation.

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Authors: J. T. Manhire

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A tax authority wants to take actions it knows will foster the greatest degree of voluntary taxpayer compliance to reduce the “tax gap.” This paper suggests that even if a tax authority could attain a state of complete knowledge, there are constraints on whether and to what extent such actions would result in reducing the macro-level tax gap. These limits are not merely a consequence of finite agency resources. They are inherent in the system itself. To show that this is one possible interpretation of the tax gap data, the paper formulates known results in a different way by analyzing tax compliance as a population with a single covariate. This leads to a standard use of the logistic map to analyze the dynamics of non-compliance growth or decay over a sequence of periods. This formulation gives the same results as the tax gap studies performed over the past fifty years in the U.S. given the published margins of error. Limitations and recommendations for future work are discussed, along with some implications for tax policy.

Keywords: Tax law, tax compliance, tax gap, income tax.

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Authors: A. Badri

Abstract:

Restructured electricity markets may provide opportunities for producers to exercise market power maintaining prices in excess of competitive levels. In this paper an oligopolistic market is presented that all Generation Companies (GenCos) bid in a Cournot model. Genetic algorithm (GA) is applied to obtain generation scheduling of each GenCo as well as hourly market clearing prices (MCP). In order to consider network constraints a multiperiod framework is presented to simulate market clearing mechanism in which the behaviors of market participants are modelled through piecewise block curves. A mixed integer linear programming (MILP) is employed to solve the problem. Impacts of market clearing process on participants- characteristic and final market prices are presented. Consequently, a novel multi-objective model is addressed for security constrained optimal bidding strategy of GenCos. The capability of price-maker GenCos to alter MCP is evaluated through introducing an effective-supply curve. In addition, the impact of exercising market power on the variation of market characteristics as well as GenCos scheduling is studied.

Keywords: Optimal bidding strategy, Cournot equilibrium, market power, network constraints, market auction mechanism

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Authors: Jong Han Joo, Jeong Hun Lee, Young Sun Kim, Jae Young Kang, Seung Ho Choi

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In this study, we propose a novel technique for acoustic echo suppression (AES) during speech recognition under barge-in conditions. Conventional AES methods based on spectral subtraction apply fixed weights to the estimated echo path transfer function (EPTF) at the current signal segment and to the EPTF estimated until the previous time interval. However, the effects of echo path changes should be considered for eliminating the undesired echoes. We describe a new approach that adaptively updates weight parameters in response to abrupt changes in the acoustic environment due to background noises or double-talk. Furthermore, we devised a voice activity detector and an initial time-delay estimator for barge-in speech recognition in communication networks. The initial time delay is estimated using log-spectral distance measure, as well as cross-correlation coefficients. The experimental results show that the developed techniques can be successfully applied in barge-in speech recognition systems.

Keywords: Acoustic echo suppression, barge-in, speech recognition, echo path transfer function, initial delay estimator, voice activity detector.

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Authors: Anant Oonsivilai, Wichai Srisuruk, Boonruang Marungsri, Thanatchai Kulworawanichpong

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Optimal routing in communication networks is a major issue to be solved. In this paper, the application of Tabu Search (TS) in the optimum routing problem where the aim is to minimize the computational time and improvement of quality of the solution in the communication have been addressed. The goal is to minimize the average delays in the communication. The effectiveness of Tabu Search method is shown by the results of simulation to solve the shortest path problem. Through this approach computational cost can be reduced.

Keywords: Communication networks, optimum routing network, tabu search algorithm, shortest path.

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Authors: Shipra Upadhyay , R. K. Nagaria, R. A. Mishra

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In this paper, we present the design and experimental evaluation of complementary energy path adiabatic logic (CEPAL) based 1 bit full adder circuit. A simulative investigation on the proposed full adder has been done using VIRTUOSO SPECTRE simulator of cadence in 0.18μm UMC technology and its performance has been compared with the conventional CMOS full adder circuit. The CEPAL based full adder circuit exhibits the energy saving of 70% to the conventional CMOS full adder circuit, at 100 MHz frequency and 1.8V operating voltage.

Keywords: Adiabatic, CEPAL, full adder, power clock

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Authors: Fariba Azizi, Firoozeh Haghighi, Viliam Makis

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In this paper, we propose a method to model the relationship between failure time and degradation for a simple step stress test where underlying degradation path is linear and different causes of failure are possible. It is assumed that the intensity function depends only on the degradation value. No assumptions are made about the distribution of the failure times. A simple step-stress test is used to shorten failure time of products and a tampered failure rate (TFR) model is proposed to describe the effect of the changing stress on the intensities. We assume that some of the products that fail during the test have a cause of failure that is only known to belong to a certain subset of all possible failures. This case is known as masking. In the presence of masking, the maximum likelihood estimates (MLEs) of the model parameters are obtained through an expectation-maximization (EM) algorithm by treating the causes of failure as missing values. The effect of incomplete information on the estimation of parameters is studied through a Monte-Carlo simulation. Finally, a real example is analyzed to illustrate the application of the proposed methods.

Keywords: Expectation-maximization (EM) algorithm, cause of failure, intensity, linear degradation path, masked data, reliability function.

