Journal of the Korean Statistical Society

  • 제24권1호
  • /
  • Pages.19-29
  • /
  • 1995
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

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)
  • 발행 : 1995.06.01
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초록

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.

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참고문헌

  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.