Sparse-traffic model serving platform

Design a multi-tenant model-hosting platform (think 'serverless inference') where thousands of customers each deploy their own custom models, most of which receive sparse, bursty traffic, many models get a request once an hour, a few get thousands per second. You can't keep every model loaded on a GPU (too expensive), but cold-starting a model takes 5-30 seconds. Design the system to serve this long-tail traffic cost-efficiently while keeping cold-start pain acceptable.