Interpolation approximations for queues in series

Tandem queues constitute a fundamental structure of queueing networks. However, exact queue times in tandem queues are notoriously difficult to compute except for some special cases. Several approximation schemes that are based on mathematical assumptions that enable approximate analyses of tandem queues have been reported in the literature. This article proposes an approximation approach that is based on observed properties of the behavior of tandem queues: the intrinsic gap and intrinsic ratio. The approach exploits the nearly linear and heavy-traffic properties of the intrinsic ratio, which appear to hold in realistic production situations. The proposed approach outperforms existing approximation methods across a broad range of examined cases. It is also demonstrated that the proposed approach has the potential when applied to historical data to achieve accurate mean queue time estimates in practical production environments.