Queueing Theory and Stochastic Modelling

• B.Sc. (Eng, Phy, Chem, Math) , 1998 , University of Jammu, Jammu
• M.Sc. (Statistics) , 2001 , Kurukshetra University, Kurukshetra
• Ph.D. (Statistics) , Awarded on Aug. 11, 2006 , Kurukshetra University, Kurukshetra
• PGDBA (Finance) , 2007 , Guru Jambheshwar University, Hisar
• PDF , 2008 , Kurukshetra University, Kurukshetra

Prof. Darvinder Kumar is currently working as a Principal in the PGDAV College (University of Delhi), Nehru Nagar, New Delhi wef 01.05.2025. He has worked as a Vice-Principal in the PGDAV College from 22.10.2024 to 30.04.2025. Dr. Kumar is a Professor in the Department of Statistics and has been teaching various courses of Statistics for the last 18 years. He has completed his B.Sc (PCM) from University of Jammu, M.Sc (Statistics), Ph.D, PDF, Diploma course in German, Certificate course in French from Kurukshetra University, Kurukshetra and PGDBA (Finance) from Guru Jambheshwar University of Science and Technology, Hisar. He was also awarded the University Research Scholarship for Ph.D Statistics from KUK and Post-Doctoral Fellowship from University Grants Commission, New Delhi. Before joining PGDAV College, he has worked as a Lecturer at the P.G. Department of Statistics, Sardar Patel University, Vallabh Vidyanagar on permanent basis.

His areas of research interest are “Queueing Theory, Stochastic and Queueing Models with Catastrophes, Feedback, Restoration effects and Environmental Changes”. He has published 29 research papers in national/ international journals of repute and presented more than 15 research papers in national/ international conferences. He has written Four Chapters of M.A. Economics, II Year course (MEC-109) for IGNOU, Maidan Garhi, New Delhi.

In the past, he was a member of various committees at the college including Admission committee, Apex committee, ICC, IQAC, Sports committee, Discipline committee, Placement cell, Canteen committee, Care Taker committee, Work load committee, Purchase committee, SAF, Student union advisor, Statistics Dept. Society 'Sankhyiki', Academic committee, Coordinator of IQAC and many more. Acted as Co-coordinator in the 10 days Online FDP on ‘NEP Orientation & Sensitization Programme’ under Malaviya Mission Teacher Training Programme of UGC organized by CPDHE in collaboration with PGDAV College, University of Delhi.

He is a life member of the six professional societies viz. ISPS, FIM, IISA, ORSI, ISMS and ISAS. He was a member of committee of undergraduate courses (B.Sc Mathematical Science) during 2011-2013, Member of Departmental Research Committee (2020-2023) and M.Phil. Committee (2021-2024) at the Department of Statistics, University of Delhi. He is also a member of Board of Moderator for various courses of Statistics and an approved supervisor for the PhD students supervision from the Dept. of Statistics, University of Delhi.

Dr Kumar is one of the founder member of the IGNOU Study Centre-07174 at the PGDAV College and worked as Part-time Assistant Coordinator-cum-Academic Counselor since inception from 24.10.2013 to 31.12.2018. Presently, he has been working as Part-time Coordinator at the study centre since January, 2019 to till date. 

Discriptive Statistics, Coorelation and Regression, Probability, Probability Distributions, Statistical Methods, Statistical Simulation, Operations Research, Linear Programming Problems, Transportation and Assignment Problems, Goal Programming, and Dynamic Programming Problems, Non Linear Problems, Applied Statistics, Index Numbers, Demand Analysis, Sampling Distributions, Large sample theory, Small sample theory, Statistical Inference, Theory of Estimation, Testing of Hypothesis, Stochastic Processes, Queueing Theory, Game theory, Inventory Models, Linear Models etc etc

Ph.D students Supervisorship: Got approval for Ph.D students Supervisorship from the Dept of Statistics, University of Delhi.

Evaluation of Ph.D Synopsis: Evaluated the Ph.D synopsis entitled “Optimization of Queuing System in Healthcare Sector with Machine Learning Approach ” for the award of the Ph.D. Degree of the Banasthali Vidyapith, Jaipur (2023).

