The busy period of the queueing system M / G /∞

@article{Stadje1985TheBP,
title={The busy period of the queueing system M / G /∞},
journal={Journal of Applied Probability},
year={1985},
volume={22},
pages={697-704}
}
• Published 1 September 1985
• Mathematics
• Journal of Applied Probability
For the queueing system M/G/oo some distributions connected with the associated busy periods are derived. QUEUES WITH UNLIMITED SERVICE
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References

SHOWING 1-10 OF 11 REFERENCES
QUEUEING OUTPUT PROCESSES
The paper reviews various aspects, mostly mathematical, concerning the output or departure process of a general queueing system G/G/s/N with general arrival process, mutually independent service
On the Measure of a Random Set
The following is perhaps the simplest non-trivial example of the type of problem to be considered in this paper. On the real number axis let N points $${x_i}(i = 1,2, \cdots ,N)$$ be chosen
Asymptotic Coverage Distributions on the Circle
Abstract : Let n arcs, each of length G sub N, be placed uniformly at random on the circumference of a circle. If the arc length sequence is chosen so that the coverage probability remains constant,
Covering the circle with random ARCS
AbstractArcs of lengthsln, 0<ln+1<=ln<1,n=1,2,…, are thrown independently and uniformly on a circumferenceC of unit length. The union of the arcs coversC with probability one if and only if
Integral geometry and geometric probability
Part I. Integral Geometry in the Plane: 1. Convex sets in the plane 2. Sets of points and Poisson processes in the plane 3. Sets of lines in the plane 4. Pairs of points and pairs of lines 5. Sets of
A Survey of Coverage Problems Associated with Point and Area Targets
At first glance the subject-matter of this paper may appear to be rather trivial. No questions of offense or defense strategies are involved; one is interested solely in calculating the probability