The document provides an introduction to queuing theory, covering key concepts such as queues, stochastic processes, Little's Law, and types of queuing systems. It discusses topics like arrival and service processes, the number of servers, system capacity, and service disciplines. Common variables in queueing analysis are defined. Relationships among variables for G/G/m queues are described, including the stability condition, number in system vs. number in queue, number vs. time relationships, and time in system vs. time in queue. Different types of stochastic processes like discrete-state, continuous-state, Markov, and birth-death processes are introduced. Properties of Poisson processes are outlined. The document concludes by noting some applications of queuing
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.
Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted
MCM,MCA,MSc, MMM, MPhil, PhD (Computer Applications)
Working as Associate Professor at Zeal Education Society, Pune for MCA Progrmme.
Having 18 Years teaching experience
Queueing Theory- Waiting Line Model, Heizer and RenderAi Lun Wu
I HOPE IT IS HELPFUL FOR YOU> BUT PLS IWANT CREDITS> OR ADD ME AND MESSAGE ME THANKS
THERE IS A NOTE FOR PRESENTERS VIEW
HAVE A GOOD DAY
KEEP CALM AND DRINK ON
NAME: Ellen Magalona
GNDR: FML
BRTHDY: FEB. 1998
@ellenmaaee
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.
Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted
MCM,MCA,MSc, MMM, MPhil, PhD (Computer Applications)
Working as Associate Professor at Zeal Education Society, Pune for MCA Progrmme.
Having 18 Years teaching experience
Queueing Theory- Waiting Line Model, Heizer and RenderAi Lun Wu
I HOPE IT IS HELPFUL FOR YOU> BUT PLS IWANT CREDITS> OR ADD ME AND MESSAGE ME THANKS
THERE IS A NOTE FOR PRESENTERS VIEW
HAVE A GOOD DAY
KEEP CALM AND DRINK ON
NAME: Ellen Magalona
GNDR: FML
BRTHDY: FEB. 1998
@ellenmaaee
Queuing theory: What is a Queuing system???
Waiting for service is part of our daily life….
Example:
we wait to eat in restaurants….
We queue up in grocery stores…
Jobs wait to be processed on machine…
Vehicles queue up at traffic signal….
Planes circle in a stack before given permission to land at an airport….
Unfortunately, we can not eliminate waiting time without incurring expenses…
But, we can hope to reduce the queue time to a tolerable levels… so that we can avoid adverse impact….
Why study???? What analytics can be drawn??? Analytics means ---- measures of performance such as
1. Average queue length
2. Average waiting time in the queue
3. Average facility utilization….
We consider a real-time multi-server system with homogeneous servers (such as overhearing devices,
unmanned aerial vehicles, machine controllers, etc.) which can be maintained/programmed for different kinds
of activities (e.g. passive or active). This system provides a service for real-time tasks arriving via several
channels (such as communication channels, surveillance regions, assembly lines, etc.) and involves
maintenance. We address the worst case analysis of the system working under maximum load with preemptive
priorities assigned for servers of different activity type. We consider a model with ample maintenance facilities
and single joint queue to all channels.
We provide various analytical approximations of steady state probabilities for these real-time systems, discuss
their quality, compare the results and choose the best one.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
2. • Queuing
• Queuing Notation
• Rules For All Queues
• Little’s Law
• Types Of Stochastic Processes
3. A queue is a waiting line of customers requiring service from
one server to another and it is a mathematical study of waiting
lines or queues.
It is extremely useful in predicting and evaluating the system
performance.
There are some applications of queuing like Traffic control ,
Health service , Ticket sales etc.
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4. 1. Arrival Process: If the students arrive at times t1,t2,...,tj
the random variables τj = tj – tj-1 are called the interarrival
times. It is generally assumed that τj form a sequence of
Independent and Identically Distributed random variables.
2. Service Time Distribution: We also need to know the
time each student spends at the terminal. This is called the
service time. It is common to assume that the service times
are random variables, which are IID.
2
5. 3. Number of Servers: The terminal room may have one or
more terminals, all are considered part of the same queuing
system since they are all identical, and any terminal may be
assigned to any student.
If all the servers are not identical, they are usually divided
into groups of identical servers with separate queues for each
group.
4. System Capacity: The maximum number of students who
can stay may be limited due to space availability and also to
avoid long waiting times. This number is called the system
capacity.
