In this paper, we present an efficient numerical method for calculating the waiting time and idle time distributions of the arithmetic GI/G/1 queue. Our method is based on the Wiener-Hopf factorization, which is briefly reviewed. Compared to the related methods suggested in the literature, our method seems to perform very well, and it is often faster by several orders of magnitude. A number of numerical examples conclude the paper.
mIn carrying out our plan for doing multicenter molecular integrals over Slater-type orbitals, it is necessary to evaluate the Lowdin a-function over a grid from the origin of the coordinate system to the displacement distance of the center of the orbital. A previous article obtained excellent results by expanding the exponentials in the a-function, for both interior and exterior regions. However, if the displacement distance multiplied by the screening constant, i.e., the ( a parameter, is larger than 16, we suggest that it may be more efficient in time and storage if we use the closed formula for the a-function for values of the radial distance r greater than 8. This remarkable rule of thumb was tested for a variety of orbitals up to ( a = 64 and one to ( a = 128. Also, in the exterior region, the formula may always be used if ( a 2 16. This strategy necessitates using the formula in quadruple precision arithmetic. 0 1996 John Wiley & Sons, Inc.
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