Abstract: A multi-stage network comprising (2×logd N)?1 stages is operated in strictly nonblocking manner for unicast includes an input stage having N/d switches with each of them having d inlet links and 2×d outgoing links connecting to second stage switches, an output stage having N/d switches with each of them having d outlet links and 2×d incoming links connecting from switches in the penultimate stage. The network also has (2×logd N)?3 middle stages with each middle stage having 2 × N d switches, and each switch in the middle stage has d incoming links connecting from the switches in its immediate preceding stage, and d outgoing links connecting to the switches in its immediate succeeding stage. Also the same multi-stage network is operated in rearrangeably nonblocking manner for arbitrary fan-out multicast and each multicast connection is set up by use of at most two outgoing links from the input stage switch.

Abstract: In one embodiment, a controller is configured to establish a new multicast connection within a network without changing a path of an existing multicast connection within the network. The network can have an input stage having a total of at least n1*r1 inlet links, an output stage including r2 output switches, and n2 outlet links for each of said r2 output switches for a total of at least n2*r2 outlet links, and a middle stage including m middle switches, where m?s*Min(n1,n2) and where s=2 when r2=[9,11], s=3 when r2=[25,48], s=4 when r2=[49,99, s=5 when r2=[100,154], s=6 when r2=155,224], and s=7 when r2=[225,278 ]. The new multicast connection from an inlet link from the n1*r1 inlet links passes through at most s middle switches.

Abstract: A rearrangeably nonblocking multicast network includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, where m?n1+n2. The network has all multicast connections set up such that each multicast connection passes through at most two middle switches to be connected to the destination outlet links.

Abstract: A three-stage network is operated in strictly nonblocking manner and includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, where m?2*n1+n2?1. In one embodiment, each multicast connection is set up through such a three-stage network by use of at most two switches in the middle stage.

Abstract: A system for scheduling multirate multicast packets through an interconnection network having a plurality of input ports, a plurality of output ports, and a plurality of input queues, comprising multirate multicast packets with rate weight, at each input port is operated in nonblocking manner in accordance with the invention by scheduling corresponding to the packet rate weight, at most as many packets equal to the number of input queues from each input port to each output port. The scheduling is performed so that each multicast packet is fan-out split through not more than two interconnection networks and not more than two switching times. The system is operated at 100% throughput, work conserving, fair, and yet deterministically thereby never congesting the output ports. The system performs arbitration in only one iteration, with mathematical minimum speedup in the interconnection network.

Abstract: A rearrangeably nonblocking multicast network includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, where m?n1+n2. The network has all multicast connections set up such that each multicast connection passes through at most two middle switches to be connected to the destination outlet links. When the number of inlet links in each input switch n1 is equal to the number of outlet links in each output switch n2, and n1=n2=n, a three-stage network is operated in rearrangeably nonblocking manner, where m?2*n.

Abstract: A three-stage network is operated in strictly nonblocking manner includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, where m???{square root over (r2)}?*MIN(n1,n2) when ??{square root over (r2)}? is >1 and odd, or when ??{square root over (r2)}?=2, m?(??{square root over (r2)}??1)*MIN(n1,n2) when ??{square root over (r2)}? is >2 and even, and m?n1+n2?1 when ??{square root over (r2)}?=1. Each multicast connection is set up through such a three-stage network by use of only one switch in the middle stage.

Abstract: A system for scheduling multicast packets through an interconnection network having a plurality of input ports, a plurality of output ports, and a plurality of input queues, comprising multicast packets, at each input port is operated in nonblocking manner in accordance with the invention by scheduling at most as many packets equal to the number of input queues from each input port to each output port. The scheduling is performed so that each multicast packet is fan-out split through not more than two interconnection networks and not more than two switching times. The system is operated at 100% throughput, work conserving, fair, and yet deterministically thereby never congesting the output ports. The system performs arbitration in only one iteration, with mathematical minimum speedup in the interconnection network. The system operates with absolutely no packet reordering issues, no internal buffering of packets in the interconnection network, and hence in a truly cut-through and distributed manner.

Abstract: A rearrangeably nonblocking multicast network in accordance with the invention includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, where m?n1+n2. The network has all multicast connections set up such that each multicast connection passes through at most two middle switches to be connected to the destination outlet links. When the number of inlet links in each input switch n1 is equal to the number of outlet links in each output switch n2, and n1=n2=n, a three-stage network is operated in rearrangeably nonblocking manner in accordance with the invention, where m?2*n.

