### Prof. Dr. Panamalai Ramarao Parthasarathy

- Allianz-Gebäude (05.20)
- Parthasarathy@stoch.uni-karlsruhe.de

LIST OF PUBLICATIONS OF P.R. PARTHASARATHY

MONOGRAPH

1. Parthasarathy, P.R. and Lenin, R.B. : Birth and Death Process (BDP) Models with Applications− Queueing,

Communication Systems, Chemical Models, Biological Models: The State-of-the-Art with a Time-Dependent

Perspective, American Series in Mathematical and Management Sciences 51,Syracuse, NY, American Sciences

?Press, Inc., 2004 (MR 2006a:60003, Zbl 1055.60081).

I QUEUEING MODELS

1. A transient solution to an M/M/1 queue - A simple approach, Adv. Appl. Prob. 19(1987), 997- 998

(MR 89h:60158, Zbl 632.60098).

2. Transient solution to the many-server Poisson queue: A simple approach, J. Appl. Prob. 26(1989),

584-594 (with M. Sharafali, MR 90k:60185, Zbl 693.60076).

3. Some notes on the total service time in certain loss systems, J. Appl. Prob. 21(1984), 616-627 (with

M.Sharafali, MR 86b:60156, Zbl 551.60095).

4. Transient solution of an M/M/1 queue with balking, Queueing systems 13(1993), 441-448 (with

B. Krishna Kumar, MR 94b:60110, Zbl 772.60077).

5. On the distribution of a busy period for the many server Poisson queue, Opsearch 26(1989), 125-132

(with M. Sharafali, MR 91h:60107, Zbl 685.60099).

6. Transient solution of state-dependent queues: A continued fraction approach, Neural Parallel and

Sci.Computations 1(1993),97-107 (with V. Vijayalakshmi, Zbl 797.60082, STMA 36/2466).

7. Busy period distribution for state dependent Multiserver queues, Asia Pacific J. Oper. Res. 11(1994),

131-140 (with V. Vijayalakshmi, Zbl 824.90065).

8. Transient solution of a state dependent many server Poisson queue with balking, J. Appl. Stat. Sci.

2(1995), 207-220 (with V. Vijayalakshmi, MR 98k:60170, Zbl 883.60087, STMA 38/0783).

9. A queue with birth process arrival and state-dependent service, Int. J. Mod. and Sim., 10(1990), 13-16

(with M. Sharafali).

10. A continued fraction approximation of the Modified Bessel function I1(t), Appl. Math. Lett. 3(1990),

13-15 (with N. Balakrishnan, Zbl 709.65013).

11. Transient solution of a state dependent multiserver Poisson queue with balking - A continued

fraction approach, J. Appl. Stat. Sci., 3(1996), 191-208 (with V. Vijayalakshmi, MR 97a:60136,

Zbl 948.60082, STMA 38/2154).

12. On quadrature approximation for the busy period density function of an M/M/1 queueing

system, Amer. J. Math. Mgmt. Sci., 18(1998), 277-289 (with V. Vijayalakshmi, MR 99k:90078,

Zbl 938.60092, STMA 41/0173).

13. On the total overtime service in some loss queueing systems. J. Appl. Stat. Sci., 5(1996), 27-37 (with

G.K. Agrafiotis, Zbl 876.60086, STMA 39/0763).

14. On the transient solution of a discrete queue, Stat. Res. Rep., 15(1990), McMaster Univ. (with

S.G.Mohanty).

15. On the numerical solution of transient probabilities of a state-dependent multi-server queue, Intern. J.

Computer Math., 66(1998), 241-255 (with R.B. Lenin, Zbl 891.65148).

16. Exact busy period distribution of discrete queue with quadratic rates, Intern. J. Computer Math.,

71(1999), 427-436 (with R.B. Lenin, MR 2000h:90018, Zbl 953.60086, STMA 40/6019).

17. On the convergence to stationarity of the many-server Poisson queue, J. Appl. Prob. 36(1999), 546-557

(with W. Stadje, Zbl 955.60094, MR 2000i:60109).

