This document analyzes a single server queueing system with fixed batch service, multiple vacations, and the possibility of catastrophes. The system uses a Poisson arrival process and exponential service times. The server provides service in batches of size k. If fewer than k customers remain after service, the server takes an exponential vacation. If a catastrophe occurs, all customers are lost and the server vacations. The document derives the generating functions and steady state probabilities for the number of customers when the server is busy or vacationing. It also provides closed form solutions for performance measures like mean number of customers and variance. Numerical studies examine these measures for varying system parameters.
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.
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.
Talks about what is Queuing and its application, practical life usage, with a complex problem statement with its solution. Pre-emptive and non-preemptive queue models and its algorithm.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, 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.
In the classical model, the fundamental building block is represented by bits exists in two states a 0 or a 1. Computations are done by logic gates on the bits to produce other bits. By increasing the number of bits, the complexity of problem and the time of computation increases. A quantum algorithm is a sequence of operations on a register to transform it into a state which when measured yields the desired result. This paper provides introduction to quantum computation by developing qubit, quantum gate and quantum circuits.
A QUANTITATIVE ANALYSIS OF HANDOVER TIME AT MAC LAYER FOR WIRELESS MOBILE NET...ijwmn
Extensive studies have been carried out for reducing the handover time of wireless mobile network at
medium access control (MAC) layer. However, none of them show the impact of reduced handover time
on the overall performance of wireless mobile networks. This paper presents a quantitative analysis to
show the impact of reduced handover time on the performance of wireless mobile networks. The proposed
quantitative model incorporates many critical performance parameters involve in reducing the handover
time for wireless mobile networks. In addition, we analyze the use of active scanning technique with
comparatively shorter beacon interval time in a handoff process. Our experiments verify that the active
scanning can reduce the overall handover time at MAC layer if comparatively shorter beacon intervals are
utilized for packet transmission. The performance measures adopted in this paper for experimental
verifications are network throughput under different network loads.
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.
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.
Talks about what is Queuing and its application, practical life usage, with a complex problem statement with its solution. Pre-emptive and non-preemptive queue models and its algorithm.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, 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.
In the classical model, the fundamental building block is represented by bits exists in two states a 0 or a 1. Computations are done by logic gates on the bits to produce other bits. By increasing the number of bits, the complexity of problem and the time of computation increases. A quantum algorithm is a sequence of operations on a register to transform it into a state which when measured yields the desired result. This paper provides introduction to quantum computation by developing qubit, quantum gate and quantum circuits.
A QUANTITATIVE ANALYSIS OF HANDOVER TIME AT MAC LAYER FOR WIRELESS MOBILE NET...ijwmn
Extensive studies have been carried out for reducing the handover time of wireless mobile network at
medium access control (MAC) layer. However, none of them show the impact of reduced handover time
on the overall performance of wireless mobile networks. This paper presents a quantitative analysis to
show the impact of reduced handover time on the performance of wireless mobile networks. The proposed
quantitative model incorporates many critical performance parameters involve in reducing the handover
time for wireless mobile networks. In addition, we analyze the use of active scanning technique with
comparatively shorter beacon interval time in a handoff process. Our experiments verify that the active
scanning can reduce the overall handover time at MAC layer if comparatively shorter beacon intervals are
utilized for packet transmission. The performance measures adopted in this paper for experimental
verifications are network throughput under different network loads.
Analysis of a Batch Arrival and Batch Service Queuing System with Multiple Va...IJMER
This paper concerns the queuing system MX
/G1, B/1, to which the customers are assumed
to arrive in batches of random size X according to a compound Poisson process and also are served in
batches. As soon as the system becomes empty, the server leaves for a vacation of random length V. If
no customers are available for service after returning from that vacation, the server keeps on taking
vacations till he finds at least one customer in the queue, then immediately begins to serve the
customers up to the service capacity B. If more than B customers are present when the server returns
from a vacation, the first B customers are taken into service. If fewer than B customers are present, all
waiting customers go into service. Late arrivals are not allowed to join the ongoing service. The steady
state behavior of this queuing system is derived by an analytic approach to study the queue size
distribution at a random point as well as a departure point of time under multiple vacation policy. It
may be noted that the results in [5] and [7] can be obtained as special cases from the results in this
paper.
Time Domain Signal Analysis Using Modified Haar and Modified Daubechies Wavel...CSCJournals
In this paper, time signal analysis and synthesis based on modified Haar and modified Daubechies wavelet transform is proposed. The optimal results for both analysis and synthesis for time domain signals were obtained with the use of the modified Haar and modified Daubechies wavelet transforms. This paper evaluates the quality of filtering using the modified Haar and modified Daubechies wavelet transform. Analysis and synthesis of the time signals is performed for 10 samples and the signal to noise ratio (SNR) of around 25-40 dB is obtained for modified Haar and 24-32 dB for modified Daubechies wavelet. We have observed that as compared to standard Haar and standard Daubechies mother wavelet our proposed method gives better signal quality, which is good for time varying signals.
