Dr. B. KRISHNA KUMAR Professor

Dr. B. KRISHNA KUMAR Professor Address : Department of Mathematics, CEG Campus, Anna University, Chennai - 600 025. E-Mail ID : drbkkumar@hotmail.com Phone : 044-2235 8528 Present Position, College of Engineering Guindy, Anna University, Chennai from April-2010. Previous Positions Associate professor, Department of Mathematics, College of Engineering Guindy, Anna University, Chennai during April-2009 and March-2010. Assistant, College of Engineering Guindy, Anna University, Chennai during April-2002 and March-2009. Degree Lecturer, Department of Mathematics, College of Engineering Guindy, Anna University, Chennai during December-1995 and March-2002. M.Sc. in MATHEMATICS,, University of Madras (1982-1984). B.Sc. in MATHEMATICS,, University of Madras (1979-1982). Research Degree Postdoctoral Research in Queueing Theory Multimedia Labs, NTT R&D Labs, Tokyo, Japan (1993-1994). Title: Some Polling Models and Their Applications. Ph.D. in Applied Probability and Stochastic Processes from Faculty of SCIENCE & HUMANITIES, IITMadras, Chennai -36, (1986-1991). Title: Some Stochastic Population Models in Ecology. M.phil. in from Faculty of SCIENCE & HUMANITIES, SRI R.M.K. VIVEKANADA COLLEGE, CHENNAI-4, University of Madras (1984-1985). Title: Stochastic Models of Some Dynamical Systems. Area of Specialisation APPLIED PROBABILITY AND STOCHASTIC PROCESSES page 1 / 7

Mathematical Statistics Reliability, Queueing Thoery, Branching Processes Membership in Professional Organization Operation Research Society of India Operation Research Society of Japan Indian Society for Probability and Statistics Research Guidance Number of Ph.D Scholars Guided : 2 Number of Ph.D Scholars Guiding : 1 Number of M.S (By Research) Students Guided : 1 Number of M.E./ M.Tech. Projects Guided : 13 Papers Published in Journals Research Papers Published in International Journals : 60 Research Papers Published in National Journals : 0 1. P.R.Parthasarathy and B.Krishna Kumar, "On the number and the sum of lifetimes of overaged cells", Indian Journal of Pure and Applied Mathematics, Vol. 21, pp. 390-395 (1990). 2. P.R.Parthasarathy and B.Krishna Kumar, "Two stochastic analogoues of the logistic process", Indian Journal of Pure and Applied Mathematics, Vol. 21, pp. 965-969 (1990). 3. P.R.Parthasarathy and B.Krishna Kumar, "Density-dependent birth and death process with state-dependent immigration", Int. Jour. Mathl. Comput. Modelling, Vol. 15, pp. 11-16 (1991). 4. P.R.Parthasarathy and B.Krishna Kumar, "The number and the sum of lifetimes of overaged cells in modified branching processes", Int. Jour. Mathl. Comput. Modelling, Vol. 15, pp. 41-47 (1991). 5. P.R.Parthasarathy and B.Krishna Kumar, "A birth and death process with logistic mean population", Communications in Statistics, Theory and Methods, Vol. 20, pp. 621-629 (1991). 6. P.R.Parthasarathy and B.Krishna Kumar, "Some logistic growth models in ecology", Handbook of the Logistic Distribution (Ed. N.Balakrishnan), Marcel Dekker, published by Marcel Dekker. pp. 540-551 (1991). 7. B.Krishna Kumar and P.R.Parthasarathy, "Number of deaths in semi-markov compartmental system with branching particles", Int. Jour. Mathl. Comput. Modelling, Vol. 16, pp. 29-36 (1992). page 2 / 7

