The input-queued Crossbar Switching is one of the most popular and crucial technologies of the high-performance switching systems.The matrix model for IQ-Crossbar fabric is given in this paper

which has provided and well-defined the precise concepts of IQ-Crossbar fabric

such as the state matrix

the queueing length matrix

the arriving matrix

and the matching matrix.Based on analyzing the mechanism of the cell’s queueing in the IQ-Crossbar

two matrix theorems of queueing length iteration as well as the state iteration are discussed and proved.The matrix model given in this paper provides the theoretical reference to IQ-Crossbar scheduling algorithms.Based on the matrix model set up in this paper and the analysis of the advantages and disadvantages of LQF algorithm

a new scheduling scheme of MM-LQF is provided

which has 3.72 times of operational efficiency

2.35 times of port gate rates

0.5 times of cell delay under heavy Bernoulli uniform load

100% throughput under Bernoulli diagonal load of the LQF algorithm.