ER Publication,
IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
Research Papers,
Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
Congestion Control through Load Balancing Technique for Mobile Networks: A Cl...IDES Editor
The Optimal Routing Path (ORP) for mobile
cellular networks is proposed in this paper with the
introduction of cluster-based approach. Here an improved
dynamic selection procedure is used to elect cluster head.
The cluster head is only responsible for the computation of
least congested path. Hence the delay is reduced with the
significant reduction on the number of backtrackings.
Experimental study of Data clustering using k- Means and modified algorithmsIJDKP
The k- Means clustering algorithm is an old algorithm that has been intensely researched owing to its ease
and simplicity of implementation. Clustering algorithm has a broad attraction and usefulness in
exploratory data analysis. This paper presents results of the experimental study of different approaches to
k- Means clustering, thereby comparing results on different datasets using Original k-Means and other
modified algorithms implemented using MATLAB R2009b. The results are calculated on some performance
measures such as no. of iterations, no. of points misclassified, accuracy, Silhouette validity index and
execution time
Joint Timing and Frequency Synchronization in OFDMidescitation
With the advent of OFDM for WLAN
communications, as exemplified by IEEE 802.11a, it has become
imperative to have efficient and reliable synchronization
algorithms for OFDM WLAN receivers. The main challenges
with synchronization deal with the frequency offset and delay
spread introduced by the wireless channel. In this paper,
research is done into OFDM timing synchronization and
frequency synchronization techniques.
Testing of Matrices Multiplication Methods on Different ProcessorsEditor IJMTER
There are many algorithms we found for matrices multiplication. Until now it has been
found that complexity of matrix multiplication is O(n3). Though Further research found that this
complexity can be decreased. This paper focus on the algorithm and its complexity of matrices
multiplication methods.
Probability-Based Analysis to Determine the Performance of Multilevel Feedbac...Eswar Publications
Operating System may work on different types of CPU scheduling algorithms with different mechanism and concepts. The Multilevel Feedback Queue (MLFQ) Scheduling manages a variety of processes among various queues in a better and efficient manner. CPU scheduler appears transition mechanism over various queues. This paper is presented with various schemes of under a probability-based model. The scheduler has random movement over queues with given time quantum. This paper designs general transition model for its functioning
and justifying comparison under different scheduling schemes through a simulation study applied on different data sets in particular cases.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Hamming Distance and Data Compression of 1-D CAcsitconf
In this paper an application of von Neumann correction technique to the output string of some
chaotic rules of 1-D Cellular Automata that are unsuitable for cryptographic pseudo random
number generation due to their non uniform distribution of the binary elements is presented.
The one dimensional (1-D) Cellular Automata (CA) Rule space will be classified by the time run
of Hamming Distance (HD). This has the advantage of determining the rules that have short
cycle lengths and therefore deemed to be unsuitable for cryptographic pseudo random number
generation. The data collected from evolution of chaotic rules that have long cycles are
subjected to the original von Neumann density correction scheme as well as a new generalized
scheme presented in this paper and tested for statistical testing fitness using Diehard battery of
tests. Results show that significant improvement in the statistical tests are obtained when the
output of a balanced chaotic rule are mutually exclusive ORed with the output of unbalanced
chaotic rule that have undergone von Neumann density correction.
Hamming Distance and Data Compression of 1-D CAcscpconf
In this paper an application of von Neumann correction technique to the output string of some chaotic rules of 1-D Cellular Automata that are unsuitable for cryptographic pseudo random number generation due to their non uniform distribution of the binary elements is presented.The one dimensional (1-D) Cellular Automata (CA) Rule space will be classified by the time run of Hamming Distance (HD). This has the advantage of determining the rules that have short cycle lengths and therefore deemed to be unsuitable for cryptographic pseudo random number generation. The data collected from evolution of chaotic rules that have long cycles are subjected to the original von Neumann density correction scheme as well as a new generalized scheme presented in this paper and tested for statistical testing fitness using Diehard battery of tests. Results show that significant improvement in the statistical tests are obtained when the output of a balanced chaotic rule are mutually exclusive ORed with the output of unbalanced
chaotic rule that have undergone von Neumann density correction.
