Riga Technical University

WHERE is the TELE-TRAFFIC here?

PROBLEM Nr1

WHERE is the TELE-TRAFFIC here?

PROBLEM Nr2

Digital Communication Flow in

Parcel Service

WHERE is the TELE-TRAFFIC here?

PROBLEM Nr3

Course (RAE-555) Life-Span

Week 1

2024.01.29

Course (RAE-555) Life-Span

Week 1

Week 2

2024.01.29

2024.02.05

WHERE is the TELE-TRAFFIC in this MODEL?

PROBLEM Nr4

WHAT is the TRAFFIC?

PROBLEM Nr5

HOW

TELE-TRAFFIC THEORY

is HELPFUL for US ?

THEORY

BUSINESS-ORIENTED LEARNING MODEL

2024.01.29

2024.05.31

WHAT is the TRAFFIC?

What are the TRAFFIC METRICS?

WHERE is the TRAFFIC?

PROBLEM Nr6

What are the TRAFFIC METRICS?

WHERE is the TRAFFIC?

PROBLEM Nr7

OPERATIONAL
MODEL instantiated as APPLICATION

METRICS & UNITS

OPERATIONAL
MODEL instantiated as APPLICATION

METRICS & UNITS

It's TIME to EXERCISE

PROBLEM Nr8

WEEK 1

Observe & Think

Develop &

Deploy

Run & Relax

Week # 2

Observing

Systems

METRICS

& UNITS

Considering Traffic as a

Service System Load

Dynamic Model

Static Model

What is the queue size?

REAL NETWORK MODEL

Considering Traffic as a

Service System Load

What is the router load?

How long will stay the yellow packet in the queue?

How long will be processed the green packet?

\overline{W}

\overline{T} \equiv

\overline{N}

\overline{L} \equiv

TRAFFIC as a

Service System Load

(Jobs, Tasks, Customers, Cars, Data packets, Bytes, etc. )

\overline{N} = \lambda \cdot \overline{W}

Math Model

Conceptual Model

Course Book

https://www.amazon.com/Fundamentals-Queueing-Theory-Probability-Statistics/dp/111894352X/ref=sr_1_6?s=books&ie=UTF8&qid=1510840499&sr=1-6&keywords=fundamentals+of+queueing

Single Node Model

Fundamental Models

\overline{N} = \lambda \cdot \overline{W}

Little's Formula

Fundamental Models

\overline{L} = \lambda \cdot \overline{T}

\rho = \frac{\lambda}{\mu}

Erlang's A Formula

Fundamental Models

\lambda = \frac{k}{T_{obs}}

Arrival Rate

Fundamental Models

T_{obs} \to System Observation Time

k \to Counted Arrived Jobs

\mu = \frac{k}{T_{busy}}

Departure Rate

Fundamental Models

T_{busy} \to Server Busy Time

k \to Counted Departered Jobs

\overline{W} = \frac{1}{\mu}

Waiting Time vs Departure Rate

Fundamental Models

\mu = \frac{1}{\overline{W}}

{\rho} = \frac{\lambda}{\mu}

Little formula and Erlang formula

Fundamental Models

\overline{N} = \lambda \cdot \overline{W} = \lambda\frac{1}{\mu}

From

OBSERVATION

to

MODEL DATA

Fundamental Models

\overline{N} = \lambda \cdot \overline{W}

ARRIVAL RATE

Fundamental Models

\overline{N} = \lambda \cdot \overline{W}

\lambda = \frac{k} {T_{obs}}

WHERE is the ARRIVAL here?

PROBLEM Nr 2.1

ARRIVAL RATE

Fundamental Models

\overline{N} = \lambda \cdot \overline{W}

\lambda = \frac{k} {T_{obs}}

Problem Domain

Fundamental Models

TRAFFIC as a PROCESS over TIME

\overline{N} = \lambda \cdot \overline{W}

Questions

Fundamental Models

Course Book

https://www.amazon.com/Fundamentals-Queueing-Theory-Probability-Statistics/dp/111894352X/ref=sr_1_6?s=books&ie=UTF8&qid=1510840499&sr=1-6&keywords=fundamentals+of+queueing

Fundamental Models

TRAFFIC as a PROCESS over TIME

PROBLEM Nr9

RTU RAE555

Teletraffic Theory (Spring 2024)

Pre-Class for Week 3

Choose any service-related Single Node System
Observe the system for some time
Analyse the system identifying primary traffic (load-related) characteristics
Demonstrate results and understanding of the topic:
1. Use slides on SLIDES.COM
2. Make a Screencast on YouTube or Vimeo (make a short video about the topic)
3. Publish the outcome on the course SLACK channel before the next meetup

The output is based on unique and individual experience

Output ( TODO )

Homework

Analysis of a Single Node Service system

(paying attention to the following characteristics)

\lambda, \mu, \bar{N}_{sys}, \bar{N}_{srv}, \bar{N}_{queue}, \bar{W}_{sys}, \bar{W}_{srv}, \bar{W}_{queue}, k, T_{obs}, T_{busy}

Just be Active!

