Search results for: single–server queue model

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: Kailash C. Madan

Abstract:

We study the steady state behaviour of a batch arrival single server queue in which the first service with general service times is compulsory and the second service with general service times is optional. We term such a two phase service as generalized Coxian-2 service. Just after completion of a service the server must take a vacation of random length of time with general vacation times. We obtain steady state probability generating functions for the queue size as well as the steady state mean queue size at a random epoch of time in explicit and closed forms. Some particular cases of interest including some known results have been derived.

Keywords: batch arrivals, compound Poisson process, generalized Coxian-2 service, steady state

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Authors: R. Sivasamy, G. Paulraj, S. Kalaimani, N.Thillaigovindan

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For profitable businesses, queues are double-edged swords and hence the pain of long wait times in a queue often frustrates customers. This paper suggests a technical way of reducing the pain of lines through a Poisson M/M1, M2/2 queueing system operated by two heterogeneous servers with an objective of minimising the mean sojourn time of customers served under the queue discipline ‘First Come First Served with an ‘m’ policy, i.e. FCFS-m policy’. Arrivals to the system form a Poisson process of rate λ and are served by two exponential servers. The service times of successive customers at server ‘j’ are independent and identically distributed (i.i.d.) random variables and each of it is exponentially distributed with rate parameter μj (j=1, 2). The primary condition for implementing the queue discipline ‘FCFS-m policy’ on these service rates μj (j=1, 2) is that either (m+1) µ2 > µ1> m µ2 or (m+1) µ1 > µ2> m µ1 must be satisfied. Further waiting customers prefer the server-1 whenever it becomes available for service, and the server-2 should be installed if and only if the queue length exceeds the value ‘m’ as a threshold. Steady-state results on queue length and waiting time distributions have been obtained. A simple way of tracing the optimal service rate μ*2 of the server-2 is illustrated in a specific numerical exercise to equalize the average queue length cost with that of the service cost. Assuming that the server-1 has to dynamically adjust the service rates as μ1 during the system size is strictly less than T=(m+2) while μ2=0, and as μ1 +μ2 where μ2>0 if the system size is more than or equal to T, corresponding steady state results of M/M1+M2/1 queues have been deduced from those of M/M1,M2/2 queues. To conclude this investigation has a viable application, results of M/M1+M2/1 queues have been used in processing of those waiting messages into a single computer node and to measure the power consumption by the node.

Keywords: two heterogeneous servers, M/M1, M2/2 queue, service cost and queue length cost, M/M1+M2/1 queue

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Authors: Fazia Rahmoune, Sofiane Ziani

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Retrial queueing systems have been extensively used to stochastically model many problems arising in computer networks, telecommunication, telephone systems, among others. In this work, we consider a $M/G/1$ retrial queue with an unreliable server with random vacations and two types of primary customers, persistent and impatient. This model involves the unreliability of the server, which can be subject to physical breakdowns and takes into account the correctives maintenances for restoring the service when a failure occurs. On the other hand, we consider random vacations, which can model the preventives maintenances for improving system performances and preventing breakdowns. We give the necessary and sufficient stability condition of the system. Then, we obtain the joint probability distribution of the server state and the number of customers in orbit and derive the more useful performance measures analytically. Moreover, we also analyze the busy period of the system. Finally, we derive the stability condition and the generating function of the stationary distribution of the number of customers in the system when there is no vacations and impatient customers, and when there is no vacations, server failures and impatient customers.

Keywords: modeling, retrial queue, unreliable server, vacation, stochastic analysis

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Authors: Amal Ezzidani, Abdelghani Ben Tahar, Mohamed Hanini

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A sequence of finite tandem queue is considered for this study. Each one has a single server, which operates under the egalitarian processor sharing discipline. External customers arrive at each queue according to a renewal input process and having a general service times distribution. Upon completing service, customers leave the current queue and enter to the next. Under mild assumptions, including critical data, we prove the existence and the uniqueness of the fluid solution. For asymptotic behavior, we provide necessary and sufficient conditions for the invariant state and the convergence to this invariant state. In the end, we establish the convergence of a correctly normalized state process to a fluid limit characterized by a system of algebraic and integral equations.

