
-
Previous Article
A new adaptive method to nonlinear semi-infinite programming
- JIMO Home
- This Issue
-
Next Article
An efficient genetic algorithm for decentralized multi-project scheduling with resource transfers
On the $ BMAP_1, BMAP_2/PH/g, c $ retrial queueing system
1. | School of Mathematical Science, Changsha Normal University, Changsha 410100, Hunan, China |
2. | School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China |
In this paper, we consider the BMAP/PH/c retrial queue with two types of customers where the rate of individual repeated attempts from the orbit is modulated according to a Markov Modulated Poisson Process. Using the theory of multi-dimensional asymptotically quasi-Toeplitz Markov chain, we obtain the algorithm for calculating the stationary distribution of the system. Main performance measures are presented. Furthermore, we investigate some optimization problems. The algorithm for determining the optimal number of guard servers and total servers is elaborated. Finally, this queueing system is applied to the cellular wireless network. Numerical results to illustrate the optimization problems and the impact of retrial on performance measures are provided. We find that the performance measures are mainly affected by the two types of customers' arrivals and service patterns, but the retrial rate plays a less crucial role.
References:
[1] |
J. R. Artalejo, Accessible bibliography on retrial queues, Mathematical and Computer Modelling, 30 (1999), 1-6. Google Scholar |
[2] |
J. R. Artalejo,
A classified bibliography of research on retrial queues: Progress in 1990-1999, Top, 7 (1999), 187-211.
doi: 10.1007/BF02564721. |
[3] |
L. Breuer, A. Dudin and V. Klimenok,
A retrial $BMAP/PH/N$ system, Queueing Systems, 40 (2002), 433-457.
doi: 10.1023/A:1015041602946. |
[4] |
S. R. Chakravarthy, The batch Markovian arrival process: A review and future work, Advances in Probability Theory and Stochastic Processes, (1999), 21–49. Google Scholar |
[5] |
A. Dudin and V. Klimenok, A retrial BMAP/PH/N queueing system with Markov modulated retrials, 2012 2nd Baltic Congress on Future Internet Communications, IEEE, (2012), 246–251.
doi: 10.1109/BCFIC.2012.6217953. |
[6] |
A. N. Dudin, G. V. Tsarenkov and V. I. Klimenok, Software "SIRIUS++" for performance evaluation of modern communication networks, Modelling and Simulation 2002. 16th European Simulation Multi-conference, Darmstadt, (2002), 489–493. Google Scholar |
[7] |
G. Falin,
A survey of retrial queues, Queueing Systems Theory Appl., 7 (1990), 127-167.
doi: 10.1007/BF01158472. |
[8] |
A. Graham, Kronecker Products and Matrix Calculus with Applications, Ellis Horwood Ltd., Chichester, Halsted Press [John Wiley & Sons, Inc.], New York, 1981,130 pp. |
[9] |
R. Guerin,
Queueing-blocking system with two arrival streams and guard channels, IEEE Transations in Communications, 36 (1988), 153-163.
doi: 10.1109/26.2745. |
[10] |
D. Hong and S.S. Rappaport, Traffic model and performance analysis for cellular mobile radio telephone systems with prioritized and nonprioritized handoff procedures, IEEE Transactions on Vehicular Technology, 35 (1996), 77-99. Google Scholar |
[11] |
C. S. Kim, V. I. Klimenok and D. S. Orlovsky,
The BMAP/PH/N retrial queue with Markovian flow of breakdowns, European Journal of Operational Research, 189 (2008), 1057-1072.
doi: 10.1016/j.ejor.2007.02.053. |
[12] |
C. S. Kim, V. Klimenok, V. Mushko and A. Dudin,
The BMAP/PH/N retrial queueing system operating in {M}arkovian random environment, Comput. Oper. Res., 37 (2010), 1228-1237.
doi: 10.1016/j.cor.2009.09.008. |
[13] |
C. S. Kim, V. I. Klimenok and A. N. Dudin,
Analysis and optimization of guard channel policy in cellular mobile networks with account of retrials, Comput. Oper. Res., 43 (2014), 181-190.
doi: 10.1016/j.cor.2013.09.005. |
[14] |
A. Klemm, C. Lindemann and M. Lohmann,
Modeling IP traffic using the batch Markovian arrival process, Performance Evaluation, 54 (2003), 149-173.