Analysis of a Batch Arrival and Batch Service Queuing System with Multiple Va...IJMER
This paper concerns the queuing system MX
/G1, B/1, to which the customers are assumed
to arrive in batches of random size X according to a compound Poisson process and also are served in
batches. As soon as the system becomes empty, the server leaves for a vacation of random length V. If
no customers are available for service after returning from that vacation, the server keeps on taking
vacations till he finds at least one customer in the queue, then immediately begins to serve the
customers up to the service capacity B. If more than B customers are present when the server returns
from a vacation, the first B customers are taken into service. If fewer than B customers are present, all
waiting customers go into service. Late arrivals are not allowed to join the ongoing service. The steady
state behavior of this queuing system is derived by an analytic approach to study the queue size
distribution at a random point as well as a departure point of time under multiple vacation policy. It
may be noted that the results in [5] and [7] can be obtained as special cases from the results in this
paper.
Time Domain Signal Analysis Using Modified Haar and Modified Daubechies Wavel...CSCJournals
In this paper, time signal analysis and synthesis based on modified Haar and modified Daubechies wavelet transform is proposed. The optimal results for both analysis and synthesis for time domain signals were obtained with the use of the modified Haar and modified Daubechies wavelet transforms. This paper evaluates the quality of filtering using the modified Haar and modified Daubechies wavelet transform. Analysis and synthesis of the time signals is performed for 10 samples and the signal to noise ratio (SNR) of around 25-40 dB is obtained for modified Haar and 24-32 dB for modified Daubechies wavelet. We have observed that as compared to standard Haar and standard Daubechies mother wavelet our proposed method gives better signal quality, which is good for time varying signals.
ER Publication,
IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
Research Papers,
Research Article,
Free Journals, Open access Journals,
erpublication.org,
Engineering Journal,
Science Journals,
Congestion Control through Load Balancing Technique for Mobile Networks: A Cl...IDES Editor
The Optimal Routing Path (ORP) for mobile
cellular networks is proposed in this paper with the
introduction of cluster-based approach. Here an improved
dynamic selection procedure is used to elect cluster head.
The cluster head is only responsible for the computation of
least congested path. Hence the delay is reduced with the
significant reduction on the number of backtrackings.
Experimental study of Data clustering using k- Means and modified algorithmsIJDKP
The k- Means clustering algorithm is an old algorithm that has been intensely researched owing to its ease
and simplicity of implementation. Clustering algorithm has a broad attraction and usefulness in
exploratory data analysis. This paper presents results of the experimental study of different approaches to
k- Means clustering, thereby comparing results on different datasets using Original k-Means and other
modified algorithms implemented using MATLAB R2009b. The results are calculated on some performance
measures such as no. of iterations, no. of points misclassified, accuracy, Silhouette validity index and
execution time
Joint Timing and Frequency Synchronization in OFDMidescitation
With the advent of OFDM for WLAN
communications, as exemplified by IEEE 802.11a, it has become
imperative to have efficient and reliable synchronization
algorithms for OFDM WLAN receivers. The main challenges
with synchronization deal with the frequency offset and delay
spread introduced by the wireless channel. In this paper,
research is done into OFDM timing synchronization and
frequency synchronization techniques.
Testing of Matrices Multiplication Methods on Different ProcessorsEditor IJMTER
There are many algorithms we found for matrices multiplication. Until now it has been
found that complexity of matrix multiplication is O(n3). Though Further research found that this
complexity can be decreased. This paper focus on the algorithm and its complexity of matrices
multiplication methods.
Probability-Based Analysis to Determine the Performance of Multilevel Feedbac...Eswar Publications
Operating System may work on different types of CPU scheduling algorithms with different mechanism and concepts. The Multilevel Feedback Queue (MLFQ) Scheduling manages a variety of processes among various queues in a better and efficient manner. CPU scheduler appears transition mechanism over various queues. This paper is presented with various schemes of under a probability-based model. The scheduler has random movement over queues with given time quantum. This paper designs general transition model for its functioning
and justifying comparison under different scheduling schemes through a simulation study applied on different data sets in particular cases.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Hamming Distance and Data Compression of 1-D CAcsitconf
In this paper an application of von Neumann correction technique to the output string of some
chaotic rules of 1-D Cellular Automata that are unsuitable for cryptographic pseudo random
number generation due to their non uniform distribution of the binary elements is presented.
The one dimensional (1-D) Cellular Automata (CA) Rule space will be classified by the time run
of Hamming Distance (HD). This has the advantage of determining the rules that have short
cycle lengths and therefore deemed to be unsuitable for cryptographic pseudo random number
generation. The data collected from evolution of chaotic rules that have long cycles are
subjected to the original von Neumann density correction scheme as well as a new generalized
scheme presented in this paper and tested for statistical testing fitness using Diehard battery of
tests. Results show that significant improvement in the statistical tests are obtained when the
output of a balanced chaotic rule are mutually exclusive ORed with the output of unbalanced
chaotic rule that have undergone von Neumann density correction.