Member of various committies at PGDAV College:

• Member, Caretaker Committee (2010-11, 2016-19)
• Member, Student Union Advisor (2011-13)
• Convener, Statistics Society (2011-12, 2019-20)
• Member, Admission Committee (2011-12, 2019-20)
• Member, Sports Committee (2011-13, 2014-15, 2017-18, 2021-22)
• College/Internal Complaint Committee (2012-21)
• Member, Purchase Committee (2012-16)
• Member, Lawn and Garden Committee (2013-14)
• Placement Cell, Teacher Coordinator (2013-14) and member 2014-17)
• Teacher Incharge (2015-16, 2022-23)
• Member, Discipline Committee (2015-21)
• Member, Work Load Committee (2016-21)
• Member, Anti- Ragging committee (2018-19)
• Member, SAF Committee (2019-21)
• Member, Canteen Committee (2019-21)
• Member, IQAC -30th March, 2021 onwards (2021-23)

  Member of Various Committees at Department of statistics, D.U.

• Member, Committee of Courses for Undergraduate Studies (Excluding Honours) in Statistics for a period of two years w.e.f 01.10.2011 (2011-13).
• Member, Sub- Committee to prepare and finalize the guidelines and pattern of the question paper for two papers STP- 303 (Statistical Methods- II) and STP- 404 (Applied Statistics) of the semester based course “B.Sc. Mathematical Sciences” implemented from 2011-12.
• Member, Sub- Committee to prepare and finalize the guidelines and pattern of the question paper for paper STP- 505 (Statistical Inference) of Semester-V of the semester-based course “B.Sc. Mathematical Sciences” implemented from 2011-12.
• Member, Committee to prepare and finalize the appropriate titles and contents of two papers of Inference under the structure of 4 year under- graduate degree programme in Statistics implemented from 2013-14.
• Member, Sub- Committee to prepare and finalize the guidelines and pattern of the question paper for paper GE-2: Introductory Probability (Semester II) of the B.Sc. (H) Statistics under CBCS implemented from 2015-16.
• Member, Sub- Committee to prepare and finalize the guidelines and pattern of the question paper for paper Core-3: Statistical Inference of the B.Sc. (Programme) Math. Sciences under CBCS implemented from 2016-17.
• Member, Sub- Committee to prepare and finalize the guidelines and pattern of the question paper for two papers Stat- Core-4: Survey Sampling and Design of Experiments of B.A. Programme Semester- IV under CBCS and Paper Core 4: Survey Sampling and Design of Experiments of B.Sc. Programme Mathematical Sciences under CBCS implemented from 2016-17.
• Member, Sub- Committee to prepare the syllabi for papers CORE-3: Statistical Inference, SEC-3: Statistical Simulation of “B.Sc. (Prog.) Mathematical Sciences” and SEC-3: Simulation Techniques in Statistics of the “B.A. (Prog.) Statistics” under CBCS (LOCF) implemented from 2019-20.
• Member, Departmental Research Committee for a period of two years with effect from 12.04.2021 in the Dept of Statistics, University of Delhi.
• Member, M.Phil Committee for a period of three years with effect from 06.08.2021 to 2024 in the Dept of Statistics, University of Delhi.
• Member, Sub-Committee to prepare and finalize the syllabus of paper Introductory Probability [GE-2(a)- 4 Credits] for B.Sc. (H) Statistics, Semester II under UGCF 2022 implemented from 2022-23.
• Member, Sub-Group to review and finalize the draft syllabus of Semester-II for the course Introduction to Probability of B.Sc. (H) Statistics as per UGCF 2022 implemented from the session 2022-23.
• Member, Sub- Committee to prepare and finalize the guidelines and pattern of the question paper for Core-1: Descriptive Statistics and Probability Theory of the course “B.Sc. (Prog.) Multidisciplinary with Statistics” Semester-I under UGCF 2022 implemented from the academic session 2022-23.
• Member, Board of Moderators for B.Sc. (Prog.) Mathematical Science (Statistics) examinations under CBCS system held in November/ December, 2022.
• Convener, Sub- Committee to prepare and finalize the syllabus for Core-4: Statistical Inference of the course “B.Sc. (Prog.) Multidisciplinary with Statistics” Semester-IV under UGCF 2022 implemented from the academic session 2022-23.
• Member, Sub- Committee to prepare and finalize the syllabus for Core-7: Stochastic Processes and Queueing Theory of the course “B.Sc. (Prog.) Multidisciplinary with Statistics” Semester-VII under UGCF 2022 implemented from the academic session 2022-23.
• Member, Sub- Committee to prepare and finalize the syllabus for DSE-6c: Multivariate Data Analysis of the course “B.Sc. (Prog.) Multidisciplinary with Statistics” Semester-VIII under UGCF 2022 implemented from the academic session 2022-23.
• Member, Sub- Committee to prepare and finalize the syllabus for DSE-6d: Statistical Simulation of the course “B.Sc. (Prog.) Multidisciplinary with Statistics” Semester-VIII under UGCF 2022 implemented from the academic session 2022-23.
• Member, Sub- Committee to prepare and finalize the syllabus for DSE-6d: Simulation Techniques in Statistics of the course “B.Sc. (H) Statistics” Semester-VIII under UGCF 2022 implemented from the academic session 2022-23.
• Convenor, Sub- Committee to prepare and finalize the guidelines and pattern of the question paper for GE2(a): Introductory Probability of B.Sc. (H) Statistics, Sem-II under UGCF 2022 implemented from the academic session 2022-23.
• Member, Sub- Committee to prepare and finalize the guidelines and pattern of the question paper for DSE1(a): Optimization Techniques of B.Sc. (H) Statistics, Sem-III under UGCF 2022 implemented from the academic session 2022-23.
• Member, Sub- Committee to prepare and finalize the guidelines and pattern of the question paper for DSE10: Statistical Simulation of B.Sc. (Prog.) Multidisciplinary with Statistics, Sem-V under UGCF 2022 implemented from the academic session 2022-23.
• Member, Sub- Committee to prepare and finalize the guidelines and pattern of the question paper DSE3(b): Simulation Techniques in Statistics of B.Sc (H) Statistics, Sem-V under UGCF 2022 implemented from the academic session 2022-23.