Q&A

2024.02.05

Week #3

From Observation to Models

Fundamental Models

\overline{N} = \overline{\lambda} \cdot \overline{W}

\overline{N}_{sys}

\overline{W}_{sys}

N(t)

\overline{W}_{q}

{W}_{q}^i

{W}_{sys}^i

{W}_{q}^i \equiv W(i)_{q}

Client

Server

\lambda(t)_1

\lambda(t)_2

\mu_1

\mu_2

Fundamental Models

Client

Server

Fundamental Models

T(obs)

PROBLEM Nr10

Fundamental Models

PROBLEM Nr11

Fundamental Models

T(obs)

Fundamental Models

In-Class problem

https://www.screencast.com/t/1DuLMLx2xV

PROBLEM Nr12

RTU RAE555

Teletraffic Theory (Spring 2024)

In-Class for Week 4

Analyse the given system identifying primary traffic characteristics
Demonstrate results and the understanding of the topic:
1. Use slides on SLIDES.COM and/or do handwriting + drawing
2. Publish the outcome on the course SLACK channel Week-7 before the current Day (2024-xx-xx) ends
3. Late submissions are allowed but not welcome.

The output is based on the given problem

Output ( TODO )

Homework

Analysis of a Single Node Service system

(paying attention to the following characteristics)

\lambda, \mu, \bar{N}_{sys}, \bar{N}_{srv}, \bar{N}_{queue}, \bar{W}_{sys}, \bar{W}_{srv}, \bar{W}_{queue}, k, T_{obs}, T_{busy}

Week #4

From Observation to Models

2024-02-19

1st Module Exam

POSTPONED

RTU RAE555

Teletraffic Theory (Spring 2024)

Homework for Week 5

Solve all the given problems related to HW1
Demonstrate results and understanding of the topic
Become ready for te Q1

The output is based on unique and individual variants

Output

Homework

Analysis of a Single Node Service system

Week #5

From Observation to Models

2024-02-26

Week 5

Moving towards Reality

Books

P_{1a}(t+h) \sim \lambda h

P_{1d}(t+h) \sim \mu h

\lambda (t)

\mu (t)

Classwork Time

Week 5

Classwork

Week 5

Classwork

Moving towards Reality

RTU RAE555

Teletraffic Theory (Spring 2024)

Activities for Week 5 (HOMEWORK for Week 6)

Participate in MADRAS UNI lectures Lec-30 and Lec-31
Demonstrate understanding of the topic, and namely,
Publish a recap of both lectures

The output can be complemented by unique and individual variants

Output

Homework

Theoretical Model of a Single Node Service system

TO DO that, proceed to

Week #6

From Observation to Models

2024-03-04

Week 6

Moving towards Reality

Week 6

FINITE SYSTEMS

Building Conceptual Understanding of

DTMC

(Discrete-Time Markov Chains)

Markov Chains

Week 6

FINITE SYSTEMS

DTMC

Markov Chains

CTMC

Books

Challenges

Markov Models

Books

https://www.wiley-vch.de/de/fachgebiete/mathematik-und-statistik/mathematik-16ma/diskrete-mathematik-16ma9/markov-chains-978-1-119-38755-8

Week 6

Homework

Another viewpoint on load-time model

Theoretical Model of a Single Node Service system

In theory, what can you reveal from the model above?

