Fundamental Conditions Governing TDM Switching Assignments in Terrestrial and Satellite Networks

We consider the traffic handling capability of a new switching architecture which generalizes upon the structure of a traditional time multiplex switching system. For the traditional approach, lowbandwidth end users are formed into groups, each of which shares a single high bandwidth time-division multiplexed (TDM) line into the central time multiplex switch. Each user synchronously generates packets of data in preassigned time slots at a rate consistent with its offered traffic, and the feeder for the TDM line serving a group of users merely time multiplexes the arriving packets prior to routing by the central switch; analogously, each output port of the switch feeds a demultiplexer which routes the packets to the appropriate user within its group. The generalized approach permits each user group to share some multitude of TDM lines interconnecting that group with the central switch, and the group multiplexers and demultiplexers are replaced by switches which route packets from users to TDM lines (and vice versa). For this structure, we derive a set of necessary and sufficient conditions on the user-touser offered traffic such that a valid, nonconflicting TDM assignment of packets-to-time slots exists. These conditions reveal that the constraints imposed by the three-tiered switching hierarchy do not limit the useable capacity of the switch. Consequently, with no loss of traffic bearing efficiency, it is possible to reduce the number of multiplexers used to serve the end-user population, achieve greater trunking efficiency since small user groups served by one TDM line are replaced by larger groups serving multiple lines, and modularly grow the system by adding TDM lines to each group commensurate with the traffic offered by that group. As a byproduct, it is shown that such a system designed to switch low-speed circuits of some particular data rate can, with no hardware change, switch circuits at lower rates (subrate switching). These conclusions have important ramifications for the design of terrestrial and satellite-based switching systems.