Search results for: open queueing network

Authors: Saulius Minkevicius, Genadijus Kulvietis

Abstract:

The modern queueing theory is one of the powerful tools for a quantitative and qualitative analysis of communication systems, computer networks, transportation systems, and many other technical systems. The paper is designated to the analysis of queueing systems, arising in the networks theory and communications theory (called open queueing network). The authors of this research in the sphere of queueing theory present the theorem about the law of the iterated logarithm (LIL) for the queue length of a customers in open queueing network and its application to the mathematical model of the open message switching system.

Keywords: Models of information systems, open message switching system, open queueing network, queue length of a customers, heavy traffic, a law of the iterated logarithm.

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Authors: Jouhra Dad, Mohammed Ouali, Yahia Lebbah

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Urban road network traffic has become one of the most studied research topics in the last decades. This is mainly due to the enlargement of the cities and the growing number of motor vehicles traveling in this road network. One of the most sensitive problems is to verify if the network is congestion-free. Another related problem is the automatic reconfiguration of the network without building new roads to alleviate congestions. These problems require an accurate model of the traffic to determine the steady state of the system. An alternative is to simulate the traffic to see if there are congestions and when and where they occur. One key issue is to find an adequate model for road intersections. Once the model established, either a large scale model is built or the intersection is represented by its performance measures and simulation for analysis. In both cases, it is important to seek the queueing model to represent the road intersection. In this paper, we propose to model the road intersection as a BCMP queueing network and we compare this analytical model against a simulation model for validation.

Keywords: Queueing theory, transportation systems, BCMPqueueing network, performance measures, modeling, simulation

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Authors: Miloš Šeda, Pavel Ošmera, Jindřich Petrucha

Abstract:

In the queueing theory, it is assumed that customer arrivals correspond to a Poisson process and service time has the exponential distribution. Using these assumptions, the behaviour of the queueing system can be described by means of Markov chains and it is possible to derive the characteristics of the system. In the paper, these theoretical approaches are presented on several types of systems and it is also shown how to compute the characteristics in a situation when these assumptions are not satisfied

Keywords: Queueing theory, Poisson process, Markov chains.

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Authors: Dimitrios Koukopoulos

Abstract:

In this work, we study the impact of dynamically changing link slowdowns on the stability properties of packetswitched networks under the Adversarial Queueing Theory framework. Especially, we consider the Adversarial, Quasi-Static Slowdown Queueing Theory model, where each link slowdown may take on values in the two-valued set of integers {1, D} with D > 1 which remain fixed for a long time, under a (w, ¤ü)-adversary. In this framework, we present an innovative systematic construction for the estimation of adversarial injection rate lower bounds, which, if exceeded, cause instability in networks that use the LIS (Longest-in- System) protocol for contention-resolution. In addition, we show that a network that uses the LIS protocol for contention-resolution may result in dropping its instability bound at injection rates ¤ü > 0 when the network size and the high slowdown D take large values. This is the best ever known instability lower bound for LIS networks.

Keywords: Network stability, quality of service, adversarial queueing theory, greedy scheduling protocols.

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Authors: Behrouz Fathi-Vajargah, Sara Ghasemalipour

Abstract:

This paper studies a random fuzzy queueing system that the interarrival times of customers arriving at the server and the service times are independent and identically distributed random fuzzy variables. We match the random fuzzy queueing system with the random fuzzy alternating renewal process and we do not use from α-pessimistic and α-optimistic values to estimate the average chance of the event ”random fuzzy queueing system is busy at time t”, we employ the fuzzy simulation method in practical applications. Some theorem is proved and finally we solve a numerical example with fuzzy simulation method.

Keywords: Random fuzzy variables, Fuzzy simulation, Queueing system, Interarrival times.

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Authors: Emad Alenany, M. Adel El-Baz

Abstract:

In this paper, the flow of different classes of patients into a hospital is modelled and analyzed by using the queueing network analyzer (QNA) algorithm and discrete event simulation. Input data for QNA are the rate and variability parameters of the arrival and service times in addition to the number of servers in each facility. Patient flows mostly match real flow for a hospital in Egypt. Based on the analysis of the waiting times, two approaches are suggested for improving performance: Separating patients into service groups, and adopting different service policies for sequencing patients through hospital units. The separation of a specific group of patients, with higher performance target, to be served separately from the rest of patients requiring lower performance target, requires the same capacity while improves performance for the selected group of patients with higher target. Besides, it is shown that adopting the shortest processing time and shortest remaining processing time service policies among other tested policies would results in, respectively, 11.47% and 13.75% reduction in average waiting time relative to first come first served policy.

