Find the Shuttle Wave on Which the Last Party Member Fits — Free
A queue can put one family member on the next shuttle and another on the following one. Count positions through the last party member before describing a rental-car transfer as one short wait.
The proof surface
Door-to-door pricing adds journey segments. This docket audits one FIFO boarding bottleneck with finite usable seats, an explicit next-departure wait and repeated headway. It distinguishes first and last boarding and flags a split party instead of predicting the whole trip.
InputQueue option | people ahead | party size | usable seats per departure | minutes until next departure; assumed departure headway (minutes)
Rare deviceDoor-to-door pricing adds journey segments. This docket audits one FIFO boarding bottleneck with finite usable seats, an explicit next-departure wait and repeated headway. It distinguishes first and last boarding and flags a split party instead of predicting the whole trip.
Output artifactLargest modeled last-member boarding wait with row-by-row context
Cost$0 local calculation · no card, paid key, subscription or signup · proposed filing price is not for sale
Sample, not your facts: Illustrative inputs: West terminal | 12 | 4 | 10 | 3; East terminal | 5 | 6 | 8 | 4. Assumed departure headway (minutes) = 10. Largest modeled last-member boarding wait: 14 minutes until last member boards. All records are invented.
Before using the boarding-wave docket
Assume a first-in-first-out queue, identical usable seat counts on every departure, no new priority boarding, and party members allowed to board in separate waves. If the operator keeps parties together, reserves seats, changes vehicles or requires particular accessibility space, this model is not the actual queue rule. Usable seats are the seats available to this queue after those constraints, not the vehicle's brochure capacity. The next-departure wait is measured from the same observation time as people ahead. Headway means time between departure opportunities, not journey duration. Alternative queue options are evaluated separately; their waits are not added. The calculator does not know live service status or guarantee a boarding time.
Why the flat version breaks
Using the first available seat as everyone's wait
A party's first and last positions can fall in different departures. At a queue boundary, one extra person can move the last member into another wave. Keep both positions and waits visible; a single next-shuttle countdown does not establish that the whole party fits.
Using advertised seats as usable seats
A vehicle can reserve space or arrive with occupants already aboard. Brochure capacity is not necessarily available to this queue. The seat input is a confirmed usable count under the stated rule, and the app cannot inspect the arriving vehicle or allocate accessibility space.
Treating constant headway as a live forecast
Traffic, loading, vehicle changes and staff instructions can break the repeated interval assumption. The source observations are not refreshed. Use the wave calculation to ask a concrete boarding question, not to promise a connection or disregard the operator's current advice.
How to work the boarding-wave docket
Ask which queue and seats the count describes
Confirm the boarding rule with the operator and identify usable seats for the relevant queue. Luggage and accessibility arrangements may remove seats from general boarding or require staff assistance. Use anonymous stop codes rather than passenger identities. Do not count parties as people if the seat model is person-based.
Observe ahead count and next wait together
Enter whole people ahead, positive whole party size, positive whole usable seats and non-negative minutes until the next departure. These must describe one moment. A count from ten minutes earlier paired with a fresh departure countdown is not a coherent queue observation. The headway is a separate supplied operating assumption.
Locate first and last party positions
The first party position is people-ahead plus one; the last is people-ahead plus party-size. Their waves are the upward-rounded positions divided by seats. Wait for wave w is next-wait plus (w-1) times headway. Compare first and last waves to reveal a split. The summary uses the largest alternative last-member wait, with each option still visible.
Confirm the operational reality before relying on it
Ask shuttle staff about party-together rules, vehicle changes and accessible boarding. If the party must travel together, get staff's actual allocation rather than assuming the first member's modeled boarding solves the trip. Add loading, travel and rental-desk time elsewhere; this docket covers only a declared boarding opportunity.
What the boarding-wave docket separates
Question
Before
Inspect this instead
Using the first available seat as everyone's wait
A party's first and last positions can fall in different departures. At a queue boundary, one extra person can move the last member into another wave. Keep both positions and waits visible; a single next-shuttle countdown does not establish that the whole party fits.
Observe ahead count and next wait together
Using advertised seats as usable seats
A vehicle can reserve space or arrive with occupants already aboard. Brochure capacity is not necessarily available to this queue. The seat input is a confirmed usable count under the stated rule, and the app cannot inspect the arriving vehicle or allocate accessibility space.
Locate first and last party positions
Treating constant headway as a live forecast
Traffic, loading, vehicle changes and staff instructions can break the repeated interval assumption. The source observations are not refreshed. Use the wave calculation to ask a concrete boarding question, not to promise a connection or disregard the operator's current advice.
Confirm the operational reality before relying on it
This boarding-wave docket replaces a manual count or calculation, not source verification or the responsible person’s review.
