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Switch Control Complexity of Diminished Three-Quarter Crossbar Switches


Pavel Selin, Hitoshi Obara


Vol. 12  No. 10  pp. 20-25


The three-quarter crossbar switch (TQ-XBS) has been known to have about 3N2/4 crosspoints, where N is the switch size, and shows a property intermediate between the crossbar switch (XBS) and the triangular switch (TAS). Its original configuration has an extra pair of input and output ports to make the analysis of the switch control complexity difficult and some major properties of TQ-XBS have been left open. In this paper, we consider a diminished TQ-XBS that has not the extra ports as a first step to examine performance of TQ-XBSs. We made a comprehensive study of the switch control complexity and the worst case scenario for rearrangement in the diminished TQ-XBS. It is shown that the switch control complexity for setting up a new connection is O(N) at most. It is also shown that the identical permutation ensures truly a worst case scenario for rearrangement and the maximum number of rearrangements for the worst case remains two regardless of N. The complexity of the rearrangement process is also given by O(N). Additionally, it is pointed out for the first time that the diminished TQ-XBS shows a better performance than the TAS regarding a newly defined figure of merit.


Three-quarter crossbar switch, Rearrangeably nonblocking, Switch control complexity, Rearrangement.