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A Time-invariant Network Flow Model for Two-person Ride-pooling Mobility-on-Demand

Fabio Paparella, Leonardo Pedroso, Theo Hofman, Mauro Salazar

TL;DR

A time-invariant network flow model capturing two-person ride-pooling that can be inte-grated within design and planning frameworks for Mobility-on-Demand systems and suggests that the higher the demands per unit time, the lower the waiting time and delay experienced by users.

Abstract

This paper presents a time-invariant network flow model capturing two-person ride-pooling that can be integrated within design and planning frameworks for Mobility-on-Demand systems. In these type of models, the arrival process of travel requests is described by a Poisson process, meaning that there is only statistical insight into request times, including the probability that two requests may be pooled together. Taking advantage of this feature, we devise a method to capture ride-pooling from a stochastic mesoscopic perspective. This way, we are able to transform the original set of requests into an equivalent set including pooled ones which can be integrated within standard network flow problems, which in turn can be efficiently solved with off-the-shelf LP solvers for a given ride-pooling request assignment. Thereby, to compute such an assignment, we devise a polynomial-time algorithm that is optimal w.r.t. an approximated version of the problem. Finally, we perform a case study of Sioux Falls, South Dakota, USA, where we quantify the effects that waiting time and experienced delay have on the vehicle-hours traveled. Our results suggest that the higher the demands per unit time, the lower the waiting time and delay experienced by users. In addition, for a sufficiently large number of demands per unit time, with a maximum waiting time and experienced delay of 5 minutes, more than 90% of the requests can be pooled.

A Time-invariant Network Flow Model for Two-person Ride-pooling Mobility-on-Demand

TL;DR

A time-invariant network flow model capturing two-person ride-pooling that can be inte-grated within design and planning frameworks for Mobility-on-Demand systems and suggests that the higher the demands per unit time, the lower the waiting time and delay experienced by users.

Abstract

This paper presents a time-invariant network flow model capturing two-person ride-pooling that can be integrated within design and planning frameworks for Mobility-on-Demand systems. In these type of models, the arrival process of travel requests is described by a Poisson process, meaning that there is only statistical insight into request times, including the probability that two requests may be pooled together. Taking advantage of this feature, we devise a method to capture ride-pooling from a stochastic mesoscopic perspective. This way, we are able to transform the original set of requests into an equivalent set including pooled ones which can be integrated within standard network flow problems, which in turn can be efficiently solved with off-the-shelf LP solvers for a given ride-pooling request assignment. Thereby, to compute such an assignment, we devise a polynomial-time algorithm that is optimal w.r.t. an approximated version of the problem. Finally, we perform a case study of Sioux Falls, South Dakota, USA, where we quantify the effects that waiting time and experienced delay have on the vehicle-hours traveled. Our results suggest that the higher the demands per unit time, the lower the waiting time and delay experienced by users. In addition, for a sufficiently large number of demands per unit time, with a maximum waiting time and experienced delay of 5 minutes, more than 90% of the requests can be pooled.
Paper Structure (14 sections, 2 theorems, 7 equations, 4 figures, 1 algorithm)

This paper contains 14 sections, 2 theorems, 7 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Ride-pooling Network Flow Model
  3. Time-invariant Network Flow Model
  4. Ride-pooling Time-invariant Network Flow Model
  5. Approximate Computation of the Demand Matrix
  6. Spatial Analysis of Ride-pooling
  7. Temporal Analysis of Ride-pooling
  8. Expected Number of Pooled Rides
  9. Optimal Ride-pooling Assignment
  10. Discussion
  11. Case Study
  12. Conclusions
  13. Proof of Lemma \ref{['lemma:finalprob']}
  14. Proof of Theorem \ref{['theorem:one']}

Key Result

Lemma II.1

Let $r_m, r_n \in \mathcal{R}$ be two requests whose arrival rate follow a Poisson process with parameters $\alpha_m$ and $\alpha_n$, respectively. The probability of each having an occurrence within a maximum time interval $\bar{t}$ is

Figures (4)

  • Figure 1: Distinct configurations for serving two requests $r_m,r_n \in \mathcal{R}$. Each arrow represents a flow of $\alpha = 1$ vehicles. The dashed arrows represent a flow with two users, whilst the solid ones represent a flow with one user.
  • Figure 2: Road network of Sioux Falls, South Dakota, USA. Prepared by Hai Yang and Meng Qiang, Hong Kong University of Science and Technology.
  • Figure 3: Percentage of pooled rides, objective function of Problem \ref{['prob:rides']}, and improvement w.r.t. no pooling as a function of the overall number of hourly demands, waiting time, and experienced delay.
  • Figure 4: Improvement of $J$ with ride-pooling w.r.t. no ride-pooling, as a function of maximum waiting time and delay.

Theorems & Definitions (7)

  • Definition II.1: Requests
  • Remark II.1
  • Remark II.2
  • Lemma II.1
  • proof
  • Theorem II.1
  • proof