How can I see how busy the cluster is?

You can get the current status of all nodes on a cluster using the command sinfo, you will get a printout like the following.

$ sinfo
PARTITION AVAIL JOB_SIZE  TIMELIMIT   CPUS  S:C:T   NODES STATE      NODELIST
compute*  up    1-infini 14-00:00:0    256 2:64:2       1 down*      compute-5
compute*  up    1-infini 14-00:00:0    256 2:64:2       4 mixed      compute-[0-2,4]
compute*  up    1-infini 14-00:00:0    256 2:64:2       1 idle       compute-3
gpu       up    1-infini 14-00:00:0     96 2:24:2       1 idle       gpu-0
hugemem   up    1-infini 14-00:00:0    256 2:64:2       1 mixed      hugemem-1
hugemem   up    1-infini 14-00:00:0    256 2:64:2       1 idle       hugemem-0
interacti up    1-infini 60-00:00:0      8  8:1:1       3 idle       interactive-[0-2]
vgpu      up    1-infini 60-00:00:0     32 32:1:1       2 drained    vgpu-[0-1]
vgpu      up    1-infini 60-00:00:0     32 32:1:1       1 allocated  vgpu-2
vgpu      up    1-infini 60-00:00:0     32 32:1:1       1 idle       vgpu-3

Each partition has a row for every state it's nodes are currently in.

For example, the compute partition currently has  1 down node, 4 mixed nodes,  no allocated nodes and  0 idle nodes.

The most common node states you are likely to see are:

State	Description
idle	All CPUs on this node are unallocated and available for use.
allocated	All CPUs on this node are currently allocated.
mixed	Some CPUs on this node are unallocated, smaller jobs are likely to land here.
down	The node is unavailable for use
reserved	This node has been reserved, and is only available for some users (in the case of the igpu partition, please contact NeSI support if you wish to use it).
draining	Jobs are currently running on this node, but is not available for new jobs.

A full list of node states can be found here.

If you are interested in the state of one partition in particular you may want to use the command squeue -p <partition> to get the current queue of the partition <partition>.