What if the key to profitable public transit was a simple saturation index?

Imagine small automated pods zipping along elevated tracks, taking you straight to your destination with no intermediate stops. That's the promise of PRT (Personal Rapid Transit) and GRT (Group Rapid Transit): eco-friendly systems designed to lure drivers out of their cars. But how do you know if such a project makes economic sense before spending billions?

A study published in *Future Transportation* offers an elegant answer: the "peak hour network saturation" index (S). Simply put, S measures how many vehicles actually circulate during rush hour compared to the theoretical maximum if they all traveled at top speed with minimum safe headways.

The brilliance lies in S condensing the biggest unknown—real demand versus supply—into a single number. Even without detailed ridership forecasts, a maximum S can be estimated. From there, an analytical formula derives profit per trip using fares, capital and maintenance costs, daily demand curves, empty vehicle share, and physical system properties.

The results? A PRT with distance-based fares turns profitable at just S > 0.25. Economic resilience improves dramatically with vehicle platooning or by adding higher-capacity GRT vehicles during peak hours. This means doubling or tripling infrastructure costs doesn't sink the project. A new tool for bold planners wanting lighter, more connected cities.

The parametric cost modeling framework introduced in the study enables rapid, transparent sensitivity analyses. The key variable, S (peak hour network saturation), is defined as the ratio of actual peak hour vehicle flow (veh/h) to theoretical line capacity (veh/h), the latter calculated as the inverse of the minimum safe headway multiplied by the number of guideways.

Profit per trip (π) is analytically derived as a function of S and certain parameters: average fare (f), annualized capital cost per vehicle-km (c_cap), operating cost per vehicle-km (c_op), empty vehicle share (ε), and daily demand profile (peak factor k). The formula π = f * (1 - ε) * g(S) - (c_cap + c_op) * h(S) highlights the non-linear dependence of profitability on saturation.

Application to three configurations — single-vehicle PRT, platooned PRT (virtual convoys with 0.5-1s headway via V2V), and mixed PRT/GRT — shows platooning shifts the break-even curve to lower S and flattens sensitivity to infrastructure costs (CAPEX). In tripled CAPEX scenarios, single PRT fails (π < 0 for S < 0.6), while platooning and GRT mix maintain π > 0 for S > 0.3-0.35. This proves operational efficiency (headway, load factor) is a more powerful lever than civil cost containment for economic viability.