Run it on the samples, right here
FIRST-LOAD
HYPOTHESIS / PROTOTYPE — checkout unavailable. Calculation is local. A draft is saved automatically in this browser profile when storage is available; Reset to sample clears it. Optional Pro history stores only five summaries and has its own deletion control. State links encode your inputs and can remain in browser history, clipboard or recipients’ records; share only non-sensitive rows. Optional external AI formatting leaves this device. The required site analytics beacon reports page activity; shared URLs contain encoded inputs. Do not treat an encoded URL as private. The calculator has no input-collection endpoint.
FIFO boarding scenario only, not a live timetable, accessible-seat assessment or connection guarantee. Ask shuttle staff to confirm usable seats, party-together rules and accessibility arrangements before relying on a modeled wave.
Data note: The boarding-wave docket processes Queue option | people ahead | party size | usable seats per departure | minutes until next departure locally. Starter/sample selection and Run compute in this tab; no input is sent by the calculator. A local draft may be saved; explicit state-link sharing or optional external AI formatting can disclose inputs. Use non-sensitive labels.
Go deeper: the companion app files the same reading as a clerk's docket sheet
The article demo above runs without limits. The companion app keeps a local history, exports the rows as CSV, prints the boarding-wave docket reading, and holds your drafts on this device — one complete free app run; the proposed $4 one-time filing layer is not for sale.
The boarding-wave docket answer stays complete for free. The proposed $4 one-time filing layer adds row CSV, print and five local reading summaries, not hidden answers. Checkout is unavailable; the article demo remains unlimited.
FIFO boarding scenario only, not a live timetable, accessible-seat assessment or connection guarantee. Ask shuttle staff to confirm usable seats, party-together rules and accessibility arrangements before relying on a modeled wave.
What this is built on
Method: The first party position is people-ahead plus one; the last is people-ahead plus party-size. Their waves are the upward-rounded positions divided by seats. Wait for wave w is next-wait plus (w-1) times headway. Compare first and last waves to reveal a split. The summary uses the largest alternative last-member wait, with each option still visible.
All sample records, dates, quantities and labels are invented. No outside policy, contract, rate, clock offset, measurement or accessibility standard is represented as verified.
Google’s official pricing documentation, fetched 2026-10-01, says AI Studio is free in available regions. Optional formatting may require a Google account; manual local entry requires none. Limits can change and free-tier content may be used to improve products. Do not send private records.
Before: the next shuttle's countdown stood in for the whole party. After: first and last positions expose capacity waves and any split-party assumption.
Three worked readings, with different inputs
Sample A — typical inputs
West terminal | 12 | 4 | 10 | 3
East terminal | 5 | 6 | 8 | 4
Setting: Assumed departure headway (minutes) = 10. Expected summary: 14 minutes until last member boards.
At West, positions 13–16 all fit in the second ten-seat departure, so the party boards after 3+10 = 13 minutes. At East, positions 6–11 span the first and second eight-seat departures: first members board at four minutes and the last at fourteen. The summary selects the larger alternative-option last-member wait, fourteen, and East is marked as a split-party model rather than described as everyone boarding at four minutes.
Setting: Assumed departure headway (minutes) = 10. Expected summary: 15 minutes until last member boards.
Regional's twelve-person party spans two eight-seat departures, with the last boarding at 5+10 = 15 minutes. Express's first member is at position sixteen and boards on the next departure at two minutes; the second is at position seventeen and waits for the next wave at twelve. The summary is fifteen among alternatives, not the sum of both options' waits.
Sample C — boundary convention
Quick stop | 0 | 8 | 8 | 0
Setting: Assumed departure headway (minutes) = 10. Expected summary: 0 minutes until last member boards.
The next departure is modeled as immediate and all eight party members fit in its eight usable seats. Both first and last boarding waits are zero. A zero next-departure wait does not mean instantaneous travel or loading. Headway remains a separate positive assumption for later waves, and real luggage, accessibility or party-together rules can alter which seats are usable.
Optional AI formatting, never the calculation
Manual entry completes this boarding-wave docket for free without signup. If available to you, the free AI Studio interface linked in the sources may format fictional or non-sensitive notes; external access may require an account. No API key or AI call is built into this tool. Free-tier content may be used to improve products. Review each cell and transcribe it to the labeled row schema; do not paste the JSON object into the row box.
Format only these fictional or non-sensitive notes for a boarding-wave docket. Return strict JSON shaped as {"rows": [{"label": "string", "cells": ["string", "string", "string", "string"]}], "setting": "string"}. The columns are Queue option | people ahead | party size | usable seats per departure | minutes until next departure; the setting is Assumed departure headway (minutes). Keep all supplied strings and quantities exactly; do not calculate, infer missing entries, invent dates or add advice. If any required value is missing, return an empty rows array and ask me for it separately. I will verify every cell against my source and manually transcribe rows using vertical bars before running the local calculator.
An AI response is not executed, fetched or trusted as a result. Missing values remain questions; the strict local parser checks the rows you actually enter.