Parking terms; speed-density and flow relations

Parking terms

• Parking accumulation: the number of vehicles parked in a study area at a given instant. Plotting it against time gives the accumulation curve; its peak gives the demand.
• Parking volume: total number of vehicles parked in an area during a given period (usually a day); it counts each vehicle once.
• Parking load: the area under the accumulation curve, in vehicle-hours (or vehicle-minutes) in a given period; it shows the total parking demand in time.
• Parking duration: the length of time a vehicle stays parked.
• Parking turnover: the rate of use of a parking space, the number of vehicles parked per bay in a given time.

$$\text{Turnover} = \frac{\text{Number of vehicles parked in the period}}{\text{Number of parking bays available}}$$

• Parking index (occupancy): the ratio of the number of bays occupied to the number of bays available, as a percentage. It measures how well the supply is used.

$$\text{Parking index} = \frac{\text{Parking load (vehicle-hours)}}{\text{Parking capacity (bay-hours)}} \times 100$$

where parking capacity = number of bays x hours of study. An index near 100 percent means the supply is exhausted; a very low value means over-supply.

Speed-density relation

Speed falls as density rises. The simplest (Greenshields) model is linear:

$$v = v_f\left(1 - \frac{k}{k_j}\right)$$

where $v_f$ is the free-flow speed (at $k \to 0$) and $k_j$ is the jam density (where $v = 0$).

 v ^
vf |*
   |   *
   |      *
   |         *
   |            *
   +---------------*--> k
   0               kj

Speed-flow relation

Since $q = vk$, eliminating $k$ gives $q = k_j\left(v - v^2/v_f\right)$, a parabola with maximum flow $q_{max} = v_f k_j/4$ at $v = v_f/2$.

 v ^
vf |*
   |  *
   |    *   uncongested
vm |- - - -*----- (v = vf/2)
   |       *  congested
   |     *
   +-----|----> q
   0   qmax

The upper branch is stable (uncongested) flow, and the lower branch is forced (congested) flow. Flow rises with density up to $k_m = k_j/2$ (capacity) and then falls to zero at jam density.