This document summarizes a study on a fuzzy queueing model of an FM/FM/1 queue with single working vacation. The arrival rate, service rates, and vacation rate are assumed to be fuzzy numbers. Membership functions are defined for the system characteristics, including the number of customers in the system, the virtual time of a customer, the probability the server is idle, and the probability the server is busy. Explicit expressions are presented for the membership functions of these performance measures in terms of the fuzzy arrival, service, and vacation rates.
An Interval Type-2 Fuzzy Approach for Process Plan Selectioninventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Abstract: The present paper analyzes a vacation queueing model with bulk service rule. Considering distribution of the system occupancy just before and after the departure epochs using discrete-time analysis. The inter-arrival times of customers are assumed to be independent and geometrically distributed. The server works at different rate, rather than completely stopping service vacations. The service times during a service period and vacation time geometric distribution. Some performance measures and a cost model have been presented and an optimum service rate has been obtained using convex function. Numerical results showing the effect of the parameters of the model on the key performance are presented.
Bridging Centrality: Identifying Bridging Nodes in Transportation NetworkEswar Publications
To identify the importance of node of a network, several centralities are used. Majority of these centrality measures are dominated by components' degree due to their nature of looking at networks’ topology. We propose a centrality to identification model, bridging centrality, based on information flow and topological aspects. We apply bridging centrality on real world networks including the transportation network and show that the nodes distinguished by bridging centrality are well located on the connecting positions between highly connected regions. Bridging centrality can discriminate bridging nodes, the nodes with more information flowed through them and locations between highly connected regions, while other centrality measures cannot.
RESOURCE ALLOCATION METHOD FOR CLOUD COMPUTING ENVIRONMENTS WITH DIFFERENT SE...IJCNCJournal
In a cloud computing environment with multiple data centers over a wide area, it is highly likely that each data center would provide the different service quality to users at different locations. It is also required to consider the nodes at the edge of the network (local cloud) which support applications such as IoTs that require low latency and location awareness. The authors proposed the joint multiple resource allocation method in a cloud computing environment that consists of multiple data centers and each data center provides the different network delay. However, the existing method does not take account of cases where requests that require a short network delay occur more than expected. Moreover, the existing method does not take account of service processing time in data centers and therefore cannot provide the optimal resource allocation when it is necessary to take the total processing time (both network delay and service processing time in a data center) into consideration in resource allocation.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
An Interval Type-2 Fuzzy Approach for Process Plan Selectioninventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Abstract: The present paper analyzes a vacation queueing model with bulk service rule. Considering distribution of the system occupancy just before and after the departure epochs using discrete-time analysis. The inter-arrival times of customers are assumed to be independent and geometrically distributed. The server works at different rate, rather than completely stopping service vacations. The service times during a service period and vacation time geometric distribution. Some performance measures and a cost model have been presented and an optimum service rate has been obtained using convex function. Numerical results showing the effect of the parameters of the model on the key performance are presented.
Bridging Centrality: Identifying Bridging Nodes in Transportation NetworkEswar Publications
To identify the importance of node of a network, several centralities are used. Majority of these centrality measures are dominated by components' degree due to their nature of looking at networks’ topology. We propose a centrality to identification model, bridging centrality, based on information flow and topological aspects. We apply bridging centrality on real world networks including the transportation network and show that the nodes distinguished by bridging centrality are well located on the connecting positions between highly connected regions. Bridging centrality can discriminate bridging nodes, the nodes with more information flowed through them and locations between highly connected regions, while other centrality measures cannot.
RESOURCE ALLOCATION METHOD FOR CLOUD COMPUTING ENVIRONMENTS WITH DIFFERENT SE...IJCNCJournal
In a cloud computing environment with multiple data centers over a wide area, it is highly likely that each data center would provide the different service quality to users at different locations. It is also required to consider the nodes at the edge of the network (local cloud) which support applications such as IoTs that require low latency and location awareness. The authors proposed the joint multiple resource allocation method in a cloud computing environment that consists of multiple data centers and each data center provides the different network delay. However, the existing method does not take account of cases where requests that require a short network delay occur more than expected. Moreover, the existing method does not take account of service processing time in data centers and therefore cannot provide the optimal resource allocation when it is necessary to take the total processing time (both network delay and service processing time in a data center) into consideration in resource allocation.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
PERFORMANCE FACTORS OF CLOUD COMPUTING DATA CENTERS USING [(M/G/1) : (∞/GDM O...ijgca
The ever-increasing status of the cloud computing h
ypothesis and the budding concept of federated clou
d
computing have enthused research efforts towards in
tellectual cloud service selection aimed at develop
ing
techniques for enabling the cloud users to gain max
imum benefit from cloud computing by selecting
services which provide optimal performance at lowes
t possible cost. Cloud computing is a novel paradig
m
for the provision of computing infrastructure, whic
h aims to shift the location of the computing
infrastructure to the network in order to reduce th
e maintenance costs of hardware and software resour
ces.
Cloud computing systems vitally provide access to l
arge pools of resources. Resources provided by clou
d
computing systems hide a great deal of services fro
m the user through virtualization. In this paper, t
he
cloud data center is modelled as
queuing system with a single task arrivals
and a task request buffer of infinite capacity.
SOLVING OPTIMAL COMPONENTS ASSIGNMENT PROBLEM FOR A MULTISTATE NETWORK USING ...ijmnct
Optimal components assignment problem subject to system reliability, total lead-time, and total cost
constraints is studied in this paper. The problem is formulated as fuzzy linear problem using fuzzy
membership functions. An approach based on genetic algorithm with fuzzy optimization to sole the
presented problem. The optimal solution found by the proposed approach is characterized by maximum
reliability, minimum total cost and minimum total lead-time. The proposed approach is tested on different
examples taken from the literature to illustrate its efficiency in comparison with other previous methods
SOLVING OPTIMAL COMPONENTS ASSIGNMENT PROBLEM FOR A MULTISTATE NETWORK USING ...ijmnct
Optimal components assignment problem subject to system reliability, total lead-time, and total cost constraints is studied in this paper. The problem is formulated as fuzzy linear problem using fuzzy membership functions. An approach based on genetic algorithm with fuzzy optimization to sole the presented problem. The optimal solution found by the proposed approach is characterized by maximum reliability, minimum total cost and minimum total lead-time. The proposed approach is tested on different examples taken from the literature to illustrate its efficiency in comparison with other previous methods.