Hamming Distance and Data Compression of 1-D CAcscpconf
In this paper an application of von Neumann correction technique to the output string of some chaotic rules of 1-D Cellular Automata that are unsuitable for cryptographic pseudo random number generation due to their non uniform distribution of the binary elements is presented.The one dimensional (1-D) Cellular Automata (CA) Rule space will be classified by the time run of Hamming Distance (HD). This has the advantage of determining the rules that have short cycle lengths and therefore deemed to be unsuitable for cryptographic pseudo random number generation. The data collected from evolution of chaotic rules that have long cycles are subjected to the original von Neumann density correction scheme as well as a new generalized scheme presented in this paper and tested for statistical testing fitness using Diehard battery of tests. Results show that significant improvement in the statistical tests are obtained when the output of a balanced chaotic rule are mutually exclusive ORed with the output of unbalanced
chaotic rule that have undergone von Neumann density correction.
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.
A MULTIPLE – CHANNEL QUEUING MODELS ON FUZZY ENVIRONMENTIAEME Publication
In this paper, we investigated a queuing model of fuzzy environment-based a multiple channel queuing model (M/M/C) ( /FCFS) and study its performance under realistic conditions. It applies a nonagonal fuzzy number to analyse the relevant performance of a multiple channel queuing model (M/M/C) ( /FCFS). Based on the sub interval average ranking method for nonagonal fuzzy number, we convert fuzzy number to crisp one. Numerical results reveal that the efficiency of this method. Intuitively, the fuzzy environment adapts well to a multiple channel queuing models (M/M/C) ( /FCFS) are very well.
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.
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Discretizing of linear systems with time-delay Using method of Euler’s and Tu...IJERA Editor
Delays deteriorate the control performance and could destabilize the overall system in the theory of discretetime
signals and dynamic systems. Whenever a computer is used in measurement, signal processing or control
applications, the data as seen from the computer and systems involved are naturally discrete-time because a
computer executes program code at discrete points of time. Theory of discrete-time dynamic signals and systems
is useful in design and analysis of control systems, signal filters, state estimators and model estimation from
time-series of process data system identification. In this paper, a new approximated discretization method and
digital design for control systems with delays is proposed. System is transformed to a discrete-time model with
time delays. To implement the digital modeling, we used the z-transfer functions matrix which is a useful model
type of discrete-time systems, being analogous to the Laplace-transform for continuous-time systems. The most
important use of the z-transform is for defining z-transfer functions matrix is employed to obtain an extended
discrete-time. The proposed method can closely approximate the step response of the original continuous timedelayed
control system by choosing various of energy loss level. Illustrative example is simulated to demonstrate
the effectiveness of the developed method.\
A tale of scale & speed: How the US Navy is enabling software delivery from l...sonjaschweigert1
Rapid and secure feature delivery is a goal across every application team and every branch of the DoD. The Navy’s DevSecOps platform, Party Barge, has achieved:
- Reduction in onboarding time from 5 weeks to 1 day
- Improved developer experience and productivity through actionable findings and reduction of false positives
- Maintenance of superior security standards and inherent policy enforcement with Authorization to Operate (ATO)
Development teams can ship efficiently and ensure applications are cyber ready for Navy Authorizing Officials (AOs). In this webinar, Sigma Defense and Anchore will give attendees a look behind the scenes and demo secure pipeline automation and security artifacts that speed up application ATO and time to production.
We will cover:
- How to remove silos in DevSecOps
- How to build efficient development pipeline roles and component templates
- How to deliver security artifacts that matter for ATO’s (SBOMs, vulnerability reports, and policy evidence)
- How to streamline operations with automated policy checks on container images
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
SAP Sapphire 2024 - ASUG301 building better apps with SAP Fiori.pdfPeter Spielvogel
Building better applications for business users with SAP Fiori.
• What is SAP Fiori and why it matters to you
• How a better user experience drives measurable business benefits
• How to get started with SAP Fiori today
• How SAP Fiori elements accelerates application development
• How SAP Build Code includes SAP Fiori tools and other generative artificial intelligence capabilities
• How SAP Fiori paves the way for using AI in SAP apps
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
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Analysis of single server fixed batch service queueing system under multiple vacation with catastrophe
1. Mathematical Theory and Modeling
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.11, 2013
www.iiste.org
Analysis of Single Server Fixed Batch Service Queueing System
under Multiple Vacation with Catastrophe
1.
2.
3.
G. Ayyappan1, G. Devipriya2*, A. Muthu Ganapathi Subramanian3
Associate Professor, Pondicherry Engineering College, Pondicherry, India
Assistant Professor, Sri Ganesh College of Engineering & Technology ,Pondicherry , India
Associate Professor, Kanchi Mamunivar Centre for Post Graduate Studies, Pondicherry, India
*E-mail of the corresponding author: devimou@yahoo.com
Abstract
Consider a single server fixed batch service queueing system under multiple vacation with a possibility of
catastrophe in which the arrival rate λ follows a Poisson process and the service time follows an exponential
distribution with parameter μ. Further we assume that the catastrophe occur at the rate of ν which follows a
Poisson process and the length of time the server in vacation follows an exponential distribution with parameter
α. Assume that the system initially contains k customers when the server enters in to the system and starts the
service immediately in a batch of size k. After completion of a service, if he finds less than k customers in the
queue, then the server goes for a multiple vacation of length α. If there are more than k customers in the queue
then the first k customers will be selected from the queue and service will be given as a batch. We are analyzing
the possibility of catastrophe that is whenever a catastrophe occurs in the system, all the customers who are in
the system will be completely destroyed and system becomes an empty and server goes for a multiple vacation.
This model is completely solved by constructing the generating function and we have derived the closed form
solutions for probability of number of customers in the queue during the server busy and in vacation. Further we
are providing the analytical solution for mean number of customers and variance of the system. Numerical
studies have been done for analysis of mean and variance of number of customers in the system for various
values of λ, µ, ν and k and also various particular cases of this model have been discussed.
Keywords: Single server queue , Fixed batch service , Catastrophe, Multiple vacation, Steady state distribution
1. Introduction
Batch service queues have numerous applications to traffic, transportation, production, and manufacturing
systems. Bailey (1954) obtained the transform solution to the fixed-size batch service queue with Poisson arrival.
Miller (1959) studied the batch arrival and batch service queues and Jaiswal (1964) have studied the batch
service queues in which service size is random. Neuts (1967) proposed the "general bulk service rule" in which
service initiates only when a certain number of customers in the queue are available. Neuts general bulk service
rule was extended by Borthakur and Medhi (1973). Studies on waiting time in a batch service queue were also
rendered by Downton (1955), Cohen (1980), Medhi (1975) and Powell (1987). Fakinos (1991) derived the
relation between limiting queue size distributions at arrival and departure epochs. Briere and Chaudhry (1989),
Grassmann and Chaudhry (1982), and Kambo and Chaudhry (1985) used numerical approaches to obtain the
performance measures. Chaudhry and Templeton (1983) gave more extensive study on batch arrival/service
queues.
The notion of catastrophes occurring at random, leading to annihilation of all the customers there and the
momentary inactivation of the service facility until a new arrival of a customer is not common in many practical
problems. The catastrophes may come either from outside the system or from another service station. In
computer systems, if a job is infected, this job transmits a virus when it is transferred to other processors.
Infected files in floppy diskettes, for instance, may also arrive at the processors according to some random
process. The infected jobs may be modeled by the catastrophe. Hence, computer networks with a virus may be
modeled by queueing networks with catastrophes.
Vacation queues have been extensively studied by many researchers. Comprehensive surveys can be found in
Doshi (1986) and Takagi (1991). Most of the studies on vacation queues have been concerned with single-unit
service systems such as M/G/1 or MX /G/1 queues. The well-known result concerning vacation queues is the
"decomposition property" by Fuhrmann and Cooper (1985) which states that the Probability Generating Function
(PGF) of the queue length of a vacation system can be factorized into the queue length of ordinary queue without
vacation and "something else", the "something else" depends on the system characteristics. Lee et al. (1994)
have analyzed the operating characteristics of batch arrival queues with N-policy and vacations, and obtained the
queue length and waiting time distributions.
For batch service queues with vacations, there have been a few related works. Dhas (1989) considered
Markovian batch service systems and obtained the queue length distributions by matrix-geometric method. Lee
et al. [1994] obtained various performance measures for M/GB/1 queue with single vacation. Dshalalow and
35
2. Mathematical Theory and Modeling
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.11, 2013
www.iiste.org
Yellen (1996) have considered a non-exhaustive batch service system with multiple vacations in which the
server starts a multiple vacation whenever the queue drops below a level r and resumes service at the end of a
vacation segment when the queue accumulates to at least r. They called such a system (r, R)-quorum system.
They have applied the theory of the first excess level (Dshalalow (1996)). Lee et al. [1994] showed that for some
batch service queues, mean queue length may even decrease in systems with server vacations. This has an
implication that for some batch service queues, customers do not have to complain about unavailability of the
server. Instead, they would rather force the server to take a vacation.
In this paper we are analyzing a special batch service queue called the fixed size batch service queue with
catastrophes under multiple vacations. The model is described in Section 2. In Section 3, we have derived the
system steady state equations and using these equations, the probability generating functions for number of
customers in the queue when the server is busy or in vacation are derived and also obtained steady state
probability distributions. Section 4 deals with stability condition of the system. In section 5, we discuss the
particular case. Closed form solutions of system performance measures are obtained in 6. A numerical study is
carried out in Section 7 to test the effectiveness of the system. We are providing the analytical solution for mean
number of customers and variance of the system. Numerical studies have been done for analysis of mean and
variance for various values of λ, µ, α ν and k and also various particular cases of this model have been discussed.