Keywords: Queueing network, discrete-event simulation, health applications, SPT.

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Authors: Dimitrios Koukopoulos

Abstract:

In this work, we study the impact of dynamically changing link slowdowns on the stability properties of packetswitched networks under the Adversarial Queueing Theory framework. Especially, we consider the Adversarial, Quasi-Static Slowdown Queueing Theory model, where each link slowdown may take on values in the two-valued set of integers {1, D} with D > 1 which remain fixed for a long time, under a (w, p)-adversary. In this framework, we present an innovative systematic construction for the estimation of adversarial injection rate lower bounds, which, if exceeded, cause instability in networks that use the LIS (Longest-in- System) protocol for contention-resolution. In addition, we show that a network that uses the LIS protocol for contention-resolution may result in dropping its instability bound at injection rates p > 0 when the network size and the high slowdown D take large values. This is the best ever known instability lower bound for LIS networks.

Keywords: Parallel computing, network stability, adversarial queuing theory, greedy scheduling protocols.

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Authors: Chun Wen, Tingzhu Huang

Abstract:

We present a new numerical method for the computation of the steady-state solution of Markov chains. Theoretical analyses show that the proposed method, with a contraction factor α, converges to the one-dimensional null space of singular linear systems of the form Ax = 0. Numerical experiments are used to illustrate the effectiveness of the proposed method, with applications to a class of interesting models in the domain of tandem queueing networks.

Keywords: Markov chains, tandem queueing networks, convergence, effectiveness.

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Authors: Arijit Ghosh, Tony Givargis

Abstract:

Video sensor networks operate on stringent requirements of latency. Packets have a deadline within which they have to be delivered. Violation of the deadline causes a packet to be treated as lost and the loss of packets ultimately affects the quality of the application. Network latency is typically a function of many interacting components. In this paper, we propose ways of reducing the forwarding latency of a packet at intermediate nodes. The forwarding latency is caused by a combination of processing delay and queueing delay. The former is incurred in order to determine the next hop in dynamic routing. We show that unless link failures in a very specific and unlikely pattern, a vast majority of these lookups are redundant. To counter this we propose source routing as the routing strategy. However, source routing suffers from issues related to scalability and being impervious to network dynamics. We propose solutions to counter these and show that source routing is definitely a viable option in practical sized video networks. We also propose a fast and fair packet scheduling algorithm that reduces queueing delay at the nodes. We support our claims through extensive simulation on realistic topologies with practical traffic loads and failure patterns.

Keywords: Sensor networks, Packet latency, Network design, Networkperformance.

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Authors: M. R. Martinez-Torres, S. L. Toral, M. Olmedilla

Abstract:

Typically, virtual communities exhibit the well-known phenomenon of participation inequality, which means that only a small percentage of users is responsible of the majority of contributions. However, the sustainability of the community requires that the group of active users must be continuously nurtured with new users that gain expertise through a participation process. This paper analyzes the time evolution of Open Source Software (OSS) communities, considering users that join/abandon the community over time and several topological properties of the network when modeled as a social network. More specifically, the paper analyzes the role of those users rejoining the community and their influence in the global characteristics of the network.

Keywords: Open source communities, social network analysis, time series, virtual communities.

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Authors: Inchae Park, Byungun Yoon

Abstract:

As open innovation has received increasingly attention in the management of innovation, the importance of identifying potential partnership is increasing. This paper suggests a methodology to identify the interested parties as one of Innovation intermediaries to enable open innovation with patent network. To implement the methodology, multi-stage patent citation analysis such as bibliographic coupling and information visualization method such as keyword vector mapping are utilized. This paper has contribution in that it can present meaningful collaboration keywords to identified potential partners in network since not only citation information but also patent textual information is used.

Keywords: Open innovation, partner selection, bibliographic coupling, Keyword vector mapping, patent network.