Keywords: fluid limit, fluid model, measure valued process, processor sharing, tandem queue

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Authors: Baya Takhedmit, Karim Abbas, Sofiane Ouazine

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The vacations queues are often employed to model many real situations such as computer systems, communication networks, manufacturing and production systems, transportation systems and so forth. These queueing models are solved at fixed parameters values. However, the parameter values themselves are determined from a finite number of observations and hence have uncertainty associated with them (epistemic uncertainty). In this paper, we consider the M/G/1/N queue with server vacation and exhaustive discipline where we assume that the vacation parameter values have uncertainty. We use the Taylor series expansions approach to estimate the expectation and variance of model output, due to epistemic uncertainties in the model input parameters.

Keywords: epistemic uncertainty, M/G/1/N queue with vacations, non-parametric sensitivity analysis, Taylor series expansion

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Authors: R. Remya

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We consider an M/M/1 multiple variant vacation queueing system and working vacation with waiting server. Here, comparing considering three models. First model, working vacation is taken after the server has exhaustively served all the customers in the system and waits random amount of time. After completing a working vacation, the server will wait for a random period of time before going on vacation. Then it goes to finite number of vacations same way. After end of J th vacation server waits in busy or served immediately. Second model, working vacation is taken after the server has exhaustively served all the customers in the system and waits random amount of time. Third model, working vacation is taken after the server has exhaustively served all the customers in the system and waits random amount of time. It is expected that service times and vacation lengths are exponentially distributed . We provide a steady-state solution and cost comparison for the stated models.

Keywords: vacation, working vacation, waiting server, steady state analysis, cost analysis

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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This study analyzed a queueing system with blocking and no waiting line. The customers arrive according to a Poisson process and the service times follow exponential distribution. There are two non-identical servers in the system. The queue discipline is FCFS, and the customers select the servers on fastest server first (FSF) basis. The service times are exponentially distributed with parameters μ1 and μ2 at servers I and II, respectively. Besides, the catastrophes occur in a Poisson manner with rate γ in the system. When server I is busy or blocked, the customer who arrives in the system leaves the system without being served. Such customers are called lost customers. The probability of losing a customer was computed for the system. The explicit time dependent probabilities of system size are obtained and a numerical example is presented in order to show the managerial insights of the model. Finally, the probability that arriving customer finds system busy and average number of server busy in steady state are obtained numerically.

Keywords: queueing system, blocking, poisson process, heterogeneous servers, queue discipline FCFS, busy period

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Authors: Shahram Jamali, Samira Hamed

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One of the open issues in Random Early Detection (RED) algorithm is how to set its parameters to reach high performance for the dynamic conditions of the network. Although original RED uses fixed values for its parameters, this paper follows a model-based approach to upgrade performance of the RED algorithm. It models the routers queue behavior by using the Markov model and uses this model to predict future conditions of the queue. This prediction helps the proposed algorithm to make some tunings over RED's parameters and provide efficiency and better performance. Widespread packet level simulations confirm that the proposed algorithm, called Markov-RED, outperforms RED and FARED in terms of queue stability, bottleneck utilization and dropped packets count.

Keywords: active queue management, RED, Markov model, random early detection algorithm

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Authors: Xiaoming Jiang, Jinqiao Shi, Qingfeng Tan, Wentao Zhang, Xuebin Wang, Muqian Chen

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Nowadays, big companies such as Google, Microsoft, which have adequate proxy servers, have perfectly implemented their web crawlers for a certain website in parallel. But due to lack of expensive proxy servers, it is still a puzzle for researchers to crawl large amounts of information from a single website in parallel. In this case, it is a good choice for researchers to use free public proxy servers which are crawled from the Internet. In order to improve efficiency of web crawler, the following two issues should be considered primarily: (1) Tasks may fail owing to the instability of free proxy servers; (2) A proxy server will be blocked if it visits a single website frequently. In this paper, we propose Proxisch, an optimization approach of large-scale unstable proxy servers scheduling, which allow anyone with extremely low cost to run a web crawler efficiently. Proxisch is designed to work efficiently by making maximum use of reliable proxy servers. To solve second problem, it establishes a frequency control mechanism which can ensure the visiting frequency of any chosen proxy server below the website’s limit. The results show that our approach performs better than the other scheduling algorithms.

