Throughput of crossbar switches using maximal matching algorithms

Crossbar switch fabrics are simple and inexpensive. Maximal matching algorithms can be used to schedule packets through a crossbar switch at a reasonable computational complexity. This paper establishes conditions that guarantee the departure rate of each of a switch's input/output pairs will equal each pair's arrival rate if the switch is using a crossbar fabric and any maximal matching algorithm. These conditions bound each pair's arrival rate in relation to the switch's speedup and the sum of the arrival rates of the other input/output pairs that share either the input or the output of the pair in question. In particular, for speedups less than 2, bounding the sum of the rates passing through each input and output independently is overly restrictive, especially if rates tend to be a sizable fraction of the line rates. This paper also establishes that the speedup required to ensure that each input/output pair's departure rate equals its arrival rate for switches using maximal matching is less than 2 if all non-zero arrival rates are equal to or greater than some minimum rate.