How bad is selfish routing in practice? Lessons from the National Science Experiment

Transcription

1 How bad is selfish routing in practice? Lessons from the National Science Experiment Barnabé Monnot, Francisco Benita, Georgios Piliouras Singapore University of Technology and Design 1

2 Efficiency and fairness Quantifying (in)efficiency opens up exploring how costs are distributed in the population Smart cities are looking at achieving several related goals: livability, sustainability, economic output. We quantify these goals with various metrics, such as efficiency and fairness. They are also interconnected: better to have a fair but inefficient system? the reverse? what do we even mean by fair? Efficiency is relatively easy to obtain (with the right data), this is our starting point. We study a large experiment on city living to explore these questions. 2

3 Contents of the talk The National Science Experiment Bounding the efficiency of a real network: the Empirical Price of Anarchy Comparing trips: public vs private transport and imitation-regret 3

4 Overview of the experiment Over students were equipped with a sensor and went about their daily activities Capable of recording location, temperature, relative humidity, atmospheric pressure, sound pressure, light level and 9-degrees of freedom motion data, every 10 seconds. 4

5 Overview of the experiment Location is determined by looking at Wi-Fi addresses collected by the sensor The sensors are equipped with Wi-Fi radio Collect MAC addresses from surrounding Wi-Fi points, used to determine location Send data points to the server remotely Figure Wi-Fi density in Singapore 5

6 Home and school recognition Home and school are recognized using temporal data Most of the time is spent by the student either at school or at home We use temporal data to assign the location of both: no active reporting Figure Homes and schools 6

7 Contents of the talk The National Science Experiment Bounding the efficiency of a real network: the Empirical Price of Anarchy Comparing trips: public vs private transport and imitation-regret 7

8 Equilibrium and optimum Congestion games offer an example of suboptimal equilibrium Congestion games, proposed by Rosenthal (1973), are one of the first models of large games. Nonatomic flow of agents on a network trying to reach a destination from their origin. Classical example: two edges network. Unit demand wants to go from green to red. If they take the upper edge, cost equal to the fraction of users on the edge. If they take the lower edge, cost equal to 1. Figure Two edges network 8

9 Equilibrium and optimum Congestion games offer an example of suboptimal equilibrium Congestion games, proposed by Rosenthal (1973), are one of the first models of large games. Nonatomic flow of agents on a network trying to reach a destination from their origin. Classical example: two edges network. Unit demand wants to go from green to red. If they take the upper edge, cost equal to the fraction of users on the edge. If they take the lower edge, cost equal to 1. Equilibrium: all take the upper edge. Cost = 1 * 1 = 1 But Optimal: half on the upper, half on the lower. Cost = 1/2 * 1/2 + 1/2 * 1 = 0.75 Figure Two edges network Up: Equilibrium. Down: Optimum. 9

10 The tension between equilibrium and optimum The Price of Anarchy gives the gap between worst equilibrium and the optimum From the previous examples, it happens (often) that players reach suboptimal states. The Price of Anarchy is defined as the ratio between the cost of the worst equilibrium and the cost of the optimal state. Price of Anarchy = Social Cost(worst equilibrium) Social Cost(optimal state) In the previous example, PoA = 4/3. Turns out this is a tight bound for affine latency functions. 10

11 PoA for real networks Lack of data made it difficult to estimate what is this ratio in real cities From the data collected during the NSE, we define the following ratio: Empirical Price of Anarchy = Cost(Recorded trip durations) Cost(Optimal trip durations) Numerator is easy to compute: add up trip durations from our dataset. Denominator is hard: need to estimate the latency functions of Singapore s road network, and solve for the optimal flow. We use another method to bound the true value of EPoA. Costs are here taken to be trip durations only, could include tolls, comfort or other psychological factors. 11

12 Upper bound of the EPoA Via a lower bound of the denominator It is true that for any trip: So: Cost(Trip in free-flow) Cost(Trip in optimum) EPoA = Cost(Recorded trip durations) Cost(Optimal trip durations) Cost(Recorded trip durations) Cost(Free-flow trip durations) 12

13 Optimal route selection We compare the trip with the suggested itinerary to determine if it was optimal The Google Directions API lets us find the fastest itinerary by car or by public transportation. Figure Optimal itinerary by car Figure Optimal itinerary by bus 13

14 Obtaining the free-flow durations Query Google Directions API Two cases: car users and public transport users. For car users, query for light traffic conditions over several time periods, API returns best conditions travel time. For public transport users, query for directions, return best time by removing any potential waiting time. 14

15 Estimations from the data Global upper bound is low, with marked differences between private and public transportation We obtain EPoA 1.26 when considering both private and public transportation users. But restricting to private transport only yields EPoA 1.84! If the real ratio is 1.84, this tells us that even if cars were photon-cars, Singapore could not improve by more than a factor of 2 between current conditions and optimal. Figure Photon-cars can go through each other to beat the traffic! 15

16 Contents of the talk The National Science Experiment Bounding the efficiency of a real network: the Empirical Price of Anarchy Comparing trips: public vs private transport and imitation-regret 16

17 Distance and time distributions Distance does not impact mode choice, but duration of public transport trips is greater 17

18 Comparing similar users We cluster users by their home locations, schools, departure times and mode Let C(h, s, t, m) be the set of users starting from cluster h around time t, going to school s with mode m. We find the fastest user in the set and compare the other users against her. Figure Clustering homes that are close to one another 18

19 Comparing similar users We cluster users by their home locations, schools, departure times and mode Imitation-regret is the difference between one user and the fastest in its set. Expected to be small, same conditions should yield same trip time. Figure Complementary distribution of imitationregret values 19

20 Sets with different modes We cluster users by their home locations, schools and departure times We drop the mode in our group: compare one student s trip with the best in the set, car or public transport. In 80% of mixed sets, car users are faster than public transport. Average regret of public transport user with respect to the fastest car in the set: 8 minutes and 30 seconds, for an average trip duration of 25 minutes across this population. 20

21 New directions Explore fairness in games from a transportation perspective We are curious to discover more ties between efficiency and fairness in large systems. Transportation offers challenges on both fronts. Happy to take questions, comments and remarks from you and discuss further in the next two days! 21

22 Coming soon... Real-time GPS tracking of cars in Singapore, complete dataset of all private transportation Source LTA Source LTA ERP1 Gantry Only at specific locations, mostly large roads ERP2 System Continuous real-time tracking of private vehicles everywhere 22