2. DESCRIBE OF THE MODEL
Consider a single server fixed batch service queueing system under multiple vacation with a possibility of
catastrophe in which the arrival rate λ follows a Poisson process and the service time follows an exponential
distribution with parameter μ. Further we assume that the catastrophe occur at the rate of ν which follows a
Poisson process and the length of time the server in vacation follows an exponential distribution with parameter
α. Assume that the system initially contains k customers when the server enters in to the system and starts the
service immediately in a batch of size k. After completion of a service, if he finds less than k customers in the
queue, then the server goes for a multiple vacation of length α. If there are more than k customers in the queue
then the first k customers will be selected from the queue and service will be given as a batch. We are analyzing
the possibility of catastrophe that is whenever a catastrophe occurs in the system, all the customers who are in
the system will be completely destroyed and system becomes an empty and server goes for a multiple vacation.
If there are less than k customers in the queue upon his return from the vacation, he immediately leaves for
another vacation and so on until he finally finds k or more customers in the queue.
Let < N(t),C(t) > be a random process where N(t) be the random variable which represents the number of
customers in queue at time t and C(t) be the random variable which represents the server status (busy/vacation)
at time t.
We define
• Pn,1(t) - Probability that the server is in busy if there are n customers in the queue at time t.
• Pn,2(t) - Probability that the server is in vacation if there are n customers in the queue at time t
The Chapman- Kolmogorov equations are
'
P0,1 (t ) = − (λ + ν + µ ) P0,1 (t ) + µ Pk ,1 (t ) +α Pk ,2 (t)
(1)
Pn ,1 (t ) = − ( λ + ν + µ ) Pn ,1 (t ) + λ Pn − 1,1 (t ) + µ Pn + k ,1 (t ) +α Pn + k , 2 (t) for n = 1,2,3,..
(2)
P (t ) = −(λ + ν ) P0,2 (t ) + µ P0,1 (t ) + ν
(3)
P (t ) = − (λ + ν ) Pn ,2 (t ) + λ Pn −1,2 (t ) + µ Pn ,1 (t ) for n = 1,2,3,...,k-1
(4)
P (t ) = −(λ + ν + α ) Pn ,2 (t ) + λ Pn −1,2 (t ) for n ≥ k
(5)
'
'
0,2
'
n ,2
'
n ,2
3. EVALUATION OF STEADY STATE PROBABILITIES
In this section, we are finding the closed form solutions for number of customers in the queue when the server is
busy or in vacation by using Generating function.
When steady state prevails, the equations (1) to (5) becomes
( λ + ν + µ ) P0 ,1 = µ Pk ,1 + α P k , 2
( λ + ν + µ ) Pn ,1 = λ Pn − 1,1 + µ Pn + k ,1 + α P n + k , 2 fo r n = 1 ,2 ,3 ,...
( λ + ν ) P0 , 2 = µ P0 ,1 + ν
( λ + ν ) Pn , 2 = λ Pn − 1, 2 + µ Pn ,1 f o r n = 1 ,2 ,... k -1
36
(6)
(7)
(8)
(9)
3. Mathematical Theory and Modeling
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.11, 2013
www.iiste.org
( λ + ν + α ) Pn , 2 = λ Pn − 1, 2 fo r n ≥ k
(10)
Generating functions for the number of customers in the queue when the server is busy or in vacation are defined
as
∞
G( z ) = ∑ Pn,1 z
∞
H ( z) = ∑ Pn,2 z n
n
n=0
n =0
and
Adding equations (6) and (7) after multiplying by 1, zn ( n = 0 to ∞) respectively we get
k −1
k −1
G( z )[λ z k +1 − (λ + µ +ν ) z k + µ ] + α H ( z ) = µ ∑ Pn ,1 z n + α ∑ Pn,2 z n
n =0
n =0
(11)
Adding equations (8), (9) and (10) after multiplying by 1, zn and zn ( n = 1,2,3, . . . ) respectively, we get
k −1
k −1
n= 0
n=0
H ( z)[α + ν + λ (1 − z)] −ν = µ ∑ Pn,1 z n + α ∑ Pn,2 z n
k −1
H ( z) =
(12)
k −1
µ ∑ Pn,1 z n + α ∑ Pn ,2 z n + ν
n=0
n=0
α +ν + λ (1 − z )
(13)
Equation (13) represents the probability generating function for the number of customers in the queue when the
server is in vacation.
