Convener(s)
| Name: | Prof Subhamay Saha | Prof. Chandan Pal |
| Mailing Address: | Assistant Professor, Department of Mathematics, IIT Guwahati, Assam, 781039. |
Assistant Professor, Department of Mathematics, IIT Guwahati, Assam, 781039. |
| Email: | saha.subhamay at iitg.ac.in | cpal at iitg.ac.in |
Most real life phenomena evolve in a random fashion. In order to model such random evolution, we need the mathematical tool called stochastic processes. Knowledge of stochastic processes is useful for both mathematicians and engineers. In this advanced instructional school, we would like to cover the basics of some important stochastic processes and also we would like to illustrate their applications in solving real life problems. In the stochastic processes part, we plan to cover discrete time Markov chains and Poisson processes in detail. The students will be introduced to basic concepts in continuous time Markov chains and renewal processes. This will comprise of 23 lectures (approx). In the applications part the participants will learnt about Markov decision processes. Markov decision processes are widely used to analyze problems in the fields of operation research, epidemiology, mathematical finance etc. Another application area that will be covered is queueing systems. Now a days queueing systems are being used to deal with real life scenarios arising in diverse fields like computer networks, telecommunication networks and so on. This will comprise of 13 lectures (approx). This school is targeted towards first year post graduate students of science and engineering. Very basic knowledge of probability will be assumed.
Dates:
Venue:
Venue Address:
Department of Mathematics,
Indian Institute of Technology Guwahati,
Assam, 781039.
Venue State:
Venue City:
PIN:
Syllabus:
Syllabus: (Each speaker is required to deliver minimum 6 lectures).
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
|
Prof. Parthanil Roy ISI Bangalore |
7.5 hrs |
Definition and examples of Discrete-time Markov chains, 1 and n-step transition probability matrices; Communication and irreducibility; Hitting times and absorption probabilities; Strong Markov Property; Recurrence and transience; Invariant distributions. limit theorems for discrete-time Markov chains. |
|
Dr. Subhamay Saha IIT Guwahati |
6 hrs |
Reversible Markov chains Definition and properties of Renewal Processes; Renewal equations and its generalizations; Elementary renewal theorem, Key renewal theorem; Excess life and age distribution; Renewal reward processes. |
|
Dr. Koushik Saha IIT Bombay
|
6 hrs |
Exponential distribution and its properties; Definition of Poisson processes, Inter-arrival times, nth arrival time, conditional arrival times; Poisson thinning, merging of two independent Poisson processes; Compound Poisson processes. |
|
Dr. Chandan Pal IIT Guwahati |
4.5 hrs |
Definition and examples of continuous-time Markov chains; Rate matrix, transition probability function, Kolmogorov forward and backward equations; Birth-death processes; Limiting probabilities. |
|
Prof. Mrinal K. Ghosh IACS, Kolkata |
6 hrs |
Discrete-time Markov decision processes; Finite horizon problems; Infinite horizon discounted and average cost problems. Semi-Markov decision processes; Infinite horizon discounted and average cost problems. |
|
Prof. N. Selvaraju IIT Guwahati |
6 hrs |
Characteristics of queueing systems, Little’s law, Markovian and non-Markovian queueing systems, embedded Markov chain applications to M/G/1, G/M/1 and related queueing systems; Networks of queues, open and closed queueing networks; Queues with vacations, priority queues. |
References:
- J. R. Norris, Markov Chains, Cambridge University Press, 1997.
- S. M. Ross, Stochastic Processes, 2nd edition, Wiley, 2008.
- S. M. Ross, Applied Probability Models with Optimization Applications, Dover Publications, 1992.
- D. Gross and C. Harris, Introduction to Queueing Theory, 3rd Edition, Wiley, 1998 (WSE Edition), 2004.
