Change one thing.
Follow the effect.

The balancing principle is informed by grid-operation sources; all capacities are editorial teaching values. With demand of 140 and response capability of 20, supply is capped at 120 and 20 units remain unmatched. Raising the assumed response capability to 40 covers that demand. This changes a chosen limit, not a forecast of what real equipment can deliver.

• The baseline demand and scheduled supply are both 100 arbitrary power units, not measurements from a real system.
• Available upward response is a second control, ranging from 0 to 60 units with a starting value of 20. Supply is assumed able to reduce to match demand below 100 units.
• Scheduled supply = min(demand, 100 + available upward response). Unmatched demand = max(0, demand − scheduled supply). Available headroom = 100 + available upward response − scheduled supply.
• The result is a static balance after response. Network losses, location, ramp rates, stored-energy duration and contingency reserves are omitted. Changing the response control does not explain how that capability would be obtained.
• The model does not calculate frequency, blackout probability, cost or emissions. An uncovered shortfall means the chosen illustrative resources are insufficient, not that a particular real protection action will occur.

Model references: Australian Energy Market Operator: Guide to Frequency Control Ancillary Services · U.S. Environmental Protection Agency: Electricity Delivery and its Environmental Impacts · U.S. Energy Information Administration: Electricity glossary

Conservation of water connects inflow, outflow and the change in storage. At the starting demand of 100 m³/h, 600 m³ lasts six hours with no inflow. At 200 m³/h it lasts three hours. Pin a scenario before changing demand to compare these assumptions directly; neither result predicts service at a particular tap.

• The chosen starting usable storage is 600 m³. This is an editorial teaching value, not a measured or typical reservoir.
• Pump inflow is zero throughout the selected interval. Requested demand is constant within each scenario and can be set from 50 to 200 m³/h; its starting value is 100 m³/h.
• Remaining usable volume = max(0, 600 − demand × elapsed hours). Unmet volume = max(0, demand × elapsed hours − 600). Total storage duration = 600 / demand.
• Remaining volume buffer = max(0, 600 / demand − elapsed hours). No alternate supply, leakage, evaporation or changing demand is included.
• Storage is assumed deliverable until its usable volume reaches zero. Real pressure can become inadequate before a tank is empty. No water-quality or pressure calculation is performed.
• The references explain real storage, pumping and pressure dependencies. The selected values and calculated durations are original illustrative arithmetic, not operational standards.

Model references: Sydney Water: Water System Planning Guideline · US Environmental Protection Agency: How to Conduct a Sanitary Survey of Drinking Water Systems · US Environmental Protection Agency: Protecting Water Quality Through Distribution System Pressure Management

Routing references explain how an alternative can be selected; delay measurements are a different question from reachability. Here the selected path has an assigned one-way delay: 20 ms through B, or the chosen delay through C after failure. The model does not derive latency from distance, measure bandwidth or calculate page-load time.

• The topology is invented: path A → B → D is preferred and A → C → D is available as an alternative. It does not represent providers, locations or actual links.
• The first control changes link A–B from available to failed. All other links and both endpoints remain available.
• After failure, routing is assumed to have converged to an allowed alternate route with sufficient capacity. Detection time, convergence, packet loss, queues and transport recovery are omitted.
• The preferred path is assigned an illustrative one-way delay of 20 ms. The alternate path delay is a second control from 20 to 120 ms, starting at 40 ms. These are editorial values, not measurements or a geographic estimate.
• The alternate-delay control affects the selected path only when A–B has failed. Real routing follows protocols and policy rather than necessarily choosing the lowest-delay path.
• A surviving path means reachability under these assumptions. It does not guarantee seamless recovery, application performance or independence from shared physical dependencies.

Model references: IETF / RFC Editor; F. Baker (editor): RFC 1812: Requirements for IP Version 4 Routers · IETF / RFC Editor; Y. Rekhter, T. Li, and S. Hares (editors): RFC 4271: A Border Gateway Protocol 4 (BGP-4) · IETF / RFC Editor; W. Eddy (editor): RFC 9293: Transmission Control Protocol (TCP) · Internet Society: The Internet Way of Networking: Defining the critical properties of the Internet · IETF / RFC Editor; G. Almes, S. Kalidindi, and M. Zekauskas: RFC 2681: A Round-trip Delay Metric for IPPM

At the starting planned interval of 120 seconds, 15 extra seconds make the station occupation 105 seconds and leave 15 seconds of margin. With 45 extra seconds, occupation is 135 seconds and the implied rate is about 26.7 trains per hour. Changing the planned interval changes the comparison; it does not establish an achievable timetable for a real railway.

• This is an original steady-state teaching model of repeated longer stops, not a simulation of one delayed train or a real timetable.
• The planned interval is a second control, from 90 to 180 seconds with a starting value of 120 seconds. A 120-second interval is equivalent to 30 trains per hour if sustained.
• The chosen baseline station occupation is 90 seconds, including the relevant occupation and clearance effects. All other constraints remain fixed.
• Effective headway = max(planned interval, 90 + extra dwell), in seconds. Illustrative sustained throughput = 3600 / effective headway.
• Remaining margin = max(0, planned interval − 90 − extra dwell). A shorter planned interval can offer more trains per hour while leaving less margin at this bottleneck.
• No passenger-crowding feedback, variable braking, junction conflict, turnback, fleet or recovery behaviour is simulated. Actual railway analysis requires these and other details.

Model references: Transportation Research Board / National Academies: Transit Capacity and Quality of Service Manual, Third Edition, Chapter 8: Rail Transit Capacity · National Academies of Sciences, Engineering, and Medicine / Transportation Research Board: Transit Capacity and Quality of Service Manual, Fourth Edition · Network Rail: The timetable