How do you route agent requests when model capability, policy, cost, and latency conflict?

An agent request may require tool calls or structured output, but available models can differ in capability, cost, and latency. Would you first apply hard eligibility checks for capability and policy, then optimize cost or latency across the remaining models? Or combine the signals in one weighted routing score? For dynamic routing, what prevents provider latency shifts from causing route flapping? Do you use a rolling window, hysteresis/cooldown, or an evaluation gate? What trade-offs have you seen in production? Disclosure: I work with nRouter on multi-model routing. I’m asking about design approaches; there is no product link.