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Real-time queueing theory: A tutorial presentation with an admission control application

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Abstract

Real-time scheduling, or scheduling with respect to a deadline, is critical in many application areas such as telecommunications, control systems, and manufacturing. This paper presents a novel approach to real-time scheduling based on a queueing theory model. Using real-time queueing theory (RTQT), one can analytically determine the distribution of the lead-time profile (i.e., the time until the deadline is reached) of customers waiting for service. Emphasis is placed on the development of the equations used to determine the lead-time profile distribution. The development of the GI/G/1 case is presented and confirmed using simulation. Simulation results confirm prior research for the M/M/1 and GI/M/1 case. As a practical application, RTQT is used to implement a packet admission control algorithm for a telecommunications network. Using this algorithm, packet lateness was reduced by up to 31%.

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References

  1. A.S. Alfa, A discrete MAP/PH/1 queue with vacations and exhaustive time-limited service, Oper. Res. Lett. 18(1) (1995) 31–40.

    Article  Google Scholar 

  2. D.Y. Burman, An analytic approach to diffusion approximations in queueing, Ph.D. dissertation, Department of Mathematics, New York University (1979).

  3. L.Y. Dar and S.C. Maw, A two-machine flowshop sequencing problem with limited waiting time constraints, Comput. Industr. Engrg. 28(1) (1995) 63–70.

    Google Scholar 

  4. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed. (Wiley, New York, 1968).

    Google Scholar 

  5. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2 (Wiley, New York, 1971).

    Google Scholar 

  6. I. Frigui and A.S. Alfa, Analysis of a time-limited polling system, Comput. Commun. 21(6) (May 1998) 558–571.

    Article  Google Scholar 

  7. J.L. Kelley and I. Namioka, Linear Topological Spaces (Van Nostrand, New Jersey, 1963).

    Google Scholar 

  8. J.F.C. Kingman, On queues in heavy traffic, J. Roy. Statist. Soc. Ser. B 24 (1962) 383–392.

    Google Scholar 

  9. L. Kleinrock, Queueing Systems, Vol. 1: Theory (Wiley, New York, 1975).

    Google Scholar 

  10. L. Kleinrock, Queueing Systems, Vol. 2: Computer Applications (Wiley, New York, 1976).

    Google Scholar 

  11. J.P. Lehoczky, Real-time queueing theory, in: Proc. of the 17th IEEE Real-Time Systems Symposium (December 1996) pp. 186–195.

  12. J.P. Lehoczky, Using real-time queueing theory to control lateness in real-time systems, Performance Evaluation Rev. 25(1) (1997) 158–168.

    Google Scholar 

  13. J.P. Lehoczky, Personal correspondence with R.O. Baldwin (5 July 1997).

  14. J.P. Lehoczky, Real-time queueing network theory, in: Proc. of the 18th IEEE Real-Time Systems Symposium (December 1997) pp. 58–67.

  15. C.L. Liu and J.W. Layland, Scheduling algorithms for multiprogramming in a hard real time environment, J. Assoc. Comput. Mach. 20(1) (1973) 46–61.

    Google Scholar 

  16. L. Liu, B.R. Kashyap and J.G. Templeton, The service system /M/M/supR/ infinity with impatient customers, Queueing Systems 2(4) (1988) 363–372.

    Article  Google Scholar 

  17. R.E. Moore, Computational Functional Analysis (Halsted Press, New York, 1985).

    Google Scholar 

  18. OPNET Modeler, MIL 3, 3400 International Drive NW, Washington.

  19. N.L. Polyayev, Nonstationary characteristics of a single channel system with a constraint on the waiting time, Soviet J. Comput. Systems Sci. 24(4) (1986) 116–121.

    Google Scholar 

  20. S.S. Panwar, D. Towsley and J.K. Wolf, Optimal scheduling policies for a class of queues with customer deadlines to the beginning of service, J. Assoc. Comput. Mach. 35(4) (1988) 832–844.

    Google Scholar 

  21. N. Sugakkai, Encyclopedic Dictionary of Mathematics (MIT Press, Cambridge, MA, 1977).

    Google Scholar 

  22. Y.Q. Zhao and A.S. Alfa, Performance analysis of a telephone system with both patient and impatient customers, Telecommunication Systems 4(3–4) (1995) 201–215.

    Article  Google Scholar 

  23. Z.X. Zhao, S.S. Panwar and D. Towsley, Queueing performance with impatient customers, in: IEEE INFOCOM '91, pp. 400–409.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH, 45433, USA

    Rusty O. Baldwin

  2. Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA

    Nathaniel J. Davis IV & Scott F. Midkiff

  3. Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA

    John E. Kobza

Authors
  1. Rusty O. Baldwin
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  2. Nathaniel J. Davis IV
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  3. John E. Kobza
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  4. Scott F. Midkiff
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Baldwin, R.O., Davis IV, N.J., Kobza, J.E. et al. Real-time queueing theory: A tutorial presentation with an admission control application. Queueing Systems 35, 1–21 (2000). https://doi.org/10.1023/A:1019177624198

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