A procedure to approximate the mean queue content in a discrete-time generalized processor sharing queue with Bernoulli arrivals

摘要

Generalized Processor Sharing is a notoriously hard model to analyze. In earlier work we derived an iterative procedure to calculate coefficients for a power series of the joint probability generating function of the stationary queue content. This procedure posed computational limitations on the possible number of coefficients calculable for the performance measures, such as mean queue content. In this paper, we propose a direct approach and derive a procedure to directly calculate the power series for these performance measures, thus eliminating the problems associated with the probability generating function. The result is a procedure of complexity O(N-3) to calculate the first N coefficients of the mean queue content. Finally, the approximations are compared and validated with simulations. (C) 2019 Elsevier B.V. All rights reserved.