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The interdeparture-time distribution for each class in the ∑ i M i /G i /1 queue

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Abstract

A stationary queueing system is described in which a single server handles several competing Poisson arrival streams on a first-come first-served basis. Each class has its own generally distributed service time characteristics. The principal result is the Laplace-Stieltjes transform, for each class, of the interdeparture time distribution function. Examples are given and applications are discussed.

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References

  1. G. Bitran and D. Tirupati, Multiproduct queueing networks with deterministic routing: decomposition approach and the notion of interference, Man. Sci. 34 (1988) 75–100.

    Google Scholar 

  2. P.J. Burke, The output of a queueing system, Operations Research 4 (1956) 699–704.

    Google Scholar 

  3. R.W. Conway, W. Maxwell and L. Miller,Theory of Scheduling (Addison-Wesley, Reading, Mass. 1967).

    Google Scholar 

  4. D.J. Daley, Queueing output processes, Adv. Appl. Prob. 8 (1976) 395–415.

    Google Scholar 

  5. D. Gross, C.M. Harris,Fundamentals of Queueing Theory (Wiley, New York, 1974).

    Google Scholar 

  6. L. Kleinrock,Queueing Systems, Vol. I: Theory (Wiley, New York, 1975).

    Google Scholar 

  7. P.J. Kuehn, Approximate analysis of general queueing networks by decomposition, IEEE Transactions on Communications, COM-27 (1979) 113–126.

    Google Scholar 

  8. K.T. Marshall, Some inequalities in queuing, Operations Research, 16 (1968) 651–665.

    Google Scholar 

  9. P. Nain, Interdeparture times from a queueing system with preemptive resume priority, Performance Evaluation 4 (1984) 93–98.

    Google Scholar 

  10. M. Segal and W. Whitt, A Queueing network analyzer for manufacturing, Proc. 12th Int'l. Teletraffic Congress, Turin, Italy, June 1988.

  11. D.A. Stanford, Modelling priority queueing characteristics in approximate analytical tools for open queueing networks, in:Modelling Techniques and Tools for Performance Analysis (Elsevier-North-Holland, 1986) pp. 131–143.

  12. L. Takács,Introduction to the Theory of Queues (Oxford University Press, 1962).

  13. W. Whitt, The queueing network analyzer, Bell System Technical Journal 62, No. 9 (1983) 1779–2815.

    Google Scholar 

  14. W. Whitt, Approximations for departure processes and queues in series, Nav. Res. Log. Qtrly. 31 (1984) 499–521.

    Google Scholar 

  15. W. Whitt, A light traffic approximation for single-class departure processes from multi-class queues, Man. Sci. 34 (1988) 1333–1346.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Dept. of Statistical & Actuarial Sciences, The University of Western Ontario, N6A 5B9, London, Ontario, Canada

    David Stanford

  2. Institute of Communications Switching and Data Techniques, University of Stuttgart, Fed. Rep. of Germany

    Wolfgang Fischer

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  1. David Stanford
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  2. Wolfgang Fischer
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Stanford, D., Fischer, W. The interdeparture-time distribution for each class in the ∑ i M i /G i /1 queue. Queueing Syst 4, 179–191 (1989). https://doi.org/10.1007/BF02100265

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  • DOI: https://doi.org/10.1007/BF02100265

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