**Table 1.**

Based on the hypothesis of a homogenous spatial distribution of activities throughout this territory, the ratio *θ*applies to both the point of origin of trips and their destination. The market potential of the ring service is thus *θ*<sup>2</sup> multiplied by

*<sup>Q</sup>*<sup>~</sup> <sup>¼</sup> <sup>P</sup>*:μ:* <sup>4</sup>*<sup>π</sup>* <sup>ℓ</sup><sup>R</sup>

<sup>¼</sup> <sup>P</sup>*:<sup>μ</sup>* A *:*

*Models and Technologies for Smart, Sustainable and Safe Transportation Systems*

<sup>¼</sup> <sup>P</sup>*:<sup>μ</sup>*

• An equivalent radius for the urban settlement RA, such as *π:*R<sup>2</sup>

The terms of the formula can thus be rearranged to show:

• Mobility generation density *μ*P*=*A,

• The width of the band 2ℓ, with exponent 2,

A <sup>2</sup>

ð Þ <sup>4</sup>*<sup>π</sup>* <sup>ℓ</sup><sup>R</sup> <sup>2</sup> A

<sup>A</sup> *:*4*π:*ð Þ <sup>2</sup><sup>ℓ</sup> <sup>2</sup> <sup>R</sup>

• The role of the radii: the ratio R*=*RA, squared, determines the potential demand.

For a given territory, the goal is to find the 'natural' proportion between R and RA. **Figure 2a,b** shows two examples from the cities of Rennes and Saint-Malo, in the Brittany region of France. **Figure 2c,d** shows two examples in the Ile-de-France region: one for the Paris-Saclay area, and another for the Greater Paris conurbation,

*Examples for (a) Rennes, (b) St Malo, (c) Paris-Saclay, (d) Grand Paris (source: Mappy, modified by the*

RA <sup>2</sup> (2)

<sup>A</sup> ¼ A.

the city's total mobility, i.e.

here labelled Grand Paris.

**Figure 2.**

*author).*

**168**

*Quantification of geographical potential.*

**Table 1** shows a high degree of similarity between the results (Q-tilde) for the two radius values envisaged: between 10,000 and 12,000 journeys per day for a radius of 3 km, or 29,000 to 34,000 journeys per day for a radius of 5 km. To put it another way, the urban conditions found in a variety of French cities all represent interesting levels of potential demand. Nevertheless, the quality of service would need to be attractive to users, in conjunction with attractive prices.