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Authors: M. P. Nanda Kumar, K. Dheeraj

Abstract:

The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense.

Keywords: Inverse Optimal Control, Radial basis function neural network, Controller Design.

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Authors: Lei Guo, Xu Zhang, Weigang Hou

Abstract:

Since the traditional network is closed and it has no architecture to create applications, it has been unable to evolve with changing demands under the rapid innovation in services. Additionally, due to the lack of the whole network profile, the quality of service cannot be well guaranteed in the traditional network. The Software Defined Network (SDN) utilizes global resources to support on-demand applications/services via open, standardized and programmable interfaces. In this paper, we implement the traffic grooming application under a real SDN environment, and the corresponding analysis is made. In our SDN: 1) we use OpenFlow protocol to control the entire network by using software applications running on the network operating system; 2) several virtual switches are combined into the data forwarding plane through Open vSwitch; 3) An OpenFlow controller, NOX, is involved as a logically centralized control plane that dynamically configures the data forwarding plane; 4) The traffic grooming based on SDN is demonstrated through dynamically modifying the idle time of flow entries. The experimental results demonstrate that the SDN-based traffic grooming effectively reduces the end-to-end delay, and the improvement ratio arrives to 99%.

Keywords: NOX, OpenFlow, software defined network, traffic grooming.

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Authors: J. P. Dubois, H. M. Chiu

Abstract:

In this paper, we study statistical multiplexing of VBR video in ATM networks. ATM promises to provide high speed realtime multi-point to central video transmission for telemedicine applications in rural hospitals and in emergency medical services. Video coders are known to produce variable bit rate (VBR) signals and the effects of aggregating these VBR signals need to be determined in order to design a telemedicine network infrastructure capable of carrying these signals. We first model the VBR video signal and simulate it using a generic continuous-data autoregressive (AR) scheme. We carry out the queueing analysis by the Fluid Approximation Model (FAM) and the Markov Modulated Poisson Process (MMPP). The study has shown a trade off: multiplexing VBR signals reduces burstiness and improves resource utilization, however, the buffer size needs to be increased with an associated economic cost. We also show that the MMPP model and the Fluid Approximation model fit best, respectively, the cell region and the burst region. Therefore, a hybrid MMPP and FAM completely characterizes the overall performance of the ATM statistical multiplexer. The ramifications of this technology are clear: speed, reliability (lower loss rate and jitter), and increased capacity in video transmission for telemedicine. With migration to full IP-based networks still a long way to achieving both high speed and high quality of service, the proposed ATM architecture will remain of significant use for telemedicine.

Keywords: ATM, multiplexing, queueing, telemedicine, VBR.

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Authors: Dong-Young Yoo, Jong-Whoi Shin, Jin-Young Choi

Abstract:

Social interest and demand on Home-Network has been increasing greatly. Although various services are being introduced to respond to such demands, they can cause serious security problems when linked to the open network such as Internet. This paper reviews the security requirements to protect the service users with assumption that the Home-Network environment is connected to Internet and then proposes the security model based on the requirement. The proposed security model can satisfy most of the requirements and further can be dynamically applied to the future ubiquitous Home-Networks.

Keywords: Home-Network, Security, Vulnerability, Response, Countermeasure.

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Authors: S. Chahba, R. Sehab, A. Akrad, C. Morel

Abstract:

Nowadays, the electric machines used in urban electric vehicles are, in most cases, three-phase electric machines with or without a magnet in the rotor. Permanent Magnet Synchronous Machine (PMSM) and Induction Machine (IM) are the main components of drive trains of electric and hybrid vehicles. These machines have very good performance in healthy operation mode, but they are not redundant to ensure safety in faulty operation mode. Faced with the continued growth in the demand for electric vehicles in the automotive market, improving the reliability of electric vehicles is necessary over the lifecycle of the electric vehicle. Multiphase electric machines respond well to this constraint because, on the one hand, they have better robustness in the event of a breakdown (opening of a phase, opening of an arm of the power stage, intern-turn short circuit) and, on the other hand, better power density. In this work, a diagnosis approach using a neural network for an open circuit fault or more of a five-phase induction machine is developed. Validation on the simulator of the vehicle drivetrain, at reduced power, is carried out, creating one and more open circuit stator phases showing the efficiency and the reliability of the new approach to detect and to locate on-line one or more open phases of a five-induction machine.

