Where capacity binds — working trial 1.4

Job and preserved intention

Compare a baseline with a resource-specific renewal/capacity intervention. The local numerical version preserves separate passenger/freight demand and service, all resource constraints, commissioning delay, temporary restriction, investment stock/spend and an infrastructure-only cash account. Five resources provide a compact synthetic example; all coefficients and costs are invented. No scenario edits propagate to other apps.

Construction and equations

Each of up to 36 monthly steps represents an editable number of service hours at a continuous average rate. Demand grows as P(t)=P0(1+gP)^t and F(t)=F0(1+gF)^t. Each resource load is aP×P+aF×F. Its usable budget is max(0,(gross budget+commissioned addition)×availability−temporary restriction), in resource-minutes per representative hour. The common served fraction is min(1, usable/load for each positive load). No demand gives a fraction of one and zero served flows. Passenger and freight outputs remain separate.

Works run from start through start+delay−1; added budget and renewed availability apply at start+delay. Equal spend over works months reconciles to the stated total investment. Income is (served P × access £/P movement + served F × access £/F movement) × representative hours. Cash is income minus operating cost and capital spend. There is no ticket revenue, depreciation, discounting or official charging methodology.

Walkthrough and reference

Use Compare intervention to move the investment from Junction to Station. Inspect month shows why the unchanged junction still binds. Change delay or works restriction and inspect both service and money tables. Update resource changes an assumption in both baseline and trial. The shared shell resets inputs and recomputes the trajectory.

Opening baseline: P=4, F=1, Junction load=5×4+10×1=30, usable budget=30×0.8=24. Track load=4×4=16, budget=32. Other resources are nonbinding. Fraction=0.8; served P=3.2 and F=0.8. Raising a nonbinding resource alone has no service effect. With the default start 2 and delay 2, commissioning first occurs in month 4. £16,000 spending is £8,000 in each of months 2 and 3.

Checks and boundaries

node --test apps/rail-capacity-renewal/app.test.mjs runs five tests: independent reference/zero demand, nonbinding counterexample, delayed commissioning and resource/cash reconciliation, reset/determinism/atomic edit, and import/presentation failure handling. The model is deterministic; no stochastic inputs or seed controls are presented.

A resource-budget spreadsheet is the simpler comparator. This is a continuous teaching allocation, not a fair/optimal policy, timetable, engineering model, calibrated forecast or investment appraisal. A real application would need validated operating constraints, resource coefficients, financial boundaries and scenario data. No operational or investment use is claimed.