• Previous Article
    Modelling and computation of optimal multiple investment timing in multi-stage capacity expansion infrastructure projects
  • JIMO Home
  • This Issue
  • Next Article
    A self adaptive inertial algorithm for solving split variational inclusion and fixed point problems with applications
January  2022, 18(1): 267-295. doi: 10.3934/jimo.2020153

Analysis of dynamic service system between regular and retrial queues with impatient customers

1. 

Department of Mathematics, College of Engineering, Anna University, Chennai 600 025, India

2. 

Department of Mathematics, Pachaiyappa's College, Chennai 600 030, India

* Corresponding author: B. Krishna Kumar

Received  January 2020 Revised  July 2020 Published  January 2022 Early access  October 2020

Fund Project: This research work is supported in part by Department of Science and Technology, New Delhi, India, under research grant INT/RUS/RFBR/377

In this article, we propose a dynamic operating of a single server service system between conventional and retrial queues with impatient customers. Necessary and sufficient conditions for the stability, and an explicit expression for the joint steady-state probability distribution are obtained. We have derived some interesting and important performance measures for the service system under consideration. The first-passage time problems are also investigated. Finally, we have presented extensive numerical examples to demonstrate the effects of the system parameters on the performance measures.

Citation: Balasubramanian Krishna Kumar, Ramachandran Navaneetha Krishnan, Rathinam Sankar, Ramasamy Rukmani. Analysis of dynamic service system between regular and retrial queues with impatient customers. Journal of Industrial and Management Optimization, 2022, 18 (1) : 267-295. doi: 10.3934/jimo.2020153
References:
[1]

M. S. AguirO. Z. AksinF. Karaesmen and Y. Dallery, On the interaction between retrials and sizing of call centers, Euro. J. Oper. Res., 191 (2008), 398-408.  doi: 10.1016/j.ejor.2007.06.051.

[2]

M. S. AguirF. KaraesmenO. Z. Aksin and F. Chauvet, The impact of retrials on call center performance, OR Spectrum, 26 (2004), 353-376.  doi: 10.1007/s00291-004-0165-7.

[3]

N. Akar and K. Sohraby, Retrial queueing models of multi-wavelength FDL feedback optical buffers, IEEE Trans. Commun., 59 (2011), 2832-2840.  doi: 10.2307/2152750.

[4]

O. Z. Aksin and P. T. Harker, Modeling a phone center: Analysis of a multichannel multiresource processor shared loss system, Management Science, 47 (2001), 324-336.  doi: 10.2307/2152750.

[5]

E. Altman and A. A. Borovkov, On the stability of retrial queues, Queueing Systems, 26 (1997), 343-363.  doi: 10.1023/A:1019193527040.

[6]

E. Altman and U. Yechiali, Analysis of customers' impatience in queues with server vacations, Queueing Systems, 52 (2006), 261-279.  doi: 10.1007/s11134-006-6134-x.

[7]

J. R. Artalejo, Accessible bibliography on retrial queues, Math. Comput. Model., 30 (1999), 1-6.  doi: 10.1016/j.mcm.2009.12.011.

[8]

J. R. Artalejo, Accessible bibliography on retrial queues: Progress in 2000–2009, Math. Comput. Model., 51 (2010), 1071-1081.  doi: 10.1016/j.mcm.2009.12.011.

[9]

J. R. Artalejo and A. Gomez-Corral, Steady state solution of a single-server queue with linear repeated requests, J. Appl. Probab., 34 (1997), 223-233.  doi: 10.2307/3215189.

[10]

J. R. Artalejo and A. Gomez-Corral, Retrial Queueing Systems: A Computational Approach, Springer-Verlag, Berlin, 2008. doi: 10.1007/978-1-4612-0873-0.

[11]

J. R. Artalejo and V. Pla, On the impact of customer balking, impatience and retrials in telecommunication systems, Comput. Math. Appl., 57 (2009), 217-229.  doi: 10.1016/j.camwa.2008.10.084.

[12]

W. J. Anderson, Continuous-Time Markov Chains: An Applications-Oriented Approach, Springer-Verlag, Berlin, 1991. doi: 10.1007/978-1-4612-0873-0.