doi: 10.1007/3-540-46029-2_6. |
[15] |
V. I. Klimenok, D. S. Orlovsky and A. N. Dudin,
A $BMAP/PH/N$ system with impatient repeated Calls, Asia-Pacific Journal of Operational Research, 24 (2007), 293-312.
doi: 10.1142/S0217595907001310. |
[16] |
V. I. Klimenok and A. N. Dudin,
Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory, Queueing Systems, 54 (2006), 245-259.
doi: 10.1007/s11134-006-0300-z. |
[17] |
G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, American Statistical Association, Alexandria, VA, 1999.
doi: 10.1137/1.9780898719734. |
[18] |
D. M. Lucantoni,
New results on the single server queue with a batch Markovian arrival process, Stochastic Models, 7 (1991), 1-46.
doi: 10.1080/15326349108807174. |
[19] |
M. Martin and J. R. Artalejo,
Analysis of an $M/G/1$ queue with two types of impatient units, Advances in Applied Probability, 27 (1995), 840-861.
doi: 10.2307/1428136. |
[20] |
E. Morozov, A. Rumyantsev, S. Dey and T. G. Deepak, Performance analysis and stability of multiclass orbit queue with constant retrial rates and balking, Performance Evaluation, 134 (2019), 102005.
doi: 10.1016/j.peva.2019.102005. |
[21] |
M. F. Neuts,
A versatile Markovian point process, Journal of Applied Probability, 16 (1979), 764-779.
doi: 10.2307/3213143. |
[22] |
M. F. Neuts, Structured Stochastic Matrices of M/G/1-type and their Applications, Probability: Pure and Applied, 5. Marcel Dekker, Inc., New York, 1989. |
[23] |
M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach,
Johns Hopkins Series in the Mathematical Sciences, 2. Johns Hopkins University Press, Baltimore, Md., 1981. |
[24] |
P. I. Panagoulias, I. D. Moscholios, P. G. Sarigiannidis and M. D. Logothetis,
Congestion probabilities in OFDM wireless networks with compound Poisson arrivals, IET Communications, 14 (2020), 674-681.
doi: 10.1049/iet-com.2019.0845. |
[25] |
K. S. Trivedi, S. Dharmaraja and X. M. Ma,
Analytic modeling of handoffs in wireless cellular networks, Information Sciences, 148 (2000), 155-166.
doi: 10.1016/S0020-0255(02)00292-X. |
[26] |
T. M. Walingo and F. Takawira,
Performance analysis of a connection admission scheme for future networks, IEEE Transactions on Wireless Communications, 14 (2015), 1994-2006.
doi: 10.1109/TWC.2014.2378777. |
[27] |
Y. L. Wu, G. Y. Min and L. T. Yang,
Performance analysis of hybrid wireless networks under bursty and correlated traffic, IEEE Transactions on Vehicular Technology, 62 (2013), 449-454.
doi: 10.1109/TVT.2012.2219890. |
[28] |
J. B. Wu, Z. M. Lian and G. Yang,
Analysis of the finite source MAP/PH/N retrial G-queue operating in a random environment, Applied Mathematical Modelling, 35 (2011), 1184-1193.
doi: 10.1016/j.apm.2010.08.006. |
[29] |
J. B. Wu and Z. T. Lian,
Analysis of $M_1, M_2/G/1$ G-queueing system with retrial customers, Nonlinear Analysis: Real World Applications, 14 (2013), 365-382.
doi: 10.1016/j.nonrwa.2012.06.009. |
show all references
References:
[1] |
J. R. Artalejo, Accessible bibliography on retrial queues, Mathematical and Computer Modelling, 30 (1999), 1-6. Google Scholar |
[2] |
J. R. Artalejo,
A classified bibliography of research on retrial queues: Progress in 1990-1999, Top, 7 (1999), 187-211.
doi: 10.1007/BF02564721. |
[3] |
L. Breuer, A. Dudin and V. Klimenok,
A retrial $BMAP/PH/N$ system, Queueing Systems, 40 (2002), 433-457.