Week 6

Classwork

Week 6

Classwork

Week 6

Week #7

From Observation to Models

2024-03-11

Classwork Time

Week 7

Classwork

Week 7

Classwork

Week 7

Classwork

Week 7

Classwork

Pre-Class Week 8

Homework - Part 1

Learning Markov Chains

1. Record your voice in AUDIO format, explaining the terms used in the Equation system.

2. Use screen recording to point to the terms you are discussing.

3. Publish your record in the Slack HOMEWORK CHANNEL.

Week #8

Infinite and Finite

2024-03-18

2nd Module Exam

APPROACHING

Theoretical Models

Service Systems

Week #8

From Observation to Models

2024-03-18

https://towardsdatascience.com/sql-joins-a-brief-example-9d015868b56a

https://www.google.com/search?q=andrey+andreyevich+markov&rlz=1C5CHFA_enLV889LV889&sxsrf=APq-WBsyI88xAvtsq7nGDiBEw2fcxhf7gg:1646897947719&tbm=isch&source=iu&ictx=1&vet=1&fir=1mWzaoYlCdvr8M%252Cv3SWMCoFghWAVM%252C%252Fm%252F0kz0%253BfJgqZDzcP0pUaM%252Co_AQCFk0WdmyFM%252C_%253BmBXNaksaj7WQ0M%252C12KOCiPVrIPXPM%252C_%253BmTj0m0tPFcUyKM%252C80KAu9zJ0rx8jM%252C_%253B18svUHl8YhDi9M%252CSgL9fpTCX3B9zM%252C_%253BVplz4lXluhbLiM%252CC613xlUTf5RX7M%252C_%253BElZthqyswocQ-M%252COGOZlLA1jJicWM%252C_%253BWIPpos0yzSuwOM%252C8POXzH7gnQ6F0M%252C_%253BVeyJaCGraCGUDM%252C8POXzH7gnQ6F0M%252C_&usg=AI4_-kR2sk7mcGr3QPtmSzFvW1MvfgN3fA&sa=X&ved=2ahUKEwjp5p35hLv2AhUhR_EDHTAhBhoQ_B16BAgpEAE#imgrc=5hEhbQsA4C8tUM

Week 8

FINITE SYSTEMS

DTMC

(Discrete-Time Markov Chains)

Markov Chains

CTMC

(Continuous-Time Markov Chains)

Challenges

Markov Models

BOOKS

https://slidetodoc.com/10-1-properties-of-markov-chains-in-this/

Professor has 4 umbrellas, Markov chain and Probability

https://www.youtube.com/results?search_query=markov+chains

SLIDES

VIDEOS

STACKEXCHANGE

Week 8

FINITE SYSTEMS

DTMC

Markov Chains

CTMC

Week 8

CLASSWORK

DTMC

Learning Markov Chains

OVERVIEW on DTMC

Aperiodic irreducible DTMCs are ergodic since each

has at least one state i with

p_{i,i} > 0

Demonstration Time

Week 8

DTMC

PROFESSOR-UMBRELLA MODEL

Learning Markov Chains

Classwork

Week 8

Classwork

Week 8

DTMC

Learning Markov Chains

PROFESSOR has 2 UMBRELLAS
For example, there is a chance of rain with one umbrella available at home, but even if the rain does, and the professor takes the umbrella to work, he/she will take it back if the precipitation occurs again. One can't take more than one umbrella, so the number of umbrellas varies from walk to walk AND from the weather conditions. But, if there is no rain occurring outdoors, the professor can forget to take an umbrella, like every one of us usually does. So, in the situation, if NO umbrellas are available, the bad (wet) things happen - you can easily guess what.
Compute and sketch the function of the probability of "getting clothes sodden" in a long term process (let's say - 60 walks) depending on the rain probability

P(getting\> wet) = f(P(rain))

P(rain)

Classwork

Week #9

From Observation to Models

2024-04-08

F.A.S.T.

https://medium.com/big-self-society/jim-kwiks-fast-method-will-help-you-learn-faster-5d3d669dc3b5

method

Week 9

Moving towards Reality

Homework - Part I and II

Learning through Models

Where is the Key of Problem Solving?

quantitative-model-checking

Week 9

FINITE SYSTEMS

DTMC

(Discrete-Time Markov Chains)

Markov Chains

CTMC

(Continuous-Time Markov Chains)

quantitative-model-checking

Demonstration Time

CTMC

(Continuous-Time Markov Chains)

Quantitative Model Checking

Week 9

Homework - Part I

CTMC

Learning Markov Chains

BARBER-SHOP
has 2 SEATS and 2 EXTRA WAITING SEATS
Two BarBERS are operating
If, ...

