In my opinion, after experimenting with different solutions, the best way to handle this is by segmenting conversations into buckets (types of issues), applying a priority level to each bucket and ensuring that the oldest conversations in each bucket are handled first. This ensures that the most important issues are handled first and the people waiting the longest are given priority.

Generally as part of a request triage process I recommend reviewing the client's stated impact to their business. If its an end user perhaps its how many users are experiencing the same issue. Then I take those most critical issues and work them hopefully leveraging knowledge already available. Once those are resolved, I would work from "smallest" to "largest" based off the effort needed of the ask. If I'm in a situation with a backlog of items some of which have been opened for weeks those "Big asks" may need to wait till we clear the backlog OR if possible go to a sales team to be turned into an intake item. Of course you must set expectations with the client.

Prioritise based on urgency. The most important ones first, moderate ones, and then those which are of lesser importance. There is another factor that needs to be considered, which is whether the customer queries are over calls, or emails? If they are calls, you have no options of prioritising and handle each query one after the other. On emails you can flag them as "high", "medium" and "low" and resolve them systematically. Additionally, remember the email TAT (Turn Around Time) as most companies have a 24 hour first response policy. Naturally, the email TAT is applicable for the "medium" and "low' priority queries. I hope that makes sense.

Categorize Requests: Use a system to classify inquiries by type (e.g., billing, technical support) to streamline responses. Assess Urgency: Assign urgency levels to the inquiries like high, medium, low—to focus on critical issues first, particularly those affecting product usability. Automate Workflows: Utilize automation to assign tasks to appropriate teams, ensuring prompt timely responses. Monitor Performance: analyze ticket resolution metrics to identify roadblocks and improve response strategies.

To efficiently prioritize urgent customer inquiries: Evaluate: Quickly assess each inquiry's urgency and impact. Categorize: Sort inquiries into categories and prioritize by urgency. Triage: Address critical issues first that affect service or cause major dissatisfaction. Set Response Times: Establish clear response times for different priorities. Use Templates: Apply response templates for common issues to save time. Delegate: Distribute tasks based on team expertise and workload. Track: Monitor inquiry status and follow up as needed. Communicate: Keep customers informed about their inquiry status and resolution time.

It's important to let them know you understand their inquirie and give them an estimate return time. Be transparent of how other inquiries could influence their case and keep the conversation clear.