Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

DISCRETE-TIME BULK-SERVICE QUEUE WITH MARKOVIAN SERVICE INTERRUPTION AND PROBABILISTIC BULK SIZE

  • Lee, Yu-Tae (Department of Information and Communication Engineering, Dongeui University)
  • Published : 2010.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper analyzes a discrete-time bulk-service queue with probabilistic bulk size, where the service process is interrupted by a Markov chain. We study the joint probability generating function of system occupancy and the state of the Markov chain. We derive several performance measures of interest, including average system occupancy and delay distribution.

Keywords

References

  1. N. Amitay, Distributed switching and control with fast resource assignmen/handoff for personal communications systems, IEEE Journal on Selected Areas in Communications 11(6) (1993), 842-849. https://doi.org/10.1109/49.232293
  2. P. Baht, I. Chlamtac and A.S. Farago, Resource assignment for integrated services in wireless ATM networks, International Journal of Communication Systems 11 (1998), 29-41. https://doi.org/10.1002/(SICI)1099-1131(199801/02)11:1<29::AID-DAC353>3.0.CO;2-0
  3. H. Bruneel and B. Kim, Discrete-time Models for Communication Systems Including ATM, Kluwar Academic Publishers, 1993.
  4. P.J. Burke, Delays in single-server queues with batch input, Operations Research 23(4) (1975), 830-833. https://doi.org/10.1287/opre.23.4.830
  5. M.Y. Chung, M.H. Chung, T.J. Lee and Y. Lee, Performance analysis of HomePlug 1.0MAC with CSMA/CA, IEEE Journl on Selected Areas in Commnications 24(7) (2006), 1411-1420.
  6. D. Fiems, B. Steyaert and H. Bruneel, Discrete-time queues with generally distributed server interruptions and renewal-type server interruptions, Performance Evaluation 55(3-4) (2004), 277-298. https://doi.org/10.1016/j.peva.2003.08.004
  7. A.T. Hoang and Y.C. Liang, A two-phase channel and power allocation scheme for cognitive radio networks, Proceedings of IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications, 2006.
  8. G.U. Hwang and K. Sohraby, Power tail asymptotic results of a discrete time queue with long range dependent input, Journal of Korean Mathematical Society 40(1) (2003), 87-107. https://doi.org/10.4134/JKMS.2003.40.1.087
  9. F. Ishizaki, Loss probability in a finite queue with service interruptions and queue length distribution in the corresponding infinite queue, Performance Evaluation 63 (2006), 682-699. https://doi.org/10.1016/j.peva.2005.06.006
  10. V. Klimenok, On the modification of Rouche's theorem for the queueing theory problems, Queueing Systems: Theory and Applications 38(4) (2001), 431-434. https://doi.org/10.1023/A:1010999928701
  11. J. Lamperti, Criteria for the recurrence or transience of stochastic process, I, Journal of Mathematical Analysis and Applcations 1 (1960), 314-330. https://doi.org/10.1016/0022-247X(60)90005-6
  12. D. Lee, Analysis of a single server queue with semi-Markovian service interruption, Queueing Systems: Theory and Applications 27(1-2) (1997), 153-178.
  13. Y. Lee, Discrete-time $Geo^{x}/G/1$ queue with preemptive resume priority, Mathematical and Computer Modeling 34 (2001), 243-250. https://doi.org/10.1016/S0895-7177(01)00057-7
  14. Y. Lee, Discrete-time $Geo^{x}/G/1$ queue with place reeservation discipline, Journal of Applied Mathematics and Computing 22(1-2) (2006), 453-460. https://doi.org/10.1007/BF02896493
  15. Y. Lee, Performance of secondary users in opportunistic spectrum access, Electronics Letters 44(16) (2008), 981-983. https://doi.org/10.1049/el:20081625
  16. Y.Lee, Opportunistic spectrum access in cognitive networks, Electronics Letters 44(17) (2008), 1022-1024. https://doi.org/10.1049/el:20081287
  17. A. Mokhtar and M. Azizoglu, Analysis of state-dependent probabilistic service interruptions in discrete-time queues, IEEE Communication Letters 8(8) (2004), 544-546. https://doi.org/10.1109/LCOMM.2004.833827
  18. T.L. Saaty, Elements of Queueing Theory with Applications, McGraw-Hill Book Company, 1961.