doi: 10.1023/A:1015041602946. |
[4] |
S. R. Chakravarthy, The batch Markovian arrival process: A review and future work, Advances in Probability Theory and Stochastic Processes, (1999), 21–49. Google Scholar |
[5] |
A. Dudin and V. Klimenok, A retrial BMAP/PH/N queueing system with Markov modulated retrials, 2012 2nd Baltic Congress on Future Internet Communications, IEEE, (2012), 246–251.
doi: 10.1109/BCFIC.2012.6217953. |
[6] |
A. N. Dudin, G. V. Tsarenkov and V. I. Klimenok, Software "SIRIUS++" for performance evaluation of modern communication networks, Modelling and Simulation 2002. 16th European Simulation Multi-conference, Darmstadt, (2002), 489–493. Google Scholar |
[7] |
G. Falin,
A survey of retrial queues, Queueing Systems Theory Appl., 7 (1990), 127-167.
doi: 10.1007/BF01158472. |
[8] |
A. Graham, Kronecker Products and Matrix Calculus with Applications, Ellis Horwood Ltd., Chichester, Halsted Press [John Wiley & Sons, Inc.], New York, 1981,130 pp. |
[9] |
R. Guerin,
Queueing-blocking system with two arrival streams and guard channels, IEEE Transations in Communications, 36 (1988), 153-163.
doi: 10.1109/26.2745. |
[10] |
D. Hong and S.S. Rappaport, Traffic model and performance analysis for cellular mobile radio telephone systems with prioritized and nonprioritized handoff procedures, IEEE Transactions on Vehicular Technology, 35 (1996), 77-99. Google Scholar |
[11] |
C. S. Kim, V. I. Klimenok and D. S. Orlovsky,
The BMAP/PH/N retrial queue with Markovian flow of breakdowns, European Journal of Operational Research, 189 (2008), 1057-1072.
doi: 10.1016/j.ejor.2007.02.053. |
[12] |
C. S. Kim, V. Klimenok, V. Mushko and A. Dudin,
The BMAP/PH/N retrial queueing system operating in {M}arkovian random environment, Comput. Oper. Res., 37 (2010), 1228-1237.
doi: 10.1016/j.cor.2009.09.008. |
[13] |
C. S. Kim, V. I. Klimenok and A. N. Dudin,
Analysis and optimization of guard channel policy in cellular mobile networks with account of retrials, Comput. Oper. Res., 43 (2014), 181-190.
doi: 10.1016/j.cor.2013.09.005. |
[14] |
A. Klemm, C. Lindemann and M. Lohmann,
Modeling IP traffic using the batch Markovian arrival process, Performance Evaluation, 54 (2003), 149-173.
doi: 10.1007/3-540-46029-2_6. |
[15] |
V. I. Klimenok, D. S. Orlovsky and A. N. Dudin,
A $BMAP/PH/N$ system with impatient repeated Calls, Asia-Pacific Journal of Operational Research, 24 (2007), 293-312.
doi: 10.1142/S0217595907001310. |
[16] |
V. I. Klimenok and A. N. Dudin,
Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory, Queueing Systems, 54 (2006), 245-259.
doi: 10.1007/s11134-006-0300-z. |
[17] |
G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, American Statistical Association, Alexandria, VA, 1999.
doi: 10.1137/1.9780898719734. |
[18] |
D. M. Lucantoni,
New results on the single server queue with a batch Markovian arrival process, Stochastic Models, 7 (1991), 1-46.
doi: 10.1080/15326349108807174. |
[19] |
M. Martin and J. R. Artalejo,
Analysis of an $M/G/1$ queue with two types of impatient units, Advances in Applied Probability, 27 (1995), 840-861.
doi: 10.2307/1428136. |
[20] |
E. Morozov, A. Rumyantsev, S. Dey and T. G. Deepak, Performance analysis and stability of multiclass orbit queue with constant retrial rates and balking, Performance Evaluation, 134 (2019), 102005.
doi: 10.1016/j.peva.2019.102005. |
[21] |
M. F. Neuts,
A versatile Markovian point process, Journal of Applied Probability, 16 (1979), 764-779.
