Queueing networks with string transitions of mixed vector additions and vector removals (Q1348603)

A model of a queueing network with string transitions of mixed vectors additions, vector removals and compensating boundary rates is presented. Specifically a sequence of nonnegative vectors is removed, and then a sequence of nonnegative is added to the network state. Extensions of the string transition networks to allow transitions of mixed vector additions and vector removals, and including assembly-transfer networks as well as networks with negative and positive signals in special cases are proved as the main result. This result is illustrated with signals and assembly networks. The results not only characterize a new class of models with a product from equilibrium distribution, but also provide a generic construction of product form models, based on partial balances that are useful in developing. Reflecting boundaries as an alternative in model are also discussed.