Keywords: proxy server, priority queue, optimization algorithm, distributed web crawling

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Authors: Yutae Lee

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This paper considers a discrete-time bulk-arrival bulkservice queueing system, where service capacity varies depending on the previous service time. By using the generating function technique and the supplementary variable method, we compute the distributions of the queue length at an arbitrary slot boundary and a departure time.

Keywords: discrete-time queue, bulk queue, variable service capacity, queue length distribution

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Authors: Andreas Ahrens, Ojaras Purvinis, Jelena Zascerinska

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A successful shopping experience without overcrowded shops and long waiting times undoubtedly leads to the release of happiness hormones and is generally considered the goal of any optimization. Factors influencing the shopping experience can be divided into internal and external ones. External factors are related, e. g. to the arrival of the customers to the shop, whereas internal are linked with the service process itself when checking out (waiting in the queue to the cash register and the scanning of the goods as well as the payment process itself) or any other non-expected delay when changing the status from a visitor to a buyer by choosing goods or items. This paper divides the customer-server interaction into five phases starting with the customer's arrival at the shop, the selection of goods, the buyer waiting in the queue to the cash register, the payment process, and ending with the customer or buyer's departure. Our simulation results show how five phases are intertwined and influence the overall shopping experience. Parameters for measuring the shopping experience are estimated based on the burstiness level in each of the five phases of the customer-server interaction.

Keywords: customers’ burstiness, cash register, customers’ wait-ing time, gap distribution function

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: stochastic integrals, single–server queue model, catastrophes, busy period

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Authors: Bagul Abhijeet

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Background: Client-Server model is the backbone of today’s internet communication. In which normal user can not have control over particular website or server? By using the same processing model one can have unauthorized access to particular server. In this paper, we discussed about application scenario of hacking for simple website or server consist of unauthorized way to access the server database. This application emerges to autonomously take direct access of simple website or server and retrieve all essential information maintain by administrator. In this system, IP address of server given as input to retrieve user-id and password of server. This leads to breaking administrative security of server and acquires the control of server database. Whereas virus helps to escape from server security by crashing the whole server. Objective: To control malicious attack and preventing all government website, and also find out illegal work to do hackers activity. Results: After implementing different hacking as well as non-hacking techniques, this system hacks simple web sites with normal security credentials. It provides access to server database and allow attacker to perform database operations from client machine. Above Figure shows the experimental result of this application upon different servers and provides satisfactory results as required. Conclusion: In this paper, we have presented a to view to hack the server which include some hacking as well as non-hacking methods. These algorithms and methods provide efficient way to hack server database. By breaking the network security allow to introduce new and better security framework. The terms “Hacking” not only consider for its illegal activities but also it should be use for strengthen our global network.

Keywords: Hacking, Vulnerabilities, Dummy request, Virus, Server monitoring

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Authors: Sadegh Abebi

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There are problems with estimating time of product process of products, especially when there is variable serving time, like control stage. These problems will cause overestimation of process time. Layout constraints, reworking constraints and inflexible product schedule in multi product lines, needs a precise planning to reduce volume in particular situation of line stock. In this article, by analyzing real queue systems with layout constraints and by using concepts and principles of Markov chain in queue theory, a hybrid model has been presented. This model can be a base to assess queue systems with probable parameters of service. Here by presenting a case study, the proposed model will be described. so, production lines of a home application manufacturer will be analyzed.

Keywords: Queuing theory, Markov Chain, layout, line balance

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Authors: Maged A. Mogalli, Abdullah I. Al-Mansour, Seongkwan Mark Lee

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In the last decades, population growth has gradually exceeded transportation infrastructure growth, and today’s transportation professionals are facing challenge on how to meet the mobility needs of a rising population especially in the absence of adequate public transport, as is the case in Saudi Arabia. The traffic movement congestion can be decreased by carrying out some appropriate alternative designs of interchanges such as diverging diamond interchange (DDI) and single diamond interchange (SPDI). In this paper, evaluation of newly implemented DDIs at the interchange of Makkah road with Prince Turki road and the interchange of King Khaled road with Prince Saud Ibn Mohammed Ibn Mugrin road in Riyadh city was carried out. The comparison between the DDI and SPDI is conducted by evaluating different measures of effectiveness (MOE) such as stop delay, average queue length, and number of stops. In this connection, each interchange type was evaluated for traffic flow at peak hours using micro-simulation program namely 'Synchro/SimTarffic' to measure its effectiveness such as stop delay, average queue length, and number of stops. The results of this study show that DDI provides a better result when compared with SPDI in terms of stope delay, average queue length, and number of stops. The stop delay for the SPDI is greater than DDI by three times. Also, the average queue length is approximately twice that of the SPDI when compared to the DDI. Furthermore, the number of stops for the SPDI is about twice as the DDI.

