
-
Previous Article
Characterizing robust weak sharp solution sets of convex optimization problems with uncertainty
- JIMO Home
- This Issue
-
Next Article
Pricing dynamic fund protection under a Regime-switching Jump-diffusion model with stochastic protection level
Admission control for finite capacity queueing model with general retrial times and state-dependent rates
Indian Institute of Technology Roorkee - 247 667, India |
The finite state dependent queueing model with $ F $-policy is investigated by considering the general retrial attempts. On arrival in the system, if the job finds the server engaged, it is forced to enter into the retrial orbit. After a random period of time, the job from the retrial orbit re-attempts for the service. According to $ F $-policy, as the system attains its full capacity, the arrivals are restricted to join the system until the number of jobs comes down to the prefixed threshold value '$ F $'. The supplementary variable corresponding to the remaining retrial time is used to frame the governing equations which are solved by using Laplace-Stieltjes transform and then applying the recursive method. Special models for machine repair and time-sharing queue are deduced by setting the state dependent rates. Several system indices are obtained explicitly which are further used to facilitate the sensitivity analysis by considering a numerical illustration. A cost function is constructed and minimized for evaluating the optimal threshold parameter and optimal service rate.
References:
[1] |
I. J. B. F. Adan and V. G. Kulkarni,
Single-server queue with Markov-dependent inter-arrival and service times, Queueing Syst., 45 (2003), 113-134.
doi: 10.1023/A:1026093622185. |
[2] |
I. Adiri and B. Avi-Itzhak,
A time-sharing queue, Manage. Sci., 15 (1969), 639-657.
doi: 10.1287/mnsc.15.11.639. |
[3] |
A. Banerjee and U. C. Gupta,
Reducing congestion in bulk-service finite-buffer queueing system using batch-size-dependent service, Perform. Eval., 69 (2012), 53-70.
doi: 10.1016/j.peva.2011.09.002. |
[4] |
M. Boualem, N. Djellab and D. Aïssani,
Stochastic bounds for a single server queue with general retrial times, Bull. Iran. Math. Soc., 40 (2014), 183-198.
|
[5] |
M. Chandrasekaran, M. Muralidhar and U. S. Dixit, Online optimization of multipass machining based on cloud computing, Int. J. Adv. Manuf. Technol., 65 (2013), 239-250. Google Scholar |
[6] |
C.-J. Chang, F.-M. Chang and J.-C. Ke, Economic application in a Bernoulli $F$-policy queueing system with server breakdown, Int. J. Prod. Res., 52 (2014), 743-756. Google Scholar |
[7] |
C.-J. Chang and J.-C. Ke,
Randomized controlling arrival for a queueing system with subject to server breakdowns, Optimization., 64 (2015), 941-955.
doi: 10.1080/02331934.2013.804076. |
[8] |
J. Chang and J. Wang,
Unreliable M/M/1/1 retrial queues with set-up time, Qual. Technol. Quant. Manag., 3703 (2017), 1-13.
doi: 10.1080/16843703.2017.1320459. |
[9] |
G. Choudhury and J.-C. Ke,
An unreliable retrial queue with delaying repair and general retrial times under Bernoulli vacation schedule, Appl. Math. Comput., 230 (2014), 436-450.
doi: 10.1016/j.amc.2013.12.108. |
[10] |
D. R. Cox, The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables, Math. Proc. Cambridge Philos. Soc., 51 (1955), 433.
doi: 10.1017/S0305004100030437. |
[11] |
S. D. Flapper, J.-P. Gayon and L. L. Lim,
On the optimal control of manufacturing and remanufacturing activities with a single shared server, Eur. J. Oper. Res., 234 (2014), 86-98.
doi: 10.1016/j.ejor.2013.10.049. |
[12] |
S. Gao, J. Wang and W. W. Li, An M/G/1 retrial queue with general retrial times, working vacations and vacation interruption, Asia-Pacific J. Oper. Res., 31 (2014), 1440006.
doi: 10.1142/S0217595914400065. |
[13] |
S. M. Gupta,
Interrelationship between controlling arrival and service in queueing systems, Comput. Oper. Res., 22 (1995), 1005-1014.
doi: 10.1016/0305-0548(94)00088-P. |
[14] |
M. Jain,
An $(m, M)$ machine repair problem with spares and state dependent rates: A diffusion process approach, Microelectron. Reliab., 37 (1997), 929-933.
doi: 10.1016/S0026-2714(96)00146-1. |
[15] |
M. Jain and A. Bhagat,
Transient analysis of finite F-policy retrial queues with delayed repair and threshold recovery, Natl. Acad. Sci. Lett., 38 (2015), 257-261.
doi: 10.1007/s40009-014-0337-1. |
[16] |
M. Jain and S. S. Sanga, Performance modeling and ANFIS computing for finite buffer retrial queue under F-policy, in Proceedings of Sixth International Conference on Soft Computing for Problem Solving, Patiala, India, 2017,248–258.
doi: 10.1007/978-981-10-3325-4_25. |
[17] |
M. Jain and S. S. Sanga,
Control F-policy for fault tolerance machining system with general retrial attempts, Natl. Acad. Sci. Lett., 40 (2017), 359-364.
doi: 10.1007/s40009-017-0573-2. |
[18] |
M. Jain and S. S. Sanga, $F$-policy for M/M/1/K retrial queueing model with state-dependent rates, in Performance Prediction and Analytics of Fuzzy, Reliability and Queuing Models (eds. K. Deep, M. Jain and S. Salhi), Springer, Singapore, 2019,127–138.
