Systems Economics • CostGuard

The Mathematics of
$0.00 Guaranteed Cloud Spend

By combining sliding-window quota rate-limiters with multi-candidate free-tier routing across Google AI Studio's Gemma 4 and Gemini 3.5 architectures, Ishita operates 24/7 without incurring a single dollar of cloud charges.

$0.00

Guaranteed Monthly Spend

14,400

Daily Gemma 4 Quota (RPD)

250,000

Context Window Tokens (TPM)

1,000

Daily Vector Embeddings

Live Simulation Tool

Interactive Quota & Cost Calculator

Adjust the projected daily volume of Instagram messages, multimodal reel analyses, and vector recall queries to verify that the zero-dollar cost invariant remains inviolable.

Daily Direct Messages (DMs): 4,500 msgs/day

0 Gemma 4 Free Cap: 14,400 RPD 20,000

Multimodal Reel & Photo QA: 150 reels/day

0 Gemini 3.5 Flash Lite Free Cap: 500 RPD 1,000

Semantic Memory Vector Searches: 400 queries/day

0 Embedding 2 Free Cap: 1,000 RPD 2,000

Calculated Infrastructure Status

Total Estimated Cloud Spend:

$0.0000 USD

Strict Free-Only Mode Enforced

Gemma 4 26B Load: 31.2% (4,500 / 14,400)

Gemini 3.5 Vision Load: 30.0% (150 / 500)

Embedding 2 Load: 40.0% (400 / 1,000)

Algorithmic Formulation

Dual Sliding-Window Quota Tracking

Google AI Studio enforces limits on two distinct horizons: Requests Per Minute (RPM) and Requests Per Day (RPD). We implement continuous atomic token buckets in Python:

Sliding-Window Equations

Incoming queries are recorded in timestamps list $T_m$. Any query older than the window is evicted with $O(\log N)$ bisect search:

N_{60s}(m, t) = |\{ \tau \in T_m \mid t - 60 \le \tau \le t \}| \le RPM(m)
N_{24h}(m, t) = |\{ \tau \in T_m \mid t - 86400 \le \tau \le t \}| \le RPD(m)

Automatic Failover Tree

When primary chat capacity exceeds 90% of RPD, the router transitions dynamically:

Primary: Gemma 4 26B (14.4K RPD)
Failover: Gemma 4 31B (14.4K RPD)
Emergency: Gemini 3.1 Flash Lite (500 RPD)
Total Daily Capacity: 29,300 Free Requests
            

The Mathematics of$0.00 Guaranteed Cloud Spend