Azure Service Bus Limit Azure Function

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We have the following architecture:

  • When a file is inserted into the blob storage the event grid call an Azure Function
  • The Azure Function read the file and insert a message into the service bus with meta information
  • An App Service is processing those Service Bus messages later.

But sometimes we have too much file add events at once and we reach the limit of insertion in the service bus so we would like to limit the number of Azure Function that could be created. Do we have a way to limit it or maybe limit the rate of the event grid trigger?

Regards,

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