We analyze a novel two-level queueing network with blocking, consisting of N level-1 parallel queues linked to M level-2 parallel queues. The processing of a customer by a level-1 server requires additional services that are exclusively offered by level-2 servers. These level-2 servers are accessed through blocking and non-blocking messages issued by level-1 servers. If a blocking message is issued, the level-1 server gets blocked until the message is fully processed at the level-2 server. The queueing network is analyzed approximately using a decomposition method, which can be viewed as a generalization of the well-known two-node decomposition algorithm used to analyze tandem queueing networks with blocking. Numerical tests show that the algorithm has a good accuracy.
