The default is unfair and inefficient
Without a defined ladder, escalation happens when a customer becomes angry enough or knows somebody senior. This punishes patient customers, rewards aggressive ones, and gives managers no early warning at all.
Build the ladder first
Agent, then team lead, then department head, with a defined interval at each step and a defined trigger — time without a reply, or breach of target. Publish it internally so nobody is ambushed by an escalation notice.
Separate escalation from reassignment
Reassignment is routine: right queue, wrong hands. Escalation is exceptional: more authority or more skill required. Conflating them fills your escalation report with noise and hides the cases that matter.
Escalate before the breach, not after
A notification at 80% of the target gives somebody a chance to prevent the failure. A notification at breach is a report, not a control.
Review what escalated
Monthly, look at what escalated and why. A recurring pattern usually points at a training gap, a permission that should have been granted, or a product problem that support is absorbing.