doi: 10.1007/978-981-13-0857-4_9. |
[19] |
M. Jain, S. S. Sanga and R. K. Meena, Control F-policy for Markovian retrial queue with server breakdowns, in 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES), New Delhi, India, 2016, 1–5.
doi: 10.1109/ICPEICES.2016.7853083. |
[20] |
M. Jain, G. C. Sharma and V. Rani,
M/M/R+r machining system with reneging, spares and interdependent controlled rates, Int. J. Math. Oper. Res., 6 (2014), 655-679.
doi: 10.1504/IJMOR.2014.065422. |
[21] |
M. Jain, G. C. Sharma and R. Sharma,
Optimal control of (N, F) policy for unreliable server queue with multi-optional phase repair and start-up, Int. J. Math. Oper. Res., 4 (2012), 152-174.
doi: 10.1504/IJMOR.2012.046375. |
[22] |
M. Jain, G. C. Sharma and C. Shekhar,
Processor-shared service systems with queue-dependent processors, Comput. Oper. Res., 32 (2005), 629-645.
doi: 10.1016/j.cor.2003.08.009. |
[23] |
M. Jain, C. Shekhar and S. Shukla,
Queueing analysis of machine repair problem with controlled rates and working vacation under F-Policy, Proc. Natl. Acad. Sci. India Sect. A Phys. Sci., 86 (2016), 21-31.
doi: 10.1007/s40010-015-0233-1. |
[24] |
J. C. Ke, C. H. Wu and Z. G. Zhang, Recent developments in vacation queueing models: A short survey, Int. J. Oper. Res., 7 (2010), 3-8. Google Scholar |
[25] |
J. Kim and B. Kim,
The processor-sharing queue with bulk arrivals and phase-type services, Perform. Eval., 64 (2007), 277-297.
doi: 10.1016/j.peva.2006.05.006. |
[26] |
E. R. Kumara and S. Dharsana, Analysis of M/M/1 queueing system with state dependent arrival and detainment of retracted customers, Malaya J. Mat., (2015), 89–98. Google Scholar |
[27] |
C. Lee,
On moment stability properties for a class of state-dependent stochastic networks, J. Korean Stat. Soc., 40 (2011), 325-336.
doi: 10.1016/j.jkss.2010.12.003. |
[28] |
C.-D. Liou,
Optimization analysis of the machine repair problem with multiple vacations and working breakdowns, J. Ind. Manag. Optim., 11 (2014), 83-104.
doi: 10.3934/jimo.2015.11.83. |
[29] |
W. A. Massey, The analysis of queues with time-varying rates for telecommunication models, Telecommun. Syst., 21 (2002), 173-204. Google Scholar |
[30] |
P. Moreno,
An M/G/1 retrial queue with recurrent customers and general retrial times, Appl. Math. Comput., 159 (2004), 651-666.
doi: 10.1016/j.amc.2003.09.019. |
[31] |
P. R. Parthasarathy and R. Sudhesh,
Time-dependent analysis of a single-server retrial queue with state-dependent rates, Oper. Res. Lett., 35 (2007), 601-611.
doi: 10.1016/j.orl.2006.12.005. |
[32] |
T. Phung-Duc and K. Kawanishi,
Multiserver retrial queue with setup time and its application to data centers, J. Ind. Manag. Optim., 15 (2019), 15-35.
|
[33] |
J. Rodrigues, S. M. Prado, N. Balakrishnan and F. Louzada,
Flexible M/G/1 queueing system with state dependent service rate, Oper. Res. Lett., 44 (2016), 383-389.
doi: 10.1016/j.orl.2016.03.011. |
[34] |
K. H. Wang,
Cost analysis of the M/M/R machine-repair problem with mixed standby spares, Microelectron. Reliab., 33 (1993), 1293-1301.
doi: 10.1016/0026-2714(93)90131-H. |
[35] |
K. H. Wang, C. C. Kuo and W. L. Pearn,
Optimal control of an M/G/1/K queueing system with combined F policy and startup time, J. Optim. Theory Appl., 135 (2007), 285-299.
doi: 10.1007/s10957-007-9253-6. |
[36] |
K.-H. Wang, C.-C. Kuo and W. L. Pearn,
A recursive method for the $F$-policy G/M/1/K queueing system with an exponential startup time, Appl. Math. Model., 32 (2008), 958-970.
doi: 10.1016/j.apm.2007.02.023. |
[37] |
K.-H. Wang and B. D. Sivazlian,
Cost analysis of the M/M/R machine repair problem with spares operating under variable service rates, Microelectron. Reliab., 32 (1992), 1171-1183.
doi: 10.1016/0026-2714(92)90035-J. |
[38] |
D.-Y. Yang, F.-M. Chang and J.-C. Ke,
On an unreliable retrial queue with general repeated attempts and J optional vacations, Appl. Math. Model., 40 (2016), 3275-3288.
doi: 10.1016/j.apm.2015.10.023. |
[39] |
D.-Y. Yang and P.-K. Chang,
A parametric programming solution to the F-policy queue with fuzzy parameters, Int. J. Syst. Sci., 46 (2015), 590-598.
doi: 10.1080/00207721.2013.792975. |
[40] |
D.-Y. Yang and Y.-D. Chang,
Sensitivity analysis of the machine repair problem with general repeated attempts, Int. J. Comput. Math., 95 (2018), 1761-1774.