Keywords: Electric vehicle drivetrain, multiphase drives, induction machine, control, open circuit fault diagnosis, artificial neural network.

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Authors: A. Ourici

Abstract:

Rapid progress in process automation and tightening quality standards result in a growing demand being placed on fault detection and diagnostics methods to provide both speed and reliability of motor quality testing. Doubly fed induction generators are used mainly for wind energy conversion in MW power plants. This paper presents a detection of an inter turn stator and an open phase faults, in a doubly fed induction machine whose stator and rotor are supplied by two pulse width modulation (PWM) inverters. The method used in this article to detect these faults, is based on Park-s Vector Approach, using a neural network.

Keywords: Doubly fed induction machine, inter turn stator fault, neural network, open phase fault, Park's vector approach, PWMinverter.

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Authors: Amir Rashid, M. Saleem Khan, Freeha Zafar

Abstract:

This work presents a new approach of securing a wireless network. The configuration is focused on securing & Protecting wireless network traffic for a small network such as a home or dorm room. The security Mechanism provided both authentication, allowing only known authorized users access to the wireless network, and encryption, preventing anyone from reading the wireless traffic. The mentioned solution utilizes the open source free S/WAN software which implements the Internet Protocol Security –IPSEC. In addition to wireless components, wireless NIC in PC and wireless access point needs a machine running Linux to act as security gateway. While the current configuration assumes that the wireless PC clients are running Linux, Windows XP/VISTA/7 based machines equipped with VPN software which will allow to interface with this configuration.

Keywords: Wireless network security, security network, authentication, encryption and internet protocol security.

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Authors: Kailash C. Madan

Abstract:

We study four models of a three server queueing system with Bernoulli schedule optional server vacations. Customers arriving at the system one by one in a Poisson process are provided identical exponential service by three parallel servers according to a first-come, first served queue discipline. In model A, all three servers may be allowed a vacation at one time, in Model B at the most two of the three servers may be allowed a vacation at one time, in model C at the most one server is allowed a vacation, and in model D no server is allowed a vacation. We study steady the state behavior of the four models and obtain steady state probability generating functions for the queue size at a random point of time for all states of the system. In model D, a known result for a three server queueing system without server vacations is derived.

Keywords: A three server queue, Bernoulli schedule server vacations, queue size distribution at a random epoch, steady state.

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Authors: Usman Sarwar, Gopinath Sinniah Rao, Zeldi Suryady, Reza Khoshdelniat

Abstract:

The low power wireless sensor devices which usually uses the low power wireless private area network (IEEE 802.15.4) standard are being widely deployed for various purposes and in different scenarios. IPv6 low power wireless private area network (6LoWPAN) was adopted as part of the IETF standard for the wireless sensor devices so that it will become an open standard compares to other dominated proprietary standards available in the market. 6LoWPAN also allows the integration and communication of sensor nodes with the Internet more viable. This paper presents a comparative study on different available IPv6 platforms for wireless sensor networks including open and close sources. It also discusses about the platforms used by these stacks. Finally it evaluates and provides appropriate suggestions which can be use for selection of required IPv6 stack for low power devices.

Keywords: 6LoWPAN Stacks, 6LoWPAN Platforms, m-Stack, NanoStack, uIPv6, PhyNet 6LoWPAN, Jennic 6LoWPAN.

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Authors: S. Dhib, S. A. Addouche, T. Loukil, A. Elmhamedi

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In this paper, a reverse supply chain network is investigated for a decision making. This decision is surrounded by complex flows of returned products, due to the increasing quantity, the type of returned products and the variety of recovery option products (reuse, recycling, and refurbishment). The most important problem in the reverse logistic network (RLN) is to orient returned products to the suitable type of recovery option. However, returned products orientations from collect sources to the recovery disposition have not well considered in performance model. In this study, we propose a performance model for designing a network configuration on reverse logistics. Conceptual and analytical models are developed with taking into account operational, economic and environmental factors on designing network.

Keywords: Reverse logistics, Network design, Performance model, Open loop configuration.