[13]

S. Asmussen, Applied Probability and Queues, Springer, New York, 2003. doi: 10.1007/978-1-4612-0873-0.

[14]

F. BaccelliP. Boyer and G. Hebuterne, Single-server queues with impatient customers, Adv. Appl. Probab., 16 (1984), 887-905.  doi: 10.2307/1427345.

[15]

F. Baccelli and G. Hebuterne, On queues with impatient customers, in Performance'81, North-Holland Publishing Company, Amsterdam, 1981,159–179. doi: 10.2307/2152750.

[16]

O. J. Boxma and P. R. de Waal, Multiserver queues with impatient customers, ITC, 14 (1994), 743-756.  doi: 10.1016/B978-0-444-82031-0.50079-2.

[17]

A. Brandt and M. Brandt, On the two-class M/M/1 system under preemptive resume and impatience of the prioritized customers, Queueing Systems, 47 (2004), 147-168.  doi: 10.1023/B:QUES.0000032805.73991.8e.

[18]

B. D. Choi and Y. Chang, Single server retrial queues with priority calls, Math. Comput. Model., 30 (1999), 7-32.  doi: 10.1016/S0895-7177(99)00129-6.

[19]

S. DimouA. Economou and D. Fakinos, The single server vacation queueing model with geometric abandonments, J. Stat. Plan. Infer., 141 (2011), 2863-2877.  doi: 10.1016/j.jspi.2011.03.010.

[20]

A. Economou and S. Kapodistria, Synchronized abandonments in a single server unreliable queue, Euro. J. Oper. Res., 203 (2010), 143-155.  doi: 10.1016/j.ejor.2009.07.014.

[21]

A. Erdelyi, Higher Transcendental Function, 1, McGraw-Hill, New York, 1953. doi: 10.1007/978-1-4612-0873-0.

[22]

G. I. Falin, A survey of retrial queues, Queueing Systems, 7 (1990), 127-168.  doi: 10.1007/BF01158472.

[23]

G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapman and Hall, London, 1997. doi: 10.1007/978-1-4899-2977-8.

[24]

G. Fayolle, A simple telephone exchange with delayed feedbacks, in Teletrafic Analysis and Computer Performance Eualuation, Elsevier, Amsterdam, 1986,245–253. doi: 10.2307/2152750.

[25]

N. GansG. Koole and A. Mandelbaum, Telephone call centers: Tutorial, review, and research prospects, Manufacturing and Service Operations Management, 5 (2003), 79-177.  doi: 10.1287/msom.5.2.79.16071.

[26]

O. GarnettA. Mandelbaum and M. Reiman, Designing a call center with impatient customers, Manufacturing and Service Operations Management, 4 (2002), 208-227.  doi: 10.1287/msom.4.3.208.7753.

[27]

D. Gross, J. F. Shortle, J. M. Thompson and C. M. Harris, Fundamentals of Queueing Theory, Wiley India (P) Ltd, New Delhi, 2014. doi: 10.1007/978-1-4612-0873-0.

[28]

F. Iravani and B. Balcioglu, On priority queues with impatient customers, Queueing Systems, 5 (2008), 239-260.  doi: 10.1007/s11134-008-9069-6.

[29]

O. Jouini and Y. Dallery, Moments of first passage times in general birth-death processes, Math. Meth. Oper. Res., 68 (2008), 49-76.  doi: 10.1007/s00186-007-0174-9.

[30]

O. JouiniG. Koole and A. Roubos, Performance indicators for call centers with impatient customers, IIE Transactions, 45 (2013), 341-354.  doi: 10.1080/0740817X.2012.712241.

[31]

S. Karlin and J. McGregor, The classification of birth and death processes, Trans. Amer. Math. Soc., 86 (1957), 366-400.  doi: 10.1090/S0002-9947-1957-0094854-8.

[32]

G. Koole and A. Mandelbaum, Queueing models of call centers: An introduction, Annals of Operations Research, 113 (2002), 41-59.  doi: 10.1023/A:1020949626017.