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6. 5. Population Size: The total number of potential students
who can ever come to the computer centre is the
population size.
6. Service Discipline: The order in which the students are
served is called the service discipline. The most common
discipline is First Come First Served (FCFS). Other
possibilities are Last Come First Served (LCFS) and Last
Come First Served with Preempt and Resume (LCFS-
PR).
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7. There are some key variables used in queueing analysis are
as follow:
τ = interarrival time, the time between two successive
arrivals.
λ = mean arrival rate.
s = service time per job.
m = number of servers.
μ= mean service rate per server.
n= number of jobs in the system. This is also called
queue length.
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8. nq = number of jobs waiting to receive service.
ns = number of jobs receiving service.
r = response time.
w = waiting time.
There are a number of relationships among these variables
that apply to G/G/m queues.
1. Stability Condition: If the number of jobs in a system
grows continuously and becomes infinite, the system is
said to be unstable. For stability the mean arrival rate
should be less than the mean service rate is
λ > mμ
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9. 2. Number in System versus Number in Queue: The
number of jobs in the system is always equal to the sum of
the number in the queue and the number receiving service:
n=nq + ns
n, nq, and ns, are random variables.
The mean number of jobs in the system is equal to the
sum of the mean number in of job in the queue and the
mean number receiving service.
E[n]=E[nq] + E[ns]
If the service rate of each server is independent of the
number in the queue, we have
Cov(nq,ns) = 0 and Var[n] = Var[nq] + Var[ns]
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10. 3. Number versus Time: If jobs are not lost due to
insufficient buffers, the mean number of jobs in a system
is related to its mean response time as follows:
Mean number of jobs in system = arrival rate × mean
response time.
Mean number of jobs in queue = arrival rate × mean
waiting time.
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11. 4. Time in System versus Time in Queue: The time
spent by a job in a queueing system.
r = w + s
r, w, and s are random variables
The mean response time is equal to the sum of the mean
waiting time and the mean service time.
E[r] = E[w] + E[s]
If the service rate is independent of the number of jobs in
the queue, we have
Cov(w,s) = 0 and Var[r] = Var[w] + Var[s]
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12. Little’s law, which was first proven by Little in 1961.
The most commonly used theorems in queuing theory is
Little’s law, which allows us to relate the mean number of
jobs in any system with the mean time spent in the system as
follows:
Mean number in the system = arrival rate × mean response
time
The law applies as long as the number of jobs entering the
system is equal to completing service, so that no new jobs
are created in the system and no jobs are lost inside the
system.
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13. The law can be applied to the part of the system
consisting of the waiting and serving positions because
once a job finds a waiting position , it is not lost.
11
14. 1. Discrete-State and Continuous-State Processes: A
process is called discrete or continuous state depending
upon the values its state can take.
If the number of possible values is finite or countable, the
process is called a discrete-state process.
The waiting time w(t) can take any value on the real line
then, w(t) is a continuous-state process.
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15. 2. Markov Process: If the future states of a process are
independent of the past and depend only on the present,
the process is called a Markov process.
It can be used to model a random system that change the
state according to transition rule that only depend on
current state.
13
16. 3. Birth-Death Processes: The discrete-space Markov
processes in which the transitions are restricted to
neighboring states only are called birth-death processes.
It is possible to represent states by integer such that a
process in state n can change only two state n+1 or n-1.
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17. 4. Poisson Processes: It is a random process which
counts the number of event and time that these event
occur in given time interval (t, t+x) has a Poisson
distribution, and then, the arrival process is referred to
as a Poisson process.
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18. Poisson process have the following properties:
Merging of k Poisson process with mean rate λi results
in a Poisson stream with mean rate λ given by
λ =
If a Poisson process is split into k substreams such that
the probability of a job going to the ith substream is pi,
each substream is also Poisson with a mean rate of piλ.
16
k
i
i
1
19. If the arrivals to a single server with exponential service
time are Poisson with mean rate λ, the departures are also
Poisson with the same rate λ, provided the arrival rate λ is
less than the service rate μ.
If the arrivals to a service facility with m service centres
are Poisson with a mean rate λ, then the departures also
a Poisson with the same rate λ and provided the arrival
rate λ is less than the total service rate
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20. Queuing theory is major for computer system
performance and also in our daily life. It can be used to
help reduce waiting times. It helps in determining the
time that the jobs spend in various queues in the system.
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