LN: A Flexible Algorithmic Framework for Layered Queueing Network Analysis

Abstract

Layered queueing networks (LQNs) are an extension of ordinary queueing networks useful to model simultaneous resource possession and stochastic call graphs in distributed systems. Existing computational algorithms for LQNs have primarily focused on mean-value analysis. However, other solution paradigms, such as normalizing constant analysis and mean-field approximation, can improve the computation of LQN mean and transient performance metrics, state probabilities, and response time distributions. Motivated by this observation, we propose the first LQN meta-solver, called LN, that allows for the dynamic selection of the performance analysis paradigm to be iteratively applied to the submodels arising from layer decomposition. We report experiments where this added flexibility helps us to reduce the LQN solution errors. We also demonstrate that the meta-solver approach eases the integration of LQNs with other formalisms, such as caching models, enabling the analysis of more general classes of layered stochastic networks. Additionally, to support the accurate evaluation of the LQN submodels, we develop novel algorithms for homogeneous queueing networks consisting of an infinite server node and a set of identical queueing stations. In particular, we propose an exact method of moment algorithms, integration techniques for normalizing constants, and a fast non-iterative mean-value analysis technique.