From equations (11) and (13), we get
k −1
k −1
µ ∑ Pn,1 z n + α ∑ Pn,2 z n +ν (ν + λ (1 − z ) ) −ν
n =0
G ( z ) = n=0
k +1
(α +ν + λ (1 − z ) ) ( λ z − (λ + µ +ν ) z k + µ )
(14)
The generating function G(z) has the property that it must converge inside the unit circle
the expression in the denominator of G(z) , λ z
k +1
− (λ + µ + ν ) z + µ has k+1 zeros. By Rouche's theorem,
z <1
numerator of G(z) and one zero lies outside the circle
z <1
and must coincide with k zeros of
. Let z0 be a zero which lies outside the circle
z <1
.
As G(z) converges, k zeros of numerator and denominator will be cancelled, we get
A
(α +ν + λ − λ z)λ ( z − z0 )
G(0) =
When z = 0,
(15)
A
(α +ν + λ )λ (− z0 )
A = P0,1 (α + ν + λ )λ ( − z0 )
G( z ) =
. We notice that
k
we notice that k zeros of this expression lies inside the circle
G( z ) =
z <1
(α +ν + λ ) z0 P0,1
(α +ν + λ − λ z)( z − z)
0
Then
By applying partial fractions, we get
(16)
n +1
∞
(α +ν + λ ) z0 P0,1 ∞ z n
λ
G( z ) =
zn
∑ n +1 − ∑
(α +ν + λ − λ z0 ) n =1 z0
n =1 (α + ν + λ )
Comparing the coefficient of zn on both sides of the equation (17), we get
37
(17)
4. Mathematical Theory and Modeling
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.11, 2013
n
r
r
Pn ,1 = P0,1 s 1 + + ... +
s
s
n
www.iiste.org
r=
for n = 1,2,3,...
1
λ
and s =
z0
λ +ν + α (18)
Where
Using equation (18) in (8) and (9) , apply recursive for n = 1,2, ...,k-1 and we get
n
n −1
n
n
n r
λ n−1 r r
r
λ λ ν
Pn,2 =
P s 1 + + ... +
s 1 + + ... + ... +
+
s
λ +ν 0,1 s s λ +ν
s
λ +ν λ +ν λ +ν
µ
for n = 0,1,2,...,k-1
(19)
λ
Pn ,2 =
λ + α +ν
n − k +1
Pk −1,2
for n ≥ k
(20)
The normalized condition is
∞
k −1
∞
n =1
n=0
n =k
P0,1 + ∑ Pn ,1 + ∑ Pn ,2 + ∑ Pn ,2 = 1
(21)
Substitute (18),(19) and (20) in (21), we get,
P0,1 =
Nr
Dr
(22)
k −1
ν λ
λ ν
Nr = 1 − ∑
−
α +ν λ +ν
n=0 λ +ν λ +ν
n
n −1
n
µ k −1 n r
λ n −1 r
1
r
r
λ
+ ... +
Dr =
s
+
1 + + ...
∑ s 1 + + ... + +
s
(1 − s)(1 − r ) λ +ν n = 0 s
s λ +ν
s
λ +ν
n
+
k
k −1
k −2
k − 1
µ k −1 r
s
λ
1 + + ... + r
+ λ sk − 2 1 + r + ... r
+ ... + λ
s
λ +ν
s
α +ν
λ +ν
s
s
λ +ν
Equations (18),(19),(20) and (22) represent the steady state probabilities for number of customers in the queue
, when the server is in busy or in vacation.
4. STABILITY CONDITION
The necessary and sufficient condition for the system to the stable is
λ
kµ
< 1.
5. PARTICULAR CASE
If we take ν = 0, the results coincides with the results of the model single server batch service under multiple
vacation.
6. SYSTEM PERFORMANCE MEASURES
In this section we will list some important performance measures along with their formulae. These measures are
used to bring out the qualitative behaviour of the queueing model under study. Numerical study has been dealt in
very large scale to study the following measures.
P0,1 =
1.
Nr
Dr
ν λ
λ ν
Nr = 1 − ∑
−
α +ν λ +ν
n=0 λ +ν λ +ν
k −1
n
38
k
5. Mathematical Theory and Modeling
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.11, 2013
Dr =
1
(1 − s )(1 − r )
+
+
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k −1
n
∑ s n 1 + r + ... + r + λ s n − 1 1 + r + ... + r
s
s
λ + ν n = 0
s λ +ν
s
µ
n −1
+ ... + λ
λ +ν
k −1
k −2
s k − 1 1 + r + ... + r
+ λ s k − 2 1 + r + ... + r
+ ... + λ
λ +ν
s
s
λ +ν
s
s
λ +ν
µ
n
k − 1 λ
α +ν
n
r
r
P0,1 s n 1 + + ... + for n = 0,1,2,...
s
s
2. Pn,1 =
n
n−1
n
n
n r
µ
r λ n−1 r r
λ λ ν
P s 1+ +... + +
s 1+ +... +.. +.