P(OneExtraSeatWillBeBusyAfter2HoursOfOperating) = \> ? \> \cdot

https://www.coursera.org/learn/quantitative-model-checking/lecture/DWlJz/definition-of-a-ctmc

quantitative-model-checking

Week 9

Homework - Part II

Demonstrate progress in the course:

https://www.coursera.org/learn/quantitative-model-checking/lecture/DWlJz/definition-of-a-ctmc

quantitative-model-checking

Week #10

From Observations to Models

2024-04-15

to PN

From

Week 9

Homework

Submit Matlab/Octave

code and plots related to BarberShop problem

Week 10

Homework - Part I

Get and Install the Snoopy tool

from Cottbus Uni

Learning Petri Nets

Demonstration Time

(Petri Nets)

MarkovChain

Petri Net

Control Element

State

Place

Transition

State Index

Number of

Tokens

Week 10

Homework - Part II

Using Snoopy

Learning Petri Nets

Transforming MC models

(e.g. BarberShop)

into simple but stochastic Petri Nets

Week #11

From Observations to Models

2024-04-15

From

Week 11

Moving towards Reality

Including all Homework Fragments

Demonstration Time

Tokens are on the Students' Court

Demonstration Time

The token is on the Instructor's Court

Week 11

Homework - Part I

Learning Petri Nets

Output

Demonstrate understanding of the topic, and namely,
Publish a handwritten recap of the lecture examples {Ex.1 .. Ex. 6} with comments

Participate in DELHI UNI Lecture:

Mod-05 Lec-08 Stochastic Petri Nets

https://www.youtube.com/watch?v=XpZEbHyHA2o

Week 11

Homework - Part II

Using Snoopy Tool and STPN Model,

Learning Petri Nets

Verify an Algebraic Model for the System M/M/1

through Load and Waiting Time metrics

Output

On YouTube published Video Report

Emotional Cycles

Week 1

Week 2

...

Week13

.END

CLASS NOTES

Week #12

From Observations to Models

2024-04-22

From

a SEMI-ULTIMATE Tool

Petri Nets in Modelling

Week 12

TODO: start thinking about the model

BW = 10 Mbps

BW = 100 Mbps

queue size?

T_{data\> transfer} = f(V, BW_1, BW_2, BW_3, \lambda, N )

Volume = {1..10} // Integer [Byte/Packet/Message]

Priority = {Low, High} // Integer

Origin = {1, 2} // Integer

Destination = {1 .. 6} // Integer

iat = { 12 .. } // Double [1/min]

lambda = { 5 .. } // Double [1/hr]

minQueueLength = {0...N}; // Integer

Server

Client 2

Client 1

Controller

Synchronous

Asynchronous

BW_k = {1,10,10,1000, \ldots} \> bps, Kbps, Mbps, \ldots

BW_1 = 100 \> bps

BW_2 = 10 \> bps

BW_3 = 1 \> bps

Asynchronous

Engineering Question: What is a value of

Scientific Research Topics

e.g. "Verifying theoretical M/M/x:x/x/x models utilising Petri Nets".
How to make queues, protocols and services better?
- e-mails, notifications, chats, bots, scheduling systems and apps
- authentication, authorisation, etc. protocols
- networking software/hardware, PLC controllers, etc.
Modelling with Higher-Order Tools
- PRISM Model Checker (from OXFORD UNI),
- UUPAAL
- ns-3,
- Fuzzy Logic Systems,
- ...

https://medium.com/literacy-discourse/what-does-imrad-reveal-about-science-7de7741ba987

Use IMRAD to demonstrate

Research Results

https://medium.com/literacy-discourse/what-does-imrad-reveal-about-science-7de7741ba987

Use IMRAD to demonstrate

Research Results

“Results are where the findings and the outcomes go.”

Week #13

From Observations to

Approved Models

2024-04-29

AND

VERIFIED BY

MODEL

CHECKER

MODEL

CHECKER

CLASS NOTES

The problem

The problem

https://www.prismmodelchecker.org/

The problem

THE PROBLEM

Week 13

Homework

using

PRISM MODEL CHECKER

Verifying Markov Chains

BARBER SHOP MODEL

Week #14

From Observations to

Reliable Models

2024-xx-xx

AND

VERIFIED BY

MODEL

CHECKER

From Observations to

Reliable Models

https://youtu.be/H6vSIM754X4

Focus
Fundamentals
Structure

That kick required is ...

PRACTICE

Demonstration Time

The token is on the Students' Court

Demonstration Time

The token is on the Students' Court

The problem

Demonstration Time

The token is on the Students' Court

Demonstration Time

The token is on the Students' Court

https://www.prismmodelchecker.org/

TODO

Initiate Your Research

Week 16

TODO (PRE-CLASS)

Do research like masters do!