8. B.Krishna Kumar and P.R.Parthasarathy, "Semi-Markov compartmental systems with branching particles", Int. Jour. Mathl. Edu. Sci. Techn., Vol. 24, pp. 875-882 (1993). 9. B.Krishna Kumar and P.R.Parthasarathy, "On the total sojourn time of particles in semi-markov compartmental system with branching particles", Communications in Statistics, Theory and Methods, Vol. 22, pp. 1207-1220 (1993). 10. B.Krishna Kumar, P.R.Parthasarathy and M.Sharafali, "Transient solution of an M/M/1 queue with balking", Queueing Systems (Theory and Applications), Vol. 13, pp. 441-448 (1993). 11. B.Krishna Kumar, P.R.Parthasarathy and M.Sharafali, "Density-dependent birth and death processes with controlled immigration", Stochastic Analysis and Applications, Vol. 11, pp. 181-196 (1993). 12. P.R.Parthasarathy and B.Krishna Kumar, "Density-dependent birth and death processes with immigration", Int. Jour. Mathl. Edu. Sci. Techn., Vol. 24, pp. 55-62 (1993). 13. Y.Takahashi and B. Krishna Kumar, "Pseudo-conservation law for discrete-time multi-queue systems with priority disciplines", J. Operations. Res. Soc. Japan, Vol. 38, pp. 450-466 (1995). 14. Y.Takahashi and B. Krishna Kumar, "Pseudo-conservation law for a priority polling systems with mixed service strategies", Performance Evaluation, Vol. 23, pp. 107-120 (1995). 15. P.R.Parthasarathy and B.Krishna Kumar, "Stochastic compartmental models with Prendville growth mechanisms", Mathematical Biosciences, Vol. 125, pp. 51-60 (1995). 16. B.Krishna Kumar, "On semi-markov birth and death compartmental models", Jour. Applied Statistical Sciences, Vol. 2, pp. 361-373 (1995). 17. B.Krishna Kumar, " busy period of an M/M/1 queue with balking", Jour. Applied Statistical Sciences, Vol. 3, pp. 209-218 (1996). 18. B.Krishna Kumar, B.Thilaka and A.Vijayakumar, "Multi-type branching processes with disasters-i: The number of particles in the system", Int. Jour. Mathl. Comput. Modelling, Vol. 28, pp. 87-102 (1998). 19. B.Krishna Kumar, B.Thilaka and A.Vijayakumar, "Multi-type branching processes with disasters-ii: Total sojourn time and number of deaths", Int. Jour. Mathl. Comput. Modelling, Vol. 28, pp. 103-114 (1998). 20. A.Vijayakumar, B.Krishna Kumar and B.Thilaka, "On semi-markov compartmental models with branching particles under the influence of disasters", Communications in Statistics, Theory and Methods, Vol. 27, pp. 1101-1122 (1998). 21. B.Krishna Kumar and D.Arivudainambi, "Transient solution of an M/M/1 queue with catastrophes", Int. Jour. Comput. Math. with Applications, Vol. 40, pp. 1233-1240 (2000). 22. B.Krishna Kumar, B. Thilaka and A.Vijayakumar, "Stochastic compartmental models with branching particles and disasters: Sojourn time and related characteristics", Communications in Statistics, Theory and Methods, Vol. 29, pp. 291-318 (2000). page 3 / 7

23. B.Krishna Kumar and D.Arivudainambi, "Semi-Markov compartmental models of invading insect populations", The Korean Journal of Computational and Applied Mathematics, Vol. 7, pp. 161-174 (2000). 24. B.Krishna Kumar and D.Arivudainambi, "An M/G/1/1 feedback queue with regular and optional services", Int. Jour. Information and Management Sciences, Vol. 12, pp. 67-73 (2001). 25. B.Krishna Kumar and D.Arivudainambi, "Transient solution of an M/M/C queue with heterogeneous server and balking", Int. Jour. Information and management Sciences, Vol. 12, pp. 15-27 (2001). 26. B.Krishna Kumar, D.Arivudainambi and A.Vijayakumar, "On the MX/G/1 retrial queue with Bernoulli schedules and general retrial times", Asia-Pacific Journal of Operations Research, Vol. 19, Issue 2, pp. 1-17 (2002). 27. B.Krishna Kumar and A.Vijayakumar, "Age-dependent branching processes with disasters", Journal of Engineering Simulation, Vol. 19, pp. 112-122 (2002). 28. B.Krishna Kumar and D.Arivudainambi, "The M/G/1 retrial queue with Bernoulli schedules and general retrial times", Int. Jour. Comput. Math. with Applications, Vol. 43, pp. 15-30 (2002). 29. B.Krishna Kumar and S.Pavai Madheswari, "Transient behaviour of the M/M/2 queue with catastrophes", Journal of Statistica, pp. 129-136 (2002). 30. B.Krishna Kumar, S.Pavai Madheswari and A.Vijayakumar, "The M/G/1 retrial queue with feedback and starting failures", Int. Jour. Appl. Mathl. Modelling, Vol. 26, pp. 1057-1075 (2002). 31. B.Krishna Kumar and D.Arivudainambi, " The M/G/1/1 queue with non-reliable server and no waiting capacity", Int. Jour. Inform. and Management Sciences, Vol. 13, Issue 2, pp. 35-50 (2002). 32. B.Krishna Kumar, D.Arivudainambi and A.Vijayakumar, "On the N-Policy of M/G/1 feedback queue with varying arrival rates", Opsearch, Vol. 39, pp. 236-314 (2002). 33. B.Krishna Kumar, A.Vijayakumar and D.Arivudainambi, "An M/G/1 retrial queueing system with two-phase service and preemptive resume", Ann. Operations Research, Vol. 113, pp. 61-79 (2002). 34. B.Krishna Kumar and S.Pavai Madheswari, " Transient solution of an M/M/2 queue with catastrophes", Mathematical Scientist, Vol. 28, pp. 98-144 (2003). 35. B.Krishna Kumar and S.Pavai Madheswari, "On MX/G/1 retrial queue with multiple vacations and starting failures", Opsearch, Vol. 40, pp. 115-137 (2003). 36. B.Krishna Kumar and A.Vijayakumar, " The sojourn time and related characteristics of an age-dependent branching process", Journal of Applied Mathematics and Computing, Vol. 143, pp. 157-172 (2004). 37. B.Krishna Kumar, S.Pavai Madheswari and K.S.VenkataKrishnan, "Transient solution of an M/M/2 queueing system with heterogeneous servers and disasters,", Stochastic Modelling and Applications, Vol. 7, pp. 27-43 (2004). page 4 / 7