0,1
+
λ +ν s
s λ +ν s s
λ +ν λ +ν λ +ν
3. P =
n,2
for n = 0,1,2,...,k-1
4.
λ
Pn ,2 =
λ + α +ν
n − k +1
Pk −1,2
for n ≥ k
∞
Ls = ∑ ( n + k ) Pn,1 + nPn,2
5.
n =0
∞
Lq = ∑ n ( Pn ,1 + Pn ,2 )
6.
7.
n=0
∞
∞
V ( x) = ∑ ( n + k ) 2 Pn ,1 + ∑ n 2 Pn ,2 − ( Ls ) 2
n =0
n =0
7. NUMERICAL STUDIES
Table 1: Steady state probabilities for various batch size when λ = 2, µ =10, ν =1, α = 5
k=1
k=2
k=3
Pi
P0,1
0.0915
0.0382
0.0202
P1,1
0.0391
0.0155
0.0081
P2,1
0.0127
0.0048
0.0025
P3,1
0.0036
0.0013
0.0007
P4,1
0.0010
0.0003
0.0001
P5,1
0.0002
0.00009
0.00004
P6,1
0.00007
0
0
P0,2
0.6383
0.4606
0.4006
P1,2
0.1595
0.3589
0.2943
P2,2
0.0398
0.0897
0.2046
P3,2
0.0099
0.0224
0.0511
P4,2
0.0024
0.0056
0.0127
P5,2
0.0006
0.0014
0.0031
P6,2
0.0001
0.0003
0.0007
P7,2
0.00003
0.00008
0.0001
P8,2
0
0
0.00004
39
6. Mathematical Theory and Modeling
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.11, 2013
www.iiste.org
Table 2: Steady state probabilities for various α when λ = 2, µ = 10, ν = 1 and k = 3
Pi
α=5
α =10
α =20
P0,1
0.0202
0.0249
0.0281
P1,1
0.0081
0.0076
0.0067
P2,1
0.0025
0.0017
0.0012
P3,1
0.0007
0.0003
0.0002
P4,1
0.0001
0.00007
0.00003
P5,1
0.00004
0
0
P6,1
0
0
0
P0,2
0.4006
0.4163
0.4276
P1,2
0.2943
0.3031
0.3072
P2,2
0.2046
0.2079
0.2090
P3,2
0.0511
0.0319
0.0181
P4,2
0.0127
0.0049
0.0015
P5,2
0.0031
0.0007
0.0001
0.0007
0.0001
0.00001
P6,2
P7,2
0.0001
0.00001
0
P8,2
0.00004
0
0
Table 3: Steady state probabilities for various ν when λ = 2, µ = 10, k = 2, α = 5
Pi
ν=1
ν = 10
ν = 50
0.0382
0.0038
0.0001.
P0,1
0.0007
0.000006
P1,1
0.0155
0.0048
0.0001
0
P2,1
0.00001
0
P3,1
0.0013
0
0
P4,1
0.0003
0.00009
0
0
P5,1
0.4606
0.8365
0.9615
P0,2
0.1400
0.0369
P1,2
0.3589
0.0164
0.0012
P2,2
0.0897
0.0224
0.0019
0.00004
P3,2
0.0002
0
P4,2
0.0056
0.00002
0
0.0014
P5,2
0.0003
0
0
P6,2
0.00008
0
0
P7,2
Table 4: System measures for various batch size when λ = 2, µ = 10, ν =1, α = 5
k=1
k=2
k=3
Ls
Lq
V(x)
0.5111
0.08072
0.66047
0.78829
0.03065
0.85402
1.03904
0.0158
1.2129
Table 5: System measures for various values of α when λ = 2, µ = 10, ν =1, k = 3
α =5
α=10
α =20
Ls
Lq
V(x)
1.03904
0.0158
1.2129
0.95427
0.01218
1.01359
0.90334
0.00982
0.908116
40
7. Mathematical Theory and Modeling
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.11, 2013
www.iiste.org
Table 6: System measures for various values of ν when λ = 2, µ = 10, α =5, k = 3
ν=1
ν = 10
ν = 50
Ls
Lq
V(x)
0.78829
0.03065
0.85402
0.18955
0.00013
0.213820
0.0398
0.00006
0.04141
8. Conclusion
The Numerical studies show the changes in the system due to impact of batch size, vacation rate and
catastrophes. The mean number of customers in the system increases as batch size increase. The mean number of
customers in the system decreases as catastrophes rate and vacation rate increases. Various special cases have
been discussed, which are particular cases of this research work. This research work can be extended further by
introducing various concepts like negative arrival, breakdown and repair etc.
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41
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