Abstract: A system for scheduling unicast packets through an interconnection network having a plurality of input ports, a plurality of output ports, and a plurality of input queues, comprising unicast packets, at each input port is operated in nonblocking manner in accordance with the invention by scheduling at most as many packets equal to the number of input queues from each input port to each output port. The system is operated at 100% throughput, work conserving, fair, and yet deterministically thereby never congesting the output ports. The system performs arbitration in only one iteration, with mathematical minimum speedup in the interconnection network. The system operates with absolutely no packet reordering issues, no internal buffering of packets in the interconnection network, and hence in a truly cut-through and distributed manner.

Abstract: A three-stage network is operated in strictly nonblocking manner in accordance with the invention includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, where m?2*n1+n2?1. In one embodiment, each multicast connection is set up through such a three-stage network by use of at most two switches in the middle stage. When the number of inlet links in each input switch n1 is equal to the number of outlet links in each output switch n2, and n1=n2=n, a three-stage network is operated in strictly nonblocking manner in accordance with the invention if m?3*n?1.

Abstract: A system for scheduling multirate unicast packets through an interconnection network having a plurality of input ports, a plurality of output ports, and a plurality of input queues, comprising multirate unicast packets with rate weight, at each input port is operated in nonblocking manner in accordance with the invention by scheduling corresponding to the packet rate weight, at most as many packets equal to the number of input queues from each input port to each output port. The system is operated at 100% throughput, work conserving, fair, and yet deterministically thereby never congesting the output ports. The system performs arbitration in only one iteration, with mathematical minimum speedup in the interconnection network. The system operates with absolutely no packet reordering issues, no internal buffering of packets in the interconnection network, and hence in a truly cut-through and distributed manner.

Abstract: A rearrangeably nonblocking multicast network in accordance with the invention includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, where m?n1+n2. The network has all multicast connections set up such that each multicast connection passes through at most two middle switches to be connected to the destination outlet links. When the number of inlet links in each input switch n1 is equal to the number of outlet links in each output switch n2, and n1=n2=n, a three-stage network is operated in rearrangeably nonblocking manner in accordance with the invention, where m?2*n.

Abstract: A three-stage network is operated in strictly nonblocking manner in accordance with the invention includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, where m??{square root}{square root over (r2)}?*MIN(n1,n2) when ?{square root}{square root over (r2)}? is >1 and odd, or when ?{square root}{square root over (r2)}?=2, m?(?{square root}{square root over (r2)}??1)*MIN(n1,n2) when ?{square root}{square root over (r2)}? is >2 and even, and m?n1+n2?1 when ?{square root}{square root over (r2)}?=1.

Abstract: A three-stage network is operated in strictly nonblocking manner in accordance with the invention includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, where m?2*n1+n2?1. In one embodiment, each multicast connection is set up through such a three-stage network by use of at most two switches in the middle stage. When the number of inlet links in each input switch n1 is equal to the number of outlet links in each output switch n2, and n1=n2=n, a three-stage network is operated in strictly nonblocking manner in accordance with the invention if m?3*n?1.

Abstract: A three-stage network is operated in strictly nonblocking manner in accordance with the invention includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, if m?s*MIN(n1,n2) where s=2 when r2=[9,11], s=3 when r2=[25,48], s=4 when r2=[49,99], s=5 when r2=[100,154], s=6 when r2=[155,224], and s=7 when r2=[225,278]. In one embodiment, each multicast connection is set up through such a three-stage network by use of at most s middle stage switches.

Abstract: A three-stage network is operated in strictly nonblocking manner in accordance with the invention includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, where m≧2*n1+n2−1. In one embodiment, each multicast connection is set up through such a three-stage network by use of at most two switches in the middle stage. When the number of inlet links in each input switch n1 is equal to the number of outlet links in each output switch n2, and n1=n2=n, a three-stage network is operated in strictly nonblocking manner in accordance with the invention if m≧3*n−1.

Abstract: A rearrangeably nonblocking multicast network in accordance with the invention includes an input stage having r1 switches and n1 inlet links for each of r1 switches, an output stage having r2 switches and n2 outlet links for each of r2 switches. The network also has a middle stage of m switches, and each middle switch has at least one link connected to each input switch for a total of at least r1 first internal links and at least one link connected to each output switch for a total of at least r2 second internal links, where m≧n1+n2. The network has all multicast connections set up such that each multicast connection passes through at most two middle switches to be connected to the destination outlet links. When the number of inlet links in each input switch n1 is equal to the number of outlet links in each output switch n2, and n1=n2=n, a three-stage network is operated in rearrangeably nonblocking manner in accordance with the invention, where m≧2*n.