Write QPS: million/month ÷ million seconds ≈ writes/sec. Peak: /sec.
Read QPS: billion/month ÷ million seconds ≈ reads/sec. Peak: /sec.
Storage: Each URL mapping is ~ bytes. million × bytes = GB/month. years = TB.
Short URL length: How many characters for million URLs? Using base62 (a-z, A-Z, -), = billion. characters is plenty with room to grow.
Notice: This is read-heavy. Optimize for reads.