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A generalization of the Reversed Compound Agent Theorem of Markovian process algebra is derived that yields separable, but non-product-form solutions for collections of interacting processes such as arise in multi-class queueing networks with Processor Sharing servers. It is based on an analysis of the minimal cycles in the state space of a multi-agent cooperation, which can be simply identified. The extended methodology leads to what we believe are new separable solutions and, more generally,doi:10.1016/j.entcs.2006.03.012 fatcat:uyf5ikzm5jau7kbcpi4gk5v764