**3. Geographical potential and technical advantages of a ring-shaped service**

#### **3.1 Geographical principles: potential locations**

What is the potential user base for a ring-shaped service operating in a relatively homogenous territory?

To answer, let us build up a simple model. Let A represent the surface area of the territory in question, and P its population. The mean density is P/A people per unit of surface area. Let *μ* represent the mobility rate per individual and per day, typically somewhere between 3 and 4 trips. In spatial terms, the hypothetical 'outbound density' is *μ*P*=*A trips per unit of surface area.

Assume further, on a provisional basis, that the ring is a circle of radius R, and that along its whole circumference it attracts passengers from within a band 2ℓ wide – i.e. from a distance of at most ℓ from the pathway of the circular transport service. The total drainage basin for this infrastructure is thus equivalent to a surface area of 4*π* ℓR (**Figure 1**).

This drainage basin can be represented as a proportion of the total surface area (A*)* of the territory:

**Figure 1.** *Area served by a ring-shaped line.*

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 the city's total mobility, i.e.

$$\begin{split} \tilde{Q} &= \text{P.} \mu \left( \frac{4 \pi \ell \mathcal{R}}{\mathcal{A}} \right)^{2} \\ &= \frac{\text{P.} \mu}{\mathcal{A}} \cdot \frac{(4 \pi \ell \mathcal{R})^{2}}{\mathcal{A}} \\ &= \frac{\text{P.} \mu}{\mathcal{A}} \cdot 4 \pi \left( 2 \ell \right)^{2} \left( \frac{\mathcal{R}}{\mathcal{R}\_{\mathcal{A}}} \right)^{2} \end{split} \tag{2}$$

**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

**City St Malo Rennes Grand Paris Ville de Paris**

Eqt radius RA (km) 5 8 25 6 Population P (thousands) 50 300 11,000 2000

Ratio 3*=*RA 59% 38% 12% 53% Ratio *θ*<sup>2</sup> if R = 3 km 74% 30% 3% 59% *Q*~ (thousands trips/day) 38.9 37.3 13.7 995 Variant if R = 5 km 107.9 103.6 38.0 2763

) 80 200 2000 100

) 0.63 1.50 5.50 20,0

Whatever the means of transportation - shuttle, taxi, car share, moped, bicycle, scooter etc. – users expect a satisfactory quality of service. While the quality of service has been adequately defined and described for collective transit systems in the Transit Capacity and Quality of Service Manual [11], for shared mobility services that are more diverse a more generic definition is required. To that end, an analysis framework comprising four components was put forward as follows [4]:

1.*Maintenance and manners*: the vehicle needs to be appropriate for this service, in terms of its mechanical condition and energy supply; it must be clean; if it is to be used collectively (shuttle), each user has a right to expect a

2.*'Pleasure', including Protection and comfort*: four-wheeled vehicles offer shelter from the elements (weather hazards) and potential impacts (shocks), along with more comfortable seating arrangements than mopeds or bicycles. At the other end of the spectrum, scooters require passengers to be standing up

3.**'***Conductance', including Efficiency, mobility and speed*: 'conductance' is the term we use to describe the aptitude of a vehicle to fulfil its transportation role, from proximity of access to arrival at final destination. A taxi offers maximum

capacities, and particularly its power source. Speed depends upon the mobility and agility of the vehicle (the latter being greater for two-wheeled vehicles) as

4.*Ease of use, including Availability*. The less time required to access a service, the more available it is. Shuttles and taxis pick up passengers directly, they

conductance. The mobility of a vehicle depends upon its mechanical

minimum level of courtesy from other passengers on board.

(although this does offer a certain degree of excitement).

well as the fluidity of traffic conditions.

need to be attractive to users, in conjunction with attractive prices.

**3.2 Quality of service: four components**

Surface A (km<sup>2</sup>

*Towards Shared Mobility Services in Ring Shape DOI: http://dx.doi.org/10.5772/intechopen.94410*

P*=*A (k people/km<sup>2</sup>

*Quantification of geographical potential.*

**Table 1.**

**169**

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


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, here labelled Grand Paris.

#### **Figure 2.**

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

*Towards Shared Mobility Services in Ring Shape DOI: http://dx.doi.org/10.5772/intechopen.94410*