𝑴[𝑿]/G/1 with Second Optional Service, Multiple Vacation, Breakdown and RepairIJRES Journal
In this paper, we present a batch arrival non- Markovian queuing model with second optional service, subject to random break downs and multiple vacations. Batches arrive in Poisson stream with mean arrival rate λ, such that all customers demand the first `essential' service, whereas only some of them demand the second `optional' service. The service times of the both first essential service and the second optional service are assumed to follow general (arbitrary) distribution with distribution function 𝐵1(𝑣) and 𝐵2(𝑣) respectively. The server may undergo breakdowns which occur Aaccording to Poisson process with breakdown rate. Once the system encounter break downs it enters the repair process and the repair time is followed by exponential distribution with repair rate𝛼. The server takes vacation each time the system becomes empty and the vacation period is assumed to be exponential distribution. On returning from vacation if the server finds no customer waiting in the system, then the server again goes for vacation until he finds at least one unit in the system. The time-dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been derived explicitly. Also the mean queue length and the mean waiting time have been found explicitly.
Mean Object Size Considering Average Waiting Latency in M/BP/1 SystemIJCNCJournal
This paper deals with the web object size which affects to the service time in multiple access environments. The M/BP/1 model can be considered because packets arrival and web service are Poission and Bound Pareto (BP) distribution respectively. We find mean object size which satisfies that the average waiting latency by deterministic model equals the mean queueing delay of the M/BP/1 model. Performance evaluation shows that the mean web object size is affected by file size bounds and shape parameter of BP distribution, however, the impact of link capacity is not significant. When the system load is low, web object size converges on half the maximum segment size (MSS). Our results can be applied to find mean web object size in the economic web service design.
A fpga implementation of data hiding using lsb matching methodeSAT Journals
Abstract
Data Hiding is one of the familiar methodologies used nowadays to authenticate and resolve the copyrights of the digital data.
This paper discusses the verilog based FPGA implementation of data hiding in grayscale image using the concept of the LSB
Matching technique. In this verilog based data hiding process the secret digital signature is hidden in the host image then
analyzed with the PSNR value and Payload capacity.
Keywords: Data hiding, Least-Significant-bit matching method, Reversible, Gray Scale Image, Real Time
LSB Embedding, FPGA- Implementation etc
A novel scheme for reliable multipath routing through node independent direct...eSAT Journals
Abstract Multipath routing is essential in the wake of voice over IP, multimedia streaming for efficient data transmission. The growing usage of such network requirements also demands fast recovery from network failures. Multipath routing is one of the promising routing schemes to accommodate the diverse requirements of the network with provision such as load balancing and improved bandwidth. Cho et al. introduced a resilient multipath routing scheme known as directed acyclic graphs. These graphs enable multipath routing with all possible edges while ensuring guaranteed recovery from single point of failures. We also built a prototype application that demonstrates the efficiency of the scheme. The simulation results revealed that the scheme is useful and can be used in real world network applications.
Index Terms – Multipath routing, failure recovery, directed acyclic graphs
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
This work constructs the membership functions of the system characteristics of a batch-arrival queuing system with multiple servers, in which the batch-arrival rate and customer service rate are all fuzzy numbers. The -cut approach is used to transform a fuzzy queue into a family of conventional crisp queues in this context. By means of the membership functions of the system characteristics, a set of parametric nonlinear programs is developed to describe the family of crisp batch-arrival queues with multiple servers. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the system characteristics are expressed and governed by the membership functions, the fuzzy batch-arrival queues with multiple servers are represented more accurately and the analytic results are more useful for system designers and practitioners.
Reliability Analysis of Identical unit System with Arbitrary Distribution Sub...ijtsrd
In this research paper, we analyzed the reliability measures of two units identical system who's each unit has operative and complete failure modes. Repairing of the failed unit is done by a server who grabs some time to turn up at the system. Also, the server makes alternate of the failed unit by fresh ones whenever he is not capable to fix the failed unit in a pre precise time. The expressions for different consideration of vital signs have been derived using semi Markov process and RPT. Using arbitrary distributions to all random variable, some numerical results have been obtained to depict the behavior of MTSF, availability and profit with respect to the replacement rate. Gitanjali "Reliability Analysis of Identical unit System with Arbitrary Distribution Subject to Appearance Time of the Server" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26408.pdfPaper URL: https://www.ijtsrd.com/mathemetics/statistics/26408/reliability-analysis-of-identical-unit-system-with-arbitrary-distribution-subject-to-appearance-time-of-the-server/gitanjali
Moment Preserving Approximation of Independent Components for the Reconstruct...rahulmonikasharma
The application of Independent Component Analysis (ICA) has found considerable success in problems where sets of observed time series may be considered as results of linearly mixed instantaneous source signals. The Independent Components (IC’s) or features can be used in the reconstruction of observed multivariate time seriesfollowing an optimal ordering process. For trend discovery and forecasting, the generated IC’s can be approximated for the purpose of noise removal and for the lossy compression of the signals.We propose a moment-preserving (MP) methodology for approximating IC’s for the reconstruction of multivariate time series.The methodologyis based on deriving the approximation in the signal domain while preserving a finite number of geometric moments in its Fourier domain.Experimental results are presented onthe approximation of both artificial time series and actual time series of currency exchange rates. Our results show that the moment-preserving (MP) approximations of time series are superior to other usual interpolation approximation methods, particularly when the signals contain significant noise components. The results also indicate that the present MP approximations have significantly higher reconstruction accuracy and can be used successfully for signal denoising while achieving in the same time high packing ratios. Moreover, we find that quite acceptable reconstructions of observed multivariate time series can be obtained with only the first few MP approximated IC’s.
