MSPs typically dispatch tickets through queue, schedule, pod, board, or first-call resolution after triage. Triage should take 10-15 minutes; anything longer signals workflow problems like overly complex processes or client confusion about service expectations.
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Most MSPs will move a ticket to triage into some form of a dispatch process next, where they decide who works the ticket in what order. This could be a queue, this could be a schedule, this could be a pod, could be a board, could be a first call resolution. It is generally accepted the triage process should be a quick process, and I like to advocate that the whole thing needs to take less than 15 minutes. The shorter the better. Many MSPs are able to triage a ticket in under 10 to 12 minutes, just to give you an idea. But I think if you're under 15 minutes, you are in a reasonable area. If triage is taking more time than that, something else is broken, and you're either doing more than just triage or MSP, or your clients are in a position where they don't understand what they're consuming from you, and this process is just taking too long.