Fluid Analysis of Queueing in Two-Stage Random Environments

A large number of random environments leads to Markov processes where average-environment (AVG) and near-complete-decomposability (DEC) approximations suffer unacceptably large errors. This is problematic for queueing networks in particular, where state-space explosion hinders the application of numerical methods. In this paper we introduce blending, a novel fluid-based approximation for queueing models in random environments. The technique is here first introduced for random environments with two stages. Blending estimates the equilibrium of the model by iteratively evaluating transient-analysis sub problems for each of the two stages. Each sub problem is solved by means of a very small system of ordinary differential equations, making the approach scalable and simple to implement. Random environments supported by blending are either state-independent, as for models with breakdown and repair, or state-dependent, such as for Markov-modulated queues where the service phase changes only during busy periods. Comparative results with AVG and DEC approximations prove that blending tackles the limitations of existing methods for evaluating queues in random environments.