doi: 10.1080/00207160.2017.1336230. |
[41] |
C. Yeh, Y.-T. Lee, C.-J. Chang and F.-M. Chang, Analysis of a two-phase queue system with <p, F>- policy, Qual. Technol. Quant. Manag., 14 (2017), 178-194. Google Scholar |
show all references
References:
[1] |
I. J. B. F. Adan and V. G. Kulkarni,
Single-server queue with Markov-dependent inter-arrival and service times, Queueing Syst., 45 (2003), 113-134.
doi: 10.1023/A:1026093622185. |
[2] |
I. Adiri and B. Avi-Itzhak,
A time-sharing queue, Manage. Sci., 15 (1969), 639-657.
doi: 10.1287/mnsc.15.11.639. |
[3] |
A. Banerjee and U. C. Gupta,
Reducing congestion in bulk-service finite-buffer queueing system using batch-size-dependent service, Perform. Eval., 69 (2012), 53-70.
doi: 10.1016/j.peva.2011.09.002. |
[4] |
M. Boualem, N. Djellab and D. Aïssani,
Stochastic bounds for a single server queue with general retrial times, Bull. Iran. Math. Soc., 40 (2014), 183-198.
|
[5] |
M. Chandrasekaran, M. Muralidhar and U. S. Dixit, Online optimization of multipass machining based on cloud computing, Int. J. Adv. Manuf. Technol., 65 (2013), 239-250. Google Scholar |
[6] |
C.-J. Chang, F.-M. Chang and J.-C. Ke, Economic application in a Bernoulli $F$-policy queueing system with server breakdown, Int. J. Prod. Res., 52 (2014), 743-756. Google Scholar |
[7] |
C.-J. Chang and J.-C. Ke,
Randomized controlling arrival for a queueing system with subject to server breakdowns, Optimization., 64 (2015), 941-955.
doi: 10.1080/02331934.2013.804076. |
[8] |
J. Chang and J. Wang,
Unreliable M/M/1/1 retrial queues with set-up time, Qual. Technol. Quant. Manag., 3703 (2017), 1-13.
doi: 10.1080/16843703.2017.1320459. |
[9] |
G. Choudhury and J.-C. Ke,
An unreliable retrial queue with delaying repair and general retrial times under Bernoulli vacation schedule, Appl. Math. Comput., 230 (2014), 436-450.
doi: 10.1016/j.amc.2013.12.108. |
[10] |
D. R. Cox, The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables, Math. Proc. Cambridge Philos. Soc., 51 (1955), 433.
doi: 10.1017/S0305004100030437. |
[11] |
S. D. Flapper, J.-P. Gayon and L. L. Lim,
On the optimal control of manufacturing and remanufacturing activities with a single shared server, Eur. J. Oper. Res., 234 (2014), 86-98.
doi: 10.1016/j.ejor.2013.10.049. |
[12] |
S. Gao, J. Wang and W. W. Li, An M/G/1 retrial queue with general retrial times, working vacations and vacation interruption, Asia-Pacific J. Oper. Res., 31 (2014), 1440006.
doi: 10.1142/S0217595914400065. |
[13] |
S. M. Gupta,
Interrelationship between controlling arrival and service in queueing systems, Comput. Oper. Res., 22 (1995), 1005-1014.
doi: 10.1016/0305-0548(94)00088-P. |
[14] |
M. Jain,
An $(m, M)$ machine repair problem with spares and state dependent rates: A diffusion process approach, Microelectron. Reliab., 37 (1997), 929-933.
doi: 10.1016/S0026-2714(96)00146-1. |
[15] |
M. Jain and A. Bhagat,
Transient analysis of finite F-policy retrial queues with delayed repair and threshold recovery, Natl. Acad. Sci. Lett., 38 (2015), 257-261.
doi: 10.1007/s40009-014-0337-1. |
[16] |
M. Jain and S. S. Sanga, Performance modeling and ANFIS computing for finite buffer retrial queue under F-policy, in Proceedings of Sixth International Conference on Soft Computing for Problem Solving, Patiala, India, 2017,248–258.
doi: 10.1007/978-981-10-3325-4_25. |
[17] |
M. Jain and S. S. Sanga,
Control F-policy for fault tolerance machining system with general retrial attempts, Natl. Acad. Sci. Lett., 40 (2017), 359-364.
doi: 10.1007/s40009-017-0573-2. |
[18] |
M. Jain and S. S. Sanga, $F$-policy for M/M/1/K retrial queueing model with state-dependent rates, in Performance Prediction and Analytics of Fuzzy, Reliability and Queuing Models (eds. K. Deep, M. Jain and S. Salhi), Springer, Singapore, 2019,127–138.
doi: 10.1007/978-981-13-0857-4_9. |
[19] |
M. Jain, S. S. Sanga and R. K. Meena, Control F-policy for Markovian retrial queue with server breakdowns, in 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES), New Delhi, India, 2016, 1–5.
doi: 10.1109/ICPEICES.2016.7853083. |
[20] |
M. Jain, G. C. Sharma and V. Rani,
M/M/R+r machining system with reneging, spares and interdependent controlled rates, Int. J. Math. Oper. Res., 6 (2014), 655-679.
doi: 10.1504/IJMOR.2014.065422. |
[21] |
M. Jain, G. C. Sharma and R. Sharma,
Optimal control of (N, F) policy for unreliable server queue with multi-optional phase repair and start-up, Int. J. Math. Oper. Res., 4 (2012), 152-174.
