The Finite-Skip Method for Multiserver Analysis

Multiserver queueing systems are found at the core of a wide variety of practical systems. Unfortunately, existing tools for analyzing multiserver models have major limitations: Techniques for exact analysis often struggle with high-dimensional models, while techniques for deriving bounds are often too specialized to handle realistic system features, such as variable service rates of jobs. New techniques are needed to handle these complex, important, high-dimensional models. In this paper we introduce the work-conserving finite-skip class of models. This class includes many important models, such as the heterogeneous M/G/k, the limited processor sharing policy for the M/G/1, the threshold parallelism model, and the multiserver-job model under a simple scheduling policy. We prove upper and lower bounds on mean response time for any model in the work-conserving finite-skip class. Our bounds are separated by an additive constant, giving a strong characterization of mean response time at all loads. When specialized to each of the models above, these bounds represent the first bounds on mean response time known for each setting.