Plauti Assign automatically attempts assignment if all your assignees are unavailable. This article goes into detail about how Plauti Assign does this.

Assignees can be unavailable for a number of reasons: they might be Out of Office, Out of Hours, Inactive, At Capacity or Unlicensed. If all the Assignees in a Match Group are unavailable, then Plauti Assign has nobody to assign the record to. In this situation, the record is temporarily assigned to the Queue User specified on the Match Group:

The Queue User can be changed on the Match Group's Settings subtab.

This Queue User doesn't have anything to do with Salesforce Queues. The Queue User above is simply a user that the record is 'parked' with until it gets assigned to one of the designated Assignees. As such it is a good idea if the person you set as the Queue User is not normally dealing with these records on a day to day basis. It can be a system administrator account, or team manager etc.

PA Automatically Attempts Assignment

On the Assign Setup tab, in Jobs & Maintenance, there is a button labeled 'Create Jobs'. This should be pressed once during initial setup of Plauti Assign, to initialize the scheduled jobs that do the automatic assignments. The only purpose of these jobs is to query Salesforce for QUEUED records, and run them through Plauti Assign rules to attempt assignment. This job runs every 10 minutes once set up.

By default these jobs will query the oldest 50 QUEUED records for each object you use Plauti Assign for. This is called the Batch Size: the number of queued records per ObjectType, per Job. So if you have Match Groups for Leads and Opportunities, and the batch size is set to 50, it will select the top 50 queued Leads and the top 50 queued Opportunities in a single scheduled job run. 
Whether these are the 50 oldest or newest records depends on your set value for ‘Sort Order for Queued Records’ in the Settings in Assign Setup; the default is oldest.

Changing The Batch Size

You may want to increase or decrease this number. For example if you receive many hundreds of leads over the weekend you may want to increase this to 200; or it might be that you use High Velocity Sales and you are hitting the 'You can only add 20 targets to a Sales Cadence at once' error - so you'll want to set the batch size to 20 or less.

To change the batch size:

1. In Plauti Assign, go to Assign Setup > Settings
2. At right, click Configure
3. At Batch Size, change the number to the desired value
4. Save

Setting the value to 0 will effectively stop the job from querying and processing any QUEUED records. For clarity we recommend not doing this, but instead use Pause Assignment if you want to temporarily halt the processing of QUEUED records.

Be aware that increasing the batch size to a high number (thousands) will consume more resources, and depending on the level of automation against your records upon update, this may cause the job to fail. Remember this job runs every 10 minutes, so if you can reduce this number and allow the QUEUED records to be processed over a period of time this will have less impact on resource usage.