Analysis of a Two-Class FCFS Queueing System with Interclass Correlation

  • Herwig Bruneel
  • Tom Maertens
  • Bart Steyaert
  • Dieter Claeys
  • Dieter Fiems
  • Joris Walraevens
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7314)

Abstract

This paper considers a discrete-time queueing system with one server and two classes of customers. All arriving customers are accommodated in one queue, and are served in a First-Come-First-Served order, regardless of their classes. The total numbers of arrivals during consecutive time slots are i.i.d. random variables with arbitrary distribution. The classes of consecutively arriving customers, however, are correlated in a Markovian way, i.e., the probability that a customer belongs to a class depends on the class of the previously arrived customer. Service-time distributions are assumed to be general but class-dependent. We use probability generating functions to study the system analytically. The major aim of the paper is to estimate the impact of the interclass correlation in the arrival stream on the queueing performance of the system, in terms of the (average) number of customers in the system and the (average) customer delay and customer waiting time.

Keywords

Service Time Arrival Process Queueing System Interclass Correlation System Content 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Borst, S.C., Boxma, O.J., Morrison, J.A., Queija, R.N.: The equivalence between processor sharing and service in random order. Operations Research Letters 31(4), 254–262 (2003)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Bruneel, H., Kim, B.G.: Discrete-time models for communication systems including ATM. Kluwer Academic, Boston (1993)CrossRefGoogle Scholar
  3. 3.
    Carter, G.M., Cooper, R.B.: Queues with service in random order. Operations Research 20(2), 389–405 (1970)CrossRefGoogle Scholar
  4. 4.
    Chen, J., Guérin, R.: Performance study of an input queueing packet switch with two priority classes. IEEE Transactions on Communications 39(1), 117–126 (1991)CrossRefGoogle Scholar
  5. 5.
    De Clercq, S., Laevens, K., Steyaert, B., Bruneel, H.: A multi-class discrete-time queueing system under the FCFS service discipline. Annals of Operations Research (accepted for publication)Google Scholar
  6. 6.
    Fiems, D., Bruneel, H.: A note on the discretization of Little’s result. Operations Research Letters 30, 17–18 (2002)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Gonzáles, M.O.: Classical complex analysis. Marcel Dekker, New York (1992)Google Scholar
  8. 8.
    Jaiswal, N.: Priority queues. Academic Press, New York (1968)MATHGoogle Scholar
  9. 9.
    Jin, X., Min, G.: Analytical modelling and evaluation of generalized processor sharing systems with heterogeneous traffic. International Journal of Communication Systems 21(6), 571–586 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kim, J., Kim, J., Kim, B.: Analysis of the M/G/1 queue with discriminatory random order service policy. Performance Evaluation 68(3), 256–270 (2011)CrossRefGoogle Scholar
  11. 11.
    Laevens, K., Bruneel, H.: Discrete-time multiserver queues with priorities. Performance Evaluation 33(4), 249–275 (1998)CrossRefGoogle Scholar
  12. 12.
    Lieshout, P., Mandjes, M.: Generalized processor sharing: Characterization of the admissible region and selection of optimal weights. Computers & Operations Research 35(8), 2497–2519 (2008)MATHCrossRefGoogle Scholar
  13. 13.
    Maertens, T., Walraevens, J., Bruneel, H.: Performance comparison of several priority schemes with priority jumps. Annals of Operations Research 180(3), 1168–1185 (2008)MathSciNetGoogle Scholar
  14. 14.
    Shortle, J.F., Fischer, M.J.: Approximation for a two-class weighted fair queueing discipline. Performance Evaluation 67(10), 946–958 (2010)CrossRefGoogle Scholar
  15. 15.
    Walraevens, J., Fiems, D., Wittevrongel, S., Bruneel, H.: Calculation of output characteristics of a priority queue through a busy period analysis. European Journal of Operational Research 198(3), 891–898 (2009)MATHCrossRefGoogle Scholar
  16. 16.
    Walraevens, J., van Leeuwaarden, J.S.H., Boxma, O.J.: Power series approximations for two-class generalized processor sharing systems. Queueing systems 66(2), 107–130 (2010)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Wang, L., Min, G., Kouvatsos, D.D., Jin, X.: Analytical modeling of an integrated priority and WFQ scheduling scheme in multi-service networks. Computer Communications 33, S93–S101 (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Herwig Bruneel
    • 1
  • Tom Maertens
    • 1
  • Bart Steyaert
    • 1
  • Dieter Claeys
    • 1
  • Dieter Fiems
    • 1
  • Joris Walraevens
    • 1
  1. 1.Department of Telecommunications and Information Processing, SMACS Research GroupGhent UniversityGhentBelgium

Personalised recommendations