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Approximating nonstationaryPh(t)/M(t)/s/c queueing systems

  • Part I Numerical Problems In Probability
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Abstract

Nonstationary phase processes are defined and a surrogate distribution approximation (SDA) method for analyzing transient and nonstationary queueing systems with nonstationary phase arrival processes is presented. Regardless of system capacityc, the SDA method requires the numerical solution of only 6K differential equations, whereK is the number of phases in the arrival process, compared to theK(c+1) Kolmogorov forward equations required for the classical method of solution. Time-dependent approximations of mean and variance of the number of entities in the system and the number of busy servers are obtained. Empirical test results over a wide range of systems indicate the SDA is quite accurate.

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References

  1. E. Çinlar,Introduction to Stochastic Processes (Prentice Hall, Englewood Cliffs, NJ, 1975).

    Google Scholar 

  2. G.M. Clark, Use of Polya distributions in approximate solutions to nonstationaryM/M/s queues, Commun. of the ACM 24, 4(1981)206.

    Google Scholar 

  3. N.L. Johnson and S. Kotz,Urn Models and Their Applications (Wiley, New York, 1977).

    Google Scholar 

  4. B.O. Koopman, Air terminal queues under time-dependent conditions, Oper. Res. 20(1972)1089.

    Google Scholar 

  5. T.C.T. Kotiah, Approximate transient analysis of some queueing systems, Oper. Res. 26, 2(1978)

  6. M.F. Neuts,Matrix-Geometric Solutions in Stochastic Models — An Algorithmic Approach (The Johns Hopkins University Press, Baltimore, 1981).

    Google Scholar 

  7. K.L. Rider, A simple approximation to the average size in the time-dependentM/M/1 queue J. of the ACM 23, 2(1976).

  8. M.H. Rothkopf and S.S. Oren, A closure approximation for the nonstationaryM/M/s queue, Management Science 25, 6(1979)522.

    Google Scholar 

  9. M.R. Taaffe, Approximating nonstationary queueing models, Ph.D. Dissertation, The Ohio State University (1982).

  10. M.R. Taaffe and G.M. Clark, Approximating nonstationary two-priority nonpreemptive queueing systems, Research Memorandum 85-2, School of Industrial Engineering, Purdue University, Indiana (1985).

    Google Scholar 

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Author notes

  1. K. L. Ong

    Present address: BDM Corporation, 7915 Jones Branch Drive, 22102, McLean, VA, USA

Authors and Affiliations

  1. School of Industrial Engineering, Purdue University, 47907, West Lafayette, Indiana, USA

    M. R. Taaffe & K. L. Ong

Authors
  1. M. R. Taaffe
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  2. K. L. Ong
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Additional information

This research was partially funded by National Science Foundation grant ECS-8404409.

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Taaffe, M.R., Ong, K.L. Approximating nonstationaryPh(t)/M(t)/s/c queueing systems. Ann Oper Res 8, 103–116 (1987). https://doi.org/10.1007/BF02187085

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  • DOI: https://doi.org/10.1007/BF02187085

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