Queue with Breakdowns and Interrupted Repairstheijes
This paper considers a queue, consisting of a Poisson input stream and a server. The server is subject to breakdowns. The times to failure of the server follows exponential distribution. The failed server requires repair at a facility, which has an unreliable repair crew. The repair times of the failed server follows exponential distribution, but the repair crew also subjects to breakdown when it is repairing. The times to failure of the repair crew is also assumed to be exponentially distributed. This paper obtains the steady-state performance of the queuewith server breakdowns and interrupted repairs.
PERFORMANCE FACTORS OF CLOUD COMPUTING DATA CENTERS USING [(M/G/1) : (∞/GDM O...ijgca
The ever-increasing status of the cloud computing h
ypothesis and the budding concept of federated clou
d
computing have enthused research efforts towards in
tellectual cloud service selection aimed at develop
ing
techniques for enabling the cloud users to gain max
imum benefit from cloud computing by selecting
services which provide optimal performance at lowes
t possible cost. Cloud computing is a novel paradig
m
for the provision of computing infrastructure, whic
h aims to shift the location of the computing
infrastructure to the network in order to reduce th
e maintenance costs of hardware and software resour
ces.
Cloud computing systems vitally provide access to l
arge pools of resources. Resources provided by clou
d
computing systems hide a great deal of services fro
m the user through virtualization. In this paper, t
he
cloud data center is modelled as
queuing system with a single task arrivals
and a task request buffer of infinite capacity.
SOLVING OPTIMAL COMPONENTS ASSIGNMENT PROBLEM FOR A MULTISTATE NETWORK USING ...ijmnct
Optimal components assignment problem subject to system reliability, total lead-time, and total cost
constraints is studied in this paper. The problem is formulated as fuzzy linear problem using fuzzy
membership functions. An approach based on genetic algorithm with fuzzy optimization to sole the
presented problem. The optimal solution found by the proposed approach is characterized by maximum
reliability, minimum total cost and minimum total lead-time. The proposed approach is tested on different
examples taken from the literature to illustrate its efficiency in comparison with other previous methods
SOLVING OPTIMAL COMPONENTS ASSIGNMENT PROBLEM FOR A MULTISTATE NETWORK USING ...ijmnct
Optimal components assignment problem subject to system reliability, total lead-time, and total cost constraints is studied in this paper. The problem is formulated as fuzzy linear problem using fuzzy membership functions. An approach based on genetic algorithm with fuzzy optimization to sole the presented problem. The optimal solution found by the proposed approach is characterized by maximum reliability, minimum total cost and minimum total lead-time. The proposed approach is tested on different examples taken from the literature to illustrate its efficiency in comparison with other previous methods.
𝑴[𝑿]/G/1 with Second Optional Service, Multiple Vacation, Breakdown and RepairIJRES Journal
In this paper, we present a batch arrival non- Markovian queuing model with second optional service, subject to random break downs and multiple vacations. Batches arrive in Poisson stream with mean arrival rate λ, such that all customers demand the first `essential' service, whereas only some of them demand the second `optional' service. The service times of the both first essential service and the second optional service are assumed to follow general (arbitrary) distribution with distribution function 𝐵1(𝑣) and 𝐵2(𝑣) respectively. The server may undergo breakdowns which occur Aaccording to Poisson process with breakdown rate. Once the system encounter break downs it enters the repair process and the repair time is followed by exponential distribution with repair rate𝛼. The server takes vacation each time the system becomes empty and the vacation period is assumed to be exponential distribution. On returning from vacation if the server finds no customer waiting in the system, then the server again goes for vacation until he finds at least one unit in the system. The time-dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been derived explicitly. Also the mean queue length and the mean waiting time have been found explicitly.
Mean Object Size Considering Average Waiting Latency in M/BP/1 SystemIJCNCJournal
This paper deals with the web object size which affects to the service time in multiple access environments. The M/BP/1 model can be considered because packets arrival and web service are Poission and Bound Pareto (BP) distribution respectively. We find mean object size which satisfies that the average waiting latency by deterministic model equals the mean queueing delay of the M/BP/1 model. Performance evaluation shows that the mean web object size is affected by file size bounds and shape parameter of BP distribution, however, the impact of link capacity is not significant. When the system load is low, web object size converges on half the maximum segment size (MSS). Our results can be applied to find mean web object size in the economic web service design.
A fpga implementation of data hiding using lsb matching methodeSAT Journals
Abstract
Data Hiding is one of the familiar methodologies used nowadays to authenticate and resolve the copyrights of the digital data.
This paper discusses the verilog based FPGA implementation of data hiding in grayscale image using the concept of the LSB
Matching technique. In this verilog based data hiding process the secret digital signature is hidden in the host image then
analyzed with the PSNR value and Payload capacity.
Keywords: Data hiding, Least-Significant-bit matching method, Reversible, Gray Scale Image, Real Time
LSB Embedding, FPGA- Implementation etc
A novel scheme for reliable multipath routing through node independent direct...eSAT Journals
Abstract Multipath routing is essential in the wake of voice over IP, multimedia streaming for efficient data transmission. The growing usage of such network requirements also demands fast recovery from network failures. Multipath routing is one of the promising routing schemes to accommodate the diverse requirements of the network with provision such as load balancing and improved bandwidth. Cho et al. introduced a resilient multipath routing scheme known as directed acyclic graphs. These graphs enable multipath routing with all possible edges while ensuring guaranteed recovery from single point of failures. We also built a prototype application that demonstrates the efficiency of the scheme. The simulation results revealed that the scheme is useful and can be used in real world network applications.