doi: 10.1504/IJMOR.2012.046375. |
[22] |
M. Jain, G. C. Sharma and C. Shekhar,
Processor-shared service systems with queue-dependent processors, Comput. Oper. Res., 32 (2005), 629-645.
doi: 10.1016/j.cor.2003.08.009. |
[23] |
M. Jain, C. Shekhar and S. Shukla,
Queueing analysis of machine repair problem with controlled rates and working vacation under F-Policy, Proc. Natl. Acad. Sci. India Sect. A Phys. Sci., 86 (2016), 21-31.
doi: 10.1007/s40010-015-0233-1. |
[24] |
J. C. Ke, C. H. Wu and Z. G. Zhang, Recent developments in vacation queueing models: A short survey, Int. J. Oper. Res., 7 (2010), 3-8. Google Scholar |
[25] |
J. Kim and B. Kim,
The processor-sharing queue with bulk arrivals and phase-type services, Perform. Eval., 64 (2007), 277-297.
doi: 10.1016/j.peva.2006.05.006. |
[26] |
E. R. Kumara and S. Dharsana, Analysis of M/M/1 queueing system with state dependent arrival and detainment of retracted customers, Malaya J. Mat., (2015), 89–98. Google Scholar |
[27] |
C. Lee,
On moment stability properties for a class of state-dependent stochastic networks, J. Korean Stat. Soc., 40 (2011), 325-336.
doi: 10.1016/j.jkss.2010.12.003. |
[28] |
C.-D. Liou,
Optimization analysis of the machine repair problem with multiple vacations and working breakdowns, J. Ind. Manag. Optim., 11 (2014), 83-104.
doi: 10.3934/jimo.2015.11.83. |
[29] |
W. A. Massey, The analysis of queues with time-varying rates for telecommunication models, Telecommun. Syst., 21 (2002), 173-204. Google Scholar |
[30] |
P. Moreno,
An M/G/1 retrial queue with recurrent customers and general retrial times, Appl. Math. Comput., 159 (2004), 651-666.
doi: 10.1016/j.amc.2003.09.019. |
[31] |
P. R. Parthasarathy and R. Sudhesh,
Time-dependent analysis of a single-server retrial queue with state-dependent rates, Oper. Res. Lett., 35 (2007), 601-611.
doi: 10.1016/j.orl.2006.12.005. |
[32] |
T. Phung-Duc and K. Kawanishi,
Multiserver retrial queue with setup time and its application to data centers, J. Ind. Manag. Optim., 15 (2019), 15-35.
|
[33] |
J. Rodrigues, S. M. Prado, N. Balakrishnan and F. Louzada,
Flexible M/G/1 queueing system with state dependent service rate, Oper. Res. Lett., 44 (2016), 383-389.
doi: 10.1016/j.orl.2016.03.011. |
[34] |
K. H. Wang,
Cost analysis of the M/M/R machine-repair problem with mixed standby spares, Microelectron. Reliab., 33 (1993), 1293-1301.
doi: 10.1016/0026-2714(93)90131-H. |
[35] |
K. H. Wang, C. C. Kuo and W. L. Pearn,
Optimal control of an M/G/1/K queueing system with combined F policy and startup time, J. Optim. Theory Appl., 135 (2007), 285-299.
doi: 10.1007/s10957-007-9253-6. |
[36] |
K.-H. Wang, C.-C. Kuo and W. L. Pearn,
A recursive method for the $F$-policy G/M/1/K queueing system with an exponential startup time, Appl. Math. Model., 32 (2008), 958-970.
doi: 10.1016/j.apm.2007.02.023. |
[37] |
K.-H. Wang and B. D. Sivazlian,
Cost analysis of the M/M/R machine repair problem with spares operating under variable service rates, Microelectron. Reliab., 32 (1992), 1171-1183.
doi: 10.1016/0026-2714(92)90035-J. |
[38] |
D.-Y. Yang, F.-M. Chang and J.-C. Ke,
On an unreliable retrial queue with general repeated attempts and J optional vacations, Appl. Math. Model., 40 (2016), 3275-3288.
doi: 10.1016/j.apm.2015.10.023. |
[39] |
D.-Y. Yang and P.-K. Chang,
A parametric programming solution to the F-policy queue with fuzzy parameters, Int. J. Syst. Sci., 46 (2015), 590-598.
doi: 10.1080/00207721.2013.792975. |
[40] |
D.-Y. Yang and Y.-D. Chang,
Sensitivity analysis of the machine repair problem with general repeated attempts, Int. J. Comput. Math., 95 (2018), 1761-1774.
