Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 350621, 10 pages
http://dx.doi.org/10.1155/2014/350621
Research Article

Analysis of Repairable Geo/G/1 Queues with Negative Customers

1Software Contents Research Lab, ETRI, Daejeon 305-700, Republic of Korea
2Department of Management Engineering, Sangmyung University, Chungnam 330-720, Republic of Korea

Received 3 September 2014; Accepted 8 December 2014; Published 24 December 2014

Academic Editor: Kannan Krithivasan

Copyright © 2014 Doo Ho Lee and Kilhwan Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. Gelenbe, “Random neural networks with negative and positive signals and product form solution,” Neural Computation, vol. 1, no. 4, pp. 502–510, 1989. View at Google Scholar
  2. R. J. Boucherie and O. J. Boxma, “The workload in the M/G/1 queue with work removal,” Probability in the Engineering and Informational Sciences, vol. 10, no. 2, pp. 261–277, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. C. Morfopoulou, “Network routing control with G-networks,” Performance Evaluation, vol. 68, no. 4, pp. 320–329, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. J. Wu and X. Yin, “An M/G/1 retrial G-Queue with non-exhaustive random vacations and an unreliable server,” Computers & Mathematics with Applications, vol. 62, no. 5, pp. 2314–2329, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. P. G. Harrison and E. Pitel, “Sojourn times in single-server queues with negative customers,” Journal of Applied Probability, vol. 30, no. 4, pp. 943–963, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  6. P. G. Harrison and E. Pitel, “The M/G/1 queue with negative customers,” Advances in Applied Probability, vol. 28, no. 2, pp. 540–566, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. W. S. Yang and K. C. Chae, “A note on the GI/M/1 queue with Poisson negative arrivals,” Journal of Applied Probability, vol. 38, no. 4, pp. 1081–1085, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  8. J. R. Artalejo, “G-networks: a versatile approach for work removal in queueing networks,” European Journal of Operational Research, vol. 126, no. 2, pp. 233–249, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. T. V. Do, “An initiative for a classified bibliography on G-networks,” Performance Evaluation, vol. 68, no. 4, pp. 385–394, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. T. V. Do, “Bibliography on G-networks, negative customers and applications,” Mathematical and Computer Modelling, vol. 53, no. 1-2, pp. 205–212, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. E. Gelenbe, “Product-form queueing networks with negative and positive customers,” Journal of Applied Probability, vol. 28, no. 3, pp. 656–663, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  12. E. Gelenbe, “G-networks: a unifying model for neural and queueing networks,” Annals of Operations Research, vol. 48, no. 5, pp. 433–461, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. E. Gelenbe, “The first decade of G-networks,” European Journal of Operational Research, vol. 126, no. 2, pp. 231–232, 2000. View at Google Scholar
  14. I. Atencia and P. Moreno, “A single-server G-queue in discrete-time with geometrical arrival and service process,” Performance Evaluation, vol. 59, no. 1, pp. 85–97, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. W. H. Zhou, “Performance analysis of discrete-time queue GI/G/1 with negative arrivals,” Applied Mathematics and Computation, vol. 170, no. 2, pp. 1349–1355, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. J. Wang and P. Zhang, “A discrete-time retrial queue with negative customers and unreliable server,” Computers and Industrial Engineering, vol. 56, no. 4, pp. 1216–1222, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. H. M. Park, W. S. Yang, and K. C. Chae, “The Geo/G/1 queue with negative customers and disasters,” Stochastic Models, vol. 25, no. 4, pp. 673–688, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. K. C. Chae, H. M. Park, and W. S. Yang, “A GI/Geo/1 queue with negative and positive customers,” Applied Mathematical Modelling, vol. 34, no. 6, pp. 1662–1671, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. J. Wu, Z. Liu, and Y. Peng, “On the BMAP/G/1 G-queues with second optional service and multiple vacations,” Applied Mathematical Modelling, vol. 33, no. 12, pp. 4314–4325, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. J. Wu, Z. Liu, and G. Yang, “Analysis of the finite source {${\rm MAP}/{\rm PH}/N$} retrial {$G$}-queue operating in a random environment,” Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, vol. 35, no. 3, pp. 1184–1193, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. D. H. Lee, W. S. Yang, and H. M. Park, “Geo/G/1 queues with disasters an d general repair times,” Applied Mathematical Modelling, vol. 35, no. 4, pp. 1561–1570, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation. Vol. 3, North-Holland, Amsterdam, The Netherlands, 1993. View at MathSciNet