IB 100% Non Blocking FAT TREE Topology Inter Connect Architecture Formula

1)IB Non Blocking Mode: Source Ports has the dedicated Channel to the destination ports without looping.

2)IB Non Blocking is made through FAT Tree Topology.

FAT Tree Topology Is one of the method.

Using 36 Port IB Switch
SS	LS	Max No Connection (or) Ports	Dedicate Connectivity Between SS & LS
SS	LS=SS* 2	LS*18	Possibility=36/LS=0
2	4	72	9
3	6	108	6
4	8	144	4.5
5	10	180	3.6
6	12	216	3
7	14	252	2.57
8	16	288	2.25
9	18	324	2
10	20	360	1.8
11	22	396	1.64
12	24	432	1.5
13	26	468	1.38
14	28	504	1.29
16	32	576	1.13
17	34	612	1.06
18	36	648	1
19	38	684	0.95
NOTE 1 : SS – Spine Switch LS – Leaf Switch NOTE 2 : Possible IB Switch connectivity are made in the light YELLOW color

Depends on the Requirement and cost we can reduce the LS. For Example : customer expectation is 48 node connectivity (2*3)=54 is enough rather than going (2*4)=72 Connectivity we can reduce 1 Leaf switch. In that perspective
-->

SS	LS	Max No Connection (or) Ports	SS to LS Cables	Free Ports On the Spine Switches – Just for Info
SS	LS=SS* 2	LS*18	Possibility=36/LS=0
2	3	54	12	18
2	4	72	9	0
3	6	108	6	0
6	9	162	4	54
6	12	216	3	0
9	12	216	3	108
9	18	324	2	0
18	36	648	1	0

Using 32 Port IB Switch
SS	LS	Max No Connection (or) Ports	Dedicate Connectivity Between SS & LS
SS	LS=SS* 2	LS*16	Possibility=32/LS=0
2	4	64	8
3	6	96	5.33
4	8	128	4
5	10	160	3.2
6	12	192	2.67
7	14	224	2.29
8	16	256	2
9	18	288	1.78
10	20	320	1.6
11	22	352	1.45
12	24	384	1.33
13	26	416	1.23
14	28	448	1.14
16	32	512	1
17	34	544	0.94
18	36	576	0.89
19	38	608	0.84

To Obtain the 1944 Compute Nodes 100% non blocking Interconnect Architecture.

	Switch Type	Quantity	Formula
SPINE Switch	648 Port Switch 56 Gbps	3	3*648=1944
LEAF  Switch	36 Port Switch 56 Gbps	108	108*18=1944

 Note 1)Spine Switch all the ports(648 p) are connected to the Leaf switch.

Note 2)Leaf Switch half ports(18 p) are connected to the Spine switch remaining half ports(18 p) connected to the Compute nodes.