doi: 10.1080/00207160.2017.1336230. |
[41] |
C. Yeh, Y.-T. Lee, C.-J. Chang and F.-M. Chang, Analysis of a two-phase queue system with <p, F>- policy, Qual. Technol. Quant. Manag., 14 (2017), 178-194. Google Scholar |









E[Nq] | PI | PSB | TC | |||||||||
μ | Exp | Е3 | D | Exp | Е3 | D | Exp | Е3 | D | Exp | Е3 | D |
1 | 3.164 | 3.110 | 3.060 | 0.303 | 0.335 | 0.354 | 0.697 | 0.665 | 0.646 | 532.25 | 543.43 | 547.66 |
2 | 2.043 | 2.013 | 1.964 | 0.492 | 0.543 | 0.569 | 0.508 | 0.457 | 0.431 | 473.61 | 506.62 | 518.70 |
3 | 1.482 | 1.477 | 1.436 | 0.580 | 0.643 | 0.G72 | 0.420 | 0.357 | 0.328 | 431.77 | 485.08 | 505.76 |
4 | 1.155 | 1.166 | 1.135 | 0.633 | 0.699 | 0.730 | 0.367 | 0.301 | 0.270 | 403.18 | 469.82 | 499.15 |
5 | 0.940 | 0.963 | 0.941 | 0.671 | 0.735 | 0.768 | 0.329 | 0.265 | 0.232 | 385.15 | 459.00 | 496.05 |
E[Nq] | PI | PSB | TC | |||||||||
μ | Exp | Е3 | D | Exp | Е3 | D | Exp | Е3 | D | Exp | Е3 | D |
1 | 3.164 | 3.110 | 3.060 | 0.303 | 0.335 | 0.354 | 0.697 | 0.665 | 0.646 | 532.25 | 543.43 | 547.66 |
2 | 2.043 | 2.013 | 1.964 | 0.492 | 0.543 | 0.569 | 0.508 | 0.457 | 0.431 | 473.61 | 506.62 | 518.70 |
3 | 1.482 | 1.477 | 1.436 | 0.580 | 0.643 | 0.G72 | 0.420 | 0.357 | 0.328 | 431.77 | 485.08 | 505.76 |
4 | 1.155 | 1.166 | 1.135 | 0.633 | 0.699 | 0.730 | 0.367 | 0.301 | 0.270 | 403.18 | 469.82 | 499.15 |
5 | 0.940 | 0.963 | 0.941 | 0.671 | 0.735 | 0.768 | 0.329 | 0.265 | 0.232 | 385.15 | 459.00 | 496.05 |
λ | E[Nq] | PI | PSB | TC | ||||||||
Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | |
1 | 1.132 | 1.060 | 0.998 | 0.704 | 0.771 | 0.793 | 0.296 | 0.229 | 0.207 | 562.12 | 599.89 | 618.34 |
2 | 1.742 | 1.604 | 1.542 | 0.644 | 0.687 | 0.702 | 0.356 | 0.313 | 0.298 | 677.66 | 662.77 | 667.59 |
3 | 2.161 | 2.026 | 1.985 | 0.582 | 0.617 | 0.626 | 0.418 | 0.383 | 0.374 | 711.49 | 688.00 | 689.76 |
4 | 2.494 | 2.372 | 2.347 | 0.530 | 0.559 | 0.564 | 0.470 | 0.441 | 0.436 | 729.36 | 704.04 | 704.74 |
5 | 2.767 | 2.661 | 2.645 | 0.486 | 0.510 | 0.514 | 0.514 | 0.490 | 0.486 | 741.01 | 715.85 | 716.15 |
λ | E[Nq] | PI | PSB | TC | ||||||||
Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | |
1 | 1.132 | 1.060 | 0.998 | 0.704 | 0.771 | 0.793 | 0.296 | 0.229 | 0.207 | 562.12 | 599.89 | 618.34 |
2 | 1.742 | 1.604 | 1.542 | 0.644 | 0.687 | 0.702 | 0.356 | 0.313 | 0.298 | 677.66 | 662.77 | 667.59 |
3 | 2.161 | 2.026 | 1.985 | 0.582 | 0.617 | 0.626 | 0.418 | 0.383 | 0.374 | 711.49 | 688.00 | 689.76 |
4 | 2.494 | 2.372 | 2.347 | 0.530 | 0.559 | 0.564 | 0.470 | 0.441 | 0.436 | 729.36 | 704.04 | 704.74 |
5 | 2.767 | 2.661 | 2.645 | 0.486 | 0.510 | 0.514 | 0.514 | 0.490 | 0.486 | 741.01 | 715.85 | 716.15 |
γ | E[Nq] | PI | PSB | TC | ||||||||
Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | |
0.5 | 0.581 | 0.633 | 0.628 | 0.745 | 0.799 | 0.830 | 0.255 | 0.201 | 0.170 | 384.56 | 448.74 | 500.10 |
0.6 | 0.562 | 0.627 | 0.637 | 0.733 | 0.784 | 0.817 | 0.267 | 0.216 | 0.183 | 365.13 | 423.37 | 477.68 |
0.7 | 0.544 | 0.617 | 0.643 | 0.723 | 0.771 | 0.805 | 0.277 | 0.229 | 0.195 | 348.73 | 403.30 | 459.70 |
0.8 | 0.527 | 0.606 | 0.645 | 0.714 | 0.760 | 0.795 | 0.286 | 0.240 | 0.205 | 334.57 | 386.37 | 444.12 |
0.9 | 0.510 | 0.593 | 0.644 | 0.706 | 0.750 | 0.784 | 0.294 | 0.250 | 0.216 | 322.17 | 371.45 | 429.80 |
γ | E[Nq] | PI | PSB | TC | ||||||||
Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | |
0.5 | 0.581 | 0.633 | 0.628 | 0.745 | 0.799 | 0.830 | 0.255 | 0.201 | 0.170 | 384.56 | 448.74 | 500.10 |
0.6 | 0.562 | 0.627 | 0.637 | 0.733 | 0.784 | 0.817 | 0.267 | 0.216 | 0.183 | 365.13 | 423.37 | 477.68 |
