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
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
Solving Of Waiting Lines Models in the Bank Using Queuing Theory Model the Pr...IOSR Journals
Waiting lines and service systems are important parts of the business world. In this article we describe several common queuing situations and present mathematical models for analyzing waiting lines following certain assumptions. Those assumptions are that (1) arrivals come from an infinite or very large population, (2) arrivals are Poisson distributed, (3) arrivals are treated on a FIFO basis and do not balk or renege, (4) service times follow the negative exponential distribution or are constant, and (5) the average service rate is faster than the average arrival rate. The model illustrated in this Bank for customers on a level with service is the multiple-channel queuing model with Poisson Arrival and Exponential Service Times (M/M/S). After a series of operating characteristics are computed, total expected costs are studied, total costs is the sum of the cost of providing service plus the cost of waiting time. Finally we find the total minimum expected cost.
Waiting Line Model is one of the decision line model.Waiting Line Model is one of the decision line model.Waiting Line Model is one of the decision line model.Waiting Line Model is one of the decision line model.
International Journal of Mathematics and Statistics Invention (IJMSI) inventionjournals
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.
Developed to provide models for forecasting behaviors of systems subject to random demand
The first problems addressed concerned congestion of telephone traffic
Erlang observed that a telephone system can be modeled by Poisson customer arrivals and exponentially distributed service times
Molina, Pollaczek, Kolmogorov, Khintchine, Palm, Crommelin followed the track
Common phenomenon of everyday life
Line maybe People / Items
Examples
– Grocery shop, Bank, Petrol refilling units, Automobile Service station, Airplane, Train etc.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Ethnobotany and Ethnopharmacology:
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The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
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2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Model Attribute Check Company Auto PropertyCeline George
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
1. Queueing Theory
Presented to :
Dr. Dibyojyoti
Bhattacharjee
Presented by :
Biswajit Bhattacharjee (19)
Bikash Choudhury (16)
Biswaraj Das Purkayastha(20)
Kunal Sengupta(37)
2. Introduction to Queueing Theory
A pioneer:
Agner Krarup Erlang
(1878-1929) the Danish
telecommunication engineer
started applying principles of
queuing theory in the area of
telecommunications.
3. What is queueing theory?
• Queueing theory is the mathematical study of waiting lines, or
queues. In queueing theory a model is constructed so that queue
lengths and waiting times can be predicted. Queueing theory is
generally considered a branch of operations research because the
results are often used when making business decisions about the
resources needed to provide a service.
• Queueing theory has its origins in research by Agner Krarup Erlang
when he created models to describe the Copenhagen telephone
exchange. The ideas have since seen applications including
telecommunications, traffic engineering, computing and the design of
factories, shops, offices and hospitals.
4. Why is queueing theory important?
• Capacity problems are very common in industry and one
of the main drivers of process redesign
– Need to balance the cost of increased capacity against the gains
of increased productivity and service
• Queuing and waiting time analysis is particularly
important in service systems
– Large costs of waiting and of lost sales due to waiting
Example – Hospital
• Patients arrive by ambulance or by their own accord
• One doctor is always on duty
• More and more patients seeks help longer waiting
times
Question: Should another MD position be instated?
5. Examples of Real World Queuing Systems?
• Commercial Queuing Systems
– Commercial organizations serving external customers
– Ex. Dentist, bank, ATM, gas stations, plumber, garage …
• Transportation service systems
– Vehicles are customers or servers
– Ex. Vehicles waiting at toll stations and traffic lights, trucks or ships waiting to
be loaded, taxi cabs, fire engines, buses …
• Business-internal service systems
– Customers receiving service are internal to the organization providing the
service
– Ex. Inspection stations, conveyor belts, computer support …
• Social service systems
– Ex. Judicial process, hospital, waiting lists for organ transplants or student
dorm rooms …
5
6. Problems of a store manger
• When and why do we get queues?
– Too many people, too few desks
• What can we do about it?
– More cash desks
• What if there are too many desks open?
costs
– Let on more people in
– First serve the people who need little service time
– Limit the time during which someone is being served
e.g. limited treatment time per client at the doctor
6
7. Problems of a customer
• Why does it always feel to us like all other queues move
faster?
• Which queue should I take? Where shall I append? How
long do I have to wait?
–
–
–
–
–
Where there are the fewest people in queue?
Where the people have the least products to dispatch?
Where the fastest cashier is?
Where one can only pay cash?
Where someone helps me bagging?
7
8. Queuing theory for studying networks
• View network as collections of queues
– FIFO data-structures
• Queuing theory provides probabilistic analysis of these
queues
• Examples:
– Average length (buffer)
– Average waiting time
– Probability queue is at a certain length
– Probability a packet will be lost
11. Assumptions
• Independent arrivals
• Exponential distributions
• Customers do not leave or change queues.
• Large queues do not discourage customers.
