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Optimizing multi-objective decision making having qualitative evaluation
Stability of a cyclic polling system with an adaptive mechanism
1. | Department of Mathematics Education, Chungbuk National University, 52 Naesudong-ro, Heungdeok-gu, Cheongju, Chungbuk, 361-763, South Korea |
2. | Department of Mathematics, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, 136-701, South Korea |
References:
[1] |
E. Altman, P. Konstantopoulos and Z. Liu, Stability, monotonicity and invariant quantities in general polling systems,, Queueing Systems, 11 (1992), 35.
doi: 10.1007/BF01159286. |
[2] |
M. A. A. Boon, R. D. van der Mei and E. M. M. Winands, Applications of polling systems,, Surveys in Operations Research and Management Science, 16 (2011), 67.
doi: 10.1016/j.sorms.2011.01.001. |
[3] |
A. A. Borovkov and R. Schassberger, Ergodicity of a polling network,, Stochastic Processes and their Applications, 50 (1994), 253.
doi: 10.1016/0304-4149(94)90122-8. |
[4] |
O. J. Boxma, J. Bruin and B. H. Fralix, Sojourn times in polling systems with various service disciplines,, Performance Evaluation, 66 (2009), 621.
doi: 10.1016/j.peva.2009.05.004. |
[5] |
M. Bramson, Stability of two families of queueing networks and a discussion of fluid limits,, Queueing Systems, 28 (1998), 7.
doi: 10.1023/A:1019182619288. |
[6] |
N. Chernova, S. Foss and B. Kim, On the stability of a polling system with an adaptive service mechanism,, Annals of Operations Research, 198 (2012), 125.
doi: 10.1007/s10479-011-0963-7. |
[7] |
J. G. Dai, On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models,, The Annals of Applied Probability, 5 (1995), 49.
doi: 10.1214/aoap/1177004828. |
[8] |
J. G. Dai and S. P. Meyn, Stability and convergence of moments for multiclass queueing networks via fluid limit models,, IEEE Transaction on Automatic Control, 40 (1995), 1889.
doi: 10.1109/9.471210. |
[9] |
D. G. Down, On the stability of polling models with multiple servers,, Journal of Applied Probability, 35 (1998), 925.
doi: 10.1239/jap/1032438388. |
[10] |
C. Fricker, M. R. Jaíbi, Monotonicity and stability of periodic polling models,, Queueing Systems, 15 (1994), 211.
doi: 10.1007/BF01189238. |
[11] |
L. Georgiadis and W. Szpankowski, Stability of token passing rings,, Queueing Systems, 11 (1992), 7.
doi: 10.1007/BF01159285. |
[12] |
H. Levy and M. Sidi, Polling systems: Applications, modeling, and optimization,, IEEE Transactions on Communications, 38 (1990), 1750.
doi: 10.1109/26.61446. |
[13] |
L. Massouli, Stability of non-Markovian polling systems,, Queueing Systems, 21 (1995), 67.
doi: 10.1007/BF01158575. |
[14] |
J. A. C. Resing, Polling systems and multitype branching processes,, Queueing Systems, 13 (1993), 409.
doi: 10.1007/BF01149263. |
[15] |
A. N. Rybko and A. L. Stolyar, Ergodicity of stochastic processes describing the operation of open queueing networks,, Problems of Information Transmission, 28 (1992), 199.
|
[16] |
Z. Saffer and M. Telek, Stability of periodic polling system with BMAP arrivals,, European Journal of Operational Research, 197 (2009), 188.
doi: 10.1016/j.ejor.2008.05.016. |
[17] |
H. Takagi, Analysis of Polling Systems,, Performance Evaluation, 5 (1985).
doi: 10.1016/0166-5316(85)90016-1. |
[18] |
V. Vishnevsky and O. Semenova, Adaptive dynamical polling in wireless networks,, Cybernetics and Information Technologies, 8 (2008), 3.
|
[19] |
V. Vishnevsky, A. N. Dudin, V. I. Klimenok and O. Semenova, Approximate method to study M/G/1-type polling system with adaptive polling mechanism,, Quality Technology & Quantitative Management, 9 (2012), 211. Google Scholar |
[20] |
A. Wierman, E. M. M. Winands and O. J. Boxma, Scheduling in polling systems,, Performance Evaluation, 64 (2007), 1009.
doi: 10.1016/j.peva.2007.06.015. |
[21] |
A. C. C. van Wijka, I. J. B. F. Adan, O. J. Boxma and A. Wierman, Fairness and efficiency for polling models with the $k$-gated service discipline,, Performance Evaluation, 69 (2012), 274. Google Scholar |
[22] |
E. M. M. Winands, I. J. B. F. Adan, G. J. van Houtum and D. G. Down, A state-dependent polling model with $k$-limited service,, Probability in the Engineering and Informational Sciences, 23 (2009), 385.
