A heuristic for the transient expected queue length of Markovian queueing systems

The authors present a heuristic for the transient expected queue length for stationary, single-server, Markovian queueing systems that begin at rest. The heuristic is closed-form, suitable for applications work, and requires knowledge only of basic system parameters and the equilibrium expected queue length. The present empirical results demonstrate the heuristic performs well over a specified portion of the transient period for systems under moderate to heavy traffic.