Blending randomness in closed queueing network models

Random environments are stochastic models used to describe events occurring in the environment a system operates in. The goal is to describe events that affect performance and reliability such as breakdowns, repairs, or temporary degradations of resource capacities due to exogenous factors. Despite having been studied for decades, models that include both random environments and queueing networks remain difficult to analyse. To cope with this problem, we introduce the blending algorithm, a novel approximation for closed queueing network models in random environments. The algorithm seeks to obtain the stationary solution of the model by iteratively evaluating the dynamics of the system in between state changes of the environment. To make the approach scalable, the computation relies on a fluid approximation of the queueing network model. A validation study on 1800 models shows that blending can save a significant amount of time compared to simulation, with an average accuracy that grows with the number of servers in each station. We also give an interpretation of this technique in terms of Laplace transforms and use this approach to determine convergence properties.