38. B.Krishna Kumar and S.Pavai Madheswari, "Mixed loss and delay retrial queueing system with two classes of customers", Statistica, Issue 1, pp. 57-73 (2004). 39. B.Krishna Kumar and S.Pavai Madheswari, " An M/M/2 Queueing System with Heterogeneous Servers and Multiple Vacations", Journal of Mathematical and Computer Modelling, Vol. 41, Issue 13, pp. 1415-1429 (2005). 40. B.Krishna Kumar and S.Pavai Madheswari, "Transient Analysis of an M/M/1 Queue Subject to Catastrophes and Server Failures", Journal of Stochastic Analysis and Applications, Vol. 23, pp. 329-340 (2005). 41. B.Krishna Kumar, S.Pavai Madheswari and D.Arivudainambi, "On the busy period of an M/G/1 retrial queueing system with two-phase service and preemptive resume", Stochastic Modelling and Applications, Vol. 8, Issue 2, pp. 18-34 (2005). 42. B.Krishna Kumar and J.Raja, "On Multiserver feedback Retrial Queues with Balking and Constant Retrial Rate", Annals of Operations Research, Vol. 141, pp. 229-252 (2006). 43. B.Krishna Kumar and D.Arivudainambi, "Some results on generalized M/G/1 feedback queue with disasters ", Annals of Operations Research, Vol. 143, pp. 275-292 (2006). 44. B.Krishna Kumar, S.Pavai Madheswari and K.S.Vankatakrishnan, "Transient Solution of an M/M/2 Queue with Heterogeneous Servers Subject to Catastrophes", International Journal of Information and Management Sciences, Vol. 18, pp. 63-80 (2007). 45. B.Krishna Kumar, A.Krishnamoorthy, S.Pavai Madheswari and S.Sadqi Basha, "Transient Analysis of a Single Server Queue with Catastrophes, Failures and Repairs", Journal of Queueing System, Vol. 56, pp. 133-141 (2007). 46. B.Krishna Kumar, A.Vijayakumar and S.Sophia, "Transient Analysis for State-Dependent Queues with Catastrophes", Stochastic Analysis and Applications, Vol. 26, Issue 6, pp. 1201-1217 (2008). 47. A.Krishnamoorthy, B.Krishna Kumar, V.C.Narayanan and T.G.Deepak, "On an (s, S) Inventory Policy with Servervice Time, Vacation to Server and Correlated Lead time", International Journal Quality Technology and Quantitative Management, Vol. 5, Issue 2, pp. 129-143 (2008). 48. B.Krishna Kumar, R.Rukmani and V.Thangaraj, "Analysis of MAP/PH(1), PH(2)/2 Queue with Bernoulli Vacations", Journal of Applied Mathematics and Stochastic Analysis, pp. 1-20 (2008). 49. B.Krishna Kumar, R.Rukmani and V.Thangaraj, "On Multiserver Feedback Queue with Finite Buffer", Applied Mathematical Modelling, Vol. 33, pp. 2062-2083 (2009). 50. B.Krishna Kumar and S.Pavai Madheswari, "Analsysis of an M/M/N Queue with Bernoulli Service Schedule", International Journal of Operational Research, Vol. 5, Issue 1, pp. 48-72 (2009). 51. B.Krishna Kumar, A.Vijayakumar and S.Sophia, "Transient Analysis of a Markovian Queue with Chain Sequence Rates and Total Catastrophes", International Journal of Operational Research, Vol. 5, Issue 4, pp. 375-391 (2009). page 5 / 7

