Nicolas Joseph

Nicolas Joseph

CTO / Entrepreneur

// ROOT/LOGS/2016-05-02// LOG ENTRY

> Cross Bar and Clos Network _

A visual explanation of why simple crossbar switches stop scaling and how Clos networks add stages to recover flexibility and non-blocking paths.

// Archived NoteAuthor // Nicolas Joseph

Network diagrams often look like a chaotic web of machines and links, but real switching systems are designed around repeatable topologies. This post starts with the basic crossbar switch and then shows why Clos networks are the scalable answer when the number of connections gets large.

Start With The Switch

At first glance, the Internet looks like a random mesh of computers connected to one another.

But that view hides the important hardware in the middle. In practice, machines are not all wired directly to one another. They are connected through intermediate devices such as routers and switches.

An old telephone operator is a useful analogy: you make a request, the operator connects your line to the destination, and the switchboard becomes the place where paths are created.

That is the piece we care about in this article: the switch, or more precisely the topology that lets many inputs reach many outputs.

Crossbar Networks

Why People Start With Crossbars

Crossbars are one of the simplest ways to connect two arrays of devices so that every input can reach every output. A good way to visualize that is as a road grid connecting two towns on one side to two towns on the other.

The highway version and the wiring version are the same pattern. The roads become wires, and the red highway interchanges become switching points in the electronic system.

Where Crossbars Break Down

The downside is cost. As the number of inputs and outputs grows, the number of switching points and connections grows quickly too. A pure crossbar becomes expensive to build and hard to scale.

That is the problem Clos networks are designed to solve.

Clos Networks

First Attempt: One Operator Board

Clos networks are built from crossbar-like stages. Start with the telephone operator analogy again: one operator board receives incoming calls and connects them to the requested outgoing lines.

That works at small scale, but a single operator becomes a bottleneck if too many calls arrive.

Second Attempt: More Operators

The first fix is to multiply the number of operators so the traffic can be shared.

That solves the capacity problem but introduces a routing problem: each incoming line and outgoing line is now tied to a particular operator board, so some pairs still cannot reach each other.

Third Attempt: Add Another Stage

To fix that limitation, add a second stage between ingress and egress operators.

Now every ingress can reach every egress, but the design is still fragile. If two callers share the same ingress operator and both need the same egress operator, they contend for the single path between those two stages.

Final Topology: Clos

Adding a middle stage solves that last structural weakness.

Now each ingress connects to every middle-stage operator, and each egress does the same. Instead of having one fixed path between ingress and egress, the network has multiple possible routes. The number of alternative paths is exactly the number of operators in the middle layer.

The point of the Clos design is not just "more switches." It is giving the network enough alternate middle paths that new connections can still be routed when traffic gets crowded.

Non-Blocking Properties

Once you can vary the number of middle-stage operators, the topology gets interesting. Let mm be the number of operators in the middle layer and nn the number of lines that need to be connected.

If m≥2n−1m ≥ 2n−1 the network is strictly non-blocking. Any new incoming call can be connected to an unused line without rearranging calls that are already in progress.

If the verified property is m ≥ n, then every incoming call can be connected to a free line but we may have to rearrange existing connections in the network to connect people through.

For sufficiently large systems, a Clos network is also cheaper to build than one giant crossbar, even though each stage is still composed of smaller crossbar-like elements.

Reference