18. Generating function analysis of some joint distributions for Poisson loss systems. Queueing Systems,

34(2000), 183-197 (with W. Stadje, Zbl 942.90012, MR 2001g:60238, STMA 42/2427).

19. Transient analysis in discrete time of Markovian queues with quadratic rates. Southwest J. Pure Appl.

Math., July (2000), 1-15 (with R.B. Lenin, Zbl 959.60086, MR 2001m:60213).

20. Transient analysis of a queue where potential customers are discouraged by queue length. Math. Prob.

Engg. 7(2001), 433-454 (with N. Selvaraju, Zbl 1008.60098).

21. Exact transient solution of a state-dependent queue in discrete time. Oper. Res. Lett. 28(2001),

243-248 (with N. Selvaraju, MR 2002i:60173, Zbl 993.60097).

22. Double-ended queues with impatience. Comp. Oper. Res. 29(2002), 2053-2072 (with B.W. Conolly

and N. Selvaraju, MR 2003f:60157, Zbl 1010.90011).

23. An Exact Solution for an M/M/1 Queue with Piecewise Constant Rates Math. Sci. 31 (2006), 48-52

(with R. Sudhesh).

24. Exact Transient Solution of a Discrete Time Queue with State-dependent Rates, To appear in American

Jour. Math. and Mgmt. Sciences (2006) (with R. Sudhesh).

25. A Single Server Queue with Gated Processor-Sharing System, To appear in Intern. J. Computer Math.,

(2006) (with K. Vasudevan).

26. A Single Server Queue with Two Types of Customers in a Varying Environment, To appear in Intern.

J. Modern Math., (2006) (with K. Vasudevan).

27. Transient Solution for a Single Server Retrial Queue with State-dependent Rates, To appear in Oper.

Res. Lett., (2006) (with R. Sudhesh).

II COMPUTER COMMUNICATIONS

28. Transient solution of multiprocessor systems with state-dependent arrivals. Intern. J. Computer Math.,

73(1999), 313-320 (with S. Dharmaraja and G. Manimaran, MR 2000m:68032 Zbl 955.68015, STMA

41/3052).

29. A paired queueing system arising in multimedia synchronization. Mathl. Comp. Modell., 30(1999),

133-140 (with N. Selvaraju and G. Manimaran, Zbl 1042.60545, STMA 41/2507).

30. On an inverse problem in Cauer Networks. Inverse Problems, 16(2000), 49-58 (with Sven Feldmann,

MR 2000j:94052, Zbl 985.94060).

31. Fluid queues driven by an M/M/1/N queue. Math. Prob. Engg., 6(2000), 439-460 (with R.B. Lenin,

MR 2004i:60139, Zbl 972.60086).

32. A computational approach for fluid queues driven by a truncated birth-death processes. Meth. Comp.

Appl. Prob., 2(2000), 373-392 (with R.B. Lenin, MR 2002h:60210, Zbl 982.60090).

33. Transient solution of a link with finite capacity supporting multiple streams. Performance Evaluation,

43(2001), 1-14 (with S. Dharmaraja, Zbl 1017.68022, STMA 42/3002).

34. The numerical solution of a birth-death process arising in multimedia synchronization. Math. Comp.

Modell., 34(2001), 887-901 (with N. Selvaraju and R.B. Lenin, MR 2002g:90014, Zbl 994.90015).

35. Transient analysis of a state-dependent queueing network with finite capacity. Int. J. Comp. Math.,

79(2002), 391-401 (with W. Stadje and R.B. Lenin, Zbl 1015.60081).

36. Exact transient analysis of a circulant queueing network. Comp. Math. Appl., 44(2002), 1297-1306

(with N. Selvaraju and G. Manimaran, MR 2003i:90013, Zbl 1039.60084).

37. An M/M/1 driven fluid queue ? continued fraction approach. Queueing Systems, 42(2002), 189-199

(with K.V. Vijayashree and R.B. Lenin, MR 2003i:60165, Zbl 1035.90025).

38. Resolving identity of webuser on-the-fly. ACM Computers and Society, June 2002, 4-9 (with Mohana

Krishnaiah).

