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Performance analysis of a Geom/Geom/1 queueing system with variable input probability
1. | Department of Applied Mathematics, College of Science, Yanshan University, Qinhuangdao 066004, China |
2. | Department of Intelligence and Informatics, Konan University, Kobe 658-8501 |
3. | Department of Applied Mathematics, College of Science Yanshan University, Qinhuangdao 066004, China |
References:
[1] |
R. Cooper, "Introduction to Queueing Theory," 2nd Edition, North Holland Publishing Co., New York-Amsterdam, 1981. |
[2] |
D. G. Kendall, Some problems in the theory of queues, Journal of the Royal Statistical Society, Series B, 13 (1951), 151-173. |
[3] |
Y. Levy and U. Yechiali, Utilization of idle time in an $M$/$G$/$1$ queueing system, Management Science, 22 (1975), 202-211.
doi: 10.1287/mnsc.22.2.202. |
[4] |
Z. Ma and N. Tian, Pure limited service $Geom$/$G$/$1$ queue with multiple adaptive vacations, Journal of Computational Information Systems, 1 (2005), 515-521. |
[5] |
T. Meisling, Discrete time queueing theory, Operations Research, 6 (1958), 96-105.
doi: 10.1287/opre.6.1.96. |
[6] |
M. Neuts, "Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach," John Hopkins Series in the Mathematical Sciences, 2, Johns Hopkins University Press, Baltimore, 1981. |
[7] |
L. Servi and S. Finn, $M$/$M$/$1$ queue with working vacations ($M$/$M$/$1$/$WV$), Performance Evaluation, 50 (2002), 41-52.
doi: 10.1016/S0166-5316(02)00057-3. |
[8] |
L. Tadj, G. Zhang and C. Tadj, A queueing analysis of multi-purpose production facility's operations, Journal of Industrial and Management Optimization, 7 (2011), 19-30.
doi: 10.3934/jimo.2011.7.19. |
[9] |
H. Takagi, "Queueing Analysis: A Foundation of Performance Evaluation," Vol. 1: Vacation and Priority Systems, Part 1, North-Holland Publishing Co., Amsterdam, 1991. |
[10] |
H. Takagi, "Queueing Analysis, Vol. 3: Discrete-Time Systems," Elsevier Science Publishers, Amsterdam, 1993. |
[11] |
Y. Tang and X. Tang, "Queueing Theory-Foundations And Analysis Technique," Science Press, Beijing, 2006 (in Chinese). |
[12] |
N. Tian, X. Xu and Z. Ma, "Discrete Time Queueing Theory," Science Press, Beijing, 2008 (in Chinese). |
[13] |
N. Tian, D. Zhang and C. Cao, The $GI$/$M$/$1$ queue with exponential vacations, Queueing Systems Theory Applications, 5 (1989), 331-344.
doi: 10.1007/BF01225323. |
[14] |
D. Wu and H. Takagi, $M$/$G$/$1$ queue with multiple working vacations, Performance Evaluation, 63 (2006), 654-681.
doi: 10.1016/j.peva.2005.05.005. |
[15] |
D. Yue and W. Yue, A heterogeneous two-server network system with balking and a Bernoulli vacation schedule, Journal of Industrial and Management Optimization, 6 (2010), 501-516.
doi: 10.3934/jimo.2010.6.501. |
show all references
References:
[1] |
R. Cooper, "Introduction to Queueing Theory," 2nd Edition, North Holland Publishing Co., New York-Amsterdam, 1981. |
[2] |
D. G. Kendall, Some problems in the theory of queues, Journal of the Royal Statistical Society, Series B, 13 (1951), 151-173. |
[3] |
Y. Levy and U. Yechiali, Utilization of idle time in an $M$/$G$/$1$ queueing system, Management Science, 22 (1975), 202-211.
doi: 10.1287/mnsc.22.2.202. |
[4] |
Z. Ma and N. Tian, Pure limited service $Geom$/$G$/$1$ queue with multiple adaptive vacations, Journal of Computational Information Systems, 1 (2005), 515-521. |
[5] |
T. Meisling, Discrete time queueing theory, Operations Research, 6 (1958), 96-105.
doi: 10.1287/opre.6.1.96. |
[6] |
M. Neuts, "Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach," John Hopkins Series in the Mathematical Sciences, 2, Johns Hopkins University Press, Baltimore, 1981. |
[7] |
L. Servi and S. Finn, $M$/$M$/$1$ queue with working vacations ($M$/$M$/$1$/$WV$), Performance Evaluation, 50 (2002), 41-52.
doi: 10.1016/S0166-5316(02)00057-3. |
[8] |
L. Tadj, G. Zhang and C. Tadj, A queueing analysis of multi-purpose production facility's operations, Journal of Industrial and Management Optimization, 7 (2011), 19-30.
doi: 10.3934/jimo.2011.7.19. |
[9] |
H. Takagi, "Queueing Analysis: A Foundation of Performance Evaluation," Vol. 1: Vacation and Priority Systems, Part 1, North-Holland Publishing Co., Amsterdam, 1991. |
[10] |
H. Takagi, "Queueing Analysis, Vol. 3: Discrete-Time Systems," Elsevier Science Publishers, Amsterdam, 1993. |
[11] |
Y. Tang and X. Tang, "Queueing Theory-Foundations And Analysis Technique," Science Press, Beijing, 2006 (in Chinese). |
[12] |
N. Tian, X. Xu and Z. Ma, "Discrete Time Queueing Theory," Science Press, Beijing, 2008 (in Chinese). |
[13] |
N. Tian, D. Zhang and C. Cao, The $GI$/$M$/$1$ queue with exponential vacations, Queueing Systems Theory Applications, 5 (1989), 331-344.
doi: 10.1007/BF01225323. |
[14] |
D. Wu and H. Takagi, $M$/$G$/$1$ queue with multiple working vacations, Performance Evaluation, 63 (2006), 654-681.
doi: 10.1016/j.peva.2005.05.005. |
[15] |
D. Yue and W. Yue, A heterogeneous two-server network system with balking and a Bernoulli vacation schedule, Journal of Industrial and Management Optimization, 6 (2010), 501-516.
doi: 10.3934/jimo.2010.6.501. |
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