doi: 10.2307/3213143. |
[22] |
M. F. Neuts, Structured Stochastic Matrices of M/G/1-type and their Applications, Probability: Pure and Applied, 5. Marcel Dekker, Inc., New York, 1989. |
[23] |
M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach,
Johns Hopkins Series in the Mathematical Sciences, 2. Johns Hopkins University Press, Baltimore, Md., 1981. |
[24] |
P. I. Panagoulias, I. D. Moscholios, P. G. Sarigiannidis and M. D. Logothetis,
Congestion probabilities in OFDM wireless networks with compound Poisson arrivals, IET Communications, 14 (2020), 674-681.
doi: 10.1049/iet-com.2019.0845. |
[25] |
K. S. Trivedi, S. Dharmaraja and X. M. Ma,
Analytic modeling of handoffs in wireless cellular networks, Information Sciences, 148 (2000), 155-166.
doi: 10.1016/S0020-0255(02)00292-X. |
[26] |
T. M. Walingo and F. Takawira,
Performance analysis of a connection admission scheme for future networks, IEEE Transactions on Wireless Communications, 14 (2015), 1994-2006.
doi: 10.1109/TWC.2014.2378777. |
[27] |
Y. L. Wu, G. Y. Min and L. T. Yang,
Performance analysis of hybrid wireless networks under bursty and correlated traffic, IEEE Transactions on Vehicular Technology, 62 (2013), 449-454.
doi: 10.1109/TVT.2012.2219890. |
[28] |
J. B. Wu, Z. M. Lian and G. Yang,
Analysis of the finite source MAP/PH/N retrial G-queue operating in a random environment, Applied Mathematical Modelling, 35 (2011), 1184-1193.
doi: 10.1016/j.apm.2010.08.006. |
[29] |
J. B. Wu and Z. T. Lian,
Analysis of $M_1, M_2/G/1$ G-queueing system with retrial customers, Nonlinear Analysis: Real World Applications, 14 (2013), 365-382.
doi: 10.1016/j.nonrwa.2012.06.009. |



$i$ $\backslash$ $b$ | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | $sum$ |
0 | 0.0467 | 0.1413 | 0.2136 | 0.2148 | 0.1604 | 0.0923 | 0.0376 | 0.0016 | 0.0001 | 0.9084 |
1 | 0.0001 | 0.0006 | 0.0020 | 0.0047 | 0.0091 | 0.0149 | 0.0208 | 0.0013 | 0.0001 | 0.0536 |
2 | 0.0000 | 0.0000 | 0.0002 | 0.0008 | 0.0023 | 0.0054 | 0.0109 | 0.0008 | 0.0000 | 0.0206 |
3 | 0.0000 | 0.0000 | 0.0000 | 0.0002 | 0.0007 | 0.0022 | 0.0055 | 0.0005 | 0.0000 | 0.0092 |
4 | 0.0000 | 0.0000 | 0.0000 | 0.0001 | 0.0002 | 0.0009 | 0.0028 | 0.0003 | 0.0000 | 0.0043 |
5 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0001 | 0.0004 | 0.0014 | 0.0001 | 0.0000 | 0.0020 |
1.0e-003 $\times$ | ||||||||||
6 | 0.0000 | 0.0001 | 0.0007 | 0.0055 | 0.0334 | 0.1661 | 0.6986 | 0.0667 | 0.0051 | 0.9761 |
1.0e-003 $\times$ | ||||||||||
7 | 0.0000 | 0.0000 | 0.0002 | 0.0019 | 0.0130 | 0.0731 | 0.3474 | 0.0337 | 0.0027 | 0.4721 |
1.0e-003$\times$ | ||||||||||
8 | 0.0000 | 0.0000 | 0.0001 | 0.0007 | 0.0052 | 0.0325 | 0.1724 | 0.0169 | 0.0014 | 0.2291 |
1.0e-004$\times$ | ||||||||||
9 | 0.0000 | 0.0000 | 0.0002 | 0.0025 | 0.0211 | 0.1460 | 0.8533 | 0.0846 | 0.0069 | 1.1145 |
1.0e-004$\times$ | ||||||||||
10 | 0.0000 | 0.0000 | 0.0001 | 0.0009 | 0.0087 | 0.0660 | 0.4217 | 0.0421 | 0.0035 | 0.5429 |
$sum$ | 0.0468 | 0.1419 | 0.2158 | 0.2206 | 0.1728 | 0.1162 | 0.0800 | 0.0047 | 0.0002 | 0.999 |
$i$ $\backslash$ $b$ | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | $sum$ |
0 | 0.0467 | 0.1413 | 0.2136 | 0.2148 | 0.1604 | 0.0923 | 0.0376 | 0.0016 | 0.0001 | 0.9084 |
1 | 0.0001 | 0.0006 | 0.0020 | 0.0047 | 0.0091 | 0.0149 | 0.0208 | 0.0013 | 0.0001 | 0.0536 |