39. Fluid queues driven by a discouraged arrivals queue. Int. J. Math. and Math. Sci., 2003(2003),

1509-1528 (with K.V. Vijayashree, MR 2004b:60219, Zbl 1020.60092)

40. Fluid queues driven by birth and death process with quadratic rates. Int. J. Comp. and Math.,

80(2003), 1385-1395. (with K.V. Vijayashree, MR 2004j:60189)

41. Fluid queues driven by a birth and death process with alternating flow rates. Mathematical Problems

in Engineering, 2004 (2004), 469-489 (with K.V. Vijayashree and R.B. Lenin, MR 2129436).

42. Exact transient solution of an M/M/1 driven fluid queue. Int. J. Comp. and Math. 82(2004), 659-671

(with B. Sericola and K.V. Vijayashree, Zbl 02187419)

43. Fluid queues driven by a birth and death process suggested by chain sequence. Journal of Applied

Mathematics and Stochastic Analysis, 2005 (2005), 143-158. (with K.V. Vijayashree and B. Sericola)

44. The Overflow Process from a State-dependent Queue Int. J. Comp. and Math., 82 (2005), 1073-1093

(with R. Sudhesh).

45. Transient Solution of a Queue with State- and Time-dependent Rates. To appear in Math. Scientist

(2006) (with R. Sudhesh).

III INVENTORY

46. On the unutilized capacity of a production-storage system, Oper. Res. Lett., 6(1987), 233-238 (with

M. Sharafali, MR 88m:90074, Zbl 637.90048).

47. Transient analysis of an (S − 1, S) inventory model - A numerical approach, Intern. J. Computer

Math., 59(1996), 177-185 (with V. Vijayalakshmi, STMA 37/4709).

IV CHEMICAL KINETICS

48. On the transient solution of birth-death master equation with an application to a chiral chemical system,

Ind. J. Chemistry, 35A(1996) 1021-1025 (STMA 38/5149).

49. A chemical queue, Math. Scientist, 22(1997), 83-91 (with B.W.Conolly and S.Dharmaraja, MR. 98h:

60125, Zbl 898.60087, STMA 39/5102).

50. The transient solution of a local-jump heterogeneous chain of diatomic systems, J. Phys. A : Math.

Gen., 31(1998), 6579-6588 (with S. Dharmaraja, Zbl 1002.82541, STMA 40/1308).

51. Exact transient solutions of kinetics of first-order reactions with end-effects, J. Math. Chem., 25(1999),

281-295 (with S. Dharmaraja, MR 2001a:92008, Zbl 953.92033).

V BIRTH AND DEATH PROCESSES

52. On the exact transient solution of finite birth and death processes with specific quadratic rates, Math.

Scientist, 22(1997), 92-105 (with R.B. Lenin, MR 98h:60124, Zbl 898.60084, STMA 39/4847).

53. On the numerical solution of transient probabilities of quadratic birth and death processes, J. Diff.

Eqns. Appl., 4(1998), 365-379 (with R.B. Lenin, MR 99g:60155, Zbl 914.60042, STMA 40/2613).

54. A birth and death process related to the Rogers-Ramanujan continued fraction, J. Math. Anal. Appl.,

224(1998), 297-315 (with R.B. Lenin, W. Schoutens and W. Van Assche, MR 99g:60156, Zbl 920.60067,

STMA 40/1039).

55. On a Ramanujan number, Math. Scientist, 23(1998), 124-125 (MR 2000j:11012, Zbl 923.11022).

56. An inverse problem in birth and death processes, Comp. Math. Appl., 38(1999), 33-40 (with R.B.

Lenin, MR 2000g:60144, Zbl 938.60089, STMA 40/5745).

57. Spectral representation of certain finite birth and death processes, Math. Scientist, 24(1999), 105-112

(with W. Van Assche and R.B. Lenin, MR 2001c:60140, Zbl 971.60085).

58. Birth and death processes and their applications, Bull. Allahabad Math. Soc., 12-13(1997-98), 1-22.

59. A birth-death process suggested by a chain sequence, Comp. Math. Appl. 40(2000), 239-247 (with

R.B. Lenin, MR 2000m:60092, Zbl 973.60099).