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Authors: C. Ardil

Abstract:

This paper presents the open science philosophy and paradigm of scientific research on how to transform classical research and innovation approaches. Open science is the practice of providing free and unrestricted online access to the products of scholarly research. Open science advocates for the immediate and unrestricted online access to published, peer-reviewed research in digital format. Open science research is made available for free in perpetuity and includes guidelines and/or licenses that communicate how researchers and readers can share and re-use the digital content. The emergence of open science has changed the scholarly research and publishing landscape, making research more broadly accessible to academic and non-academic audiences alike. Consequently, open science philosophy and its practice are discussed to cover all aspects of cyberscience in the context of research and innovation excellence for the benefit of global society.

Keywords: Open science, open data, open access, cyberscience , cybertechnology.

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Authors: Yuanyuan Zhang, Guang Sun, Li Su, Depeng Jin, Lieguang Zeng

Abstract:

Since Network-on-Chip (NoC) uses network interfaces (NIs) to improve the design productivity, by now, there have been a few papers addressing the design and implementation of a NI module. However, none of them considered the difference of address encoding methods between NoC and the traditional bus-shared architecture. On the basis of this difference, in the paper, we introduce a transmit mechanism to solve such a problem for global asynchronous locally synchronous (GALS) NoC. Furthermore, we give the concrete implementation of the NI module in this transmit mechanism. Finally, we evaluate its performance and area overhead by a VHDL-based cycle-accurate RTL model and simulation results confirm the validity of this address-oriented transmit mechanism.

Keywords: Network-on-Chip, Network Interface, Open CoreProtocol, Address.

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Authors: Brett E. Shelton, Joel Duffin, Yuxuan Wang, Justin Ball

Abstract:

With a growing number of digital libraries and other open education repositories being made available throughout the world, effective search and retrieval tools are necessary to access the desired materials that surpass the effectiveness of traditional, allinclusive search engines. This paper discusses the design and use of Folksemantic, a platform that integrates OpenCourseWare search, Open Educational Resource recommendations, and social network functionality into a single open source project. The paper describes how the system was originally envisioned, its goals for users, and data that provides insight into how it is actually being used. Data sources include website click-through data, query logs, web server log files and user account data. Based on a descriptive analysis of its current use, modifications to the platform's design are recommended to better address goals of the system, along with recommendations for additional phases of research.

Keywords: Digital libraries, open education, recommendation system, social networks

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Authors: Khalid Ali, Manar Jammal

Abstract:

In order to meet the stringent latency and reliability requirements of the upcoming 5G networks, Open Radio Access Networks (O-RAN) have been proposed. The virtualization of O-RAN has allowed it to be treated as a Network Function Virtualization (NFV) architecture, while its components are considered Virtualized Network Functions (VNFs). Hence, intelligent Machine Learning (ML) based solutions can be utilized to apply different resource management and allocation techniques on O-RAN. However, intelligently allocating resources for O-RAN VNFs can prove challenging due to the dynamicity of traffic in mobile networks. Network providers need to dynamically scale the allocated resources in response to the incoming traffic. Elastically allocating resources can provide a higher level of flexibility in the network in addition to reducing the OPerational EXpenditure (OPEX) and increasing the resources utilization. Most of the existing elastic solutions are reactive in nature, despite the fact that proactive approaches are more agile since they scale instances ahead of time by predicting the incoming traffic. In this work, we propose and evaluate traffic forecasting models based on the ML algorithm. The algorithms aim at predicting future O-RAN traffic by using previous traffic data. Detailed analysis of the traffic data was carried out to validate the quality and applicability of the traffic dataset. Hence, two ML models were proposed and evaluated based on their prediction capabilities.

Keywords: O-RAN, traffic forecasting, NFV, ARIMA, LSTM, elasticity.

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Authors: Han Xiao, Xiaoyan Zhu

Abstract:

Margin-Based Principle has been proposed for a long time, it has been proved that this principle could reduce the structural risk and improve the performance in both theoretical and practical aspects. Meanwhile, feed-forward neural network is a traditional classifier, which is very hot at present with a deeper architecture. However, the training algorithm of feed-forward neural network is developed and generated from Widrow-Hoff Principle that means to minimize the squared error. In this paper, we propose a new training algorithm for feed-forward neural networks based on Margin-Based Principle, which could effectively promote the accuracy and generalization ability of neural network classifiers with less labelled samples and flexible network. We have conducted experiments on four UCI open datasets and achieved good results as expected. In conclusion, our model could handle more sparse labelled and more high-dimension dataset in a high accuracy while modification from old ANN method to our method is easy and almost free of work.

