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Transient and steady state analysis of an M/M/1 queue with balking, catastrophes, server failures and repairs
1. | Mathematics Department, Damietta Faculty of Science, New Damietta, Egypt |
References:
[1] |
M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions," New York, Dover, 1970. |
[2] |
C. J. Jr. Ancker and A. V. Gafarian, Some queueing problems with balking and reneging: I, Operations Research., 11 (1963), 88-100.
doi: 10.1287/opre.11.1.88. |
[3] |
C. J. Jr. Ancker and A. V. Gafarian, Some queueing problems with balking and reneging: II, Operations Research, 11 (1963), 928-937.
doi: 10.1287/opre.11.6.928. |
[4] |
I. Atencia and P. Moreno, The discrete time $Geo$/$Geo$/$1$ queue with negative customers and disasters, Computers and Operations Research, 9 (2004), 1537-1548.
doi: 10.1016/S0305-0548(03)00107-2. |
[5] |
X. Chao, A queueing network model with catastrophes and product form solution, Operations Research Letters., 18 (1995), 75-79.
doi: 10.1016/0167-6377(95)00029-0. |
[6] |
E. Gelenbe, Production-form queueing networks with negative and positive customers, Journal of Applied Probability, 28 (1991), 656-663.
doi: 10.2307/3214499. |
[7] |
F. A. Haight, Queueing with balking, Biometrika., 44 (1957), 360-369. |
[8] |
F. A. Haight, Queueing with balking, Biometrika., 47 (1960), 285-296. |
[9] |
B. Krishna Kumar and D. Arivudainambi, Transient solution of an $M$/$M$/$1$ queue with catastrophes, Computers and Mathematics with Applications, 40 (2000), 1233-1240.
doi: 10.1016/S0898-1221(00)00234-0. |
[10] |
B. Krishna Kumar and S. Pavai Madheswari, Transient analysis of an $M$/$M$/$1$ queue subject to catastrophes and server failures, Stochastic Analysis and Applications, 23 (2005), 329-340.
doi: 10.1081/SAP-200050101. |
[11] |
B. Krishna Kumar, A. Krishnamoorthy, S. Pavai Madheswari and S. Sadiq Basha, Transient analysis of a single server queue with catastrophes, failures and repairs, Queueing Systems., 56 (2007), 133-141.
doi: 10.1007/s11134-007-9014-0. |
[12] |
B. Krishna Kumar, P. R. Parthasarathy and M. Sharafali, Transient solution of an $M$/$M$/$1$ queue with balking, Queueing Systems Theory Appl., 13 (1993), 441-448.
doi: 10.1007/BF01149265. |
[13] |
A. Montazer-Haghighi, J. Medhi and S. G. Mohanty, On a multiserver Markovian queueing system with balking and reneging, Comput. Oper. Res., 13 (1986), 421-425.
doi: 10.1016/0305-0548(86)90029-8. |
[14] |
P. R. Parthasarathy and M. Sharafali, Transient solution to the many-server Poisson queue: A simple approach, Journal of Applied Probability, 26 (1986), 584-594.
doi: 10.2307/3214415. |
[15] |
S. N. Raju and U. N. Bhat, A computationally oriented analysis of the $G$/$M$/$1$ queue, Opsearch, 19 (1982), 67-83. |
[16] |
L. Takács, "The Transient Behaviour of a Single Server Queueing Process with a Poisson Input," Proc. 4th Berkeley Symp. On Mathematical Statistics and Probability, Vol. II, Univ. California Press, Berkeley, Calif., (1961), 535-567. |
[17] |
A. M. K. Tarabia, Transient analysis of a non-empty $M$/$M$/$1$/$N$ queue-an alternative approach, Opsearch, 38 (2001), 431-440. |
[18] |
A. M. K. Tarabia, A new formula for the transient behaviour of a non-empty $M$/$M$/$1$/$infty$ queue, Applied Mathematics and Computation, 132 (2002), 1-10.
doi: 10.1016/S0096-3003(01)00145-X. |
[19] |
K.-H. Wang and Y.-C Chang, Cost analysis of a finite $M$/$M$/$R$ queueing system with balking, reneging, and server breakdowns, Mathematical Methods of Operations Research, 56 (2002), 169-180.
