Simple Product-Form Bounds for Queueing Networks with Finite Clusters

Queueing networks are studied with finite capacity constraints forclusters of stations. First, by an instructive tandemcluster example it is shown how a product-form modification methodfor networks with finite stations can be extended tonetworks with finite clusters. Next, a general result is establishedby which networks with finite clusters can be studied atcluster level by merely keeping track of the total number of jobs atthese clusters, that is, by regarding these clusters asaggregate stations. This result is of practical interest to concludesimple performance bounds at global network level. Anumber of illustrative examples with numerical support are provided.