• Convenor, Sub- Committee to prepare and finalize the guidelines and pattern of the question paper for DSE3(a): Index Numbers and Time Series Analysis of B.Sc. (Prog.) Multidisciplinary with Statistics, Sem-III under UGCF 2022 implemented from the session 2022-23.

• Member, Board of Moderators for B.A (Prog.)/B.Sc. (Prog.) with Statistics, Semester-I, III & V under CBCS/UGCF 2022 (NEP) examinations held in November/ December, 2023.
• Member, Board of Moderators for B.A (Prog.)/B.Sc. (Prog.) with Statistics, Semester-II, IV & VI under CBCS/UGCF 2022 (NEP) examinations held in May/ June, 2024.

Some Queueing Models Incorporating the Effects of Environmental Change and Catastrophes

BOOK CHAPTERS WRITTEN:

• Four units of the course MEC-109 on Research Methods in Economics, M.A. Economics (Part- II) Programme of IGNOU Maidan Garhi, New Delhi during 2015-16.

1. Transient Analysis of a Queue with Environmental and Catastrophic Effects, International Journal of Information and Management Sciences.

2. A Catastrophic Queueing System with State Dependent Service and Environmental change, Proceedings of National Conference on Applications of Mathematics in Engineering & Technology and 7th Annual Conference of ISITA.

3. A Catastrophic Queue with State Dependent Environmental change parameter, South East Asian Journal of Mathematics and Mathematical Sci.

4. Comparative Study of Various Mutual Funds Schemes in India, Amity Global Business Review.

5. Combating the Pandemic With ICT-Based Learning Tools and Applications: A Case of Indian Higher Education Platforms, International J. of Virtual and Personal Learning Environments.

6. Trend Analysis and Export Competitiveness of Coffee Production in India, IAHRW, International Journal of Social Sciences Review.