Index Terms – Multipath routing, failure recovery, directed acyclic graphs
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
This work constructs the membership functions of the system characteristics of a batch-arrival queuing system with multiple servers, in which the batch-arrival rate and customer service rate are all fuzzy numbers. The -cut approach is used to transform a fuzzy queue into a family of conventional crisp queues in this context. By means of the membership functions of the system characteristics, a set of parametric nonlinear programs is developed to describe the family of crisp batch-arrival queues with multiple servers. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the system characteristics are expressed and governed by the membership functions, the fuzzy batch-arrival queues with multiple servers are represented more accurately and the analytic results are more useful for system designers and practitioners.
Reliability Analysis of Identical unit System with Arbitrary Distribution Sub...ijtsrd
In this research paper, we analyzed the reliability measures of two units identical system who's each unit has operative and complete failure modes. Repairing of the failed unit is done by a server who grabs some time to turn up at the system. Also, the server makes alternate of the failed unit by fresh ones whenever he is not capable to fix the failed unit in a pre precise time. The expressions for different consideration of vital signs have been derived using semi Markov process and RPT. Using arbitrary distributions to all random variable, some numerical results have been obtained to depict the behavior of MTSF, availability and profit with respect to the replacement rate. Gitanjali "Reliability Analysis of Identical unit System with Arbitrary Distribution Subject to Appearance Time of the Server" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26408.pdfPaper URL: https://www.ijtsrd.com/mathemetics/statistics/26408/reliability-analysis-of-identical-unit-system-with-arbitrary-distribution-subject-to-appearance-time-of-the-server/gitanjali
Moment Preserving Approximation of Independent Components for the Reconstruct...rahulmonikasharma
The application of Independent Component Analysis (ICA) has found considerable success in problems where sets of observed time series may be considered as results of linearly mixed instantaneous source signals. The Independent Components (IC’s) or features can be used in the reconstruction of observed multivariate time seriesfollowing an optimal ordering process. For trend discovery and forecasting, the generated IC’s can be approximated for the purpose of noise removal and for the lossy compression of the signals.We propose a moment-preserving (MP) methodology for approximating IC’s for the reconstruction of multivariate time series.The methodologyis based on deriving the approximation in the signal domain while preserving a finite number of geometric moments in its Fourier domain.Experimental results are presented onthe approximation of both artificial time series and actual time series of currency exchange rates. Our results show that the moment-preserving (MP) approximations of time series are superior to other usual interpolation approximation methods, particularly when the signals contain significant noise components. The results also indicate that the present MP approximations have significantly higher reconstruction accuracy and can be used successfully for signal denoising while achieving in the same time high packing ratios. Moreover, we find that quite acceptable reconstructions of observed multivariate time series can be obtained with only the first few MP approximated IC’s.
Queue with Breakdowns and Interrupted Repairstheijes
This paper considers a queue, consisting of a Poisson input stream and a server. The server is subject to breakdowns. The times to failure of the server follows exponential distribution. The failed server requires repair at a facility, which has an unreliable repair crew. The repair times of the failed server follows exponential distribution, but the repair crew also subjects to breakdown when it is repairing. The times to failure of the repair crew is also assumed to be exponentially distributed. This paper obtains the steady-state performance of the queuewith server breakdowns and interrupted repairs.
Delayed feedback control of nonlinear phenomena in indirect field oriented co...eSAT Journals
Abstract The Indirect Field Oriented Controlled (IFOC) Induction Motor often shows the nonlinearity in time domain response of its speed and current due to the instability of the periodic orbits. The system undergoes Hopf bifurcation which is essentially caused by the unstable equilibrium points. In this work our aim is directed towards the stabilization of the unstable periodic orbits (UPOs) by continuously perturbing the system by a time delayed version of any state variable in a feedback form. The clarification of controlling the system from any periodic even chaotic mode to any stable periodic mode is presented by both numerical analysis and software simulation. Index Terms: IFOC-IM, Hopf Bifurcation, Time Delayed Feedback Control, Control of Nonlinear Dynamics.
Delayed feedback control of nonlinear phenomena in indirect field oriented co...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Discrete Time Batch Arrival Queue with Multiple VacationsIJERDJOURNAL
ABSTRACT:- In this paper we consider a discrete time batch arrival queueing system with multiple vacations. It is assume that the service of customers arrived in the system between a fixed intervals of time after which the service goes on vacations after completion of one service of cycle is taken up at the boundaries of the fixed duration of time. This is the case of late arrival. In case of early arrival i.e. arrival before the start of next cycles of service. If the customer finds the system empty, it is served immediately. We prove the Stochastic decomposition property for queue length and waiting time distribution for both the models.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Fuzzy Retrial Queues with Priority using DSW Algorithmijceronline
In this paper we study the priority queueing model under fuzzy environment.It optimize a fuzzy priority queueing model (preemptive priority, non-preemptive priority) in which arrival rate ,service rate,retrial rate are fuzzy numbers.Approximate method of Extension namely DSW (Dong, Shah and Wong) algorithm is used to define membership functions of the performance measures of priority queuing system . DSW algorithm is based on the cut representation of fuzzy sets in a standard interval analysis. Numerical example is also illustrated to check the validity of the model.
Similar to The FM / FM / 1queue with Single Working Vacation (20)
Data Mining is a significant field in today’s data-driven world. Understanding and implementing its concepts can lead to discovery of useful insights. This paper discusses the main concepts of data mining, focusing on two main concepts namely Association Rule Mining and Time Series Analysis
A Review on Real Time Integrated CCTV System Using Face Detection for Vehicle...rahulmonikasharma
We are describes the technique for real time human face detection and counting the number of passengers in vehicle and also gender of the passengers.The Image processing technology is very popular,now at present all are going to use it for various purpose. It can be applied to various applications for detecting and processing the digital images. Face detection is a part of image processing. It is used for finding the face of human in a given area. Face detection is used in many applications such as face recognition, people tracking, or photography. In this paper,The webcam is installed in public vehicle and connected with Raspberry Pi model. We use face detection technique for detecting and counting the number of passengers in public vehicle via webcam with the help of image processing and Raspberry Pi.