52. B.Krishna Kumar, Rukmani and V.Thangaraj, "An M/M/c Retrial Queueing System with Bernoulli Vacations", J. System Science and System Engineering, Vol. 18, Issue 2, pp. 222-242 (2009). 53. B.Krishna Kumar, Rukmani V.Thangaraj and Udo Krieger, " A Single Server Retrial Queue with Bernoulli Feedback and Collision", Journal of Statistical Theory and Practice, Vol. 4, Issue 2, pp. 243-260 (2010). 54. B. Krishna Kumar, G.Vijayalakshmi, A.Krishnamoorthy and S.Sadiq Basha, " A single server feedback retrial queue with collision", Computers and Operations Research, published by Elsiver. Vol. 37, pp. 1247-1255 (2010). 55. B.Krishna Kumar, S.Pavai Madheswari, and S.R.Anantha Lakshmi, " Controlled batch arrival and server under maintenance", Journal of TOP, Vol. 19, pp. 351-379 (2011). 56. Di Cresenzo, A., B. Krishna Kumar., and A.G Nobile., " A random walk with catastrophes, repair and its continuous approximation", Journal of Methodology and Computing in Applied Probability, Vol. 14, pp. 937-954 (2012). 57. B.Krishna Kumar, S.Anbrasu and S.R. Anantha Lakshmi, " Performance Analysis for Queuing Systems with Server Under Maintenance and Closedown Period", International Journal of Systems Science, (2013). 58. B.Krishna Kumar, S.Pavai madheswari, and S.R.Anantha Lakshmi, " Transient and Steady-state Analysis of Queueing System with Catastrophes and Impatient Customers", International Journal of Mathematical Operations Research, (2013). 59. B.Krishna Kumar, S.Pavai Madheswari, and S.R.Anantha Lakshmi, " Retrial queue with negative customers and two types of Bernoulli feedback of customrs,", Operational Research An International Journal, (2013). 60. B.Krishna Kumar, R.Rukmani and S.R.Anantha Lakshmi, " Performance analysis of M/G/1 queueing system under Bernoulli vacation schedules with server setup and close down periods", International Journal of Computer and Industrial Engineering, (2013). Experience Abroad 1. Visited N.T.T. Multimedia Network Labs, R&D division, Tokyo, Japan from 15-Sep-1993 to 14-Sep-1994. Purpose of visit :Post-Doctoral Research Fellow. 2. Visited University of Madrid Madrid, Spain from 01-Jul-2002 to 07-Jul-2002. Purpose of visit :Participated in International Conference on Queueing Theory. 3. Visited Department of Medical Biometry, University of Tuebingen, Tuebingen, Germany from 08-Jul-2002 to 20-Jul-2002. Purpose of visit :Joint work on Mathematical Modelling of Biomedical Problems. 4. Visited Department of Computer Science, Otto-Friedch of University Bamberg, Bamberg, Germany from 27-Jun-2006 to 02-Jul-2006. Purpose of visit :Joint work on Queueing Network Models. page 6 / 7

Powered by TCPDF (www.tcpdf.org) Dr. KRISHNA KUMAR 5. Visited Complutense University of Madrid, Madrid, Spain from 03-Jul-2006 to 11-Jul-2006. Purpose of visit :Participated in International Conference on Queueing Theory & Workshop on Retrial Queues. 6. Visited Department of Mathematics and OR, University of Athen, Athen, Greece from 09-Jul-2008 to 21-Jul-2008. Purpose of visit :Participated in 7th International Workshop on Retrial Queue. 7. Visited Department of Mathematics and Information Technology, University of Salerno, Salerno, Italy from 07-Jun-2009 to 14-Jun-2009. Purpose of visit :Joint work on Diffusion Processes of Random Walk with Catastrophes. 8. Visited International Centre for Theoretical Physics, Trieste, Italy from 15-Jun-2009 to 22-Jun-2009. Purpose of visit :Participated Workshop on Integrable System and Scientific Computing. 9. Visited Complutense University of Madrid, Madrid, Spain from 27-Jun-2010 to 01-Jul-2010. Purpose of visit :Third Madrid Conference on Queueing Theory. page 7 / 7