1. T-Share: A Large-Scale Dynamic Taxi Ridesharing Service
Shuo Ma, Yu Zheng, Ouri Wolfson
Microsoft Research Asia
University of Illinois at Chicago
This is a joint work with…
Overview, taxi-sharing, accept user queries, subject to capacity and time constraints, and minimize the increase of travel distance for each query.

2. Background
Taxi-sharing is of great social and environmental importance
Serving more demands: Peak hours vs Off-peak hours
Reduce energy consumption and air pollutants emission
Could save taxi fares while increasing the income of taxi drivers
Taxi is a transportation modes between public transportation and public transportation, providing door-to-door commuting services
However, peak hours, simply increasing the number.. Does not work
Taxi sharing can increase the capacity of the taxi system without adding new taxis.

5. Background Challenges Wide range of applications Dynamic:
Dynamic queries: anytime and anywhere, lazy users
Dynamic taxis
Real-time query processing
large-scale: millions of users and tens of thousands of taxis
Wide range of applications
Private vehicles
Logistic industry for transporting goods

6. Value Government Passengers
Save 800 million liter gasoline per year
Supporting 1M cars for 10 months
Worth about 1 billion USD
1.64 billion KG CO2 emission
Passengers
Serving rate increased 300%
Save 42% expense on average
Taxi drivers increase profit 16% on average

7. Problem Definition Query 𝑄=< 𝑄.𝑜 , 𝑄.𝑑 ,𝑄.𝑤𝑝, 𝑄.𝑤𝑑 >
Origin and destination: 𝑄.𝑜 and 𝑄.𝑑
Time window for pickup: 𝑄.𝑤𝑝 =(𝑄.𝑤𝑝.𝑒, 𝑄.𝑤𝑝.𝑙)
Time window for delivery: 𝑄.𝑤𝑑 =(𝑄.𝑤𝑑.𝑒, 𝑄.𝑤𝑑.𝑙)
Given a fixed number of taxis traveling on a road network and a stream of queries, we aim to serve each query 𝑄 in the stream by dispatching the taxi which satisfies 𝑄 with the minimum increase in travel distance.
Query, satisfy, problem (optimize for each query, with minimum travel distance)

8. Architecture
Update (status)

9. Spatio-Temporal Index
Grid-based approximation
Select an anchor node in each grid

10. Spatio-Temporal Index
For each Grid
Spatially-ordered grid cell list 𝑔. 𝑙 𝑑 (spatial closeness)
Temporally-ordered grid cell list 𝑔. 𝑙 𝑡 (temporal closeness)
Taxi list 𝑔. 𝑙 𝑣 sorted by the arrival time

11. Taxi Searching
Update (status)

12. Taxi Searching Single-side taxi search Problem 𝑄.𝑜 is located in 𝑔 7
𝑡 𝑖7 + 𝑡 𝑐𝑢𝑟 ≤ 𝑄.𝑤𝑝.𝑙
Merge taxi lists
Problem
Many candidate taxis
Scheduling process is heavy
𝑔 3
𝑔 5
𝑔 9

13. Dual-Side Taxi Searching
Origin side
𝑄.𝑜 in 𝑔 7
𝑡 𝑖7 + 𝑡 𝑐𝑢𝑟 ≤ 𝑄.𝑤𝑝.𝑙
Destination side
𝑄.𝑑 in 𝑔 2
𝑡 𝑐𝑢𝑟 + 𝑡 𝑗2 ≤𝑄.𝑤𝑑.𝑙
𝑔 1
𝑔 2
𝑔 3
𝑔 5
𝑔 9
𝑔 7
𝑔 6

14. Reduce candidate taxis, allow first fit search

15. Scheduling Module
Calculate schedule for each candidate taxi

16. Scheduling Module Feasibility check
Two steps: first insert 𝑄.𝑜 and then 𝑄.𝑑
Do not change the order of an existing schedule
Minimize the increase of travel distance
Given a schedule 𝑉.𝑠 composed of 𝑛 points
𝑛+1 positions to insert 𝑄.𝑜
𝑛−𝑖+1 positions to insert 𝑄.𝑑
𝑂( 𝑛 2 ) possible ways of insertion