Keywords: single point diamond interchange, diverging diamond interchange, measures of effectiveness, simulation

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Authors: Sina Saadati, Mohammadreza Razzazi

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Since Java is an object-oriented language, It can be used to solve a wide range of problems. One of the considerable usages of this language can be found in Agent-based modeling and simulation. Despite the significant power of Java, There is not an easy method to render a 3-dimensional human model. In this article, we are about to develop a library which helps modelers present a 3D human model and control it with Java. The library runs two server programs. The first one is a web page server that can connect to any browser and present an HTML code. The second server connects to the browser and controls the movement of the model. So, the modeler will be able to develop a simulation and display a good-looking human model without any knowledge of any graphical tools.

Keywords: agent-based modeling and simulation, human model, graphics, Java, distributed systems

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Authors: Manish Kumar Rajak, Sanjay Gupta

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Mobile ad hoc networks (MANETs) are infrastructure less and intercommunicate using single-hop and multi-hop paths. Network based congestion avoidance which involves managing the queues in the network devices is an integral part of any network. QoS: A set of service requirements that are met by the network while transferring a packet stream from a source to a destination. Especially in MANETs, packet loss results in increased overheads. This paper presents a new algorithm to avoid congestion using one or more queue on nodes and corresponding flow rate decided in advance for each node. When any node attains an initial value of queue then it sends this status to its downstream nodes which in turn uses the pre-decided flow rate of packet transfer to its upstream nodes. The flow rate on each node is adjusted according to the status received from its upstream nodes. This proposed algorithm uses the existing infrastructure to inform to other nodes about its current queue status.

Keywords: mesh networks, MANET, packet count, threshold, throughput

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Authors: Pradeep M. C. Chand

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Virtual infrastructure initiatives often spring from data center server consolidation projects, which focus on reducing existing infrastructure “box count”, retiring older hardware or life-extending legacy applications. Server consolidation benefits result from a reduction in the overall number of systems and related recurring costs (power, cooling, rack space, etc.) and also helps in the reduction of heat to the environment.

Keywords: server virtualization, data center, consolidation, project

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Authors: S. Hameed, S. Anwer, M. Saad, M. Saady

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For autonomic recovery with server virtualization, a cogent plan that includes recovery techniques and backups with virtualized servers can be developed instead of assigning an idle server to backup operations. In addition to hardware cost reduction and data center trail, the disaster recovery plan can ensure system uptime and to meet objectives of high availability, recovery time, recovery point, server provisioning, and quality of services. This autonomic solution would also support disaster management, testing, and development of the recovery site. In this research, a workflow plan is proposed for supporting disaster recovery with virtualization providing virtual monitoring, requirements engineering, solution decision making, quality testing, and disaster management. This recovery model would make disaster recovery a lot easier, faster, and less error prone.

Keywords: autonomous intelligence, disaster recovery, cloud computing, server virtualization

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Authors: Reni M. Sagayaraj, Anand Gnana S. Selvam, Reynald R. Susainathan

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In this paper, we consider stochastic queueing models for Steady-state behavior of a multi-phase M/M/1 queue in random evolution subject to catastrophe failure. The arrival flow of customers is described by a marked Markovian arrival process. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. This model contains a repair state, when a catastrophe occurs the system is transferred to the failure state. The paper focuses on the steady-state equation, and observes that, the steady-state behavior of the underlying queueing model along with the average queue size is analyzed.

Keywords: M/G/1 queuing system, multi-phase, random evolution, steady-state equation, catastrophe failure

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Authors: Ezil Sam Leni, Shalen S.