[33]

V. G. Kulkarni and H. M. Liang, Retrial queues revisited, in Frontiers in Queueing: Models and Applications in Science and Engineering, CRC Press, Boca Raton, FL, 1997, 19-34. doi: 10.2307/2152750.

[34]

A. Mandelbaum and S. Zeltyn, Staffing many-server queues with impatient customers: Constraint satisfaction in call centers, Oper. Res., 57 (2009), 1189-1205.  doi: 10.1287/opre.1080.0651.

[35]

A. Movaghar, On queueing with customer impatience until the beginning of service, Queueing Systems, 29 (1998), 337-350.  doi: 10.1023/A:1019196416987.

[36]

T. Phung-Duc and K. Kawanishi, Performance analysis of call centers with abandonment, retrial and after-call work, Perform. Eval., 80 (2014), 43-62.  doi: 10.1016/j.peva.2014.03.001.

[37]

Y. M. Shin and T. S. Choo, $M/M/s$ queue with impatient customers and retrials, Appl. Math. Model., 33 (2009), 2596-2606.  doi: 10.1016/j.apm.2008.07.018.

[38]

H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation-Vacation and Priority System, 1, Elsevier Publishers, Amsterdam, 1991., doi: 10.1007/978-1-4612-0873-0.

[39]

H. M. Taylor and S. Karlin, An Introduction to Stochastic Modeling, Academic Press, New York, 1998., doi: 10.1007/978-1-4612-0873-0.

[40]

K. Wang, N. Li and Z. Jiang, Queueing system with impatient customers: A review, IEEE proceedings, (2010), 82–87. doi: 10.1109/SOLI.2010.5551611.

[41]

W. Whitt, Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues, Springer-Verlag, Berlin, 2002., doi: 10.1007/978-1-4612-0873-0.

[42]

P. WuchnerJ. Sztrik and H. D. Meer, Finite-source $M/M/S$ retrial queue with search for balking and impatient customers from the orbit, Computer Networks, 53 (2009), 1264-1273.  doi: 10.1016/j.comnet.2009.02.015.

[43]

D. YueW. Yue and G. Zhao, Analysis of an $M/M/1$ queue with vacations and impatience timers which depend on the server's states, J. Industr. Manag. Optim., 12 (2016), 653-666.  doi: 10.2307/2152750.

[44]

S. Zeltyn and S. Mandelbaum, Call centers with impatient customers: Many-server asymptotics of the $M/M/n+G$ queue, Queueing Systems, 51 (2005), 361-402.  doi: 10.1007/s11134-005-3699-8.

show all references

References:
[1]

M. S. AguirO. Z. AksinF. Karaesmen and Y. Dallery, On the interaction between retrials and sizing of call centers, Euro. J. Oper. Res., 191 (2008), 398-408.  doi: 10.1016/j.ejor.2007.06.051.

[2]

M. S. AguirF. KaraesmenO. Z. Aksin and F. Chauvet, The impact of retrials on call center performance, OR Spectrum, 26 (2004), 353-376.  doi: 10.1007/s00291-004-0165-7.

[3]

N. Akar and K. Sohraby, Retrial queueing models of multi-wavelength FDL feedback optical buffers, IEEE Trans. Commun., 59 (2011), 2832-2840.  doi: 10.2307/2152750.

[4]

O. Z. Aksin and P. T. Harker, Modeling a phone center: Analysis of a multichannel multiresource processor shared loss system, Management Science, 47 (2001), 324-336.  doi: 10.2307/2152750.

[5]

E. Altman and A. A. Borovkov, On the stability of retrial queues, Queueing Systems, 26 (1997), 343-363.  doi: 10.1023/A:1019193527040.

[6]

E. Altman and U. Yechiali, Analysis of customers' impatience in queues with server vacations, Queueing Systems, 52 (2006), 261-279.  doi: 10.1007/s11134-006-6134-x.

[7]

J. R. Artalejo, Accessible bibliography on retrial queues, Math. Comput. Model., 30 (1999), 1-6.  doi: 10.1016/j.mcm.2009.12.011.