2 | 0.0000 | 0.0000 | 0.0002 | 0.0008 | 0.0023 | 0.0054 | 0.0109 | 0.0008 | 0.0000 | 0.0206 |
3 | 0.0000 | 0.0000 | 0.0000 | 0.0002 | 0.0007 | 0.0022 | 0.0055 | 0.0005 | 0.0000 | 0.0092 |
4 | 0.0000 | 0.0000 | 0.0000 | 0.0001 | 0.0002 | 0.0009 | 0.0028 | 0.0003 | 0.0000 | 0.0043 |
5 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0001 | 0.0004 | 0.0014 | 0.0001 | 0.0000 | 0.0020 |
1.0e-003 $\times$ | ||||||||||
6 | 0.0000 | 0.0001 | 0.0007 | 0.0055 | 0.0334 | 0.1661 | 0.6986 | 0.0667 | 0.0051 | 0.9761 |
1.0e-003 $\times$ | ||||||||||
7 | 0.0000 | 0.0000 | 0.0002 | 0.0019 | 0.0130 | 0.0731 | 0.3474 | 0.0337 | 0.0027 | 0.4721 |
1.0e-003$\times$ | ||||||||||
8 | 0.0000 | 0.0000 | 0.0001 | 0.0007 | 0.0052 | 0.0325 | 0.1724 | 0.0169 | 0.0014 | 0.2291 |
1.0e-004$\times$ | ||||||||||
9 | 0.0000 | 0.0000 | 0.0002 | 0.0025 | 0.0211 | 0.1460 | 0.8533 | 0.0846 | 0.0069 | 1.1145 |
1.0e-004$\times$ | ||||||||||
10 | 0.0000 | 0.0000 | 0.0001 | 0.0009 | 0.0087 | 0.0660 | 0.4217 | 0.0421 | 0.0035 | 0.5429 |
$sum$ | 0.0468 | 0.1419 | 0.2158 | 0.2206 | 0.1728 | 0.1162 | 0.0800 | 0.0047 | 0.0002 | 0.999 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 20 | |
1 | 18 | 18 | 18 | 17 | 17 | 17 | 16 | 16 | 16 | 16 | 15 | 15 | 15 | 14 | 14 | 13 |
10 | 18 | 18 | 18 | 17 | 17 | 17 | 16 | 16 | 16 | 16 | 15 | 15 | 15 | 14 | 14 | 13 |
20 | 18 | 18 | 18 | 17 | 17 | 17 | 16 | 16 | 16 | 16 | 15 | 15 | 15 | 14 | 14 | 13 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 20 | |
1 | 18 | 18 | 18 | 17 | 17 | 17 | 16 | 16 | 16 | 16 | 15 | 15 | 15 | 14 | 14 | 13 |
10 | 18 | 18 | 18 | 17 | 17 | 17 | 16 | 16 | 16 | 16 | 15 | 15 | 15 | 14 | 14 | 13 |
20 | 18 | 18 | 18 | 17 | 17 | 17 | 16 | 16 | 16 | 16 | 15 | 15 | 15 | 14 | 14 | 13 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 20 | |
1 | 8 | 11 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 29 | 31 | 33 | 35 | 37 | 45 |
5 | 10 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 30 | 32 | 34 | 36 | 38 | 46 |
10 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | 32 | 34 | 36 | 37 | 39 | 47 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 20 | |
1 | 8 | 11 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 29 | 31 | 33 | 35 | 37 | 45 |
5 | 10 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 30 | 32 | 34 | 36 | 38 | 46 |
10 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | 32 | 34 | 36 | 37 | 39 | 47 |
[1] |
Shoufeng Ji, Jinhuan Tang, Minghe Sun, Rongjuan Luo. Multi-objective optimization for a combined location-routing-inventory system considering carbon-capped differences. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021051 |
[2] |
Yi Peng, Jinbiao Wu. Analysis of a batch arrival retrial queue with impatient customers subject to the server disasters. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2243-2264. doi: 10.3934/jimo.2020067 |
[3] |
Namsu Ahn, Soochan Kim. Optimal and heuristic algorithms for the multi-objective vehicle routing problem with drones for military surveillance operations. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021037 |
[4] |
Wenjuan Zhao, Shunfu Jin, Wuyi Yue. A stochastic model and social optimization of a blockchain system based on a general limited batch service queue. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1845-1861. doi: 10.3934/jimo.2020049 |
[5] |
