Devansh Jalota 14 Kiril Solovey 24 Stephen Zoepf 3 Marco Pavone 24 1 Institute for Computational and Mathematical Engineering Stanford University 2 Department of Aeronautics and Astronautics ID: 935081
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Balancing Efficiency and Fairness in Traffic Routing via Interpolated Traffic Assignment
Devansh
Jalota
14
,
Kiril Solovey24, Stephen Zoepf3, Marco Pavone241 Institute for Computational and Mathematical Engineering, Stanford University 2 Department of Aeronautics and Astronautics, Stanford University3 Lacuna Technologies, Palo Alto4 Autonomous Systems Laboratory, Stanford University
Comparison to State-of-the-art
Pareto frontiers depicting the trade-off between efficiency and fairness for the (
i
) I-TAP method with a step size s = 0.01, (ii) I-TAP method with s = 0.05, (iii) I-Solution method with s = 0.01, and (iv) Jahn et al.’s method with s = 0.05.
Developing tighter theoretical bounds
Investigating notions of fairness that compare travel times of users travelling between different O-D pairs
Generalizing framework to costs beyond travel times
Future Work
Implementing Flows Through Pricing
Comparison between the inefficiency ratio and level of unfairness of the solution of I-TAP on the to their corresponding theoretical bounds
Homogeneous Users
Heterogeneous Users
Computational Tractability
Interpolated Marginal Cost Pricing
Dual Multipliers of Linear Program parametrized by
Goal
:
Price roads such that travel cost of users in the same commodity is equal
I-TAP objective is equal to the following UE-TAP objective:
Since I-TAP is equivalent to a parametric UE-TAP problem, it can be computed several orders of magnitude faster than previous work
Dense Sampling Method
Interpolated Traffic Assignment Problem
I-TAP Method
: Solve I-TAP for
from a finite set with step size s, and return solution with the lowest total travel time that is at most
-unfair
Performance Metrics
Efficiency
Fairness
Ratio of total travel time of a traffic assignment to the system optimum
Maximum ratio of travel times for users travelling between same O-D pair
Goal
:
Minimize Total Travel Time subject to Unfairness Constraint
Introduction and Motivation
Interpolate between UE-TAP and SO-TAP objectives to achieve best of both worlds – high level of fairness at a low total travel time
System Optimum (SO) routing copes with inefficiencies of selfish routing that results in a user equilibrium (UE). However, SO routing is impractical due to its unfairness to users.
SO-TAP: Efficient but Unfair
UE-TAP: Fair but Inefficient
Minimum System Travel Time
Users between a given O-D pair incur same travel time
Our approach:
Intermediate outcome between the two solutions
UE
SO
I-TAP