Abstract: The present invention is a system and a method for connection scheduling of crossbar switches having at least one ingress and at least one egress, each of the egresses is connected to at least one port, comprising at least one scheduler for scheduling matches between the ingresses and the egresses, which is in communication with the crossbar switch and at least one memory for holding data which is useful in the process of scheduling the crossbar switch. The memory is in communication with the scheduler. The scheduler schedules the matches between the ingresses and the egresses using data stored in the memory regarding the ingresses, egresses, and the ports. The scheduler operates in accordance with a selection algorithm, which is based on prioritizing of the ports. Selections are performed hierarchically as will be detailed hereinbelow. The scheduler efficiently matches between plurality of inputs and plurality of outputs, especially in crossbar systems having a large number of inputs and outputs.