Mohsen Abdolhosseinzadeh, Mir Mohammad Alipour. Design of experiment for tuning parameters of an ant colony optimization method for the constrained shortest Hamiltonian path problem in the grid networks. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 321-332. doi: 10.3934/naco.2020028 |
[6] |
Emma D'Aniello, Saber Elaydi. The structure of $ \omega $-limit sets of asymptotically non-autonomous discrete dynamical systems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 903-915. doi: 10.3934/dcdsb.2019195 |
[7] |
Guanwei Chen, Martin Schechter. Multiple solutions for Schrödinger lattice systems with asymptotically linear terms and perturbed terms. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021124 |
[8] |
Hong Seng Sim, Wah June Leong, Chuei Yee Chen, Siti Nur Iqmal Ibrahim. Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 377-387. doi: 10.3934/naco.2018024 |
[9] |
Ajay Jasra, Kody J. H. Law, Yaxian Xu. Markov chain simulation for multilevel Monte Carlo. Foundations of Data Science, 2021, 3 (1) : 27-47. doi: 10.3934/fods.2021004 |
[10] |
Zhenquan Zhang, Meiling Chen, Jiajun Zhang, Tianshou Zhou. Analysis of non-Markovian effects in generalized birth-death models. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3717-3735. doi: 10.3934/dcdsb.2020254 |
[11] |
Juan Manuel Pastor, Javier García-Algarra, José M. Iriondo, José J. Ramasco, Javier Galeano. Dragging in mutualistic networks. Networks & Heterogeneous Media, 2015, 10 (1) : 37-52. doi: 10.3934/nhm.2015.10.37 |
[12] |
Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu. Single-target networks. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021065 |
[13] |
Gelasio Salaza, Edgardo Ugalde, Jesús Urías. Master--slave synchronization of affine cellular automaton pairs. Discrete & Continuous Dynamical Systems, 2005, 13 (2) : 491-502. doi: 10.3934/dcds.2005.13.491 |
[14] |
Lakmi Niwanthi Wadippuli, Ivan Gudoshnikov, Oleg Makarenkov. Global asymptotic stability of nonconvex sweeping processes. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1129-1139. doi: 10.3934/dcdsb.2019212 |
[15] |
Marzia Bisi, Maria Groppi, Giorgio Martalò, Romina Travaglini. Optimal control of leachate recirculation for anaerobic processes in landfills. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2957-2976. doi: 10.3934/dcdsb.2020215 |
[16] |
Xu Zhang, Xiang Li. Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 393-403. doi: 10.3934/naco.2015.5.393 |
[17] |
Xiaohong Li, Mingxin Sun, Zhaohua Gong, Enmin Feng. Multistage optimal control for microbial fed-batch fermentation process. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021040 |
[18] |
Gheorghe Craciun, Abhishek Deshpande, Hyejin Jenny Yeon. Quasi-toric differential inclusions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2343-2359. doi: 10.3934/dcdsb.2020181 |
[19] |
Alessandro Gondolo, Fernando Guevara Vasquez. Characterization and synthesis of Rayleigh damped elastodynamic networks. Networks & Heterogeneous Media, 2014, 9 (2) : 299-314. doi: 10.3934/nhm.2014.9.299 |
[20] |
Juan Manuel Pastor, Javier García-Algarra, Javier Galeano, José María Iriondo, José J. Ramasco. A simple and bounded model of population dynamics for mutualistic networks. Networks & Heterogeneous Media, 2015, 10 (1) : 53-70. doi: 10.3934/nhm.2015.10.53 |
2019 Impact Factor: 1.366
Tools
Article outline
Figures and Tables
[Back to Top]