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What do the Number of Messages and Max Threads settings do in Portrait Dialogue Output Channel Properties

Product Feature: Channel Types
 
These "Output Channel" settings control the send service, for the actual transmission of the messages to the designated back end system (i.e. an smtp server).

"Number or messages to send per transaction"
Once messages have been merged and sent to the Outbox or the Send Queue, the next step, as in your example, is to actually send them to the smtp server. 
This setting configures how many messages get sent at once, in each batch, to the smtp server. 
This should be set based on the constraints and/or robustness of your smtp server. 
By default, email messages will be sent to the smtp server in batches of 100.

"Max number of threads used to send messages" 
Similarly, depending on your output channel, smtp for example, your provider may allow multiple connections when sending messages. 
This setting depends of the smtp provider. 
By default the mas threads is set to 8. 
In this scenario, it is possible that 8 batches of 100 messages will be sent to your smtp server simultaneously.  

In both cases, if your provider can process more, or is not able to process this much, you should modify these settings accordingly. 
The exact same scenario applies to any output channel, SMS, Print, Fax, etc.  
 
UPDATED:  December 13, 2017