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Transport service monitoring and upkeep are essential components of smart city initiatives. The main risks to the relevant departments and authorities are the ever-increasing vehicular traffic and the conditions of the roads. In India, the economy is greatly impacted by the road transport sector. In 2021, the Ministry of Road Transport and Highways Transport, Government of India, produced a report with statistical data on traffic accidents. The data included the number of fatalities, injuries, and other pertinent criteria. This study proposes a distributed infrastructure for the monitoring, detection, and reporting of potholes to the appropriate authorities. In a distributed environment, the nodes are the edge devices, and local edge servers, and global servers. The edge devices receive the initial model to be employed from the global server. The YOLOv8 model for pothole detection is used in the edge devices. The edge devices run the pothole detection model, gather the pothole images on their path, and send the updates to the nearby edge server. The local edge server selects the clients for its aggregation process, aggregates the model updates and sends the updates to the global server. The global server collects the updates from the local edge servers, performs aggregation and derives the updated model. The updated model has the information about the potholes received from the local edge servers and notifies the updates to the local edge servers and concerned authorities for monitoring and maintenance of road conditions. The entire process is implemented in FedCV distributed environment with the implementation using the client-server model and aggregation entities. After choosing the clients for its aggregation process, the local edge server gathers the model updates and transmits them to the global server. After gathering the updates from the regional edge servers, the global server aggregates them and creates the updated model. Performance indicators and the experimentation environment are assessed, discussed, and presented. Accelerometer data may be taken into consideration for improved performance in the future development of this study, in addition to the images captured from the transportation routes.

Keywords: federated Learning, pothole detection, distributed framework, federated averaging

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Authors: Wanqing You, Kai Qian, Ying Qian

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The concepts of Cloud Computing provide users with infrastructure, platform and software as service, which make those services more accessible for people via Internet. To better analysis the performance of Cloud Computing provisioning policies as well as resources allocation strategies, a toolkit named CloudSim proposed. With CloudSim, the Cloud Computing environment can be easily constructed by modelling and simulating cloud computing components, such as datacenter, host, and virtual machine. A good scheduling strategy is the key to achieve the load balancing among different machines as well as to improve the utilization of basic resources. Recently, the existing scheduling algorithms may work well in some presumptive cases in a single machine; however they are unable to make the best decision for the unforeseen future. In real world scenario, there would be numbers of tasks as well as several virtual machines working in parallel. Based on the concepts of multi-queue, this paper presents a new scheduling algorithm to schedule tasks with CloudSim by taking into account several parameters, the machines’ capacity, the priority of tasks and the history log.

Keywords: hierarchical queue, load balancing, CloudSim, information technology

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Authors: Hong Kai, Zhong Jun Jie, Chen Lin Qi, Wang Chen Guang

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There are inefficient global scheduling parallelism and local scheduling parallelism prone to processor starvation in current scheduling algorithms. Regarding this issue, this paper proposed a load-aware queue partitioning scheduling strategy by first allocating the queues according to the number of processor cores, calculating the load factor to specify the load queue capacity, and it assigned the awaiting nodes to the appropriate perceptual queues through the precursor nodes and the communication computation overhead. At the same time, real-time computation of the load factor could effectively prevent the processor from being starved for a long time. Experimental comparison with two classical algorithms shows that there is a certain improvement in both performance metrics of scheduling length and task speedup ratio.

Keywords: load-aware, scheduling algorithm, perceptual queue, heterogeneous multi-core

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Authors: Joel Weymouth, Ramesh K. Karne, Alexander L. Wijesinha

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Bare Machine Internet is part of the Bare Machine Computing (BMC) paradigm. It is used in programming application ns to run directly on a device. It is software that runs directly against the hardware using CPU, Memory, and I/O. The software application runs without an Operating System and resident mass storage. An important part of the BMC paradigm is the Bare Machine Internet. It utilizes an Application Development model software that interfaces directly with the hardware on a network server and file server. Because it is “bare,” it is a powerful teaching and research tool that can readily display the internals of the network protocols, software, and hardware of the applications running on the Bare Server. It was also demonstrated that the bare server was accessible by laptop and by smartphone/android. The purpose was to show the further practicality of Bare Internet in Computer Engineering and Computer Science Education and Research. It was also to show that an undergraduate student could take advantage of a bare server with any device and any browser at any release version connected to the internet. This paper presents the Bare Web Server as an educational tool. We will discuss possible applications of this paradigm.

