Nonexistence of Brownian models for certain multiclass queueing networks (Q1801805)

Two multiclass queueing open networks are considered where Harrison and Nguyen Brownian models do not exist. Such example is constructed for 2- node network when self-feedback is allowed (i.e. a customer leaving a node may immediately visit to the same station). For 3-node network without self-feedback the example is constructed also. These examples show that it is difficult to formulate a correct Brownian model for general multiclass networks.