60. Families of birth-death processes with similar time-dependent behaviour, J. Appl. Prob., 37(2000),

835-849 (with R.B. Lenin, W.R.W. Scheinhandt, E.A. van Doorn, MR 2001e:60177, Zbl 973.60087,

STMA 42/5449).

61. Some unusual birth and death processes. Math. Sci., 28(2003), 79-90 (MR 2004j:60180).

62. Hypergeometric functions and birth-death process Math. Sci.30(2005), 98-111 (Zbl 1086.60056).

63. Exact Transient Solution of State-Dependent Birth-Death Processes, Journal of Applied Mathematics

and Stochastic Analysis, 2006(2006), 1-16 (with R. Sudhesh) ( Zbl pre 05050259).

64. A Formula for the Coefficients of Orthogonal Polynomials from the Three-Term Recurrence Relations.

To appear in Applied Mathematical Letters, (2006) (with R. Sudhesh).

65. Summation Identities. To appear in Inter. Jour. Modern Math.(2006) (with R. Sudhesh).

VI RELIABILITY

66. Number of repairs for a 2-unit system, IEEE Trans. Rel., 28(1979), 172 (Zbl 409.90036).

67. An intermittently used two-unit system with semi-Markov need process, Mathl. Comput. Modelling,

17(1993), 83-90 (with R. Natarajan, Zbl 770.60081, STMA 36/1532).

68. Cost analysis for 2-unit systems, IEEE Trans. Rel., R-28(1979), 268-269 (Zbl 411.62074).

69. Number of repairs and total repair time for a 2-unit warm standby system, Math. Oper. Stat. Ser.

Opt., 10(1979), 591-595 (with R. Ramanarayanan, MR 81f:90051, Zbl 429.90032).

70. On the total working time of a repaired unit, Zast. Math., 18(1983), 1-7 (with B. Kopocinski,

MR 85i:60073, Zbl 529.60090).

71. Excess repair time for a repairable system, Microelec. and Rel. 30(1990), 507-509 (with G.K. Agrafiotis).

72. A complex two unit system with stochastic demand, Microelec. Tran. Reliab., 28(1988), 359-361 (with

M. Sharafali).

73. Transient analysis of multiple unit redundant systems - A continued fraction approach, Optimization,

35(1995), 171-185 (with V. Vijayalakshmi, MR 96f:90055, Zbl 839.90054, STMA 37/2146).

74. On the exact transient availability in discrete time of parellel redundant repairable systems with quadratic

rates, J. Appl. Stat. Sci., 7(1998), 89-101 (with R.B. Lenin, MR 99g:60160, Zbl 910.90146, STMA

40/4390).

75. On the exact transient availability of parellel redundant repairable systems with quadratic transition

rates, IAPQR Transactions, 24(1999), 81-89 (with R.B. Lenin, Zbl 1004.90027, STMA 42/1189).

VII BRANCHING PROCESSES

76. Supercritical age-dependent branching processes with immigration, J. Appl. Prob., 11(1974), 695-702

(with K.B. Athreya, MR 50 #11491, Zbl 308.60048).

77. Some convergence rate results for the Bellman-Harris process with immigration, Math. Biosci. ,

26(1975), 207-216 (with A.G. Pakes, MR 52 #9400, Zbl 323.60080).

78. Compounding Bellman-Harris processes allowing immigration, Math. Biosci., 37(1977), 105-111 (with

A. Krishnamoorthy, MR 58 #31426, Zbl 371.92021).

79. On a modified Markov branching process, J. Math. Biol., 7(1979), 95-97 (MR 83e:600084, Zbl

397.60068).

80. Age-dependent branching processes with immigration when inter-arrival times are correlated, J. Indian

Stat. Assoc., 16(1978), 83-96 , MR 82n:60105).

81. Age-dependent branching processes with birth process immigration, Int. J. Math. Edu. Sci. Technol.,

22(1991), 317-320 (with M. Sharafali, Zbl 719.92504).

VIII COMPARTMENTAL MODELS

82. Stochastic compartmental model with branching particles, Bull. Math. Biol., 43(1981), 347-360 (with

P. Mayilswamy, MR 84h:92007, Zbl 516.92001).

83. Stochastic compartmental models with branching and immigrant particles, Bull. Math. Biol., 44(1982),

75-86 (with P. Mayilswamy, MR 84i:92037, Zbl 475.93059).

