East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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QUEUEING SYSTEMS WITH N-LIMITED NONSTOP FORWARDING

  • LEE, YUTAE (DEPARTMENT OF INFORMATION AND COMMUNICATION ENGINEERING DONGEUI UNIVERSITY)
  • Received : 2015.02.24
  • Accepted : 2015.09.21
  • Published : 2015.09.30
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Abstract

We consider a queueing system with N-limited nonstop forwarding. In this queueing system, when the server breaks down, up to N customers can be serviced during the repair time. It can be used to model an assembly line consisting of several automatic stations and a manual backup station. Within the framework of $Geo^X/D/1$ queue, the matrix analytic approach is used to obtain the performance of the system. Some numerical examples are provided.

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References

  1. W. L. Wang and G. Q. Xu, The well-posedness of an M/G/1 queue with second optional service and server breakdown, Computers & Mathematics with Applications 57 (2009), no. 5, pp. 223-227.
  2. D. Perry and M. J. M. Posner, A correlated M/G/1-type queue with randomized server repair and maintenance modes, Operations Research Letters 26 (2000), no. 3, pp. 137-147. https://doi.org/10.1016/S0167-6377(99)00067-X
  3. N. P. Sherman and J. P. Kharoufeh, An M/M/1 retrial queue with unreliable server, Operations Research Letters 34 (2006), no. 6, pp. 697-705. https://doi.org/10.1016/j.orl.2005.11.003
  4. A. Econimou and S. Kanta, Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs, Operations Research Letters 36 (2008), no. 6, pp. 696-699. https://doi.org/10.1016/j.orl.2008.06.006
  5. Y. Lee, Discrete-time bulk-service queue with Markovian service interruption and prob-abilistic bulk size, J. Appl. Math. & Informatics 28 (2010), no. 1-2, pp. 275-282.
  6. G. Falin, An M/G/1 retrial queue with an unreliable server and general repair times, Perform. Evaluation 67 (2010), no. 7, pp. 569-582. https://doi.org/10.1016/j.peva.2010.01.007
  7. F. Zhang and Z. Zhu, A discrete-time unreliable Geo/G/1 retrial queue with balking customers, second optional service, and general retrial times, Mathematical Problems in Engineering 2013 (2013), pp. 1-12.
  8. C. T. Do, N. H. Tran, C. S. Hong, S. Lee, J.-J. Lee, and W. Lee, A lightweight algo-rithm for probability-based spectrum decision scheme in multiple channels cognitive radio networks, IEEE Commun. Lett. 17 (2013), no. 3, pp. 509-512. https://doi.org/10.1109/LCOMM.2013.012313.122589
  9. G. Choudhury and J.-C. Ke, An unreliable retrial queue with delaying repair and general retrial times under Bernoulli vacation schedule, Applied Mathematics and Computation 230 (2014), pp. 436-450. https://doi.org/10.1016/j.amc.2013.12.108
  10. N. Gharbi, B. Nemmouchi, L. Mokdad, and J. Ben-Othman, The impact of breakdowns disciplines and repeated attempts on performance of small cell networks, J. Computa-tional Science 5 (2014), no. 4, pp. 633-644. https://doi.org/10.1016/j.jocs.2014.02.011
  11. Shin, F., Ram, B., Gupta, A., Yu, X., Menassa, R., A decision tool for assembly line breakdown action, Proc. 2004 Winter Simulation Conference, 2004, pp. 1122-1127.
  12. M. F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Applications, Marcel Dekker, New York, NY, 1989.
  13. D. A. Bini, B. Meini, and V. Ramaswami, Analyzing M/G/1 paradigms through QBDs:the role of the block structure in computing the matrix G, In G. Latouche and P. Taylor, editors, Advances in Matrix-Analytic Methods for Stochastic Models, Notable Publications Inc. NJ, 2000, pp. 87-97.
  14. V. Ramaswami, A stable recursion for the steady state vector in markov chains of M/G/1 type, Comm. Statist. Stochastic Models 4 (1988), pp. 183-263. https://doi.org/10.1080/15326348808807077
  15. B. Meini, An improved FFT-based version of Ramaswami's formular, Comm. Statist. Stochastic Models 13 (1997), pp. 223-238. https://doi.org/10.1080/15326349708807423
  16. B. Meini, Solving M/G/1 type Markov chains: Recent advances and applications, Comm. Statist. Stochastic Models 14 (1988), no. 1-2, pp. 479-496.
  17. A. Riska and E. Smirni, An exact aggregation approach for M/G/1-type Markov chains, Proc. ACM International Conference on Measurement and Modeling of Computer Sys-tems (ACM SIGMETRICS '02), Marina Del Rey, CA, 2002, pp. 86-96.
  18. J. Walraevens, D. Fiems, and H. Bruneel, Performance analysis of priority queueing system in discrete time, Network Performance Engineering, Lecture Notes in Computer Science 5233 (2011), pp 203-232.