[8]

J. R. Artalejo, Accessible bibliography on retrial queues: Progress in 2000–2009, Math. Comput. Model., 51 (2010), 1071-1081.  doi: 10.1016/j.mcm.2009.12.011.

[9]

J. R. Artalejo and A. Gomez-Corral, Steady state solution of a single-server queue with linear repeated requests, J. Appl. Probab., 34 (1997), 223-233.  doi: 10.2307/3215189.

[10]

J. R. Artalejo and A. Gomez-Corral, Retrial Queueing Systems: A Computational Approach, Springer-Verlag, Berlin, 2008. doi: 10.1007/978-1-4612-0873-0.

[11]

J. R. Artalejo and V. Pla, On the impact of customer balking, impatience and retrials in telecommunication systems, Comput. Math. Appl., 57 (2009), 217-229.  doi: 10.1016/j.camwa.2008.10.084.

[12]

W. J. Anderson, Continuous-Time Markov Chains: An Applications-Oriented Approach, Springer-Verlag, Berlin, 1991. doi: 10.1007/978-1-4612-0873-0.

[13]

S. Asmussen, Applied Probability and Queues, Springer, New York, 2003. doi: 10.1007/978-1-4612-0873-0.

[14]

F. BaccelliP. Boyer and G. Hebuterne, Single-server queues with impatient customers, Adv. Appl. Probab., 16 (1984), 887-905.  doi: 10.2307/1427345.

[15]

F. Baccelli and G. Hebuterne, On queues with impatient customers, in Performance'81, North-Holland Publishing Company, Amsterdam, 1981,159–179. doi: 10.2307/2152750.

[16]

O. J. Boxma and P. R. de Waal, Multiserver queues with impatient customers, ITC, 14 (1994), 743-756.  doi: 10.1016/B978-0-444-82031-0.50079-2.

[17]

A. Brandt and M. Brandt, On the two-class M/M/1 system under preemptive resume and impatience of the prioritized customers, Queueing Systems, 47 (2004), 147-168.  doi: 10.1023/B:QUES.0000032805.73991.8e.

[18]

B. D. Choi and Y. Chang, Single server retrial queues with priority calls, Math. Comput. Model., 30 (1999), 7-32.  doi: 10.1016/S0895-7177(99)00129-6.

[19]

S. DimouA. Economou and D. Fakinos, The single server vacation queueing model with geometric abandonments, J. Stat. Plan. Infer., 141 (2011), 2863-2877.  doi: 10.1016/j.jspi.2011.03.010.

[20]

A. Economou and S. Kapodistria, Synchronized abandonments in a single server unreliable queue, Euro. J. Oper. Res., 203 (2010), 143-155.  doi: 10.1016/j.ejor.2009.07.014.

[21]

A. Erdelyi, Higher Transcendental Function, 1, McGraw-Hill, New York, 1953. doi: 10.1007/978-1-4612-0873-0.

[22]

G. I. Falin, A survey of retrial queues, Queueing Systems, 7 (1990), 127-168.  doi: 10.1007/BF01158472.

[23]

G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapman and Hall, London, 1997. doi: 10.1007/978-1-4899-2977-8.

[24]

G. Fayolle, A simple telephone exchange with delayed feedbacks, in Teletrafic Analysis and Computer Performance Eualuation, Elsevier, Amsterdam, 1986,245–253. doi: 10.2307/2152750.

[25]

N. GansG. Koole and A. Mandelbaum, Telephone call centers: Tutorial, review, and research prospects, Manufacturing and Service Operations Management, 5 (2003), 79-177.  doi: 10.1287/msom.5.2.79.16071.

[26]

O. GarnettA. Mandelbaum and M. Reiman, Designing a call center with impatient customers, Manufacturing and Service Operations Management, 4 (2002), 208-227.  doi: 10.1287/msom.4.3.208.7753.

[27]

D. Gross, J. F. Shortle, J. M. Thompson and C. M. Harris, Fundamentals of Queueing Theory, Wiley India (P) Ltd, New Delhi, 2014. doi: 10.1007/978-1-4612-0873-0.