doi: 10.1007/s001860200206. |
show all references
References:
[1] |
M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions," New York, Dover, 1970. |
[2] |
C. J. Jr. Ancker and A. V. Gafarian, Some queueing problems with balking and reneging: I, Operations Research., 11 (1963), 88-100.
doi: 10.1287/opre.11.1.88. |
[3] |
C. J. Jr. Ancker and A. V. Gafarian, Some queueing problems with balking and reneging: II, Operations Research, 11 (1963), 928-937.
doi: 10.1287/opre.11.6.928. |
[4] |
I. Atencia and P. Moreno, The discrete time $Geo$/$Geo$/$1$ queue with negative customers and disasters, Computers and Operations Research, 9 (2004), 1537-1548.
doi: 10.1016/S0305-0548(03)00107-2. |
[5] |
X. Chao, A queueing network model with catastrophes and product form solution, Operations Research Letters., 18 (1995), 75-79.
doi: 10.1016/0167-6377(95)00029-0. |
[6] |
E. Gelenbe, Production-form queueing networks with negative and positive customers, Journal of Applied Probability, 28 (1991), 656-663.
doi: 10.2307/3214499. |
[7] |
F. A. Haight, Queueing with balking, Biometrika., 44 (1957), 360-369. |
[8] |
F. A. Haight, Queueing with balking, Biometrika., 47 (1960), 285-296. |
[9] |
B. Krishna Kumar and D. Arivudainambi, Transient solution of an $M$/$M$/$1$ queue with catastrophes, Computers and Mathematics with Applications, 40 (2000), 1233-1240.
doi: 10.1016/S0898-1221(00)00234-0. |
[10] |
B. Krishna Kumar and S. Pavai Madheswari, Transient analysis of an $M$/$M$/$1$ queue subject to catastrophes and server failures, Stochastic Analysis and Applications, 23 (2005), 329-340.
doi: 10.1081/SAP-200050101. |
[11] |
B. Krishna Kumar, A. Krishnamoorthy, S. Pavai Madheswari and S. Sadiq Basha, Transient analysis of a single server queue with catastrophes, failures and repairs, Queueing Systems., 56 (2007), 133-141.
doi: 10.1007/s11134-007-9014-0. |
[12] |
B. Krishna Kumar, P. R. Parthasarathy and M. Sharafali, Transient solution of an $M$/$M$/$1$ queue with balking, Queueing Systems Theory Appl., 13 (1993), 441-448.
doi: 10.1007/BF01149265. |
[13] |
A. Montazer-Haghighi, J. Medhi and S. G. Mohanty, On a multiserver Markovian queueing system with balking and reneging, Comput. Oper. Res., 13 (1986), 421-425.
doi: 10.1016/0305-0548(86)90029-8. |
[14] |
P. R. Parthasarathy and M. Sharafali, Transient solution to the many-server Poisson queue: A simple approach, Journal of Applied Probability, 26 (1986), 584-594.
doi: 10.2307/3214415. |
[15] |
S. N. Raju and U. N. Bhat, A computationally oriented analysis of the $G$/$M$/$1$ queue, Opsearch, 19 (1982), 67-83. |
[16] |
L. Takács, "The Transient Behaviour of a Single Server Queueing Process with a Poisson Input," Proc. 4th Berkeley Symp. On Mathematical Statistics and Probability, Vol. II, Univ. California Press, Berkeley, Calif., (1961), 535-567. |
[17] |
A. M. K. Tarabia, Transient analysis of a non-empty $M$/$M$/$1$/$N$ queue-an alternative approach, Opsearch, 38 (2001), 431-440. |
[18] |
A. M. K. Tarabia, A new formula for the transient behaviour of a non-empty $M$/$M$/$1$/$infty$ queue, Applied Mathematics and Computation, 132 (2002), 1-10.
doi: 10.1016/S0096-3003(01)00145-X. |
[19] |
K.-H. Wang and Y.-C Chang, Cost analysis of a finite $M$/$M$/$R$ queueing system with balking, reneging, and server breakdowns, Mathematical Methods of Operations Research, 56 (2002), 169-180.
doi: 10.1007/s001860200206. |
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