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Authors: Dorota Galeza

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This paper argues that networks, such as the ECN and the American network, are affected by certain small events which are inherent to path dependence and preclude the full evolution towards efficiency. It is advocated that the American network is superior to the ECN in many respects due to its greater flexibility and longer history. This stems in particular from the creation of the American network, which was based on a small number of cases. Such a structure encourages further changes and modifications which are not necessarily radical. The ECN, by contrast, was established by legislative action, which explains its rigid structure and resistance to change. This paper is an attempt to transpose the superiority of the American network on to the ECN. It looks at concepts such as judicial cooperation, harmonisation of procedure, peer review and regulatory impact assessments (RIAs), and dispute resolution procedures.

Keywords: Antitrust, Competition, Networks, Path Dependence.

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Authors: Reza Cheraghi Kootiani, Ariffin Bin Samsuri

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To derive the fractional flow equation oil displacement will be assumed to take place under the so-called diffusive flow condition. The constraints are that fluid saturations at any point in the linear displacement path are uniformly distributed with respect to thickness; this allows the displacement to be described mathematically in one dimension. The simultaneous flow of oil and water can be modeled using thickness averaged relative permeability, along the centerline of the reservoir. The condition for fluid potential equilibrium is simply that of hydrostatic equilibrium for which the saturation distribution can be determined as a function of capillary pressure and therefore, height. That is the fluids are distributed in accordance with capillary-gravity equilibrium. This paper focused on the fraction flow of water versus cumulative oil recoveries using Buckley Leverett method. Several field cases have been developed to aid in analysis. Producing watercut (at surface conditions) will be compared with the cumulative oil recovery at breakthrough for the flowing fluid.

Keywords: Fractional Flow, Fluid Saturations, Permeability, Cumulative Oil Recoveries, Buckley Leverett Method.

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Authors: Samee Ullah Khan, C. Ardil

Abstract:

The problem of mapping tasks onto a computational grid with the aim to minimize the power consumption and the makespan subject to the constraints of deadlines and architectural requirements is considered in this paper. To solve this problem, we propose a solution from cooperative game theory based on the concept of Nash Bargaining Solution. The proposed game theoretical technique is compared against several traditional techniques. The experimental results show that when the deadline constraints are tight, the proposed technique achieves superior performance and reports competitive performance relative to the optimal solution.

Keywords: Energy efficient algorithms, resource allocation, resource management, cooperative game theory.

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Authors: Amira Elsonbaty, Rawya Rizk, Mohamed Elksas, Mofreh Salem

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In this paper, a Cooperative Multi-robot for Carrying Targets (CMCT) algorithm is proposed. The multi-robot team consists of three robots, one is a supervisor and the others are workers for carrying boxes in a store of 100×100 m2. Each robot has a self recharging mechanism. The CMCT minimizes robot-s worked time for carrying many boxes during day by working in parallel. That is, the supervisor detects the required variables in the same time another robots work with previous variables. It works with straightforward mechanical models by using simple cosine laws. It detects the robot-s shortest path for reaching the target position avoiding obstacles by using a proposed CMCT path planning (CMCT-PP) algorithm. It prevents the collision between robots during moving. The robots interact in an ad hoc wireless network. Simulation results show that the proposed system that consists of CMCT algorithm and its accomplished CMCT-PP algorithm achieves a high improvement in time and distance while performing the required tasks over the already existed algorithms.

Keywords: Ad hoc network, Computer vision based positioning, Dynamic collision avoidance, Multi-robot, Path planning algorithms, Self recharging.

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Authors: S. Aneeka, S.M. Phyoe, R. Guo, Z.W. Zhong

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Arrival flights tend to spend long waiting times at holding stacks if the arrival airport is congested. However, the waiting time spent in the air in the vicinity of the arrival airport may be reduced if the delays are distributed to the cruising phase of the arrival flights by means of speed control. Here, a case study was conducted for the flights arriving at Changi Airport. The flights that were assigned holdings were simulated to fly at a reduced speed during the cruising phase. As the study involves a single airport and is limited to imposing speed constraints to arrivals within 200 NM from its location, the simulation setup in this study could be considered as an application of the Extended Arrival Management (E-AMAN) technique, which is proven to result in considerable fuel savings and more efficient management of delays. The objective of this experiment was to quantify the benefits of imposing cruise speed constraints to arrivals at Changi Airport and to assess the effects on controllers’ workload. The simulation results indicated considerable fuel savings, reduced aircraft emissions and reduced controller workload.

Keywords: Aircraft emissions, air traffic flow management, controller workload, fuel consumption.

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Authors: Zdravka Aljinović, Snježana Pivac, Boško Šego

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According to the interaction of inflation and unemployment, expectation of the rate of inflation in Croatia is estimated. The interaction between inflation and unemployment is shown by model based on three first-order differential i.e. difference equations: Phillips relation, adaptive expectations equation and monetary-policy equation. The resulting equation is second order differential i.e. difference equation which describes the time path of inflation. The data of the rate of inflation and the rate of unemployment are used for parameters estimation. On the basis of the estimated time paths, the stability and convergence analysis is done for the rate of inflation.

Keywords: Differencing, inflation, time path, unemployment.

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