Considering Two Sides of One Review Using Stanford NLP Frameworkrahulmonikasharma
Sentiment analysis is a type of natural language processing for tracking the mood of the public about a particular product or a topic and is useful in several ways. Polarity shift is the most classical task which aims at classifying the reviews either positive or negative. But in many cases, in addition to the positive and negative reviews, there still many neutral reviews exist. However, the performance sometimes limited due to the fundamental deficiencies in handling the polarity shift problem. We propose an Improvised Dual Sentiment Analysis (IDSA) model to address this problem for sentiment classification. We first propose a novel data expansion technique by creating sentiment-reversed review for each training and test review. We develop a corpus based method to construct a pseudo-antonym dictionary. It removes DSA’s dependency on an external antonym dictionary for review reversion. We conduct a range of experiments and the results demonstrates the effectiveness of DSA in addressing the polarity shift in sentiment classification. .
A New Detection and Decoding Technique for (2×N_r ) MIMO Communication Systemsrahulmonikasharma
The requirements of fifth generation new radio (5G- NR) access networks are very high capacity and ultra-reliability. In this paper, we proposed a V-BLAST2 × N_r MIMO system that is analyzed, improved, and expected to achieve both very high throughput and ultra- reliability simultaneously.A new detection technique called parallel detection algorithm is proposed. The performance of the proposed algorithm compared with existing linear detection algorithms. It was seen that the proposed technique increases the speed of signal transmission and prevents error propagation which may be present in serial decoding techniques. The new algorithm reduces the bit error probability and increases the capacity simultaneouslywithout using a standard STC technique. However, it was seen that the BER of systems using the proposed algorithm is slightly higher than a similar system using only STC technique. Simulation results show the advantages of using the proposed technique.
Broadcasting Scenario under Different Protocols in MANET: A Surveyrahulmonikasharma
A wireless network enables people to communicate and access applications and information without wires. This provides freedom of movement and the ability to extend applications to different parts of a building, city, or nearly anywhere in the world. Wireless networks allow people to interact with e-mail or browse the Internet from a location that they prefer. Adhoc Networks are self-organizing wireless networks, absent any fixed infrastructure. broadcasting of data through proper channel is essential. Various protocols are designed to avoid the loss of data. In this paper an overview of different broadcast protocols are discussed.
Sybil Attack Analysis and Detection Techniques in MANETrahulmonikasharma
Security is important for many sensor network applications. A particularly harmful attack against sensor and ad hoc networks is known as the Sybil attack [6], where a node Illegitimately claims multiple identities.Mobility cause a main problem when we talk about security in Mobile Ad-hoc networks. It doesn’t depend on fixed architecture, the nodes are continuously moving in a random fashion. In this article we will focus on identifying the Sybil attack in MANET. It uses air medium for communication so it is more prone to the attack. Sybil attack is one in which single node present multiple fake identities to other nodes, which cause destruction.
A Landmark Based Shortest Path Detection by Using A* and Haversine Formularahulmonikasharma
In 1900, less than 20 percent of the world populace lived in cities, in 2007, fair more than 50 percent of the world populace lived in cities. In 2050, it has been anticipated that more than 70 percent of the worldwide population (about 6.4 billion individuals) will be city tenants. There's more weight being set on cities through this increment in population [1]. With approach of keen cities, data and communication technology is progressively transforming the way city regions and city inhabitants organize and work in reaction to urban development. In this paper, we create a nonspecific plot for navigating a route throughout city A asked route is given by utilizing combination of A* Algorithm and Haversine equation. Haversine Equation gives least distance between any two focuses on spherical body by utilizing latitude and longitude. This least distance is at that point given to A* calculation to calculate minimum distance. The method for identifying the shortest path is specify in this paper.
Processing Over Encrypted Query Data In Internet of Things (IoTs) : CryptDBs,...rahulmonikasharma
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1. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 648 – 654
_______________________________________________________________________________________________
648
IJRITCC | July 2017, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
The FM / FM / 1queue with Single Working Vacation
G. Kannadasan1
Department of Mathematics
Annamalai University
Annamalainager-608002,India
klsk.g.21@gmail.com1
N. Sathiyamoorthi2
Department of Mathematics
Annamalai University
Annamalainager-608002, India
n.satyamurthi@gmail.com2
Abstract—In this paper, we study aFM / FM / 1 queue with single working vacation for this fuzzy queueing model. We obtain some system
characteristic such as the number of customer in the system in steady state, the virtual time of a customer in the system, the server is in idle
period, the server is in regular busy period. Finally, numerical results for all the performance measure are presented to show the effects of system
parameters.
Keywords-FM / FM / 1 queue, Single working vacation, Server is in idle period, Server is in regular busy period, The virtual time of a customer
in the system
__________________________________________________*****_________________________________________________
I. INTRODUCTION
During last two decades, vacation queue havebeen
investigated extensively because of their applications in
computer systems, communication networks, production
managing and so forth. In various vacation queue models, the
server completely stops serving customers during a vacation,
but may perform other supplementary jobs. Proposing of
various vacation policies provides more flexibility for optional
design and operation control of the system. The details can be
seen in the monographs of Takagi [13] and Tian and Zhang
[15], the surveys of Doshi [2] and Teghem [14].
Recently, Servi and Finn [13] introduced a class of semi-
vacation polices: the server works at a lower rate rather than
completely stopping service during a vacation. Such a vacation
is called a working vacation (wv). Part of servers keeps the
system operating in a lower rate and the other parts of break or
accomplish else assistant work during a vacation. If service
rate degenerates into zero in a working vacation, then the
working vacation queue becomes a classical vacation queue
model. Therefore, the working vacation queue is an extension
of classical vacation queue. Tian and Zhang [16] studied multi
server queues with partial server’s vacation where vacation
servers completely stop service.
