My process is triggered by external applications. Can I define the maximum numbe

Try to create a report that shows the number of running instances and check this when starting the process. If the number is too high, go to an end node.

Thanks Shelzie, but this solution doesn't work for us.
Because it is an external request I must execute the process, I can’t skip to the end node. I wish, if limit was reached, the solicitation stay on standby.

OK. You want to block your external application. Right ?
You could use a SQL DB to save the number of running instances and use this value from the external application. Or you can build a queue in the external application and call a webservice (in external app) at the end of the process that tells the external application to trigger the next process.

I was looking something out of the box. Thanks

The process triggered by the external application could simply update a queue table in a database. Then you could have another process that would periodically check that table for new records and only start if there are new records.

As far as I can say there no OOTB solution for this case. But building some process models to solve this is kind of OOTB as this is the way to build things in Appian.

I had to build a message queuing mechanism to ensure that messages are processes by the target process in the same order as they were created. A small model "queue item" checks periodically whether it is the first item in the queue and sends the message to the target process. The target process sends a confirmation message back as soon as it processed it and the queue item completes.