7 Evaluation of Genetic Variation in Indian mustard (Brassica Juncea L Czern & Coss) Using Multivariate Techniques, J. of Agriculture Research and Technology

8. Transient solution of a two homogeneous servers Queueing system with Environmental change, Catastrophic and Restoration effects, Shodh Disha

9. Analysis of a Queueing System with Catastrophe, State Dependent Input Parameter and Randomly Changing Environmental effects, Shodh Disha.

10. Optimization of cultural conditions for chitosan production from Aspergillus flavus strain AF2118, The Pharma Innovation Journal.

11. Regression weather-yield models for western-zonal cotton yield prediction of Haryana, International J. of Statistics and Applied Mathematics.

12. A Queueing System with Catastrophe, State dependent Input Parameter and Environmental change, International J. of Applied Math and Statistical Sciences.

13. Parameter estimation of Type-II extreme value distribution for censored data, International Journal of Statistics and Applied Mathematics.

14. A Queueing system incorporating the effects of Environmental change and Catastrophes, International Journal of Mathematics and Statistics Invention. 

15. A Queueing system with Catastrophe, State dependent Service and Environmental change, Bulletin of Mathematics and Statistics Research.

16. A Statistical analysis of knowledge-attitude-practice on crypto currency in Madurai City, J. of Mathematical Problems, Equations and Statistics.

17. Price analysis of onion cultivation in Mewat District of Haryana, International Journal of Statistics and Applied Mathematics.

18. Transient solution of a two homogeneous servers Markovian Queueing system with Environmental, Catastrophic and Restoration effects, International J. of Math and Statistics Studies

19. Transient Analysis of A Limited Capacity Queueing Model With Environmental Change and Catastrophic Effects, IOSR- Journal of Mathematics

20. An Exploratory Research On Indian Digital Payment, International Journal of Information Engineering and Electronic Business.

21. Performance analysis of a limited capacity Queueing model incorporating the effects of two Environmental changing states and Catastrophes, Journal of Computational Analysis and Applications.

22. A Queueing system with Catastrophe, Feedback, State dependent Service and Environmental change, Cuestiones de Fisioterapia

23. Transient Analysis of a Finite Capacity Queueing System with Catastrophes and State-Dependent Environmental Change Parameter, J. of Research in Applied Math.

24. Transient Analysis of a Queueing System with Feedback, Catastrophes and State-Dependent Environmental Change Parameter, Journal of Electrical Systems

25. Transient analysis of a Queueing system incorporating the effects of Feedback, Randomly changing states and Catastrophes, International J. of Intelligent Systems and applications in Engineering

26. A Queueing System with Feedback, Catastrophe,  State Dependent Input Parameter and Randomly Changing states, Panamerican Mathematical Journal

27. Statistical Model Comparison for the National Stock Exchange (NSE) Stock Price Prediction, Communications on Applied Nonlinear Analysis.

28. Time Dependent solution of a two homogeneous servers Markovian Queueing system with Feedback, Environmental, Catastrophic and Restoration effects, Strad Research Journal.