There is quite difference between working vacation queue and
classical queue. During a vacation, customers in the forever
may finish service and depart the system, however, customers
in the latter can impossibly depart the system. On the other
hand, during a vacation, the number of customers in the latter
can only increases. Therefore, the working vacation models
have more complicated modalities and the analysis of this kind
of models is more difficult then classical vacation queue.
Liu, Xu and Tian [7] gave simple explicit expressions of
distribution for the stationary queue length and waiting time
which have intuituioustic probability sense. Furthermore, the
authors got stochastic decomposition structures of stationary
indices, derived the distributions of additional queue length
and additional delay and obtained expected regular busy
period and expected busy cycle. Kin, Choi and Chae [5], Wu
and Takagi [18] generalized the work of servi and Finn [13] to
an M/G/1 queue with multiple working vacations. Bala [1]
investigated a GI/M/1 queue with multiple working vacations.
K.Julia Rose Mery and T.Gokilavani [4] investigate
the performance measure of an 𝑀 𝑋
/M/1 Multiple Working
Vacation (MWV) queuing model in a fuzzy environment.
Mary George and Jayalekshmi [9] studied on the analysis of
G/M(n)/1/k queuing system with multiple exponential
vacations and vacations of fuzzy length. J.Pavithra and K.Julia
Rose Mary [11] gave the analysis of FM/M (a,b)/1/MWV
queuing model. The analysis of the general bulk service
queuing model to find the mean queue length probability that
the system is in vacation and the probability that the system is
in busy state are expressed in terms of crisp value for
FM/M(a,b)/1 under multiple working vacation with fuzzy
numbers. R.Ramesh and S.Kumara G Ghuru [12] constructs
the membership function of the system characteristics of a
batch-arrival queuing system with multiple servers, in which
the batch-arrival rate and customer service rate are all fuzzy
numbers.
II. THE CRISP MODEL
Introducing a single working vacation policy into a
classical / /1M M queue with arrival rate and service
rate b in a regular busy period. The server beings a working
vacation of random length V at the instant when the queue
becomes empty, and vacation duration V follows an
exponential distribution with Parameter . During a working
vacation an arriving customer is served at a rate of . When
a vacation ends, if there are customers in the queue, the server
changes service rate from bto , and a regular busy period
starts. Otherwise, the server enters idle period, and a new
regular busy period starts when a customer arrival occurs.
Working vacation V is a operation period in a lower rate.
When the number of customers in the system is relatively few,
2. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 648 – 654
_______________________________________________________________________________________________
649
IJRITCC | July 2017, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
we set a lower rate operation period in order to economize
operation cost together with serving customers. Therefore, this
single working vacation policy has practical significance in
optimal design of the system.We assume that inter arrival
times, service times, and working vacation times are mutually
independent. In addition, the service order is first in first out
(FIFO).
Let ( )Q t be the number of customers in the system
at time t, and let
1,
0, " "
( ) =
" "the system is not i
the sys
n a working
tem is in a working vacation period a
vacation period at tim
t time t
J
e
t
t
Then, ( ), ( )Q t J t is a Markov process with the state space
= (0,0) ( , ) / 0, = 0,1k j k j .
Where the state (0,1) denotes that the system is in idle
period; state ( ,1), 1k k indicates that the system is in
regular busy period; state ( ,0), 0k k indicates that the
system is in working vacation period and there are k customers
in the queue.
III. THE MODEL IN FUZZY ENVIRONMENT
In this section the arrival rate , service rate b in
a regular busy period, working vacation an arriving customer
is served at a rate of , working vacation are assumed to
be fuzzy numbers respectively. Now:
, ( ); ( )w w w S
, , ( ); ( )b
x x x S ,
, ( ); ( )y y y S and , ( ); ( )z z z S
Where, ( )S , ( )S , ( )S and ( )S are the universal
sets of the arrival rate, service rate in a regular busy period,
working vacation an arriving customer is served at a rate, and
working vacation respectively. Define ( , , , )f w x y z as the
system performance measure related to the above defined
fuzzy queuing model which depends on the fuzzy membership
function ( , , , ).f
Applying Zadeh's extension principle (1978) [15] the
membership function of the performance measure
( , , , )f can be defined as:
( , , , )
( )
( )
( )
( )
( ) sup ( ), ( ), ( ), ( )/ ( , , , )f
w S
x S
y S
z S
H w x y z H f w x y z
(1)
If the - cuts of ( , , , )f degenerate to some fixed
value, then the system performance is a crisp number,
otherwise it is a fuzzy number.
The Number of Customer in the System in Steady State
( ) ( )d
b
E L E Q
2
( ) 2 ( ( ) 4 )
2b
1
2
( ( ) 4 )
2
b
b
2
2
( ( ) 4 )
2 ( ( ) 4 )
b
b
The Virtual Time of a Customer in the System
2
3 2
( )(2 ( ( ) 4 ))1
( )
2b b
E W
1
2
( ) 4
2
b
b
2
2
( ) 4
(2 ( ( ) 4 ))
b
b
The server is in idle period
2
0
2 ( ( ) 4 )
2
b
b
P
2
2 ( ( ) 4 )
2
b
2
2
( ( ) 4 )
2 [ 2 ( ) 4 ]
b
b b b
1
2
2 ( ( ) 4 )
2 b
The Server is in Regular Busy Period
2
1 2
( ( ) 4 )
2 ( ( ) 4 )b
P
3. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 648 – 654
_______________________________________________________________________________________________
650
IJRITCC | July 2017, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
2 2
( ( ) )(2 ( ( ) 4 ))
2 b
2
2 ( ( ) 4 )
2
b
b
b
b
2
2
( ( ) 4 )
2 ( ( ) 4 )b b
1
2
2 ( ( ) 4 )
2 b
Under the study state condition
.We obtain the
membership function of some performance measures namely
the number of customer in the system in steady state, the
virtual time of a customer in the system,the server is in idle
period, the server is in regular busy period.
