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The FIFO single-server queue with disasters and multiple Markovian arrival streams
1. | Department of Information and Communications Technology, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita 565-0871, Japan |
References:
[1] |
E. Çinlar, "Introduction to Stochastic Processes,", Prentice-Hall, (1975).
|
[2] |
A. Dudin and S. Nishimura, A BMAP/SM/1 queueing system with Markovian arrival input of disasters,, J. Appl. Prob., 36 (1999), 868.
doi: 10.1239/jap/1032374640. |
[3] |
A. Dudin and O. Semenova, A stable algorithm for stationary distribution calculation for a BMAP/SM/1 queueing system with Markovian arrival input of disasters,, J. Appl. Prob., 41 (2004), 547.
doi: 10.1239/jap/1082999085. |
[4] |
F. R. Gantmacher, "The Theory of Matrices, Vol. 2,'', Translated by K. A. Hirsch Chelsea Publishing Co., (1959).
|
[5] |
Q.-M. He, Queues with marked customers,, Adv. Appl. Prob., 28 (1996), 567.
doi: 10.2307/1428072. |
[6] |
D. P. Heyman and S. Stidham, Jr., The relation between customer and time averages in queues,, Oper. Res., 28 (1980), 983.
doi: 10.1287/opre.28.4.983. |
[7] |
G. Jain and K. Sigman, A Pollaczek-Khintchine formula for M/G/1 queues with disasters,, J. Appl. Prob., 33 (1996), 1191.
doi: 10.2307/3214996. |
[8] |
H. Masuyama and T. Takine, Analysis and computation of the joint queue length distribution in a FIFO single-server queue with multiple batch Markovian arrival streams,, Stoch. Models, 19 (2003), 349.
doi: 10.1081/STM-120023565. |
[9] |
V. Ramaswami, A stable recursion for the steady state vector in Markov chains of M/G/1 type,, Stoch. Models, 4 (1988), 183.
doi: 10.1080/15326348808807077. |
[10] |
Y. W. Shin, BMAP/G/1 queue with correlated arrivals of customers and disasters,, Oper. Res. Lett., 32 (2004), 364.
doi: 10.1016/j.orl.2003.09.005. |
[11] |
T. Takine, Queue length distribution in a FIFO single-server queue with multiple arrival streams having different service time distributions,, Queueing Syst., 39 (2001), 349.
doi: 10.1023/A:1013961710829. |
[12] |
T. Takine, Matrix product-form solution for an LCFS-PR single-server queue with multiple arrival streams governed by a Markov chain,, Queueing Syst., 42 (2002), 131.
doi: 10.1023/A:1020152920794. |
[13] |
T. Takine and T. Hasegawa, The workload in the MAP/G/1 queue with state-dependent services: Its application to a queue with preemptive resume priority,, Comm. Statist. Stochastic Models, 10 (1994), 183.
doi: 10.1080/15326349408807292. |
[14] |
H. C. Tijms, "Stochastic Models, An Algorithmic Approach,'', Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons, (1994).
|
show all references
References:
[1] |
E. Çinlar, "Introduction to Stochastic Processes,", Prentice-Hall, (1975).
|
[2] |
A. Dudin and S. Nishimura, A BMAP/SM/1 queueing system with Markovian arrival input of disasters,, J. Appl. Prob., 36 (1999), 868.
doi: 10.1239/jap/1032374640. |
[3] |
A. Dudin and O. Semenova, A stable algorithm for stationary distribution calculation for a BMAP/SM/1 queueing system with Markovian arrival input of disasters,, J. Appl. Prob., 41 (2004), 547.
doi: 10.1239/jap/1082999085. |
[4] |
F. R. Gantmacher, "The Theory of Matrices, Vol. 2,'', Translated by K. A. Hirsch Chelsea Publishing Co., (1959).
|
[5] |
Q.-M. He, Queues with marked customers,, Adv. Appl. Prob., 28 (1996), 567.
doi: 10.2307/1428072. |
[6] |
D. P. Heyman and S. Stidham, Jr., The relation between customer and time averages in queues,, Oper. Res., 28 (1980), 983.
doi: 10.1287/opre.28.4.983. |
[7] |
G. Jain and K. Sigman, A Pollaczek-Khintchine formula for M/G/1 queues with disasters,, J. Appl. Prob., 33 (1996), 1191.
doi: 10.2307/3214996. |
[8] |
H. Masuyama and T. Takine, Analysis and computation of the joint queue length distribution in a FIFO single-server queue with multiple batch Markovian arrival streams,, Stoch. Models, 19 (2003), 349.
doi: 10.1081/STM-120023565. |
[9] |
V. Ramaswami, A stable recursion for the steady state vector in Markov chains of M/G/1 type,, Stoch. Models, 4 (1988), 183.
doi: 10.1080/15326348808807077. |
[10] |
Y. W. Shin, BMAP/G/1 queue with correlated arrivals of customers and disasters,, Oper. Res. Lett., 32 (2004), 364.
doi: 10.1016/j.orl.2003.09.005. |
[11] |
T. Takine, Queue length distribution in a FIFO single-server queue with multiple arrival streams having different service time distributions,, Queueing Syst., 39 (2001), 349.
doi: 10.1023/A:1013961710829. |
[12] |
T. Takine, Matrix product-form solution for an LCFS-PR single-server queue with multiple arrival streams governed by a Markov chain,, Queueing Syst., 42 (2002), 131.
doi: 10.1023/A:1020152920794. |
[13] |
T. Takine and T. Hasegawa, The workload in the MAP/G/1 queue with state-dependent services: Its application to a queue with preemptive resume priority,, Comm. Statist. Stochastic Models, 10 (1994), 183.
doi: 10.1080/15326349408807292. |
[14] |
H. C. Tijms, "Stochastic Models, An Algorithmic Approach,'', Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons, (1994).
|
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