17. Scheduling Module Feasibility check (using 𝑄.𝑜 as an example)
𝑡 𝑑 = 𝑄 2 .𝑜→𝑄.𝑜 + 𝑄.𝑜→ 𝑄 1 .𝑑 + 𝑡 𝑤 − 𝑄 2 .𝑜→ 𝑄 1 .𝑑
𝑡 𝑤 : the time spent on waiting for the passenger
(𝑄. 𝑜) 𝑠𝑡 =𝑄.𝑤𝑝.𝑙− 𝑎 𝑝
(𝑄. 𝑑) 𝑠𝑡 =𝑄.𝑤𝑑.𝑙− 𝑎 𝑑
If 𝒕 𝒅 ≥𝑴𝒊𝒏{ 𝑸 𝟏 .𝒅 𝒔𝒕 , 𝑸 𝟐 .𝒅 𝒔𝒕 }, fail

18. Scheduling Module Lazy Shortest Path Calculation
Find a lower bounder of travel time between two points
𝑡 𝑂𝐷 ≥ 𝑡 𝑖𝑗 −( 𝑐 𝑖 →𝑂)−(𝐷→ 𝑐 𝑗 )
1. 𝑐 𝑖 →𝑂 + 𝑡 𝑂𝐷 ≥ (𝑐 𝑖 →𝐷)
2. (𝑐 𝑖 →𝐷)+(𝐷→ 𝑐 𝑗 ) ≥ 𝑡 𝑖𝑗 O D
(𝑐 𝑖 →𝐷)≥ 𝑡 𝑖𝑗 - (𝐷→ 𝑐 𝑗 )
3. 𝑐 𝑖 →𝑂 + 𝑡 𝑂𝐷 ≥ 𝑡 𝑖𝑗 − (𝐷→ 𝑐 𝑗 )

19. Pricing Scheme
Taxi fare per mile is higher for multiple passengers than for a single passenger
The taxi fare of shared distances is evenly split among the riding passengers
𝐹𝑎𝑟𝑒= 𝑝 (𝑑 1 + ∑ 𝑚=2 𝑐 𝛼+1 ∗ 𝑑 𝑚 𝑚 )
𝑇𝑜𝑡𝑎𝑙_𝑃𝑟𝑜𝑓𝑖𝑡=𝑝( 𝐷 𝑛 + 1+𝛼 ∗ 𝐷 𝑟 )

20. Evaluation Settings Big data
A trajectory dataset generated by over 33,000 taxis in Beijing over 3 months
Built experimental platform based on the data
Big data
400 million kilometres
790 million points
20 million trips (46% occupied)

21. Evaluation Experimental platform
Learn the distribution of queries on the road network over time of day from the data
Assume the arrival of queries follows a Poisson distribution
Learn the transition probability between different road segments
𝒓 𝟏
𝒓 𝟐
𝒑 𝒊𝟏
𝒑 𝒊𝟐
#. Of queries
𝒓 𝒊

22. Settings of experimental platform
Definition
Value
The start time of simulation
9 am
The end time of simulation
9:30 am
The number of taxis
2,980
The pickup window size
5 minute
The length of a time bin
The # of time bins in a frame 12
Number of queries
27,000

23. Evaluation Baselines No ridesharing
Single-side and First Fit Ridesharing (SF)
Single-side and Best-fit Ridesharing (SB)
Dual-side and First Fit Ridesharing (DF)
Dual-side and Best-fit Ridesharing (DB)

24. Results
Effectiveness

25. Results
Efficiency

26. Conclusion Win-win-win scenario
Candidate taxi selection based on a spatio-temporal index
Dual-side search saves 50% computational load
Have the similar effectiveness as compared with the single-side search
Taxi scheduling based on
Feasibility check
Lazy shortest path computing saves 83% computational load
Serve 720k queries per hour on a single machine
Future work
Consider more constraints: monetary constraints
Dynamic time estimation
Other factors: like social trust and credit

27. Thanks!
Yu Zheng
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