A discrete-time Geo[X]/G/1 retrial queue with general retrial time and M-additional options for service

Muthukrishnan Senthil Kumar

RAIRO - Operations Research (2011)

  • Volume: 45, Issue: 2, page 131-152
  • ISSN: 0399-0559

Abstract

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This paper concerns a discrete time Geo[X]/G/1 retrial queue with general retrial time in which all the arriving customers require first essential service with probability α 0 while only some of them demand one of other optional services: type − r (r = 1, 2, 3,...M) service with probability α r . The system state distribution, the orbit size and the system size distributions are obtained in terms of generating functions. The stochastic decomposition law holds for the proposed model. Performance measures of the system in steady state are obtained.  Finally, some numerical illustrations are presented to justify the influence of parameters on several performance characteristics.

How to cite

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Senthil Kumar, Muthukrishnan. "A discrete-time Geo[X]/G/1 retrial queue with general retrial time and M-additional options for service." RAIRO - Operations Research 45.2 (2011): 131-152. <http://eudml.org/doc/276358>.

@article{SenthilKumar2011,
abstract = { This paper concerns a discrete time Geo[X]/G/1 retrial queue with general retrial time in which all the arriving customers require first essential service with probability $\alpha_\{0\}$ while only some of them demand one of other optional services: type − r (r = 1, 2, 3,...M) service with probability $\alpha_\{r\}$. The system state distribution, the orbit size and the system size distributions are obtained in terms of generating functions. The stochastic decomposition law holds for the proposed model. Performance measures of the system in steady state are obtained.  Finally, some numerical illustrations are presented to justify the influence of parameters on several performance characteristics. },
author = {Senthil Kumar, Muthukrishnan},
journal = {RAIRO - Operations Research},
keywords = {Discrete-time queue; first essential service (FES); multi- optional service; retrial queue ; discrete-time queue; retrial queue},
language = {eng},
month = {9},
number = {2},
pages = {131-152},
publisher = {EDP Sciences},
title = {A discrete-time Geo[X]/G/1 retrial queue with general retrial time and M-additional options for service},
url = {http://eudml.org/doc/276358},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Senthil Kumar, Muthukrishnan
TI - A discrete-time Geo[X]/G/1 retrial queue with general retrial time and M-additional options for service
JO - RAIRO - Operations Research
DA - 2011/9//
PB - EDP Sciences
VL - 45
IS - 2
SP - 131
EP - 152
AB - This paper concerns a discrete time Geo[X]/G/1 retrial queue with general retrial time in which all the arriving customers require first essential service with probability $\alpha_{0}$ while only some of them demand one of other optional services: type − r (r = 1, 2, 3,...M) service with probability $\alpha_{r}$. The system state distribution, the orbit size and the system size distributions are obtained in terms of generating functions. The stochastic decomposition law holds for the proposed model. Performance measures of the system in steady state are obtained.  Finally, some numerical illustrations are presented to justify the influence of parameters on several performance characteristics.
LA - eng
KW - Discrete-time queue; first essential service (FES); multi- optional service; retrial queue ; discrete-time queue; retrial queue
UR - http://eudml.org/doc/276358
ER -

