I have found this on the rabbitmq website it is near the bottom so I have quoted the relevant part below.
The tl;dr version is that you should have 1 connection per application and 1 channel per thread. Hope that helps.
Connections
AMQP connections are typically long-lived. AMQP is an application
level protocol that uses TCP for reliable delivery. AMQP connections
use authentication and can be protected using TLS (SSL). When an
application no longer needs to be connected to an AMQP broker, it
should gracefully close the AMQP connection instead of abruptly
closing the underlying TCP connection.
Channels
Some applications need multiple connections to an AMQP broker.
However, it is undesirable to keep many TCP connections open at the
same time because doing so consumes system resources and makes it more
difficult to configure firewalls. AMQP 0-9-1 connections are
multiplexed with channels that can be thought of as "lightweight
connections that share a single TCP connection".
For applications that use multiple threads/processes for processing,
it is very common to open a new channel per thread/process and not
share channels between them.
Communication on a particular channel is completely separate from
communication on another channel, therefore every AMQP method also
carries a channel number that clients use to figure out which channel
the method is for (and thus, which event handler needs to be invoked,
for example).
It is advised that there is 1 channel per thread, even though they are thread safe, so you could have multiple threads sending through one channel. In terms of your application I would suggest that you stick with 1 channel per thread though.
Additionally it is advised to only have 1 consumer per channel.
These are only guidelines so you will have to do some testing to see what works best for you.
This thread has some insights here and here.
Despite all these guidelines this post suggests that it will most likely not affect performance by having multiple connections. Though it is not specific whether it is talking about client side or server(rabbitmq) side. With the one point that it will of course use more systems resources with more connections. If this is not a problem and you wish to have more throughput it may indeed be better to have multiple connections as this post suggests multiple connections will allow you more throughput. The reason seems to be that even if there are multiple channels only one message goes through the connection at one time. Therefore a large message will block the whole connection or many unimportant messages on one channel may block an important message on the same connection but a different channel. Again resources are an issue. If you are using up all the bandwidth with one connection then adding an additional connection will have no increase performance over having two channels on the one connection. Also each connection will use more memory, cpu and filehandles, but that may well not be a concern though might be an issue when scaling.
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