Parallel connection control ("PCC") processes and switching networks are described. Various aspects of these PCC processes and networks relate to the provision of an alternative switching connection setup to achieve bandwidth savings or lower cost networks with acceptable setup delay. The new approach provides an alternative to existing switch-by-switch sequential connection setup approaches. In the new approach, segments of the connection are set up by executing operations in parallel. The algorithm and network are also extended to address complex control connection tasks, such as the complex bearer control tasks of third-party connection control, unidirectional multicast connection setup, and multiparty-to-multiparty connection control.