Equation 1 · AI Datacenter Interconnects in Practice: An Advanced Technical Guide
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol mu
mu is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol s
s is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
See an illustrated explanation →How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
NCCLGO and NCCROTO select which collective algorithm and wire protocol a given operation uses; NCCCA filters which InfiniBand host channel adapters, ports and rails are eligible for a job, in a format that can descend to individual rail and plane; NCCOCKEFNAME performs the equivalent filtering for the out-of-band control interfaces [ 1 ] . On the InfiniBand transport specifically, NCCIMEOUT sets the retransmission timeout as 4.096\ s 2^{} , with the library’s own default raised to 20 as of version 2.23, and NCCETRNT defaults to seven retry attempts before a queue pair gives up [ 1 ] — both are tuned upward on fabrics with longer…
Read the full surrounding passage
NCCLGO and NCCROTO select which collective algorithm and wire protocol a given operation uses; NCCCA filters which InfiniBand host channel adapters, ports and rails are eligible for a job, in a format that can descend to individual rail and plane; NCCOCKEFNAME performs the equivalent filtering for the out-of-band control interfaces [ 1 ] . On the InfiniBand transport specifically, NCCIMEOUT sets the retransmission timeout as 4.096\ s 2^{} , with the library’s own default raised to 20 as of version 2.23, and NCCETRNT defaults to seven retry attempts before a queue pair gives up [ 1 ] — both are tuned upward on fabrics with longer queueing or higher loss, and tuned down when a practitioner wants failures to surface quickly rather than be masked by retries. NCCEDEVEL governs how aggressively GPUDirect RDMA is used for a given GPU-to-NIC distance, expressed as PCIe topology levels from same-device ( LOC ) out to crossing a NUMA boundary ( SYS ) [ 1 ] , and it interacts directly with GPUDirect RDMA’s own hard requirement that the GPU and the network adapter share a PCIe root complex for the peer-to-peer path to work at all [ 3 ] . A GDR level set too permissively on a server whose GPU and NIC sit behind different root complexes does not fail loudly; it silently falls back to a slower path, and the first symptom an operator sees is a bandwidth number that looks wrong without an accompanying error.
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
Return to AI Datacenter Interconnects in Practice: An Advanced Technical Guide