1. Paper entitled "Transient Solution of a Queue with Environmental and Catastrophic Effects", presented in Eleventh International Conference- SCRA 2004- FIM held at University of Lucknow during December 27-29, 2004.
2. Paper entitled "A Catastrophic Queue with State Dependent Environmental change parameter", presented in Eleventh International Conference- SCRA 2004- FIM held at University of Lucknow during December 27-29, 2004.
3. Paper entitled "A Queueing System Incorporating the Effects of Environmental change and Catastrophes", presented in 37th Annual Convention ORSI held at IIM Ahmedabad during January 8-11, 2005.
4. Paper entitled "A Catastrophic Queueing System with State Dependent Input parameter and Environmental change", presented in Ist J&K State Science Congress held at University of Jammu during Feb.7-9, 2005.
5. Paper entitled "A Catastrophic Queueing System with State Dependent Service and Environmental change", presented in National Conference on Applications of Math in Engineering & Technology and 7th Annual Conference of ISITA held at MIMIT Malout during March 26-28, 2005.
6. Paper entitled "Transient Solution of a Queue with Environmental Effects and Catastrophic Effects" presented in Eighteenth International Conference- IMST 2009-FIM XVIII held at JayPee University of Information Technology, Waknaghat, Solan during August 02-04, 2009.
7. Paper entitled “Transient analysis of a queueing model with feedback, two  environmental changing states and catastrophes” presented in International Conference on Recent Advances and Innovations in Biological and Applied Sciences held at SGT University, Gurugram, Haryana during June 14-16, 2022.
8. Paper entitled “Transient Analysis of a queue with random environment subject to catastrophe” presented (online) in the 1st International Conference on Mathematical and Statistical Sciences (ICMSS-1) organized by Namibia University of Science and Technology during July 3-4, 2023.
9. Paper entitled “Transient analysis of a Queueing system incorporating the effects of Environmental change and Catastrophes” presented in International Conference on Recent Trends in Mathematics, Statistics and Engineering organized by the School of Technology, Management and Engineering, SVKM's NMIMS (Deemed-to-be University), Indore in Hybrid Mode during December 22-23, 2023.
10. Paper entitled “Transient Analysis of a Queueing Model with Environmental Change and Catastrophic Effects” presented in Fifth International Conference on Emerging Trends in Mathematical Sciences & Computing organized by Department of Basic Science & Humanities, Institute of Engineering & Management, Kolkata in Hybrid Mode during 2-4 February, 2024.
11. Paper entitled “Transient analysis of a Queueing system with Catastrophe, State dependent Service and Environmental change” presented in International Conference on Recent Advances of Probability and Statistics in Interdisciplinary Research-2024 during February 06-08, 2024.

    CONFERENCES INVITED SESSION/SESSION CHAIRED:

12.  Chaired a session in International Conference on RAIBAS-2022 held at SGT University, Gurugram during June 14-16, 2022.
13.  Paper entitled “A Queueing system with Catastrophe, State dependent Service and Environmental change” presented as Invited Session in International Conference on RAPSIR-2024 organized by Dept. of Statistics, University of Allahabad during February 06-08, 2024.

FDP/ Conference/ workshop organized:

• Acted as Co-coordinator in the 10 days Online FDP on ‘NEP Orientation & Sensitization Programme’ under Malaviya Mission Teacher Training Programme (MM-TTP) of UGC organized by CPDHE in collaboration with PGDAV College, University of Delhi  during 19th– 28th  November, 2024.

E- WORKSHOP/ WEBINAR/ CONFERENCES/FDP ATTENDED:

• Attended Five Days E-Workshop on “Stochastic Modelling, Optimization and Soft computing” (SMOSC 2020), organized by Dept. of Mathematics and Statistics, Manipal University Jaipur during 10-14 August 2020.
• Attended Three Days Webinar Series (Professional) organized by IQAC, PGDAV College on "Transforming Teaching-Learning Process using ICT Tools" during 28-30 August 2020.
• Attended one day webinar organized by the Statistics Society ‘SANKHYIKI' of PGDAV College to celebrate the 14th National Statistics Day in the memory of Prof. P.C. Mahalanobis on 29th June 2020. 
• Attended First International Webinar Conference on “Uncertainty Theory and Decision Making” (FIWC-UTDM) jointly organized by the School of Applied Science & Humanities, Department of Computer Applications, Haldia Institute of Technology in collaboration with the Department of Applied Science, Maulana Abdul Kalam Azad University of Technology, West Bangal, India from 28–30 November, 2020.
• Attended National Webinar on “First Help in Medical Emergence” organized by Health & Hygiene Committee, Maitreyi College, University of Delhi on 27th December, 2020.
• Attended one week online workshop on “Role of Technology and some specific tools in Research” organized by Shree Guru Gobind Singh Tricentenary (SGT) University, Gurugram during 28 June-03 July, 2021.
• Attended Five Days E-Workshop on “LaTex”, organized by the Department of Mathematics, Gandhi Institute of Technology and Management (GITAM), Banguluru during 05-09 July, 2021.
• Attended International Conference (Virtual Mode) on ‘Emerging Trends in Statistics and Data Science’ in conjunction with the 40th Annual Convention of ISPS during 07-10 September, 2021.
• Attended 3-Days Workshop on “Data Analysis Using SPSS” held at Department of Statistics, Manipur University in virtual mode during 18-20 October, 2021.
• Attended International Webinar Series on “Applications of Stochastic Models and Queueing Theory” organized by the Department of Mathematics, Central University of Rajasthan, held on six days during October 11, 2021 - November 11, 2021.
• Attended 27th international conference of IAPS (online) on Recent Advances in Mathematics & Computational Optimizations (RAMCO), jointly organized by School of Computational and Integrative Sciences, JNU New Delhi & International Academy of Physical Sciences (IAPS) during Oct. 26-28, 2021.
• Attended International Workshop on ‘Integrated Approaches of Stochastic Modelling and Data Science for Sustainable Development’ in conjunction with Diamond Jubilee Celebrations (1962-2022) of Dept of Statistics, S.V. University jointly organized with ISPS during 07-11, September, 2022.
• Attended one-week Virtual FDP on ”Mathematical Modelling and Computation in Engineering" organized by the Department of Mathematics, SRMIST, Delhi-NCR Campus, Ghaziabad, India from 24-30 July, 2023. 
• Attended Annual Seminar on “Statistical Methods and Applications in Interdisciplinary Areas” (SMAIA-2024) organized by the Dept. of Statistics, University of Delhi during March 8-9, 2024.
• Attended One-Week Online Workshop on “Research Methodology & Data Analysis” organized by the IQAC, Mata Sundri College for women (University of Delhi) in collaboration with Resilient Foundation For Academic Innovation & Scientific Research, New Delhi (Registered with NITI Aayog, Govt of India) during 22-28 April, 2024.
• Attended one day online workshop on ”Selection of UGC Care/ Web of Science/ Scopus Journals for publication of Research Papers" organized by the Dept of Population Studies & Social Work, Sri Venkateswara University, Tirupati, Andhara Pradesh on 15th July, 2024. 
• Attended Five-Days Faculty Development Program on ‘'Recent Trends in Computational Sciences'' jointly organized by the Department of Statistics and Department of Mathematics, Amity Institute of Applied Sciences, Amity University Kolkata from 22nd  July - 26th  July, 2024.
• Attended one-week online Faculty Development Program (FDP) on ‘Data Analytics and Decision Making with Statistical Software for Entrepreneurs and Innovators’ organized by Department of Mathematics & Statistics, Manipal University Jaipur, Rajasthan from  August 27 to 31, 2024.

•  

LIFE MEMBERSHIP OF PROFESSIONAL BODIES:

1. Life Member of Forum for Interdisciplinary Mathematics (FIM).
2. Life Member of International Indian Statistical Asso. (India Chapter).
3. Life Member of Indian Society for Probability and Statistics (ISPS).
4. Operational Research Society of India (ORSI).
5. Indian Society of Agricultural Statistics (ISAS).
6. Indian Society for Medical Statistics (ISMS).

a. Nominated as an Observer by the University Grant Commission/ CBSE, New Delhi for JRF and eligibility for Lectureship examination at the various centres.

b. Nominated as an Observer by the Central Board of Secondary Education, New Delhi for JEE (Main) examination at the various centres.

• ORIENTATION PROGRAMME / REFRESHER COURSES ATTENDED:

1. Attended 94th 4-Week Orientation Programme Organized by UGC- ASC, Jamia Millia Islamia, New Delhi during 18 October –16 November, 2010.
2. Attended 5th 3- Week Refresher Course in Basic Sciences (ID) Organized by UGC- HRDC, Jamia Millia Islamia, New Delhi during 05–25 May, 2015.
3. Attended 3-week Refresher Course on Maths, Statisticss and Operations Research organized by UGC-HRDC, GGV, Bilaspur during 1–21 Dec, 2016.
4. Attended 1st 3-Week Refresher Course in Computational and Math. Studies organized by UGC- H.R.D.C, Jamia Millia Islamia, Delhi during 29 Aug–19 Sept, 2018.
5. Attended 80th 2-Week Refresher Course in Mathematics and Statistics Sciences organized by UGC- H.R.D.C, Punjabi University, Patiala during 16–28 Nov, 2020.