Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Asymptotic Distributions of Maximum Queue Lengths for M/G/1 and GI/M/i Systems

  • Park, You-Sung (Department of Statistics, Korea University, Seoul 136-701)
  • Published : 1995.06.01
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Abstract

In this paper, we investigate the asymptotic distributions of maximum queue length for M/G/1 and GI/M/1 systems which are positive recurrent. It is well knwon that for any positive recurrent queueing systems, the distributions of their maxima linearly normalized do not have non-degenerate limits. We show, however, that by concerning an array of queueing processes limiting behaviors of these maximum queue lengths can be established under certain conditions.

Keywords

References

  1. Applied Probability and Queues Asmussen,S.
  2. The Single Server Queue Cohen,J.W.
  3. Fundamentals of Queueing Theory(2nd ed.) Gross,D.;Harris,C.M.
  4. Queueing and Related Models Approximating the distribution of the maximum queue length for M/M/s queues McCormick,W.P.;Park,Y.S.;Bhat,U.N.(ed.);Basawa,I.V.(ed.)
  5. Stochastic Processes and Their Applications v.27 Extreme values of birth and death processes and queues Serfozo,R.F.
  6. Mathematics of Operations Research v.13 Extreme values of queue lengths in M/G/1 and GI/M/1 systems Serfozo,R.F.