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2 results

  • Busy periods in time-dependent M/G/1 queues

  • Stig. I. Rosenlund
  • Journal:
    Advances in Applied Probability / Volume 8 / Issue 1 / March 1976
    Published online by Cambridge University Press:
    01 July 2016, pp. 195-208
    Print publication:
    March 1976

  • A single-server queue with batch arrivals in a non-homogeneous Poisson process and with balking is studied with respect to the busy period, using supplementary variables. A system of integral equations is obtained on the base of which the transforms are expressed in series. For the homogeneous case, assuming finite waiting room, the solutions are obtained via Cramer's rule. This gives asymptotic expressions for the expectations for large arrival intensity. An efficiency measure giving the long run loss probability is given. For a special case contour integral representations are given as solutions.

  • Busy period of a finite queue with phase type service

  • Stig I. Rosenlund
  • Journal:
    Journal of Applied Probability / Volume 12 / Issue 1 / March 1975
    Published online by Cambridge University Press:
    14 July 2016, pp. 201-204
    Print publication:
    March 1975

  • An M/G/1 service system with finite waiting room is studied. A customer is served by one server in two phases, during the first of which a place in the waiting room is occupied. Starting from a determinant expression for the Laplace-Stieltjes transform of the busy period given in [2] we obtain contour integral expressions for the transform and the expectation, thereby generalising a result by Cohen [1]. This is effected by developing the determinants along the first row.