Week 16

TODO (PRE-CLASS)

T = f(V, BW_1, BW_2, BW_3, \lambda, N )

Volume = {1..10} // Integer [Byte]

Priority = {1 .. 3} // Integer

Origin = {1.. 2} // Integer

Destination = {1 .. 6} // Integer

iat = { 12 .. } // Double [1/min]

lambda = { 5 .. } // Double [1/hr]

Integer minQueueLength = {0...N}; N_max = 1000

Server

Client 2

Client 1

Controller

Synchronous

Asynchronous

BW_k = {1,10,10,1000, \ldots} \> bps, Kbps, Mbps, \ldots

BW_1 = 100 \> bps

BW_2 = 10 \> bps

BW_3 = 1 \> bps

Asynchronous

Studying principles of Traffic Models in Packet-based Network
Mapping real network observations to empirical Theoretical Models

https://arxiv.org/pdf/1105.1347.pdf

T = f(V)

http://www0.cs.ucl.ac.uk/staff/m.handley/slides/nnfn-tcp.pdf

Week 16

TODO (PRE-CLASS)

Demonstration Time

The token is on the Instructor's Court

Studying principles of Traffic Models in Packet-based Network
Mapping real network observations to empirical Theoretical Models

Experiments with TCP flow finding an approximating function representing a waiting time for varying amount of data; 
e.g. 1KB  ... 100MB transferred from Server Instance to Client using 100 Mbps link on local PC machine.

Repeat the experiment, utilizing UDP protocol with up to 8 simultaneous flows.

 Prepare video report providing relevant experiment objectives, describing experiment, and presenting code, diagrams, and outcome discussion.

Week 16

TODO (PRE-CLASS)

Studying principles of Traffic Models in Packet-based Network
Mapping real network observations to empirical Theoretical Models

Week 16

TODO (PRE-CLASS)

Studying principles of Traffic Models in Packet-based Network
Mapping real network observations to empirical Theoretical Models

Week 16

TODO (PRE-CLASS)

Studying principles of Traffic Models in Packet-based Network
Mapping real network observations to empirical Theoretical Models

Week 16

TODO (PRE-CLASS)

T = f(V, BW_1, BW_2, BW_3, \lambda, N )

Volume = {1..10} // Integer [Byte]

Priority = {1 .. 3} // Integer

Origin = {1.. 2} // Integer

Destination = {1 .. 6} // Integer

iat = { 12 .. } // Double [1/min]

lambda = { 5 .. } // Double [1/hr]

Integer minQueueLength = {0...N}; N_max = 1000

Server

Client 2

Client 1

Controller

Synchronous

Asynchronous

BW_k = {1,10,10,1000, \ldots} \> bps, Kbps, Mbps, \ldots

BW_1 = 100 \> bps

BW_2 = 10 \> bps

BW_3 = 1 \> bps

Asynchronous

Week 16

TODO (PRE-CLASS)

T = f(V, BW_1, BW_2, BW_3, \lambda, N )

Volume = {1..10} // int [Byte]

Priority = {1 .. 3} // int

Origin = {1.. 6} // int

Destination = {1 .. 6} // int

iat = { 12 .. } // Double [1/min]

lambda = { 5 .. } // Double [1/hr]

BW = 1 bps

BW = 100 bps

int minQueueLength = 0;

Week 16

TODO (PRE-CLASS)

BW = 10 Mbps

BW = 100 Mbps

queue size?

ns-3

Week 16

TODO (PRE-CLASS)

queue size?

REAL NETWORK

Week 16

TODO (PRE-CLASS)

TODO

Week 16

TODO (PRE-CLASS)

Reflection on another Research

Week #15

From Passive Observation

to Wise Action

2024-05-13

F.A.S.T.

with

F.A.S.T.

do Forget

be Active

find the State

Teach the others

Jim Kwik

EXAM

time

It's about

Week 15

Homework - part I

with

PRISM MODEL CHECKER

Verifying

ANY

Queueing Model

Week 15

Homework - part II

with

Rabbit-MQ

Running, Validating and Verifying

ANY

Queueing Model

That kick required to become FAST is ...

PRACTICE

PRACTICE PARADIGM

What is Rabbit-MQ ?

https://www.rabbitmq.com/

One broker to queue them all

What is Rabbit-MQ ?

https://www.rabbitmq.com/

One broker to queue them all

RabbitMQ is a reliable and mature messaging and streaming broker, which is easy to deploy on cloud environments, on-premises, and on your local machine. It is currently used by millions worldwide.

Simplest BROKER

WORK QUEUES