Isochrone service

Design an isochrone service that answers 'what area can I reach within 15 minutes by car (or walking, or transit) from this point, given current traffic?' Used for store-coverage analysis, real-estate search, and 'restaurants reachable in 20 min'. It must handle arbitrary origin points, multiple travel modes, live traffic, and return a polygon in <500ms, at thousands of requests/second. Describe the graph traversal that computes reachability, how you turn reached nodes into a polygon, the live-traffic and multi-mode handling, and the precompute vs on-the-fly trade-off.