Azure Functions - Limiting parallel execution

There isn't a way to specify a maximum concurrency for Event Hubs triggered functions, but you can control batch size and fetching options as described here.

The maximum number of concurrent invocations may also vary depending on your workload and resource utilization.

If concurrency limits are needed, this is (currently) something you'd need to handle, and the following posts discuss some patterns you may find useful:

Throttling Azure Storage Queue processing in Azure Function App

Limiting the number of concurrent jobs on Azure Functions queue

Just for reference, I came across here in my search for throttling. You can use the [Singleton] attribute on your function ensuring only one-at-a-time execution. Maybe not really what you were looking for and a very rigorous way of throttling, but still, it is an option.

https://docs.microsoft.com/en-us/azure/app-service/webjobs-sdk-how-to#singleton-attribute

Microsoft has added a new setting which can be used to limit concurrency of function execution. The setting is WEBSITE_MAX_DYNAMIC_APPLICATION_SCALE_OUT and can be used to limit how many function instances will execute in parallel. However, according to Microsoft, it isn't fully implemented yet.

https://github.com/Azure/azure-functions-host/wiki/Configuration-Settings