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The generating functions for the serial covariances for number in system in the stationary GI/M/1 bulk arrival queue with fixed bulk sizes, and the GI/Em/1 queue, are derived. Expressions for the infinite sum of the serial correlation coefficients are also presented, as well as the first serial correlation coefficient in the case of the bulk arrival queue. Several numerical examples are considered.

Various generalizations of the Maxwell characterization of the multivariate standard normal distribution are derived. For example the following is proved: If for a k-dimensional random vector X there exists an n ∈ {l, …, k − l} such that for each n-dimensional linear subspace H Rk the projections of X on H and H⊥ are independent, X is normal. If X has a rotationally symmetric density and its projection on some H has a density of the same functional form, X is normal. Finally we give a variational inequality for the multivariate normal distribution which resembles the isoperimetric inequality for the surface measure on the sphere.

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On the serial correlation for number in system in the stationary GI/M/1 bulk arrival and GI/Em/1 queues

A Characterization and a Variational Inequality for the Multivariate Normal Distribution

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102 results in 62Hxx

On the serial correlation for number in system in the stationary GI/M/1 bulk arrival and GI/Em/1 queues

A Characterization and a Variational Inequality for the Multivariate Normal Distribution