Routing page: adopt shared cost engine with cached token pricing

[aditisaluja5]

Problem

The routing economics page (lib/routing/calc.ts) uses a naive cost calculation for frontier API pricing:

cost = (tokensIn / 1M) × pricePerMInput + (tokensOut / 1M) × pricePerMOutput

This overstates frontier API cost because it ignores cached token discounts. Cloud APIs (OpenAI, Anthropic, Google) charge ~50% less for recently-seen input tokens. Without modeling this, the self-hosted savings shown on the routing page are inflated.

What needs to change

1. Use the shared cost engine being built in Cost comparison: self-hosted on-prem vs cloud API cost per million tokens #10. That engine implements the blended cost model:

   • Input tokens (full price)
   • Cached input tokens (~50% discount, based on cache hit rate)
   • Output tokens
   • Breakeven utilization curve (self-hosted GPUs aren't always at 100%)

2. Add pricePerMCached to FrontierModel interface — currently only has pricePerMInput and pricePerMOutput. Needs a third field for cached input token pricing.

3. Add cache hit rate input per tier — the routing page lets you configure tokens in/out per tier, but has no cache hit rate slider. Different tiers will have different cache rates (e.g., RAG/doc processing = high cache, conversational = low).

4. Add utilization modeling — current self-hosted calc assumes GPUs run 24/7 at full capacity. In reality, utilization varies. The standalone calculator models the breakeven utilization % where self-hosting becomes cheaper.

Context

• Standalone cost calculator with cached token blending: https://openshift-psap.github.io/self-hosted-llm-cost-calculator/
• Issue Cost comparison: self-hosted on-prem vs cloud API cost per million tokens #10 covers building the cost comparison engine with this logic
• This issue is about wiring that engine into the existing routing economics page so both tools use the same accurate cost model
• Team identified per-use-case token ratios and cache expiry as key refinements

Current routing calc location

• lib/routing/calc.ts — computeFrontierCost() and computeSelfHostedCost()
• lib/pricing/frontier-models.ts — model pricing catalog (needs pricePerMCached field)

Blocked by

• Cost comparison: self-hosted on-prem vs cloud API cost per million tokens #10 (shared cost engine must be built first)
• Parent: Cost experience: unified cost views for sizing-to-economics flow #13 (cost experience umbrella)