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Pré-Publication, Document De Travail Année : 2019

On a Ring-Shaped Service of Collective Taxis, Part 1: Traffic Physics and Service Quality

Fabien Leurent

Résumé

In the digital era of mobility, the generalization of connectivity for customers as well as for vehicles has enabled for the development of different kinds of platform-based shared mobility services. Here we consider a service of collective taxis that combines on-demand access and egress of customers and "transit cycles" of vehicles along a ring-shaped circuit to serve mobility demand. The paper brings about a physical theory of customer and vehicle traffic in an abstract ring-shaped service of collective taxis. The traffic system is parameterized by (i) on the infrastructure side, the ring circumference and the average run speed, (ii) on the vehicle side, the cab passenger capacity and the stop time required to pick up and drop off a passenger, (iii) on the service side, the fleet size and the time span of daily operations, (iv) on the demand side, the trip volume and the average ride length. Spatial and temporal homogeneity are postulated to devise a mathematical formulation of (i) cab occupancy and the availability of vacant places to potential customers, (ii) Circulating, Alighting and Boarding phases (CAB), (iii) average service speed, in the operator perspective, (iv) average commercial speed, in the user perspective, yielding typical ride time, (v) access length and typical access time to an incoming user. The mathematical treatment is based on a stochastic Markov chain model of one collective cab with state vector that combines the C/A/B status with the number of riders. We establish the stationary regime of this dynamical stochastic system and characterize its stochastic equilibrium as a Fundamental Equation of Service Traffic in one scalar variable of load factor. The solution is unique and it exists if a capacity requirement is satisfied. Closed-form analytical formulas are provided to characterize every model outcome, together with sensitivity properties with respect to all system parameters.
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hal-02090947 , version 1 (05-04-2019)

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  • HAL Id : hal-02090947 , version 1

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Fabien Leurent. On a Ring-Shaped Service of Collective Taxis, Part 1: Traffic Physics and Service Quality. 2019. ⟨hal-02090947⟩
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