For the system in terms of membership function are:
( )
( )
( )
( )
( )
( ) sup ( ), ( ), ( ), ( ) /E L
w S
x S
y S
z S
A w x y z A
(2)Where,
w
A
x w
2
( )(2 ( ( ) 4 ))
2
z w y w z y w z y wy
wy
1
2
( ( ) 4 )
2
w z y w z y wy x y
y x
2
2
( ) 4
2 ( ( ) 4 )
w z y w z y wyx y
x y w z y w z y wy
( )
( )
( )
( )
( )
( ) sup ( ), ( ), ( ), ( ) /E W
w S
x S
y S
z S
B w x y z B
(3)
Where,
2
3 2
( )(2 ( ( ) 4 ))1
2
z w y w z y w z y wy
B
x x w wy
2
( ) 4
2
w z y w z y wy x y
y y
2
2
( ) 4
(2 ( ( ) ))
w z y w z y wyx y
x w y w z y w z y
0
( )
( )
( )
( )
( ) sup ( ), ( ), ( ), ( ) /P
w S
x S
y S
z S
C w x y z C
(4)
Where,
C
x w
x
2
2 ( ( ) 4 )
2
yz zw w z y w z y wyx z
z wy
1
2
2 ( ( ) 4 )
2
zy z w z y w z y wy
yx
1
( )
( )
( )
( )
( ) sup ( ), ( ), ( ), ( ) /P
w S
x S
y S
z S
D w x y z D
(5)
Where,
2
2
( ( ) 4 )
2 ( ( ) 4 )
z w z y w z y wy
D
xy w z y w z y wy
2 2
( ( ) 4 ).(2 ( ( ) 4 ))
2
z w z y w z y wy y w z y w z y wy
xy
2
2 ( ( ) 4 )
2
zy z w z y w z y wyx w x w
x wy x
x
2
2
( ( ) 4 )
2 ( ( ) 4 )
z w z y w z y wy
zy z w z y w z y wy
1
2
2 ( ( ) 4 )
2
zy z w z y w z y wy
xy
4. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 648 – 654
_______________________________________________________________________________________________
651
IJRITCC | July 2017, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
Using the fuzzy analysis technique explained we can find the
membership of 0 1( ), ( ),E L E W P and P as a function of
the parameter , thus the -cut approach can be used to
develop the membership function of 0( ), ( ),E L E W P and
1P .
Performance of measure
The following Performance measure are studied for this model
in fuzzy environment.
The Number of Customers in the System in Steady State
Based on Zadeh’s extension Principle ( ) ( )E L A is the
supremum of minimum over
( ), ( ), ( ), ( )}w x y z
to satisfying
( ) ( ) , 0 1E L A .
The following four cases arise:
Case ( )i ( ) , ( ) , ( ) , ( )w x y z
,
Case ( )ii ( ) , ( ) , ( ) , ( )w x y z
,
Case ( )iii ( ) , ( ) , ( ) , ( )w x y z
,
Case ( )iv ( ) , ( ) , ( ) , ( )w x y z
.
For case ( )i the lower and upper bound of - cuts of ( )E L
can be obtained through the corresponding
parametric non-linear programs:
1
[ ( )] minL
E L A
& 1
[ ( )] maxU
E L A
.
Similarly, we can calculate the lower and upper bounds of the
-cuts of ( )E L for the case ( ),( ) ( )&ii iii iv .By
considering the cases, simulatuosly the lower and upper
bounds of the -cuts of ( )E L can be written as:
[ ( )] minL
E L A
& [ ( )] maxU
E L A
such that,
, , ,L U L U L U L U
a aw w w x x x y y y z z z .
If both ( ( ))L
E L and ( ( ))U
E L are invertible with respect to
, the left and right shape function,
1
( ) [( ( )) ]L
L A E L
and
1
( ) [( ( )) ]U
R A E L
can be
derived from which the membership function ( )
( )E L
A can
be constructed as:
=0 =0
=1 =1( )
=0 =0
( ), ( ( )) ( ( ))
( ) = 1, ( ( )) ( ( ))
( ), ( ( )) ( ( ))
L U
L U
E L
L U
L A E L A E L
A E L A E L
R A E L A E L
(6)In
the same way as we said before we get the following results.
The Virtual time of a Customer in the System
=0 =0
=1 =1( )
=0 =0
( ), ( ( ) ( ( )
( ) = 1, ( ( ) ( ( )
( ), ( ( ) ( ( )
L U
L U
E W
L U
L B E W B E W
B E W B E W
R B E W B E W
(7)
The Server is in idle period
0
0 =0 0 =0
0 =1 0 =1
0 =0 0 =0
( ), ( ) ( )
( ) = 1, ( ) ( )
( ), ( ) ( )
L U
L U
P
L U
L C P C P
C P C P
R C P C P
(8)
The Server is in Regular Busy Period
1
1 =0 1 =0
1 =1 1 =1
1 =0 1 =0
( ), ( ) ( )
( ) = 1, ( ) ( )
( ), ( ) ( )
L U
L U
P
L U
L D P D P
D P D P
R D P D P
(9)
Numerical study
The Number of Customers in the System in Steady State
Suppose the arrival rate , the service rate , the vacation
rate & busy period are assumed to be trapezoidal fuzzy
numbers described by:
[11,12,13,14] , [91,92,93,94] ,
[161,162,163,164] & [71,72,73,74] per mins
respectively. Then:
( )
11, 11 12
( ) min{ ( ), 11 , 12 13 ,
14 , 13 14
w s
w w
w s w
w w
( )
11, 11 12
max{ ( ), 11 , 12 13 .
