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The M/M/1 queue is Bernoulli

100%

Keane M., O'Connell N.

Colloquium Mathematicum

2008

tom 110

nr 1

205-210

The classical output theorem for the M/M/1 queue, due to Burke (1956), states that the departure process from a stationary M/M/1 queue, in equilibrium, has the same law as the arrivals process, that is, it is a Poisson process. We show that the associated measure-preserving transformation is metrically isomorphic to a two-sided Bernoulli shift. We also discuss some extensions of Burke's theorem where it remains an open problem to determine if, or under what conditions, the analogue of this result holds.

The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition

81%

Keane M., Károly K., Solomyak B.

Fundamenta Mathematicae

2003

tom 180

nr 3

279-292

Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Fundamenta Mathematicae

2 Keane M.

1 Károly K.

1 O'Connell N.

1 Solomyak B.

1 2008

1 2003

Wyniki wyszukiwania

The M/M/1 queue is Bernoulli

The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition