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Some Topics in Queueing Network Theory

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 98))

Abstract

In this paper we present results obtained in the study of queueing networks. Such a network is illustrated in Fig. 1. Although numerous examples of queueing networks exist in real life, the study of such systems has not progressed at a pace commensurate with its importance. Rather, the theory of waiting line processes has proceeded largely as a study of single server systems. Isolated “network” results do exist but as yet no comprehensive treatment of the subject has appeared.

Research supported in part by the Office of Naval Research under Contract N00014-67-A-0181-0047 (NR 042-296)

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References

  1. Agnew, R. A., “Transformations on Uniform and Stationary Point Processes,” Doctoral Dissertation, Northwestern University, 1968.

    Google Scholar 

  2. Anderson, L. B., “Filtered Semi-Markov Procésses,” Masters Thesis, Northwestern University, 1967.

    Google Scholar 

  3. Cherry, W. P., “The Superposition of Two Independent Markov Renewal Processes,” Doctoral Dissertation, Department of Industrial and Operations Engineering, University of Michigan, 1972.

    Google Scholar 

  4. Cinlar, E., “Analysis of Systems of Queues in Parallel,” Doctoral Dissertation, Department of Industrial Engineering, University of Michigan, 1965.

    Google Scholar 

  5. Cinlar, E., “Queues with Semi-Markov Arrivals,”J.Appl. Probability, 4, 1967, pp. 365–379.

    Article  MATH  MathSciNet  Google Scholar 

  6. Cinlar, E., “On Semi-Markov Processes on Arbitrary State Spaces,” Proc. Cambridge Philos. Soc., 66, 1969, pp. 381–392.

    Article  MATH  MathSciNet  Google Scholar 

  7. Cinlar, E., “Superposition of Point Processes,”Stochastic Point Processes: Statistical Analysis, Theory and Applications(P. A. W. Lewis, ed.), John Wiley & Sons, Inc., New York, 1972.

    Google Scholar 

  8. Daley, D. J. and Vere-Jones, D., “A Summary of the Theory of Point Processes,” Stochastic Point Processes: Statistical Analysis, Theory and Applications(P. A. W. Lewis, Ed.), John Wiley & Sons, Inc, New York, 1972.

    Google Scholar 

  9. Davignon, G. R., “Queues with Dependend Feedback,” Department of Industrial and Operations Engineering Technical Report, University of Michigan, 1972.

    Google Scholar 

  10. Disney, R. L. and Morais, P. R. de, “Some Properties of Departure Processes from M/G/1/N Queues,” Department of Industrial and Operations Engineering Technical Report, University of Michigan, 1971.

    Google Scholar 

  11. Disney, R. L., “A Matrix Solution for the Two Server Queue with Overflow,” Management Sci., 19, 1972, pp. 254–265.

    Article  MATH  MathSciNet  Google Scholar 

  12. Disney, R. L., Farrell, R. L., and Morais, P. R. de, “A Characterization of M/G/1/N Queues with Renewal Departure Processes,” Management Sci., to appear.

    Google Scholar 

  13. Hall, W. K., “A Queueing Theoretic Approach to the Allocation and Distribution of Ambulances in an Urban Area,” Doctoral Dissertation, School of Business Administration, University of Michigan, 1969.

    Google Scholar 

  14. Hall, W. K.and Disney, R. L., “Finite Queues in Parallel with a Generalized Channel Selection Rule, ” J. Appl. Probability, 8, 1971, pp. 413–416.

    Article  MATH  MathSciNet  Google Scholar 

  15. Jackson, J. R., “Networks of Waiting Lines,” Operations Res., 5, 1957, pp. 518–521.

    Article  MathSciNet  Google Scholar 

  16. Kemeny, J. and Snell, L. Finite Markov Chains, D. Van Nostrand, Inc., 1959.

    Google Scholar 

  17. King, R. A., “The Covariance Properties of the Departure Process from Single Channel Queues,” Doctoral Dissertation, Department of Industrial Engineering, University of Michigan, 1967.

    Google Scholar 

  18. Prabhu, U. N., Queues and Inventories, John Wiley & Sons, 1965.

    Google Scholar 

  19. Solberg, J. J., “A Graph Theoretic Approach to the Study of Networks of Queues,” Doctoral Dissertation, Department of Industrial Engineering, University of Michigan, 1969.

    Google Scholar 

  20. Takacs, L., “A Single-Server Queue with Feedback,” Bell System Tech. J., 42, 1963, pp. 505–519.

    MathSciNet  Google Scholar 

  21. Vlach, T., “The Departure Process from the GI/G/1 Queue,” Doctoral Dissertation, Department of Industrial Engineering, University of Michigan, 1969.

    Google Scholar 

  22. Wallace, V. L., “The Solution of Quasi Birth-Death Processes Arising from Multiple Access Computer Systems,” Doctoral Dissertation, Department of Electrical Engineering, University of Michigan, 1969.

    Google Scholar 

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© 1974 Springer-Verlag Berlin · Heidelberg

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Disney, R.L., Cherry, W.P. (1974). Some Topics in Queueing Network Theory. In: Clarke, A.B. (eds) Mathematical Methods in Queueing Theory. Lecture Notes in Economics and Mathematical Systems, vol 98. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80838-8_2

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  • DOI: https://doi.org/10.1007/978-3-642-80838-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06763-4

  • Online ISBN: 978-3-642-80838-8

  • eBook Packages: Springer Book Archive

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