0.7 | 0.544 | 0.617 | 0.643 | 0.723 | 0.771 | 0.805 | 0.277 | 0.229 | 0.195 | 348.73 | 403.30 | 459.70 |
0.8 | 0.527 | 0.606 | 0.645 | 0.714 | 0.760 | 0.795 | 0.286 | 0.240 | 0.205 | 334.57 | 386.37 | 444.12 |
0.9 | 0.510 | 0.593 | 0.644 | 0.706 | 0.750 | 0.784 | 0.294 | 0.250 | 0.216 | 322.17 | 371.45 | 429.80 |
Cost Set | |||||
Ⅰ | 30 | 30 | 50 | 70 | 40 |
Ⅱ | 10 | 10 | 120 | 15 | 90 |
Ⅲ | 15 | 5 | 120 | 15 | 90 |
Ⅳ | 20 | 20 | 100 | 15 | 90 |
Cost Set | |||||
Ⅰ | 30 | 30 | 50 | 70 | 40 |
Ⅱ | 10 | 10 | 120 | 15 | 90 |
Ⅲ | 15 | 5 | 120 | 15 | 90 |
Ⅳ | 20 | 20 | 100 | 15 | 90 |
γ | |||
Exp | E3 | D | |
0.3 | (12,852.01) | (14,898.49) | (15,937.18) |
0.5 | (10,821.20) | (12,848.52) | (13,874.16) |
0.7 | (8,806.92) | (10,821.04) | (11,836.66) |
γ | |||
Exp | E3 | D | |
0.3 | (12,852.01) | (14,898.49) | (15,937.18) |
0.5 | (10,821.20) | (12,848.52) | (13,874.16) |
0.7 | (8,806.92) | (10,821.04) | (11,836.66) |
Iterations | F* | μ | TC(F*, μ) | Max. tolerance |
0 | 10 | 1 | 853.525 | 9.87E+01 |
1 | 10 | 2 | 842.70 | 5.69E+01 |
2 | 10 | 1.6344 | 823.783 | 3.5E+01 |
3 | 10 | 1.0491 | 821.311 | 8.28 |
4 | 10 | 1.5255 | 821.207 | 2.27 |
5 | 10 | 1.4917 | 821.199 | 6.35E-02 |
6 | 10 | 1.4990 | 821.199 | 4Л2Е-04 |
7 | 10 | 1.4988 | 821.199 | 1.02E-05 |
Iterations | F* | μ | TC(F*, μ) | Max. tolerance |
0 | 10 | 1 | 853.525 | 9.87E+01 |
1 | 10 | 2 | 842.70 | 5.69E+01 |
2 | 10 | 1.6344 | 823.783 | 3.5E+01 |
3 | 10 | 1.0491 | 821.311 | 8.28 |
4 | 10 | 1.5255 | 821.207 | 2.27 |
5 | 10 | 1.4917 | 821.199 | 6.35E-02 |
6 | 10 | 1.4990 | 821.199 | 4Л2Е-04 |
7 | 10 | 1.4988 | 821.199 | 1.02E-05 |
γ | |||
Exp | E3 | D | |
0.3 | (12, 1.601,851.05) | (14, 1.668,897.73) | (15, 1.323,936.78) |
0.5 | (10, 1.499,821.20) | (12, 1.579,847.89) | (13, 1.691,872.05) |
0.7 | (8, 1.489,806.90) | (10, 1.543,820.77) | (11, 1.627,834.89) |
γ | |||
Exp | E3 | D | |
0.3 | (12, 1.601,851.05) | (14, 1.668,897.73) | (15, 1.323,936.78) |
0.5 | (10, 1.499,821.20) | (12, 1.579,847.89) | (13, 1.691,872.05) |
0.7 | (8, 1.489,806.90) | (10, 1.543,820.77) | (11, 1.627,834.89) |
μ | E[Nq] | PI | PSB | TC | ||||||||
Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | |
6 | 0.876 | 0.995 | 1.041 | 0.552 | 0.557 | 0.564 | 0.448 | 0.443 | 0.436 | 274.65 | 307.11 | 323.69 |
8 | 0.476 | 0.570 | 0.623 | 0.654 | 0.656 | 0.659 | 0.346 | 0.344 | 0.341 | 241.50 | 270.93 | 290.14 |
10 | 0.286 | 0.352 | 0.399 | 0.721 | 0.722 | 0.723 | 0.279 | 0.278 | 0.277 | 237.26 | 261.73 | 280.32 |
12 | 0.187 | 0.235 | 0.272 | 0.767 | 0.767 | 0.768 | 0.233 | 0.233 | 0.232 | 247.50 | 267.75 | 284.72 |
14 | 0.131 | 0.166 | 0.196 | 0.800 | 0.800 | 0.801 | 0.200 | 0.200 | 0.199 | 265.16 | 282.20 | 297.46 |
μ | E[Nq] | PI | PSB | TC | ||||||||
Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | |
6 | 0.876 | 0.995 | 1.041 | 0.552 | 0.557 | 0.564 | 0.448 | 0.443 | 0.436 | 274.65 | 307.11 | 323.69 |
8 | 0.476 | 0.570 | 0.623 | 0.654 | 0.656 | 0.659 | 0.346 | 0.344 | 0.341 | 241.50 | 270.93 | 290.14 |
10 | 0.286 | 0.352 | 0.399 | 0.721 | 0.722 | 0.723 | 0.279 | 0.278 | 0.277 | 237.26 | 261.73 | 280.32 |
12 | 0.187 | 0.235 | 0.272 | 0.767 | 0.767 | 0.768 | 0.233 | 0.233 | 0.232 | 247.50 | 267.75 | 284.72 |
14 | 0.131 | 0.166 | 0.196 | 0.800 | 0.800 | 0.801 | 0.200 | 0.200 | 0.199 | 265.16 | 282.20 | 297.46 |
λ | E[Nq] | PI | PSB | TC | ||||||||
Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | |
2 | 0.107 | 0.124 | 0.138 | 0.800 | 0.800 | 0.800 | 0.200 | 0.200 | 0.200 | 193.36 | 201.93 | 208.81 |
4 | 0.783 | 0.948 | 1.014 | 0.613 | 0.619 | 0.628 | 0.387 | 0.381 | 0.372 | 341.33 | 391.91 | 418.07 |
