If I were doing this, I would be looking at data warehousing systems. 1.7PB of, say, Parquet files in S3 is not terribly expensive. 1.7PB of Parquet files in on-prem or collocated object storage, even replicated a zillion times, is quite cheap. And quite a few companies and open-source projects are currently competing aggressively to provide awesome tools for querying that data.
The hot data would fit on basically anything — the choice should be about robustness and barely even consider cost per TiB. Datomic got written up recently and seems credible for this type of application. FoundationDB is bulletproof. Postgres could probably handle it without breaking a sweat, although active/active replication isn’t free. Heck, writes straight to a warehouse with a cache in front to help with reads seems credible — Uber rides rarely go for longer than a couple hours, and back-of-the-envelope math suggests that the total data rate is maybe 50GB/hour. An entire day of data for an entire country would fit on a single very ordinary commodity server, and the live data for the entire world would fit on one mildly beefy server. The indexes involved sound straightforward.