[28]

F. Iravani and B. Balcioglu, On priority queues with impatient customers, Queueing Systems, 5 (2008), 239-260.  doi: 10.1007/s11134-008-9069-6.

[29]

O. Jouini and Y. Dallery, Moments of first passage times in general birth-death processes, Math. Meth. Oper. Res., 68 (2008), 49-76.  doi: 10.1007/s00186-007-0174-9.

[30]

O. JouiniG. Koole and A. Roubos, Performance indicators for call centers with impatient customers, IIE Transactions, 45 (2013), 341-354.  doi: 10.1080/0740817X.2012.712241.

[31]

S. Karlin and J. McGregor, The classification of birth and death processes, Trans. Amer. Math. Soc., 86 (1957), 366-400.  doi: 10.1090/S0002-9947-1957-0094854-8.

[32]

G. Koole and A. Mandelbaum, Queueing models of call centers: An introduction, Annals of Operations Research, 113 (2002), 41-59.  doi: 10.1023/A:1020949626017.

[33]

V. G. Kulkarni and H. M. Liang, Retrial queues revisited, in Frontiers in Queueing: Models and Applications in Science and Engineering, CRC Press, Boca Raton, FL, 1997, 19-34. doi: 10.2307/2152750.

[34]

A. Mandelbaum and S. Zeltyn, Staffing many-server queues with impatient customers: Constraint satisfaction in call centers, Oper. Res., 57 (2009), 1189-1205.  doi: 10.1287/opre.1080.0651.

[35]

A. Movaghar, On queueing with customer impatience until the beginning of service, Queueing Systems, 29 (1998), 337-350.  doi: 10.1023/A:1019196416987.

[36]

T. Phung-Duc and K. Kawanishi, Performance analysis of call centers with abandonment, retrial and after-call work, Perform. Eval., 80 (2014), 43-62.  doi: 10.1016/j.peva.2014.03.001.

[37]

Y. M. Shin and T. S. Choo, $M/M/s$ queue with impatient customers and retrials, Appl. Math. Model., 33 (2009), 2596-2606.  doi: 10.1016/j.apm.2008.07.018.

[38]

H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation-Vacation and Priority System, 1, Elsevier Publishers, Amsterdam, 1991., doi: 10.1007/978-1-4612-0873-0.

[39]

H. M. Taylor and S. Karlin, An Introduction to Stochastic Modeling, Academic Press, New York, 1998., doi: 10.1007/978-1-4612-0873-0.

[40]

K. Wang, N. Li and Z. Jiang, Queueing system with impatient customers: A review, IEEE proceedings, (2010), 82–87. doi: 10.1109/SOLI.2010.5551611.

[41]

W. Whitt, Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues, Springer-Verlag, Berlin, 2002., doi: 10.1007/978-1-4612-0873-0.

[42]

P. WuchnerJ. Sztrik and H. D. Meer, Finite-source $M/M/S$ retrial queue with search for balking and impatient customers from the orbit, Computer Networks, 53 (2009), 1264-1273.  doi: 10.1016/j.comnet.2009.02.015.

[43]

D. YueW. Yue and G. Zhao, Analysis of an $M/M/1$ queue with vacations and impatience timers which depend on the server's states, J. Industr. Manag. Optim., 12 (2016), 653-666.  doi: 10.2307/2152750.

[44]

S. Zeltyn and S. Mandelbaum, Call centers with impatient customers: Many-server asymptotics of the $M/M/n+G$ queue, Queueing Systems, 51 (2005), 361-402.  doi: 10.1007/s11134-005-3699-8.