Many assumptions are not always true, but queuing
theory gives good results anyway
12. Measuring the Queue Performance
There are a number of measure that can help a
manager to balance the capacity and waiting costs:
–
–
–
–
–
–
Average time in a queue
Average length of a queue
Average customer time in the system
Number of customers in a queue
Probability of numbers in a queue
Probability of system being unused
The last two above, looking at probability is where most of the work on
queue theory goes on
You will need to understand more about statistics, particularly Poisson
distribution) to delve deeper into this
13. Components of a Basic Queuing Process
Input Source
Calling
Population
The Queuing System
Jobs
Service
Mechanism
Queue
Served
Jobs
leave the
system
Queue
Discipline
Arrival
Process
Queue
Configuration
Service
Process
13
15. 1. The Calling Population
• Population of customers or jobs
• The size can be finite or infinite
– The latter is most common
• Can be homogeneous
– Only one type of customers/ jobs
• Or heterogeneous
– Several different kinds of customers/jobs
15
16. 2. Arrival Process
• In what pattern do jobs / customers arrive to
the queueing system?
– Distribution of arrival times?
– Batch arrivals?
– Finite population?
– Finite queue length?
• Poisson arrival process often assumed
– Many real-world arrival processes can be modeled
using a Poisson process
16
17. 3. Service Process
• How long does it take to service a job or
customer?
– Distribution of arrival times?
– Rework or repair?
– Service center (machine) breakdown?
• Exponential service times often assumed
– Works well for maintenance or unscheduled
service situations
17
18. 4. Number of Servers
• How many servers are available?
Single Server Queue
Multiple Server Queue
18
19. Example – Two Queue Configurations
Multiple Queues
Servers
Single Queue
Servers
19
20. Multiple vs Single Customer Queue
Configuration
Multiple Line Advantages
1. The service provided can be
differentiated
– Ex. Supermarket express lanes
2. Labor specialization possible
3. Customer has more flexibility
4. Balking behavior may be
deterred
– Several medium-length lines are
less intimidating than one very
long line
Single Line Advantages
1. Guarantees fairness
– FIFO applied to all arrivals
2. No customer anxiety regarding
choice of queue
3. Avoids “cutting in” problems
4. The most efficient set up for
minimizing time in the queue
5. Jockeying (line switching) is
avoided
20
21. 5. Queue Discipline
• How are jobs / customers selected from the
queue for service?
– First Come First Served (FCFS)
– Shortest Processing Time (SPT)
– Earliest Due Date (EDD)
– Priority (jobs are in different priority classes)
• FCFS default assumption for most models
21
22. Three queuing disciplines used in
Telephone Networks
• First In First Out – This principle states that
customers are served one at a time and that the
customer that has been waiting the longest is
served first.
• Last In First Out – This principle also serves
customers one at a time, however the customer
with the shortest waiting time will be served first.
• Processor Sharing – Customers are served equally.
Network capacity is shared between customers and
they all effectively experience the same delay
30. Types of Queues of Interest
• Analytical Models for Estimating Capacity and
Related Metrics
– Single Server
• M/M/1, M/G/1, M/D/1, G/G/1
– Multiple Server
• M/M/c, M/G/∞ etc.
– Multiple Stage
• Markov Chain models
31. Infinite-Source Queuing Models
• Single channel, exponential service time
(M/M/1)
• Single channel, constant service time (M/D/1)
• Multiple channel, exponential service time
(M/M/S)
• Multiple priority service, exponential service
time
32. BUSINESS APPLICATIONS
• It is a practical operations management technique that is commonly used to
determine staffing, scheduling and calculating inventory levels.
• To improve customer satisfaction.
• Six Sigma professionals – through their knowledge of probability distributions,
process mapping and basic process improvement techniques – can help
organizations design and implement robust queuing models to create this
competitive advantage.
• Timeliness: Businesses conduct studies using mathematical models and formulas
to determine the best way of serving the greatest number of customers, given
their staffing resources. In retail businesses, the volume of transactions is
extremely important in maximizing revenues and profitability
• Remove Inefficiencies: for eg., bank, needs to stick to its model once it's been
determined that maximum efficiency can be achieved, both in labor costs and
customers served, by using a centralized queue based on staffing at least three
tellers during peak hours.
33. Limitations of Queuing theory
• The assumptions of classical queuing theory may be too restrictive to be able to
model real-world situations exactly.
• The complexity of production lines with product-specific characteristics cannot be
handled with those models. Often, although the bounds do exist, they can be safely
ignored.
• Because the differences between the real-world and theory is not statistically
significant, as the probability that such boundary situations might occur is remote
compared to the expected normal situation.
• Furthermore, several studies show the robustness of queuing models outside their
assumptions.
• In other cases the theoretical solution may either prove intractable or insufficiently
informative to be useful.
•Alternative means of analysis have thus been devised in order to provide
some insight into problems that do not fall under the scope of queuing theory,
•Although they are often scenario-specific because they generally consist of
computer analysis of experimental data.
33