Jira provides a good support for querying issues by their SLAs. There are also more advanced and very useful processes that you can set up with the help of JQL Search Extensions.
Find Jira issues that are awaiting response
Special issue status: Waiting for customer
You are in the simplest situation if your workflow has a special issue type to which issues are moved when they are waiting for the customer response. JSD administrators usually set up automation rules that transition issues to Waiting for customer status whenever an operator adds a comment.
You can simply search for issues in the Waiting for customer status:
project="JQL Search Extensions" AND issuetype="Waiting for customer"
Last commented by operator
Alternatively, you can search for issues that were last commented by an operator. We assume it’s the customer’s turn to respond:
commentLastCreatedBy in membersof(jsd-operators-staff) AND resolution is EMPTY
Time since last commented
You can also identify the tickets that nobody commented on for a while. To find issues that were last commented on over 3 days ago:
commentLastCreatedOnDate < -3d
And to find the issues that require the operator’s attention:
commentLastCreatedOnDate < -1d AND commentLastCreatedBy not in membersof(jsd-operators-staff) AND resolution is EMPTY
In the above query, the last comment was created by a customer because they are not in the jse-operator-staff user group.