Tutorial Assistants:
|
S. No. |
Name |
Affiliation |
|
1 |
Bivakar Bose |
IIT Guwahati |
|
2 |
Amit Ghosh |
IIT Guwahati |
|
3 |
Pratim Dey |
IIT Guwahati |
Time Table:
Time-Table (with names of speakers and course associates/tutors):
|
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.05 To |
Lecture 2 (11.30 |
Lunch (1.05 |
Tutorial (2.30 |
Tea (3.35 to |
Tutorial (4.00 |
Snacks 5.05 to |
|
|
|
(name of the speaker) |
|
(name of the speaker) |
|
(name of the speaker + tutors) |
|
(name of the speaker + tutors) |
|
|
Mon |
13/5 |
DTMC-1(PR) |
|
DTMC-2(PR) |
|
PR+PD+AG |
|
PR+PD+AG |
|
|
Tues |
14/5 |
PP-1(KS) |
|
DTMC-3(PR) |
|
KS+PD+AG |
|
PR+PD+AG |
|
|
Wed |
15/5 |
DTMC-4(PR) |
|
PP-2(KS) |
|
PR+PD+BB |
|
KS+BB+AG |
|
|
Thu |
16/5 |
DTMC-5(PR) |
|
PP-3(KS) |
|
PR+BB+AG |
|
KS+BB+PD |
|
|
Fri |
17/5 |
DTMC-6(SS) |
|
PP-4(KS) |
|
SS+BB+AG |
|
KS+PD+BB |
|
|
Sat |
18/5 |
RP-1(SS) |
|
CTMC-1(CP) |
|
SS+PD+AG |
|
CP+BB+AG |
|
|
SUNDAY: OFF |
|||||||||
|
Mon |
20/5 |
RP-2(SS) |
|
CTMC-2(CP) |
|
SS+AG+BB |
|
CP+BB+PD |
|
|
Tues |
21/5 |
RP-3(SS) |
|
CTMC-3(CP) |
|
SS+BB+PD |
|
CP+BB+AG |
|
|
Wed |
22/5 |
MDP-1(MKG) |
|
QT-1(NS) |
|
MKG+PD+AG |
|
NS+PD+BB |
|
|
Thu |
23/5 |
MDP-2(MKG) |
|
QT-2(NS) |
|
MKG+PD+AG |
|
NS+AG+BB |
|
|
Fri |
24/5 |
MDP-3(MKG) |
|
QT-3(NS) |
|
MKG+PD+AG |
|
NS+PD+BB |
|
|
Sat |
25/5 |
MDP-4(MKG) |
|
QT-4(NS) |
|
MKG+BB+PD |
|
NS+AG+BB |
|
DTMC- Discrete-time Markov Chains
PP- Poisson Processes
RP- Renewal Processes
CTMC- Continuous-time Markov Chains
MDP- Markov Decision Processes
QT- Queueing Theory
Full forms for the abbreviations of speakers and tutors:
PR: Parthanil Roy
KS: Koushik Saha
SS: Subhamay Saha
CP: Chandan Pal
MKG: Mrinal K. Ghosh
NS: N Selvaraju
PD: Pratim Dey
AG: Amit Ghosh
BB: Bivakar Bose
Selected Applicants:
| sr.n | SID | Full Name | Gender | Affiliation | Position in College/University | Year of Passing M.Sc./M.A | Ph.D. Degree Date |
| 1 | 54303 | Mr. Raktim Ray | Male | Jadavpur University | MSc Student | Awaiting Result | |
| 2 | 54322 | Mr. Jyotishko Sarkar | Male | Jadavpur University | Msc Student | Awaiting Result | |
| 3 | 54336 | Mr. Subramanian G | Male | Bharathiar University | M.Sc Student | Awaiting Result | |
| 4 | 54350 | Mr. Poleen Kumar | Male | Indian Institute of Technology, BHU | Ph.D. Scholar | 2020 | |
| 5 | 54379 | Mr. Abdul Rahman | Male | IIT Madras | MSc Student | Awaiting Result | |
| 6 | 54393 | Ms. Savita Chaturvedi | Female | IIT BHU | PhD | 2018 | |
| 7 | 54422 | Ms. Vaishnavi Nampally | Female | Osmania Univeristy | Research Scholar | 2021 | |
| 8 | 54487 | Ms. Shilpa . | Female | Central University of Punjab | PhD | 2023 | |
| 9 | 54493 | Ms. Pooja Yadav | Female | Birla Institute of Technology and Science Pilani, Pilani Campus | PhD | 2018 | |
| 10 | 54500 | Mr. Pradeep Vishwakarma | Male | IIT Bhilai | PhD | 2022 | |
| 11 | 54503 | Ms. Manisha . | Female | Indian Institute of Technology Bhilai | PhD student | 2020 | |
| 12 | 54504 | Ms. Pooja Balhara | Female | BITS Pilani | PhD | 2017 | |
| 13 | 54510 | Ms. Ashwini Soundararajan | Female | BITS Pilani Hyderabad Campus | Ph.D. | 2017 | |
| 14 | 54558 | Mr. Rajdeep Pathak | Male | Indian Institute of Technology Hyderabad | MSc Student | ||
| 15 | 54560 | Ms. Rohini Bhagwanrao Pote | Female | Indian Institute of Technology Bhilai | PhD | 2021 | |
