Facilitating load-dependent queueing analysis through factorization

Abstract

We propose novel exact and approximate solutions for mean-value and probabilistic analysis of closed queueing networks with limited load-dependent nodes. The main result is the derivation of an exact correction factor between the equilibrium solution of a load-dependent model and the one of a related model with fixed-rate queueing stations. This enables the reuse of state-of-the-art methods for fixed-rate stations in the computation of performance metrics for load-dependent systems. As many such algorithms are available, our findings significantly increase the range of techniques available to study load-dependence. We further interpret the correction factor as a load-dependent normalizing constant and propose two novel integral forms, in the real and in the complex domains, which can be used for its efficient computation. These integral forms are also shown to be applicable to evaluate more general limited load-dependent systems, as we illustrate in a sojourn time distribution analysis problem. Lastly, the proposed algorithms are numerically examined through thousands of experiments, which reveal accuracy in the range 1%–6% mean absolute relative error.