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On infinite server queues with batch arrivals

  • D. N. Shanbhag (a1)

Extract

The queueing system studied in this paper is the one in which

  1. (i)there are an infinite number of servers,
  2. (ii)initially (at t = 0) all the servers are idle,
  3. (iii)one server serves only one customer at a time and the service times are independent and identically distributed with distribution function B(t) (t > 0) and mean β(< ∞),
  4. (iv)the arrivals are in batches such that a batch arrives during (t, t + δt) with probability λ(tt + ot) (λ(t) > 0) and no arrival takes place during (t, t + δt) with the probability 1 –λ(tt + ot),
  5. (v)the batch sizes are independent and identically distributed with mean α(< ∞), and the probability that a batch size equals r is given by a r(r ≧ 1),
  6. (vi)the batch sizes, the service times and the arrivals are independent.

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References

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[1] Downton, F. (1962) Congestion system with incomplete service. J. R. Statist. Soc. B 24, 107111.
[2] Mirasol, N. M. (1963) The output of an M/G/8 queueing system is Poisson. Operat. Res. 11, 282284.
[3] Shanbhag, D. N. (1964) On a problem of servicing a Poisson flow of demands. Ann. Math. Statist. 35, 461462 (abstract).
[4] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press.
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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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