What does this equation mean?

Self-hosting is the limiting case, where the commitment term is effectively indefinite and the fixed cost is capital and operating expense rather than an hourly rate — and it inherits the identical discipline. The serving-stack parameters covered earlier are the mechanism by which a fixed hardware footprint’s effective $Q_{\max}$ is set: vLLM’s guidance that gp$u_m$emor$y_u$tilization , ma$x_n$u$m_b$atche$d_t$okens , and ma$x_n$u$m_s$eqs are the highest-impact throughput knobs [ 17 ] , and Mooncake’s demonstration that disaggregating the KV-cache tier can shift throughput by a reported multiple in specific scenarios [ 15 ] , are the difference between a fleet’s real utilization ceiling and the number on a spec sheet. Evaluating self-hosting against a vendor’s on-demand rate without first establishing what the hardware can do compares a vendor’s optimized number against an unoptimized one, and will reliably conclude self-hosting costs more than it needs to.