Distribution of Processor-Sharing Customers for a Large Closed System with Multiple Classes SIAM Journal on Applied Mathematics Volume 60, Number 4 pp. Yaakov Kogan Abstract. 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. 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 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.