Keywords: bare machine computing, online research, network technology, visualizing network internals

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Authors: Saulius Minkevicius, Edvinas Greicius

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The paper is devoted to the analysis of queueing systems in the context of the network and communications theory. We investigate the inequality in an open queueing network and its applications to the theorems in heavy traffic conditions (fluid approximation, functional limit theorem, and law of the iterated logarithm) for a queue of customers in an open queueing network.

Keywords: fluid approximation, heavy traffic, models of information systems, open queueing network, queue length of customers, queueing theory

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Authors: Bodhayan Nandi, Shubhajit Roy Chowdhury

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This paper presents the development of a portable blood glucose monitoring device based on Near-Infrared Spectroscopy. The system supports Internet connectivity through WiFi and uploads the time series data of glucose concentration of patients to a server. In addition, the server is given sufficient intelligence to predict the future pathophysiological state of a patient given the current and past pathophysiological data. This will enable to prognosticate the approaching critical condition of the patient much before the critical condition actually occurs.The server hosts web applications to allow authorized users to monitor the data remotely.

Keywords: non invasive, blood glucose concentration, microcontroller, IoT, application server, database server

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Authors: Amirhossein Mohajerzadeh, Abolghasem Mohajerzadeh

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In this paper, target parameter is estimated with desirable precision in hierarchical wireless sensor networks (WSN) while the proposed algorithm also tries to prolong network lifetime as much as possible, using efficient data collecting algorithm. Target parameter distribution function is considered unknown. Sensor nodes sense the environment and send the data to the base station called fusion center (FC) using hierarchical data collecting algorithm. FC builds underlying phenomena based on collected data. Considering the aggregation level, x, the goal is providing the essential infrastructure to find the best value for aggregation level in order to prolong network lifetime as much as possible, while desirable accuracy is guaranteed (required sample size is fully depended on desirable precision). First, the sample size calculation algorithm is discussed, second, the average queue length based on M/M[x]/1/K queue model is determined and it is used for energy consumption calculation. Nodes can decrease transmission cost by aggregating incoming data. Furthermore, the performance of the new algorithm is evaluated in terms of lifetime and estimation accuracy.

Keywords: aggregation, estimation, queuing, wireless sensor network

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Authors: Kartik Mahajan

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DevOps methodologies streamline software development and operations, promoting collaboration and automation. Traditional server management often relies on manual, repetitive tasks, leading to inefficiencies, potential errors, and increased operational costs. Ansible, as a configuration management tool, presents a compelling solution for automating infrastructure management processes. This review paper explores the implementation and testing of Ansible for server management, specifically focusing on automated user account configuration. By replacing manual procedures with Ansible playbooks, we aim to optimize server management, reduce human error, and potentially mitigate operational expenses. This study offers insights into Ansible’s efficacy within a DevOps context, highlighting its potential to transform server administration practices.

Keywords: cloud, Devops, automation, ansible

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Authors: Yoshiaki Shikata, Nobutane Hanayama

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We present a prioritized, limited multi-server processor sharing (PS) system where each server has various capacities, and N (≥2) priority classes are allowed in each PS server. In each prioritized, limited server, different service ratio is assigned to each class request, and the number of requests to be processed is limited to less than a certain number. Routing strategies of such prioritized, limited multi-server PS systems that take into account the capacity of each server are also presented, and a performance evaluation procedure for these strategies is discussed. Practical performance measures of these strategies, such as loss probability, mean waiting time, and mean sojourn time, are evaluated via simulation. In the PS server, at the arrival (or departure) of a request, the extension (shortening) of the remaining sojourn time of each request receiving service can be calculated by using the number of requests of each class and the priority ratio. Utilising a simulation program which executes these events and calculations, the performance of the proposed prioritized, limited multi-server PS rule can be analyzed. From the evaluation results, most suitable routing strategy for the loss or waiting system is clarified.

Keywords: processor sharing, multi-server, various capacity, N-priority classes, routing strategy, loss probability, mean sojourn time, mean waiting time, simulation

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