84. Stochastic compartmental models with birth, death and immigration of particles, Comm. in Stat.

Theory and Meth., 11(1982), 1625-1642 (with P. Mayilswamy, MR 83g:92035, Zbl 505.60094).

85. Sojourn time distribution in a stochastic compartmental system, Comm. in Stat. Theory and Meth.,

12(1983), 1619-1635 (with P. Mayilswamy, MR 85f:92003, Zbl 556.93056).

86. Number of deaths in semi-Markov compartmental system with branching particles, Math. and Comp.

Mod., 16(1992), 29-36 (with B. Krishna Kumar, MR 93h:60143, Zbl 782.60070, STMA 36/0981).

87. On the total sojourn time of particles in semi-Markov compartmental system with branching particles,

Comm. in Stat. Theory and Meth., 22(1993), 1207-1220 (with B.Krishna Kumar, MR 94g:60164, Zbl

782.60060, STMA 34/4322).

88. Stochastic compartmental models with Prendville growth mechanisms, Math. Biosci., 125(1995), 51-60

(with B. Krishna Kumar, Zbl 820.92020).

89. Semi-Markov compartmental systems with branching particles, Int. J. Math. Edu. Sci. Tech.,

24(1993), 875-882 (with B. Krishna Kumar, MR 94i: 60108, STMA 36/0982).

90. The Total sojourn time distribution in a stochastic compartmental model, Mathl. Comput. Modelling,

12(1989), 1167-1173 (with M. Sharafali, MR 90g:92032, Zbl 698.60072).

91. The number and sum of lifetimes of overaged cells in modified branching processes, Mathl. Comput.

Modelling, 15(1991), 41-47 (with B.Krishna Kumar, MR 92f:60146, Zbl 721.92020).

IX ECOLOGY

92. Density-dependent birth and death processes with controlled immigration, Stoch. Anal. and Appl.,

11(1993), 181-196 (with B. Krishna Kumar, MR 94c:60138, Zbl 774.60072, STMA 34/4316).

93. Density-dependent birth and death process with state-dependent immigration, Mathl. Comput. Modelling,

15(1991), 11-16 (with B. Krishna Kumar, MR 92b:60082, Zbl 721.92019).

94. A birth and death process with logistic mean population, Commun. Statist. Theory Meth., 20(1991),

621-629 (with B. Krishna Kumar, MR 93d:60141).

95. Density-dependent birth and death processes with immigration, Int. J. Math. Edu. Sci. Technol.,

24(1993), 55-62 (with B. Krishna Kumar, MR 94f:60108, Zbl 773.60082, STMA 36/0972).

96. Two stochastic analogues of the logistic process, Indian. J. Pure Appl. Math., 21(1990), 965-969

(with B. Krishna Kumar, MR 91m:60155, Zbl 714.92017).

97. On the number and sum of lifetimes of overaged cells, Indian J. Pure Appl. Math., 21(1990), 390-395

(with B. Krishna Kumar, Zbl 701.92014).

98. The effect of superinfection on the distribution of the infectious period - A continued fraction approximation,

IMA J. Math. Appl. in Med. &r Biol., 14(1997), 113-123 (Zbl 871.92028).

99. Using density-dependent birth-death-migration models for analyzing Muskrat spread in the Netherlands,

J. Indian Soc. Agric. Statist., 49(1996), 139-156 (with J.H. Matis, STMA 40/1328).

100. On the cumulants of population size for the stochastic power law logistic model, Theor. Pop. Biol.,

53(1998), 16-29 (with J.H. Matis, Zbl 894.92026).

101. On the numerical solution of transient probabilities of a stochastic power law logistic model. Nonlinear

analysis, 37(1999), 677-688 (with J.H. Matis and R.B. Lenin, Zbl 947.60084).

102. Exact representations for tumour incidence for some density-dependent models. Int. J. of Math. Math.

Sci., 2005(2005), 2655-2667 (with Klaus Dietz) (MR 2006h:92019, Zbl 1085.92021).