Public transport, walking, cycling and inclusive networks

Follow the whole route

A network needs continuous usable connections, not merely isolated pieces of good infrastructure. A barrier at one crossing or entrance can interrupt a complete journey. Different people experience distance, slopes, surfaces, information and boarding conditions differently; a single average journey does not establish inclusion.

The U.S. Access Board’s route guidance provides one named framework for thinking about connecting elements. Its legal and dimensional requirements are jurisdiction-specific. Here the transferable question is continuity: identify the complete path and the places where its user requirements change.

Distinguish frequency from regularity

Headway is the time between successive departures or arrivals at a stated point. Frequency is departures per time interval. A service can have the same average frequency but different gaps, making its passenger experience different. Report the observation point and period rather than treating a route as having one universal headway.

Under independent uniformly timed passenger arrivals, regular headway h and guaranteed boarding of the first vehicle, mean waiting time is h/2. This follows because the remaining time to the next departure is uniform from zero to h. It need not describe passengers who plan around a sparse timetable, miss a transfer or cannot board.

With unequal repeating gaps, more passengers arrive during the longer gap. Weight each gap’s mean remaining wait by its fraction of elapsed time. Averaging the gap lengths alone loses this passenger weighting. The figure compares two invented services under exactly those assumptions.

Keep capacity and service quality distinct

Vehicle places multiplied by departures give a supplied carrying opportunity at a point. Actual passenger throughput also depends on occupancy, boarding, alighting and available space. Count a passenger journey consistently when transfers occur; summing boardings measures something different.

Reliability interventions can trade platform waiting against time already spent onboard. Walking access, cycling connections, dwell and transfer coordination also matter. A useful assessment states whose time is counted and retains the constraints, rather than optimizing one average while ignoring everyone else.

Weight waiting by elapsed time

Service A repeats departures every 10 minutes. Service B repeats gaps of 6 and 14 minutes. Both have two departures per 20-minute cycle, or six per hour. Assume passengers arrive uniformly over the entire cycle, independently of departures, with no denied boarding.

For A, mean wait is 5 minutes. For B, arrivals spend 6/20 of their time in the short gap with mean remaining wait 3 minutes, and 14/20 in the long gap with mean 7 minutes. The result is (6/20)×3+(14/20)×7=5.8 minutes, equivalently(6²+14²)/(2×20). Equal average frequency has not produced equal waiting.

If each supplied vehicle offers 30 passenger places, six departures offer 180 places/h at the point considered. This is neither an observed passenger count nor proof that every stop has enough space. The whole journey and passenger-arrival assumptions still need checking.

Try the reasoning

1. Why are the two gaps not equally weighted?

   Show the answer and reasoning

   Uniform arrivals over time place more passengers in the longer gap; its weight is 14/20, not one-half.

2. What is the mean wait for a perfectly regular 8-minute headway under these assumptions?

   Show the answer and reasoning

   4 minutes, provided arrivals are independent and uniform and the first departure can be boarded.

3. Does a continuous route on a map establish usability?

   Show the answer and reasoning

   No. Its crossings, surfaces, entrances, information and service connections must meet the intended users’ needs.

What to carry forward

Assess complete journeys and passenger-weighted service, alongside the vehicles.