| Zusammenfassung: | A closed processor-sharing (PS) system with multiple customer classes is considered. The system consists of one infinite server (IS) station and one PS station. For a system with a large number of customers, a saturated PS station, and an arbitrary number of customer classes, asymptotic approximations to the stationary distribution of the total number of customers at the PS station are derived. The asymptotics for the probability mass function is described by a quasipotential function, which defines the exponential decay for the distribution, and a state-dependent preexponential factor. Both functions have an explicit expression in terms of the solution at each point x of a polynomial equation whose order equals the number of classes and whose coefficients are explicit functions of x. The quasi-potential function at its minimum point provides the logarithmic asymptotics for the normalization constant, and the asymptotic approximation for the variance is inversely proportional to the second derivative of the quasi-potential function at its minimum point. The complementary probability distribution is computed using the normal approximation and its refinements, which do not require repeated solution of polynomial equations. Numerical results demonstrate the range of applicability of the approximations. The results can be applied to the problem of dimensioning bandwidth and of admission control for different data sources in packet-switched communication networks.
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