Figure 1.  Dynamic oscillating queue with threshold and impatience
Figure 2(a).  $\pi(0, 0) ~\text { versus }~ \xi ~\text { for }~ \alpha = 3, \mu = 4, \mathrm{N} = 5$
Figure 2(b).  $\text { E(L) versus }~ \xi~ \text { for } ~\alpha = 3, \mu = 4, N = 5$
Figure 2(c).  $\mathrm{E}\left(\mathrm{W}_{\mathrm{S}}\right) ~~\text { versus } ~~\xi ~~\text { for }~~ \alpha = 3, \mu = 4, \mathrm{N} = 5$
Figure 2(d).  $\mathrm{R}_{\mathrm{A}} ~~\text { versus } ~~\xi ~~\text { for }~~ \alpha = 3, \mu = 4, \mathrm{N} = 5$
Figure 2(e).  $\mathrm{P}_{\mathrm{S}} ~~\text { versus } ~~\xi ~~\text { for }~~ \alpha = 3, \mu = 4, \mathrm{N} = 5$
Figure 3(a).  $\pi(0, 0) \text { versus } \mu \text { for } \alpha = 3, \xi = 5, \mathrm{N} = 5$
Figure 3(b).  $\mathrm{E}(\mathrm{L}) \text { versus } \mu \text { for } \xi = 5, \alpha = 3, \mathrm{N} = 5$
Figure 3(c).  $\mathrm{E}\left(\mathrm{W}_{\mathrm{S}}\right) \text { versus } \mu \text { for } \xi = 5, \alpha = 3, \mathrm{N} = 5$
Figure 3(d).  $\mathrm{R}_{\mathrm{A}} \text { versus } \mu \text { for } \xi = 5, \alpha = 3, \mathrm{N} = 5$
Figure 3(e).  $\mathrm{P}_{\mathrm{S}} \text { versus } \mu \text { for } \xi = 5, \alpha = 3, \mathrm{N} = 5$
Figure 4(a).  $\mathrm{E}\left(\tau_{\mathrm{j}}\right) ~~\text { versus } ~~\xi ~~\text { for }~~ \alpha = 3, \mu = 4, \mathrm{N} = 5, \mathrm{j} = 10$
Figure 4(b).  $\mathrm{E}\left(\tau_{\mathrm{j}}\right) \text { versus } \mu \text { for } \xi = 5, \alpha = 3, \mathrm{N} = 5, \mathrm{j} = 10$
Figure 4(c).  $\mathrm{E}\left(\tau_{\mathrm{j}}\right) ~~\text { versus } ~~\xi ~~\text { for }~~ \lambda = 18, \nu = 20, \alpha = 3, \mu = 4, \mathrm{N} = 5$
Figure 4(d).  $\mathrm{E}\left(\tau_{\mathrm{i}}\right) \text { versus } \mu \text { for } \lambda = 18, \nu = 20, \xi = 5, \alpha = 3, \mathrm{N} = 5$
Figure 4(e).  $\mathrm{E}\left(\tau_{\mathrm{j}}\right) \text { versus } \lambda \text { for } \xi = 5, \nu = 20, \mu = 4, \alpha = 3, \mathrm{N} = 5$
Figure 4(f).  $\mathrm{E}\left(\tau_{\mathrm{j}}\right) \text { versus } \nu \text { for } \lambda = 18, \xi = 5, \alpha = 3, \mu = 4, \mathrm{N} = 5$
[1]

Omer Gursoy, Kamal Adli Mehr, Nail Akar. Steady-state and first passage time distributions for waiting times in the $ MAP/M/s+G $ queueing model with generally distributed patience times. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021078

[2]

Qiuying Li, Lifang Huang, Jianshe Yu. Modulation of first-passage time for bursty gene expression via random signals. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1261-1277. doi: 10.3934/mbe.2017065

[3]

Ikuo Arizono, Yasuhiko Takemoto. Statistical mechanics approach for steady-state analysis in M/M/s queueing system with balking. Journal of Industrial and Management Optimization, 2022, 18 (1) : 25-44. doi: 10.3934/jimo.2020141

[4]

Shihe Xu, Fangwei Zhang, Meng Bai. Stability of positive steady-state solutions to a time-delayed system with some applications. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021286

[5]

Shaojun Lan, Yinghui Tang. Performance analysis of a discrete-time $ Geo/G/1$ retrial queue with non-preemptive priority, working vacations and vacation interruption. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1421-1446. doi: 10.3934/jimo.2018102

[6]