6 | 1.726 | 1.843 | 1.829 | 0.493 | 0.516 | 0.535 | 0.507 | 0.484 | 0.465 | 504.56 | 547.33 | 559.06 |
8 | 2.340 | 2.357 | 2.303 | 0.426 | 0.456 | 0.478 | 0.574 | 0.544 | 0.522 | 589.23 | 614.24 | 619.62 |
10 | 2.737 | 2.699 | 2.632 | 0.380 | 0.412 | 0.434 | 0.620 | 0.588 | 0.566 | 634.09 | 649.61 | 652.77 |
λ | E[Nq] | PI | PSB | TC | ||||||||
Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | |
2 | 0.107 | 0.124 | 0.138 | 0.800 | 0.800 | 0.800 | 0.200 | 0.200 | 0.200 | 193.36 | 201.93 | 208.81 |
4 | 0.783 | 0.948 | 1.014 | 0.613 | 0.619 | 0.628 | 0.387 | 0.381 | 0.372 | 341.33 | 391.91 | 418.07 |
6 | 1.726 | 1.843 | 1.829 | 0.493 | 0.516 | 0.535 | 0.507 | 0.484 | 0.465 | 504.56 | 547.33 | 559.06 |
8 | 2.340 | 2.357 | 2.303 | 0.426 | 0.456 | 0.478 | 0.574 | 0.544 | 0.522 | 589.23 | 614.24 | 619.62 |
10 | 2.737 | 2.699 | 2.632 | 0.380 | 0.412 | 0.434 | 0.620 | 0.588 | 0.566 | 634.09 | 649.61 | 652.77 |
γ | E[Nq] | PI | PSB | TC | ||||||||
Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | |
1 | 0.286 | 0.352 | 0.399 | 0.721 | 0.722 | 0.723 | 0.279 | 0.278 | 0.277 | 237.26 | 261.73 | 280.32 |
1.5 | 0.225 | 0.256 | 0.276 | 0.719 | 0.721 | 0.722 | 0.281 | 0.279 | 0.278 | 214.93 | 226.13 | 234.03 |
2 | 0.195 | 0.212 | 0.223 | 0.718 | 0.720 | 0.721 | 0.282 | 0.280 | 0.279 | 204.02 | 210.31 | 214.43 |
2.5 | 0.177 | 0.188 | 0.194 | 0.717 | 0.719 | 0.720 | 0.283 | 0.281 | 0.280 | 197.58 | 201.59 | 204.06 |
3 | 0.165 | 0.173 | 0.177 | 0.716 | 0.718 | 0.719 | 0.284 | 0.282 | 0.281 | 193.35 | 196.12 | 197.75 |
γ | E[Nq] | PI | PSB | TC | ||||||||
Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | Exp | E3 | D | |
1 | 0.286 | 0.352 | 0.399 | 0.721 | 0.722 | 0.723 | 0.279 | 0.278 | 0.277 | 237.26 | 261.73 | 280.32 |
1.5 | 0.225 | 0.256 | 0.276 | 0.719 | 0.721 | 0.722 | 0.281 | 0.279 | 0.278 | 214.93 | 226.13 | 234.03 |
2 | 0.195 | 0.212 | 0.223 | 0.718 | 0.720 | 0.721 | 0.282 | 0.280 | 0.279 | 204.02 | 210.31 | 214.43 |
2.5 | 0.177 | 0.188 | 0.194 | 0.717 | 0.719 | 0.720 | 0.283 | 0.281 | 0.280 | 197.58 | 201.59 | 204.06 |
3 | 0.165 | 0.173 | 0.177 | 0.716 | 0.718 | 0.719 | 0.284 | 0.282 | 0.281 | 193.35 | 196.12 | 197.75 |
Cost Set | |||||
Ⅰ | 30 | 40 | 120 | 60 | 90 |
Ⅱ | 10 | 10 | 120 | 15 | 90 |
Ⅲ | 15 | 5 | 120 | 15 | 90 |
Ⅳ | 10 | 10 | 100 | 15 | 110 |
Cost Set | |||||
Ⅰ | 30 | 40 | 120 | 60 | 90 |
Ⅱ | 10 | 10 | 120 | 15 | 90 |
Ⅲ | 15 | 5 | 120 | 15 | 90 |
Ⅳ | 10 | 10 | 100 | 15 | 110 |
γ | |||
Exp | E3 | D | |
1 | (2,822.28) | (1,858.94) | (1,872.35) |
3 | (5,665.29) | (5,678.51) | (5,687.12) |
5 | (6,627.96) | (6,632.94) | (6,635.92) |
γ | |||
Exp | E3 | D | |
1 | (2,822.28) | (1,858.94) | (1,872.35) |
3 | (5,665.29) | (5,678.51) | (5,687.12) |
5 | (6,627.96) | (6,632.94) | (6,635.92) |
Iterations | F* | μ | TC(F*, μ) | Max. tolerance |
0 | 5 | 8 | 665.286 | 1.58E+01 |
1 | 5 | 7 | 660.172 | 7.35 |
2 | 5 | 7.3170 | 669.221 | 1.16 |
3 | 5 | 7.2739 | 659.194 | 6.86E-02 |
4 | 5 | 7.2712 | 659.194 | 7.04E-04 |
5 | 5 | 7.2712 | 659.194 | 0 |
Iterations | F* | μ | TC(F*, μ) | Max. tolerance |
0 | 5 | 8 | 665.286 | 1.58E+01 |
1 | 5 | 7 | 660.172 | 7.35 |
2 | 5 | 7.3170 | 669.221 | 1.16 |
3 | 5 | 7.2739 | 659.194 | 6.86E-02 |
4 | 5 | 7.2712 | 659.194 | 7.04E-04 |
5 | 5 | 7.2712 | 659.194 | 0 |
γ | |||
Exp | E3 | D | |
1 | (2, 6.169,803.45) | (1, 5.854,809.85) | (1, 6.092,820.80) |
3 | (5, 7.271,659.19) | (5, 7.341,673.70) | (5, 7.378,682.92) |
5 | (6, 7.012,615.23) | (6, 7.048,621.22) | (6, 7.068,624.76) |
γ | |||
Exp | E3 | D | |
1 | (2, 6.169,803.45) | (1, 5.854,809.85) | (1, 6.092,820.80) |
3 | (5, 7.271,659.19) | (5, 7.341,673.70) | (5, 7.378,682.92) |