Keywords: Max-Margin Principle, Feed-Forward Neural Network, Classifier.

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Authors: R. Sudhesh Solomon, P. Y. K. L. Srinivas, Abhay Narayan, Amitava Das

Abstract:

Users in social networks either unicast or broadcast their messages. At mention is the popular way of unicasting for Twitter whereas general tweeting could be considered as broadcasting method. Understanding the information flow and dynamics within a Social Network and modeling the same is a promising and an open research area called Information Diffusion. This paper seeks an answer to a fundamental question - understanding if the at-mention network or the unicasting pattern in social media is purely random in nature or is there any user specific selectional preference? To answer the question we present an empirical analysis to understand the sociological aspects of Twitter mentions network within a social network community. To understand the sociological behavior we analyze the values (Schwartz model: Achievement, Benevolence, Conformity, Hedonism, Power, Security, Self-Direction, Stimulation, Traditional and Universalism) of all the users. Empirical results suggest that values traits are indeed salient cue to understand how the mention-based communication network functions. For example, we notice that individuals possessing similar values unicast among themselves more often than with other value type people. We also observe that traditional and self-directed people do not maintain very close relationship in the network with the people of different values traits.

Keywords: Social network analysis, information diffusion, personality and values, Twitter Mentions Network.

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Authors: Martin Lnenicka

Abstract:

Governments collect and produce large amounts of data. Increasingly, governments worldwide have started to implement open data initiatives and also launch open data portals to enable the release of these data in open and reusable formats. Therefore, a large number of open data repositories, catalogues and portals have been emerging in the world. The greater availability of interoperable and linkable open government data catalyzes secondary use of such data, so they can be used for building useful applications which leverage their value, allow insight, provide access to government services, and support transparency. The efficient development of successful open data portals makes it necessary to evaluate them systematic, in order to understand them better and assess the various types of value they generate, and identify the required improvements for increasing this value. Thus, the attention of this paper is directed particularly to the field of open data portals. The main aim of this paper is to compare the selected open data portals on the national level using content analysis and propose a new evaluation framework, which further improves the quality of these portals. It also establishes a set of considerations for involving businesses and citizens to create eservices and applications that leverage on the datasets available from these portals.

Keywords: Big data, content analysis, criteria comparison, data quality, open data, open data portals, public sector.

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Authors: Marko A. Rodriguez

Abstract:

There exists an injective, information-preserving function that maps a semantic network (i.e a directed labeled network) to a directed network (i.e. a directed unlabeled network). The edge label in the semantic network is represented as a topological feature of the directed network. Also, there exists an injective function that maps a directed network to an undirected network (i.e. an undirected unlabeled network). The edge directionality in the directed network is represented as a topological feature of the undirected network. Through function composition, there exists an injective function that maps a semantic network to an undirected network. Thus, aside from space constraints, the semantic network construct does not have any modeling functionality that is not possible with either a directed or undirected network representation. Two proofs of this idea will be presented. The first is a proof of the aforementioned function composition concept. The second is a simpler proof involving an undirected binary encoding of a semantic network.

Keywords: general-modeling, multi-relational networks, semantic networks

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Authors: Weng Ming Chu

Abstract:

When faced with stochastic networks with an uncertain duration for their activities, the securing of network completion time becomes problematical, not only because of the non-identical pdf of duration for each node, but also because of the interdependence of network paths. As evidenced by Adlakha & Kulkarni [1], many methods and algorithms have been put forward in attempt to resolve this issue, but most have encountered this same large-size network problem. Therefore, in this research, we focus on network reduction through a Series/Parallel combined mechanism. Our suggested algorithm, named the Activity Network Reduction Algorithm (ANRA), can efficiently transfer a large-size network into an S/P Irreducible Network (SPIN). SPIN can enhance stochastic network analysis, as well as serve as the judgment of symmetry for the Graph Theory.

Keywords: Series/Parallel network, Stochastic network, Network reduction, Interdictive Graph, Complexity Index.

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