Advertisement

Imbedded Markov Chain Analysis of Time-Division Multiplexing

  • Jeremiah F. Hayes
Part of the Applications of Communications Theory book series (ACTH)

Abstract

In general terms, multiplexing is a means for sharing facilities among a number of users and sources. As we have seen in Section 2.4, the standard techniques for doing this in the telephone networks are frequency-division multiplexing (FDM) and time-division multiplexing (TDM). The explosive growth of digital technology has favored the development of TDM for sharing the capacity of transmission lines. Moreover, the digital basis of time-division multiplexing makes it a natural vehicle for data traffic. In this chapter we shall analyze the performance of time-division multiplexing and a variant, asynchronous time-division multiplexing. This analysis is closely related to the analysis of the M/G/1 queue in the previous chapter inasmuch as both use the imbedded Markov chain approach.

Keywords

Arrival Process Average Delay Data Unit Idle Period State Transition Probability 
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.
    R. J. Camrass and R. G. Gallager, “Encoding Message Lengths for Data Transmission,” IEEE Transactions on Information Theory, IT-24, July 1978.Google Scholar
  2. 2.
    W. W. Chu, “A Study of Asynchronous TDM for Time Sharing Computer Systems,” AFIPS Conference Proceedings, Fall Joint Computer Conference (1969), Vol. 35, pp. 669–678.Google Scholar
  3. 3.
    W. W. Chu and A. G. Konheim, “On the Analysis and Modeling of a Class of Computer Communication Systems,” IEEE Transactions on Communications, 20(3), P. II, 645–660, June (1972).CrossRefGoogle Scholar
  4. 4.
    H. Rudin, “Performance of Simple Multiplexer Concentrators for Data Communications,” IEEE Transactions on Communications Technology, Com-19(2), 178–187, April (1971).CrossRefGoogle Scholar
  5. 5.
    G. J. Foschini and B. Gopinath, “Sharing Memory Optimally,” IEEE Transactions on Communications, Com-31(3), 352–360, March (1983).CrossRefGoogle Scholar
  6. 6.
    F. Kamoun and L. Kleinrock, “Analysis of Shared Finite Storage in a Computer Network Environment,” IEEE Transactions on Communications, Com-28(7), 992–1003, June (1980).MathSciNetCrossRefGoogle Scholar
  7. 7.
    D. P. Gaver and P. A. W. Lewis, “Probability Models for Buffer Storage Allocation Problems,” Journal of the ACM, 18(2), 186–197, April (1977).MathSciNetCrossRefGoogle Scholar
  8. 8.
    N. T. J. Bailey, “On Queueing Processes with Bulk Service,” Journal of the Royal Statistical Society (1954).Google Scholar
  9. 9.
    K. Knopf, Theory of Functions. Part II: Application and Further Development of the General Theory. Dover, New York (1947).Google Scholar
  10. 10.
    P. E. Boudreau, J. S. Griffin, and M. Kac, “An Elementary Queueing Problem,” American Mathematical Monthly, 69, 713–724 (1962).MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    J. F. Hayes, “Performance Models of an Experimental Computer Communications Network,” Bell System Technical Journal, 53(2), 225–259, February (1974).MathSciNetGoogle Scholar
  12. 12.
    G. J. Foschini, B. Gopinath, and J. F. Hayes, “Subframe Switching for Data Communications,” International Telemetry Conference, Los Angeles (1978).Google Scholar
  13. 13.
    I. Rubin, “Message Delays in FDMA and TDMA Communications Channels,” IEEE Transactions on Communications, Com-27, 769–778, (1979).CrossRefGoogle Scholar
  14. 14.
    S. S. Lam, “Delay Analysis of a Time-Division Multiple Access Channel,” IEEE Transactions on Communications, Com-25(12), 1489–1494, December (1977).CrossRefGoogle Scholar
  15. 15.
    R. R. Anderson, G. J. Foschini, and B. Gopinath, “A Queueing Model for a Hybrid Data Multiplexer”, Bell System Technical Journal, 58(2), 279–301, February (1979).MathSciNetMATHGoogle Scholar
  16. 16.
    M. Kaplan, “A Single-Server Queue with Cyclostationary Arrivals and Arithmetic Service,” Operations Research (in press).Google Scholar
  17. 17.
    D. Towsley and J. Wolf, “On the Statistical Analysis of Queue Lengths and Waiting Times for Statistical Multiplexers with ARQ Retransmission,” IEEE Transactions on Communications, 27(4), 693–703, April (1979).MATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Jeremiah F. Hayes
    • 1
  1. 1.Concordia UniversityMontrealCanada

Personalised recommendations