doi: 10.1017/S0269964809000217. |
show all references
References:
[1] |
E. Altman, P. Konstantopoulos and Z. Liu, Stability, monotonicity and invariant quantities in general polling systems,, Queueing Systems, 11 (1992), 35.
doi: 10.1007/BF01159286. |
[2] |
M. A. A. Boon, R. D. van der Mei and E. M. M. Winands, Applications of polling systems,, Surveys in Operations Research and Management Science, 16 (2011), 67.
doi: 10.1016/j.sorms.2011.01.001. |
[3] |
A. A. Borovkov and R. Schassberger, Ergodicity of a polling network,, Stochastic Processes and their Applications, 50 (1994), 253.
doi: 10.1016/0304-4149(94)90122-8. |
[4] |
O. J. Boxma, J. Bruin and B. H. Fralix, Sojourn times in polling systems with various service disciplines,, Performance Evaluation, 66 (2009), 621.
doi: 10.1016/j.peva.2009.05.004. |
[5] |
M. Bramson, Stability of two families of queueing networks and a discussion of fluid limits,, Queueing Systems, 28 (1998), 7.
doi: 10.1023/A:1019182619288. |
[6] |
N. Chernova, S. Foss and B. Kim, On the stability of a polling system with an adaptive service mechanism,, Annals of Operations Research, 198 (2012), 125.
doi: 10.1007/s10479-011-0963-7. |
[7] |
J. G. Dai, On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models,, The Annals of Applied Probability, 5 (1995), 49.
doi: 10.1214/aoap/1177004828. |
[8] |
J. G. Dai and S. P. Meyn, Stability and convergence of moments for multiclass queueing networks via fluid limit models,, IEEE Transaction on Automatic Control, 40 (1995), 1889.
doi: 10.1109/9.471210. |
[9] |
D. G. Down, On the stability of polling models with multiple servers,, Journal of Applied Probability, 35 (1998), 925.
doi: 10.1239/jap/1032438388. |
[10] |
C. Fricker, M. R. Jaíbi, Monotonicity and stability of periodic polling models,, Queueing Systems, 15 (1994), 211.
doi: 10.1007/BF01189238. |
[11] |
L. Georgiadis and W. Szpankowski, Stability of token passing rings,, Queueing Systems, 11 (1992), 7.
doi: 10.1007/BF01159285. |
[12] |
H. Levy and M. Sidi, Polling systems: Applications, modeling, and optimization,, IEEE Transactions on Communications, 38 (1990), 1750.
doi: 10.1109/26.61446. |
[13] |
L. Massouli, Stability of non-Markovian polling systems,, Queueing Systems, 21 (1995), 67.
doi: 10.1007/BF01158575. |
[14] |
J. A. C. Resing, Polling systems and multitype branching processes,, Queueing Systems, 13 (1993), 409.
doi: 10.1007/BF01149263. |
[15] |
A. N. Rybko and A. L. Stolyar, Ergodicity of stochastic processes describing the operation of open queueing networks,, Problems of Information Transmission, 28 (1992), 199.
|
[16] |
Z. Saffer and M. Telek, Stability of periodic polling system with BMAP arrivals,, European Journal of Operational Research, 197 (2009), 188.
doi: 10.1016/j.ejor.2008.05.016. |
[17] |
H. Takagi, Analysis of Polling Systems,, Performance Evaluation, 5 (1985).
doi: 10.1016/0166-5316(85)90016-1. |
[18] |
V. Vishnevsky and O. Semenova, Adaptive dynamical polling in wireless networks,, Cybernetics and Information Technologies, 8 (2008), 3.
|
[19] |
V. Vishnevsky, A. N. Dudin, V. I. Klimenok and O. Semenova, Approximate method to study M/G/1-type polling system with adaptive polling mechanism,, Quality Technology & Quantitative Management, 9 (2012), 211. Google Scholar |
[20] |
A. Wierman, E. M. M. Winands and O. J. Boxma, Scheduling in polling systems,, Performance Evaluation, 64 (2007), 1009.
doi: 10.1016/j.peva.2007.06.015. |
[21] |
A. C. C. van Wijka, I. J. B. F. Adan, O. J. Boxma and A. Wierman, Fairness and efficiency for polling models with the $k$-gated service discipline,, Performance Evaluation, 69 (2012), 274. Google Scholar |
[22] |
E. M. M. Winands, I. J. B. F. Adan, G. J. van Houtum and D. G. Down, A state-dependent polling model with $k$-limited service,, Probability in the Engineering and Informational Sciences, 23 (2009), 385.
doi: 10.1017/S0269964809000217. |
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