5 | (6, 7.012,615.23) | (6, 7.048,621.22) | (6, 7.068,624.76) |
[1] |
Seung-Yeal Ha, Shi Jin. Local sensitivity analysis for the Cucker-Smale model with random inputs. Kinetic & Related Models, 2018, 11 (4) : 859-889. doi: 10.3934/krm.2018034 |
[2] |
Carlos Fresneda-Portillo, Sergey E. Mikhailov. Analysis of Boundary-Domain Integral Equations to the mixed BVP for a compressible stokes system with variable viscosity. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3059-3088. doi: 10.3934/cpaa.2019137 |
[3] |
W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349 |
[4] |
Martin Bohner, Sabrina Streipert. Optimal harvesting policy for the Beverton--Holt model. Mathematical Biosciences & Engineering, 2016, 13 (4) : 673-695. doi: 10.3934/mbe.2016014 |
[5] |
Todd Hurst, Volker Rehbock. Optimizing micro-algae production in a raceway pond with variable depth. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021027 |
[6] |
Arseny Egorov. Morse coding for a Fuchsian group of finite covolume. Journal of Modern Dynamics, 2009, 3 (4) : 637-646. doi: 10.3934/jmd.2009.3.637 |
[7] |
Xianming Liu, Guangyue Han. A Wong-Zakai approximation of stochastic differential equations driven by a general semimartingale. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2499-2508. doi: 10.3934/dcdsb.2020192 |
[8] |
Jan Prüss, Laurent Pujo-Menjouet, G.F. Webb, Rico Zacher. Analysis of a model for the dynamics of prions. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 225-235. doi: 10.3934/dcdsb.2006.6.225 |
[9] |
Murat Uzunca, Ayşe Sarıaydın-Filibelioǧlu. Adaptive discontinuous galerkin finite elements for advective Allen-Cahn equation. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 269-281. doi: 10.3934/naco.2020025 |
[10] |
Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023 |
[11] |
Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399 |
[12] |
Sohana Jahan. Discriminant analysis of regularized multidimensional scaling. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 255-267. doi: 10.3934/naco.2020024 |
[13] |
Marian Gidea, Rafael de la Llave, Tere M. Seara. A general mechanism of instability in Hamiltonian systems: Skipping along a normally hyperbolic invariant manifold. Discrete & Continuous Dynamical Systems - A, 2020, 40 (12) : 6795-6813. doi: 10.3934/dcds.2020166 |
[14] |
Manfred Einsiedler, Elon Lindenstrauss. On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method. Journal of Modern Dynamics, 2008, 2 (1) : 83-128. doi: 10.3934/jmd.2008.2.83 |
[15] |
A. Aghajani, S. F. Mottaghi. Regularity of extremal solutions of semilinaer fourth-order elliptic problems with general nonlinearities. Communications on Pure & Applied Analysis, 2018, 17 (3) : 887-898. doi: 10.3934/cpaa.2018044 |
[16] |
Hakan Özadam, Ferruh Özbudak. A note on negacyclic and cyclic codes of length $p^s$ over a finite field of characteristic $p$. Advances in Mathematics of Communications, 2009, 3 (3) : 265-271. doi: 10.3934/amc.2009.3.265 |
[17] |
Lunji Song, Wenya Qi, Kaifang Liu, Qingxian Gu. A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2581-2598. doi: 10.3934/dcdsb.2020196 |
[18] |
Zengyun Wang, Jinde Cao, Zuowei Cai, Lihong Huang. Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2677-2692. doi: 10.3934/dcdsb.2020200 |
[19] |
Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327 |
[20] |
Vieri Benci, Sunra Mosconi, Marco Squassina. Preface: Applications of mathematical analysis to problems in theoretical physics. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : i-i. doi: 10.3934/dcdss.2020446 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]