Arnaud Devos, Joris Walraevens, Tuan Phung-Duc, Herwig Bruneel. Analysis of the queue lengths in a priority retrial queue with constant retrial policy. Journal of Industrial and Management Optimization, 2020, 16 (6) : 2813-2842. doi: 10.3934/jimo.2019082

[7]

Dequan Yue, Wuyi Yue, Gang Xu. Analysis of customers' impatience in an M/M/1 queue with working vacations. Journal of Industrial and Management Optimization, 2012, 8 (4) : 895-908. doi: 10.3934/jimo.2012.8.895

[8]

Zhenzhen Zheng, Ching-Shan Chou, Tau-Mu Yi, Qing Nie. Mathematical analysis of steady-state solutions in compartment and continuum models of cell polarization. Mathematical Biosciences & Engineering, 2011, 8 (4) : 1135-1168. doi: 10.3934/mbe.2011.8.1135

[9]

Zsolt Saffer, Wuyi Yue. A dual tandem queueing system with GI service time at the first queue. Journal of Industrial and Management Optimization, 2014, 10 (1) : 167-192. doi: 10.3934/jimo.2014.10.167

[10]

Ahmed M. K. Tarabia. Transient and steady state analysis of an M/M/1 queue with balking, catastrophes, server failures and repairs. Journal of Industrial and Management Optimization, 2011, 7 (4) : 811-823. doi: 10.3934/jimo.2011.7.811

[11]

Zhanyou Ma, Wenbo Wang, Linmin Hu. Performance evaluation and analysis of a discrete queue system with multiple working vacations and non-preemptive priority. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1135-1148. doi: 10.3934/jimo.2018196

[12]

Dequan Yue, Wuyi Yue, Guoxi Zhao. Analysis of an M/M/1 queue with vacations and impatience timers which depend on the server's states. Journal of Industrial and Management Optimization, 2016, 12 (2) : 653-666. doi: 10.3934/jimo.2016.12.653

[13]

Federica Di Michele, Bruno Rubino, Rosella Sampalmieri. A steady-state mathematical model for an EOS capacitor: The effect of the size exclusion. Networks and Heterogeneous Media, 2016, 11 (4) : 603-625. doi: 10.3934/nhm.2016011

[14]

Mei-hua Wei, Jianhua Wu, Yinnian He. Steady-state solutions and stability for a cubic autocatalysis model. Communications on Pure and Applied Analysis, 2015, 14 (3) : 1147-1167. doi: 10.3934/cpaa.2015.14.1147

[15]

Yi Peng, Jinbiao Wu. Analysis of a batch arrival retrial queue with impatient customers subject to the server disasters. Journal of Industrial and Management Optimization, 2021, 17 (4) : 2243-2264. doi: 10.3934/jimo.2020067

[16]

Tuan Phung-Duc, Ken'ichi Kawanishi. Multiserver retrial queue with setup time and its application to data centers. Journal of Industrial and Management Optimization, 2019, 15 (1) : 15-35. doi: 10.3934/jimo.2018030

[17]

Tuan Phung-Duc, Wouter Rogiest, Sabine Wittevrongel. Single server retrial queues with speed scaling: Analysis and performance evaluation. Journal of Industrial and Management Optimization, 2017, 13 (4) : 1927-1943. doi: 10.3934/jimo.2017025

[18]

Kazimierz Malanowski, Helmut Maurer. Sensitivity analysis for state constrained optimal control problems. Discrete and Continuous Dynamical Systems, 1998, 4 (2) : 241-272. doi: 10.3934/dcds.1998.4.241

[19]

Theodore Kolokolnikov, Michael J. Ward, Juncheng Wei. The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime. Discrete and Continuous Dynamical Systems - B, 2014, 19 (5) : 1373-1410. doi: 10.3934/dcdsb.2014.19.1373

[20]

Tomoyuki Miyaji, Yoshio Tsutsumi. Steady-state mode interactions of radially symmetric modes for the Lugiato-Lefever equation on a disk. Communications on Pure and Applied Analysis, 2018, 17 (4) : 1633-1650. doi: 10.3934/cpaa.2018078

[Back to Top]