TRN-34

Parking accumulation

N = (V t̄) / T. Spaces occupied = arrivals in period T times mean duration.

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ParkingParking accumulation

Governing equation

N=V\bar t/T

$\bar t \in \left[0.2, 8\right]$

where

V: Arrivals in T (veh)
\bar t: Mean duration (h)
T: Period (h)
N: Accumulation (stalls)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

N=V\bar t/T

$\bar t \in \left[0.2, 8\right]$

$\bar t = 0.2$ $N = 5.5$

Along the curve

②

Domain of the variable — blue

\bar t_{\min} = 0.2,\quad \bar t_{\max} = 8

$\bar t \in \left[0.2, 8\right]$

$\bar t = 0.2$ $\bar t = 0.2$

Along the curve

③

Response curve — green

N=V\bar t/T

$\bar t \in \left[0.2, 8\right]$

$\bar t = 0.2$ $N = 5.5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}N}{\mathrm{d}\bar t}

$\bar t \in \left[0.2, 8\right]$

$\bar t = 0.249$ $N^{\prime} = 27.5$

Along the curve

Lecture brief

Historical brief

Highway and traffic theory crystallized with Greenshields’ 1935 speed–density line, then AASHTO stopping sight and equivalent axles. The lab is that operational arithmetic of flow, braking and pavement load. This sheet (TRN-34 — Parking accumulation) is the form associated with Parking accumulation. Working symbols: $V$ , $\bar t$ , $T$ $\rightarrow$ $N$ . Little's law in a car park. Turnover = T / t̄. Supply must cover the peak accumulation plus a reserve.

Purpose

Purpose: compute

N

from

V

\bar t

T

in Transport via

N=V\bar t/T

N = (V t̄) / T. Spaces occupied = arrivals in period T times mean duration. Use it when a real transport question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

V = 220.000\,\mathrm{veh}

\bar t = 1.500\,\mathrm{h}

T = 8.000\,\mathrm{h}

, the governing relation

N=V\bar t/T

yields

N = 41.3\,\mathrm{stalls}

. Arrivals, a dwell time, an occupied-stall count. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Arrivals in T V220 vehMean duration \bar t1.5 hPeriod T8 h

Outputs

Accumulation N41.3 stalls

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Narration of this film

Arrivals, a dwell time, an occupied-stall count.

Little's law in a car park. Turnover = T / t̄. Supply must cover the peak accumulation plus a reserve.

Reading speed

Watch on YouTube