Clos fabrics and a declared bisection

Use the conventional three-stage k-ary fat-tree construction with even k and identical k-port switches. There are k pods, each containing k/2 edge switches and k/2 aggregation switches. Every edge switch uses k/2 ports for hosts and k/2 for aggregation links. The core contains (k/2)² switches. All links in this declared construction have the same full-duplex line rate; other designs called Clos may use different radix, speeds, or oversubscription.

Each aggregation switch connects to the appropriate core group, providing multiple equal-length paths between pods. Count endpoints separately from switch ports: every inter-switch cable consumes a port at both ends, while a host-facing cable consumes one switch port. Adding host ports without matching upstream capacity changes the design's oversubscription. Real deployments may reserve ports, combine switch roles, or use breakout links, so validate the bill of materials rather than extrapolating directly from the ideal construction.

Split the hosts into equal halves and consider traffic sent from one half to the other. With H hosts each attached at rate r, their total offered rate cannot exceed Hr/2 in that direction. A nonoversubscribed construction has enough ideal cut capacity to support full host injection for suitable admissible traffic and routing. Summing both directions gives a different number. Always specify whether a vendor's aggregate figure counts transmit and receive together.

Capacity is a necessary resource budget, not proof that a collection of flows will realize it. Flow hashing can concentrate large flows, individual destinations can receive more than their access links support, and failures remove paths. A permutation with each host sending to one distinct destination differs from many senders converging on one receiver. Define admissibility at ingress, egress, and internal cuts before comparing a workload with a full-bisection claim.

Map training ranks and storage clients onto the topology, then estimate which stage carries their synchronized transfers. An intra-node operation may never use an external fabric link, while an all-to-all across pods can stress several cuts. Compare endpoint injection, rack uplinks, and cross-pod capacity separately. A test that reaches one host's line rate cannot establish bisection capacity, and a random traffic average can hide a consistently overloaded placement.

The queue lab is an abstract rate-budget exercise. Reset and set both λ=4 and μ=2, predict growth from four jobs, then Step. Reset again and set λ=2 and μ=4 before predicting decline and stepping. This illustrates offered demand exceeding a service budget, not Clos routing, packet buffers, or bit-rate conversion. Editing controls recomputes the whole trajectory at retained time; Reset makes the comparisons independent. The separately labeled stochastic waiting-time formula has additional assumptions.