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Some results for infinite server poisson queues

  • Mark Brown (a1) and Sheldon M. Ross (a2)

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We consider a queueing model in which arrivals occur according to a non-homogeneous Poisson process in batches of varying size, and in which a customer is served immediately upon arrival by one of an infinite number of servers.

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References

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[1] Brown, M. (1968) An invariance property of Poisson processes arising in traffic flow theory. Stanford University Technical Report.
[2] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol. II. Wiley, New York.
[3] Karlin, S. (1966) A First Course in Stochastic Processes. Academic Press, New York.
[4] Pyke, R. (1958) On renewal processes related to type I and type II counter models. Ann. Math. Statist. 29, 737754.
[5] Rao, , Sudarsana, J. (1966) An application of stationary point processes to queueing and textile research. J. Appl. Prob. 3, 231246.
[6] Riordan, J. (1962) Stochastic Service Systems. Wiley, New York.
[7] Shanbhag, D. N. (1966) On infinite server queues with batch arrivals. J. Appl. Prob. 3, 274279.
[8] Takács, L. (1957) On certain sojourn time problems in the theory of stochastic processes. Acta Math. Acad. Sci. Hung. III, 169191.
[9] Benes, V. E. (1965) Mathematical Theory of Connecting Networks and Telephone Traffic. Academic Press, New York.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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