References

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  1. A.K. Aboul-Hassan, S. Rabia and A. Kadry, A recursive approach for analyzing a discrete-time retrial queue with balking customers and early arrival scheme. Alexandria Engineering Journal.44 (2005) 919–925.  
  2. A.K. Aboul-Hassan, S. Rabia and F. Taboly, A discrete-time Geo/G/1 retrial queue with general retrial times and balking customers. Journal of the Korean Statistical Society37 (2008) 335–348.  
  3. A.K. Aboul-Hassan, S. Rabia and F. Taboly, Performance evaluation of a discrete-time Geo [ X ] /G/1 retrial queue with general retrial times. Comput. Math. Appl.58 (2009) 548–557.  
  4. J.R. Artalejo, A classified bibliography of research on retrial queues: Progress in 1990–1999. Top7 (1999) 187–211.  
  5. J.R. Artalejo, I. Atencia and P. Moreno, A discrete-time Geo [ X ] /G/1 retrial queue with control of admission. Appl. Math. Modell.29 (2005) 1100–1120.  
  6. J.R. Artalejo and A. Gómez-Corral, Retrial Queueing Systems: A Computational Approach. Springer, Berlin (2008).  
  7. I. Atencia and P. Moreno, A discrete-time Geo/G/1 retrial queue with general retrial times. Queueing Syst.48 (2004) 5–21.  
  8. I. Atencia and P. Moreno, Discrete-time Geo [ X ] / G H / 1 retrial queue with Bernoulli feedback. Comput. Math. Appl.47 (2004) 1273–1294.  
  9. I. Atencia and P. Moreno, A discrete-time Geo/G/1 retrial queue with server breakdowns. Asia Pac. J. Oper. Res.23 (2006a) 247–271.  
  10. I. Atencia and P. Moreno, A discrete-time Geo/G/1 retrial queue with the server subject to starting failures. Ann. Oper. Res.141 (2006b) 85–107.  
  11. H. Bruneel and B.G. Kim, Discrete-Time Models for Communication Systems Including ATM. Kluwer Academic Publishers, Boston (1993).  
  12. M.L. Chaudhry and J.G.C. Templeton, A First Course in Bulk Queues. Wiley, New York (1983).  
  13. B.D. Choi and J.W. Kim, Discrete-time Geo1, Geo2/G/1 retrial queueing systems with two types of calls. Comput. Math. Appl.33 (1997) 79–88.  
  14. G.I. Falin, Survey of retrial queues. Queueing Syst.7 (1990) 127–167.  
  15. G.I. Falin and J.G.C. Templeton, Retrial Queues. Chapman & Hall, London (1997).  
  16. S.W. Fuhrmann and R.B. Cooper, Stochastic decomposition in the M/G/1 queue with generalized vacations. Oper. Res.33 (1985) 1117–1129.  
  17. J.J. Hunter, Mathematical Techniques of Applied Probability, in Discrete-Time Models: Techniques and Applications2. Academic Press, New York (1983).  
  18. J.-C. Ke, An M [ x ] /G/1 system with startup server and J additional options for service. Appl. Math. Modell.32 (2008) 443–458.  
  19. V. Kulkarni and H. Liang, Retrial queues revisited, in Frontiers in Queueing, edited by J. Dshalalow. CRC Press, Boca Raton (1997) 19–34.  
  20. H. Li and T. Yang, Geo/G/1 discrete-time retrial queue with Bernoulli schedule. Eur. J. Oper. Res.111 (1998) 629–649.  
  21. K.C. Madan, An M/G/1 queue with second optional service. Queueing Syst.34 (2000) 37–46.  
  22. J. Medhi, A single server Poisson input queue with a second optional channel. Queueing Syst.42 (2002) 239–242.  
  23. T. Meisling, Discrete time queueing theory. Oper. Res.6 (1958) 96–105.  
  24. P. Moreno, A discrete-time retrial queue with unreliable server and general server lifetime. J. Math. Sci.132 (2006) 643–655.  
  25. B. Powell and B. Avi-Itzhak, Queueing systems with enforced idle times. Oper. Res.15 (1967) 1145–56.  
  26. M. Senthil Kumar and R. Arumuganathan, On the single server Batch Arrival Retrial Queue with General vacation Time under Bernoulli schedule and two phases of Heterogeneous service. Quality Technology and Quantitative Management5 (2008) 145–160.  
  27. H. Takagi, Queueing Analysis: A foundation of Performance Evaluation, in Discrete-Time Systems3. North-Holland, Amsterdam (1993).  
  28. M. Takahashi, H. Osawa and T. Fujisawa, Geo [ X ] /G/1 retrial queue with non-preemptive priority. Asia Pac. J. Oper. Res.16 (1999) 215–234.  
  29. J. Wang and Q. Zhao, A discrete-time Geo/G/1 retrial queue with starting failures and second optional service. Comput. Math. Appl.53 (2007) 115–127.  
  30. J. Wang and Q. Zhao, Discrete-time Geo/G/1 retrial queue with general retrial times and starting failures. Math. Comput. Modell.45 (2007) 853–863.  
  31. M.E. Woodward, Communication and Computer Networks: Modelling with Discrete-Time Queues. IEEE Computer Soc. Press, Los Alamitos, CA (1994).  
  32. T. Yang and H. Li, On the steady-state queue size distribution of the discrete-time Geo/G/1 queue with repeated customers. Queueing Syst.21 (1995) 199–215.  
  33. T. Yang and J.G.C. Templeton, A survey on retrial queues. Queueing Syst.2 (1987) 201–233.  

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