Three stage tandem queue with blocking

An analysis is given of the state and first-come, first-served waiting time processes for a three stage queueing system with no waiting space between stages, but with limited space before the first. Although the basic processes are exponential, no detailed analysis in this generality appears to have been made before; the nearest analyses entail the simplifying assumption that the first stage is never empty. A sufficient condition is derived easily for equilibrium to exist and it can be asserted with virtual certainty that it is also necessary; the complexity of calculation has so far excluded a proper proof, though this is in principle a possibility.The objective is to provide a theoretical framework easily adaptable for a numerical assessment of system performance to be made. Some typical tables with comments are given.