Advertisement

Mathematical Methods of Operations Research

, Volume 67, Issue 2, pp 269–284 | Cite as

Analytic study of multiserver buffers with two-state Markovian arrivals and constant service times of multiple slots

  • Peixia Gao
  • Sabine Wittevrongel
  • Joris Walraevens
  • Herwig Bruneel
Original Article

Abstract

In this paper, we study the behavior of a discrete-time multiserver buffer system with infinite buffer size. Packets arrive at the system according to a two-state Markovian arrival process. The service times of the packets are assumed to be constant, equal to multiple slots. The behavior of the system is analyzed by means of an analytical technique based on probability generating functions (PGF’s). Explicit expressions are obtained for the PGF’s of the system contents and the packet delay. From these, the mean values, the variances and the tail distributions of the system contents and the packet delay are calculated. Numerical examples are given to show the influence of various model parameters on the system behavior.

Keywords

Discrete-time queueing model Correlated arrivals Multiple servers Performance analysis Generating functions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Artalejo J, Hernandez-Lerma O (2003) Performance analysis and optimal control of the Geo/Geo/c queue. Perform Eval 52(1):15–39CrossRefGoogle Scholar
  2. Bisdikian C, Lew J, Tantawi A (1993) On the tail approximation of the blocking probability of single server queues with finite buffer capacity. In: Proceedings of the 2nd international conference on queueing networks with finite capacity, Research Triangle Park, pp 267–80Google Scholar
  3. Blondia C (1993) A discrete-time batch Markovian arrival process as B-ISDN traffic model. Belg J Oper Res Stat Comput Sci (JORBEL) 32(3–4):3–23Google Scholar
  4. Bruneel H, Kim BG (1993) Discrete-time models for communication systems including ATM. Kluwer, BostonGoogle Scholar
  5. Bruneel H, Steyaert B, Desmet E, Petit G (1992) An analytical technique for the derivation of the delay performance of ATM switches with multiserver output queues. Int J Digit Analog Commun Syst 5:193–201CrossRefGoogle Scholar
  6. Bruneel H, Wuyts I (1994) Analysis of discrete-time multiserver queueing models with constant service times. Oper Res Lett 15:231–236zbMATHCrossRefGoogle Scholar
  7. Chaudhry ML, Gupta UC, Goswami V (2001) Modeling and analysis of discrete-time multiserver queues with batch arrivals: GI(X)/Geom/m. INFORMS J Comput 13(3):172–180CrossRefMathSciNetGoogle Scholar
  8. Chaudhry ML, Gupta UC, Goswami V (2004) On discrete-time multiserver queues with finite buffer: GI/Geom/m/N. Comput Oper Res 31(13):2137–2150zbMATHCrossRefMathSciNetGoogle Scholar
  9. Daniels T, Blondia C (2000) Tail transitions in queues with long range dependent input. Lect Notes Comput Sci 1815:264–274CrossRefGoogle Scholar
  10. Gantmacher FR (1998) The theory of matrices, vol 1. AMS Chelsea Publishing, ProvidencezbMATHGoogle Scholar
  11. Gao P (2006) Discrete-time multiserver queues with generalized service times. PhD thesis, Ghent UniversityGoogle Scholar
  12. Gao P, Wittevrongel S, Bruneel H (2003) Delay against system contents in discrete-time G/Geom/c queue. Electron Lett 39(17):1290–1292CrossRefGoogle Scholar
  13. Gao P, Wittevrongel S, Bruneel H (2004a) Delay analysis for a discrete-time GI-D-c queue with arbitrary-length service times. In Proceedings of EPEW 2004, Lecture Notes in Computer Science, vol 3236, Toledo, pp 184–195Google Scholar
  14. Gao P, Wittevrongel S, Bruneel H (2004b) Discrete-time multiserver queues with geometric service times. Comput Oper Res 31(1):81–99zbMATHCrossRefGoogle Scholar
  15. Gao P, Wittevrongel S, Bruneel H (2004c) On the behavior of multiserver buffers with geometric service times and bursty input traffic. IEICE Trans Commun E87-B(12):3576–3583Google Scholar
  16. Gao P, Wittevrongel S, Bruneel H (2005) Relationship between delay and partial system contents in multiserver queues with constant service times. In: Booklet of abstracts of ORBEL 19, Louvain-la-Neuve, pp 72–74Google Scholar
  17. Kleinrock L (1975) Queueing systems, volume I: theory. Wiley, New YorkGoogle Scholar
  18. Kravanja P, Van Barel M (2000) Computing the zeros of analytic functions. Lect Notes Math 1727:1–59MathSciNetCrossRefGoogle Scholar
  19. Rubin I, Zhang Z (1991) Message delay and queue-size analysis for circuit-switched TDMA systems. IEEE Trans Commun 39:905–914zbMATHCrossRefGoogle Scholar
  20. Wittevrongel S, Bruneel H (1999) Discrete-time queues with correlated arrivals and constant service times. Comput Oper Res 26(2):93–108zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Peixia Gao
    • 1
  • Sabine Wittevrongel
    • 1
  • Joris Walraevens
    • 1
  • Herwig Bruneel
    • 1
  1. 1.Stochastic Modeling and Analysis of Communication Systems (SMACS) Research Group, Department of Telecommunications and Information Processing (TELIN)Ghent UniversityGentBelgium

Personalised recommendations