| 16 | 54602 | Ms. Sowmica S | Female | Bharathiar University | PhD | 2020 | |
| 17 | 54660 | Mr. Utpal Jyoti Deba Sarma | Male | Indian Institute of Technology Delhi | Ph.D. | 2021 | |
| 18 | 54668 | Mr. Akhil Vijayan R | Male | Central University of Kerala | PhD | 2019 | |
| 19 | 54670 | Mr. Santo Sali | Male | Central university of kerala | PhD | 2019 | |
| 20 | 54694 | Mr Arif Ali | Male | Indian Institute of Science Education and Research Thiruvananthapuram (IISER TVM) | MSc Student | 2020 | |
| 21 | 54773 | Mr. Piyush Gupta | Male | J.C. Bose University of Science and Technology, YMCA | Ph.D. Student | 2019 | |
| 22 | 54800 | Mr. Jaswinderpal Singh | Male | Indian Institute of Technology, Ropar | PhD. Student | 2023 | |
| 23 | 54909 | Ms. Trisha Rani | Female | IIT Ropar | PhD | 2023 | |
| 24 | 54924 | Mr. Sandip Roy | Male | Indian Institute of Technology Indore | Ph.D Student | 2022 | |
| 25 | 54968 | Mrs. Ananya Biswas | Female | IISER-KOLKATA | MSc Student | Appeared / Awaiting Result | |
| 26 | 54969 | Mr. Raj Karan Gupta | Male | Indian Institute of Technology Roorkee | PhD | 2022 | |
| 27 | 55490 | Mr. Hirak Jyoti Sarma | Male | Institute of Advanced Study in Science and Technology | PhD | 2020 | |
| 28 | 55522 | Ms. Sanjeevni Goel | Female | IIT ROPAR | PhD | 2021 | |
| 29 | 55725 | Mr. Joydip Roy | Male | Indian Institute Of Technology,Tirupati | MSc | Awaiting Result | |
| 30 | 55878 | Mr. Gaurav Kandpal | Male | Indian Institute of Technology Kharagpur | PhD | 2022 | |
| Local Patricipant | |||||||
| 1 | 54586 | Mr. Asad Uddin | Male | Indian Institute of Information Technology, Guwahati | phD | 2022 | |
| 2 | 55457 | Ms Bratati Pal | Female | Indian Institute of Information Technology, Guwahati | PhD | 2022 | |
| 3 | 55914 | Dr. Anjana Begum | Female | Nowgong Girls' College | Assistant Professor | 2015 | |
| Waiting list | |||||||
| 1 | 55030 | Ms. Ritu Attri | Female | TIFR Centre for Applicable Mathematics | Int PhD | ||
| 2 | 55031 | Mr. Ajith Krishna Deyan | Male | TIFR centre for applicable mathematics | Integrated Phd student | ||
| 3 | 55032 | Mr Raquibul Karim | Male | TIFR CAM | Int. Phd student | ||
| 4 | 55583 | Ms. Aindrila Rakshit | Female | Tata Institute of Fundamental Research, Mumbai | Integrated PhD (Research Scholar) | ||
| 5 | 54995 | Ms. Amita Maurya | Female | IIT BHU | PhD | 2018 | |
| 6 | 54927 | Mr.Pankaj Pankaj Saha | Male | IIT Indore | MSc student | Awaiting Result | |
| 7 | 54663 | Ms Evana Islam Sarkar | Female | IIT Bhubaneswar | PhD Student | 2019 | |
| 8 | 54571 | Mr Somnath Mondal | Male | Indian Institute of Technology Bhilai | PhD | 2021 | |
| 9 | 54545 | Ms. Amina Fayeque Ali Ulde | Female | Institute of Chemical Technology | MSc Student | ||
| 10 | 54507 | Mr. Ritik Soni | Male | Central University of Punjab, Bathinda | Research Scholar(PhD) | 2019 | |
| 11 | 54502 | Mr. Bipattaran Mandal | Male | IIT Jodhpur | MSc- MTech Student | 2023 | |
| 12 | 54438 | Mr Aditya Sharma | Male | IIT INDORE | PhD | 2020 | |
| 13 | 55116 | Mr. Saptarshi Halder | Male | Indian Statistical Institute, Bangalore Centre | M.Math Student | Awaiting Result | |
| 14 | 55186 | Mr. Md Rahil Miraj | Male | Indian Statistical Institute, Bangalore | M.Math Student | ||
| 15 | 54416 | Ms. Shinjini Paul | Female | Indian Institute of Science Education and Research, Pune | MSc Student | Awaiting Result | |
How to Reach:
TBA