14 , 13 14
w s
w w
w s w
w w
(i.e.).,
( ) [11 ,14 ], ( ) [91 ,94 ],
( ) [161 ,164 ] &
( ) [71 ,74 ].
It is clear that, when , , &U U U U
w w x x y y z z ,
A attains its maximum value and when
, , &L L L L
w w x x y y z z , A attains its
minimum value.From the generated for the given input value
of &, , ,v .
i) For fixed values of &, ,w x y A decreases as z increase.
ii) For fixed values of &, ,x y z A decreases as w
increase.
5. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 648 – 654
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652
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iii) For fixed values of &, ,y z w A decreases as x
increase.
iv) For fixed values of &, ,z w x A decreases as y
increase.
The smallest value of occurs when w-takes its lower bound.
i.e)., 11w and x y and z, take their upper bounds given
by 94 , 164 ,x and y 74and z
respectively. And maximum value of ( )E L occurs when
14 , 91 ,w x 161 , 71 .y z If
both &( ) ( )L
UE L E L
are invertible with respect to '
then the left shape function
1
( ) [ ( ) ]L
L A E L
and right
shape function
1
( ) [ ( ) ]U
R A E L
can be obtained and from
which the membership function ( )
( )E L
A can be constructed
as:
1 2
2 3( )
3 4
( ),
( ) = 1,
( ),
E L
L A A A A
A A A A
R A A A A
(10)
The values of 1 2 3 4, , &A A A A as obtained from (10) are:
( )
( ), 0.0935 0.1011
( ) = 1, 0.1011 0.1143
( ), 0.1143 0.1244
E L
L A A
A A
R A A
In the same way as we said before we get the following
results.
The Virtual time of a Customer in the System
The smallest value of ( )E W occurs, when w take its lower
bound.
i,e)., &11w , &y z s take their upper bounds.
Given by 94 , 164x y 4& 7z
respectively. And maximum value of ( )E W occurs ,when
14 , 91 ,w x &161 71 .y z if
both &( ) ( )L U
E W W are invertible with respect to
then left shape function
1
( ) [( ( ) ]L
L B E W
and right shape
function
1
( ) [( ( ) ]U
R B E W
can be obtained from which
the membership function ( ( )
( )E W
B Can be written as:
1 2
2 3( )
3 4
( ),
( ) = 1,
( ),
E W
L B B B B
B B B B
R B B B B
(11)
The values of 1 2 3 4, , &B B B B as obtained from (11) are:
( )
( ), 0.2874 0.7687
( ) = 1, 0.7687 1.2691
( ), 1.2691 1.8571
E W
L B B
B B
R B B
The Server is in idle period
The smallest values of 0P occurs when w-take its lower
bound.
i.e)., 11 , ,& , &w x y z take their upper bounds
given by 94 , 164x y & 74z
respectively. And maximum value of 0P occurs when
14 , 91 ,w x 161y 1& 7 .z If
both 0 0&( ) ( )L U
P P are invertible with respect to then
the left shape function
1
0( ) [( ) ]L
L C P
and the right shape
function
1
0( ) [( ) ]U
R C P
Can be obtained from which the
membership function
0( )
( )P
C Can be written as:
0
1 2
2 3
3 4
( ),
( ) = 1,
( ),
P
L C C C C
C C C C
R C C C C
(12)
The values of 1 2 3 4, , &C C C C as obtained from (12) are
0
( ), 0.2741 0.3258
( ) = 1, 0.3258 0.3612
( ), 0.3612 0.4993
P
L C C
C C
R C C
The Server is in Regular Busy Period
The smallest value of 1P occurs, when x take its lower bound.
i,e)., 11 , ,& , &w x y z take their upper bounds
given b 94 , 164 &x y 74z
respectively. And maximum value of 1P occurs when
14 , 91 161w x y 71 .& z
If both 1 1&( ) ( )L U
P P are invertible with respect to then
the left shape function
1
1( ) [( ) ]L
L D P
and the right shape
function
1
1( ) [( ) ]U
R D P
can be obtained from which the
membership function
1( )
( )P
D Can be written as:
1
1 2
2 3
3 4
( ),
( ) = 1,
( ),
P
L D D D D
D D D D
R D D D D
(13)
The values of 1 2 3 4, , &D D D D as obtained from (13) are:
6. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 648 – 654
_______________________________________________________________________________________________
653
IJRITCC | July 2017, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
1
( ), 0.8654 0.8896
( ) = 1, 0.8896 0.8925
( ), 0.8925 0.9079
P
L D D
D D
R D D
Further by fixing the vacation rate by a crisp value 𝜃=76.4 and
𝑣=161.3 taking arrival rate 𝜆=[11,12,13,14], service rate
=[91,92,93,94] both trapezoidal fuzzy numbers the values of
the number of system in the steady state are generated and are
plotted in the figure 1, it can be observed that as 𝜆 increases
the number of system in steady state increases for the fixed
value of the service rate, whereas for fixed value of arrival
rate, the number of system in steady state decreases as service
rate increases. Similar conclusion can be obtained for the case
=73.6, 𝑣=163.8 Again for fixed values of 𝜆=[11,12,13,14],
=[91,92,93,94] the graphs of the virtual time of a customer
in the system are drawn in figure 2 respectively, these figure
show that as arrival rate increases that the virtual time also
increases, while the virtual time decreases as the service rate
increases in both the case.
It is also observed from the data generated that the
membership value of the number of system in steady state is
1.7 and the membership value of the mean virtual time 1.85
when the ranges of arrival rate, service rate, and the vacation
rate lie in the intervals (12,13.4), (93,93.6), & (161.8,162.4)
respectively.
ACKNOWLEDGMENT
We would like to thank the referees for valuable comments.
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7. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 648 – 654
_______________________________________________________________________________________________
654
IJRITCC | July 2017, Available @ http://www.ijritcc.org
_______________________________________________________________________________________