T-Share: A Large-Scale Dynamic
Taxi Ridesharing Service
Shuo Ma, Yu Zheng, Ouri Wolfson
Microsoft Research Asia
University of Illinois at Chicago
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
Next Pickup Point
: in 1.2km
Next Delivery Point
: in 6.3km, $13.2
Original route
Newly scheduled route
Scheduled route
Pickup Point
Delivery Point
T -Share
Pick your role
Ride Request
Driver
From
Current Position
To
Huaxing Cinema
Number of riders
Confirmation
2
ZX3G18126781
Rider
Earliest
Taxi
ID: departure
Now
京B 1203785
Estimated
pickup time:
Latest arrival
Estimated taxi fare:
Send
OK
08:32
09:30
$ 5.3
Cancel
Ride Joining Request
Number of riders added:
2
Fare saving:
$1.5
Travel time delay:
Accept
2 min
Reject
Background
• Challenges
– 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
Value
• Government
– 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
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.
Architecture
Scheduling
Index Updating
Rv
{Taxis}
R
{V}
Taxi Searching
Ru
Spatio-Temporal
index of taxis
Q
Communication Interface
Q
Rv
Service providing data flow
Q=<t, o, wp , d, wd>;
R=Ru || Rv;
V
Rv
V
Taxi status updating flow
V=real time pos
Spatio-Temporal Index
• Grid-based approximation
• Select an anchor node in each grid
g0
gj
ci
gi
gj
gn
 D01
D10 
D0j
D0n
D1j
D1n
gi
Di0 Di1
Dij
Din
gn
Dn0 Dn1
Dnj

g0
cj
g1
g1
M=
Dij = ( tij , dij )
A) Grid-partitioned map
B) Grid distance matrix
Spatio-Temporal Index
• For each Grid
– Spatially-ordered grid cell list 𝑔. 𝑙𝑑 (spatial closeness)
– Temporally-ordered grid cell list 𝑔. 𝑙𝑡 (temporal closeness)
– Taxi list 𝑔. 𝑙𝑣 sorted by the arrival time
gi
g0 g1
gj
ci
gi
t7i
g2
g7
dn'i
gn'
tni
gn
d7i
D1n
gi
Di0 Di1
Dij
Din
gn
Dn0 Dn1
Dnj

g1
Dij = ( tij , dij )
A) Grid-partitioned map
t2i
d2i
g7
g2
D0n
M=
B) Grid distance matrix
earliest
nearest
gn
 D01 D0j
D10  D1j
g0
cj
gj
spatial
furthest
Taxi2 :ta
Taxi7 :ta
temporal
Taxim :ta
latest
Taxi Searching
Scheduling
Index Updating
Rv
{Taxis}
R
{V}
Taxi Searching
Ru
Spatio-Temporal
index of taxis
Q
Communication Interface
Q
Rv
Service providing data flow
Q=<t, o, wp , d, wd>;
R=Ru || Rv;
V
Rv
V
Taxi status updating flow
V=real time pos
Taxi Searching
• Single-side taxi search
g7
Temporal Closeness
nearest
– 𝑄. 𝑜 is located in 𝑔7
– 𝑡𝑖7 + 𝑡𝑐𝑢𝑟 ≤ 𝑄. 𝑤𝑝. 𝑙
– Merge taxi lists
𝑔3
g7
O
𝑔5
𝑔9
– Many candidate taxis
– Scheduling process is heavy
gi
t2i
d2i
g7
g2
t7i
g2
g7
dn'i
gn'
tni
gn
furthest
g9
furthest
g3 g3
g7 g7
earliest
earliest
earliest
nearest
spatial
g5
gn
• Problem
d7i
g3
Taxi2 :ta
Taxi7 :ta
tcur tcur
Taxim :ta
latest
cur tcur
Taxi5Taxi5
Selected
Taxies
Selected
Taxies
Selected
Taxies
Selected Taxies
Taxi8Taxi8
Taxi7Taxi7
Taxi2Taxi2
Q.wp.l
Q.wp.l
temporal
earliest
earliest
t
TaxixTaxix
latestlatest
Q.wp.l-t
37 37
Q.wp.l-t
TaxiyTaxiy
latestlatest
Dual-Side Taxi Searching
• Origin side
• Destination side
– 𝑄. 𝑜 in 𝑔7
– 𝑡𝑖7 + 𝑡𝑐𝑢𝑟 ≤ 𝑄. 𝑤𝑝. 𝑙
g3
g5
g9
gn
furthest
g2
nearest
Spatial Closeness
Temporal Closeness
nearest
g7
g3
g9
g8
g5
𝑔1
𝑔g77
𝑔3
𝑔2
D
𝑔5
𝑔6
nearest
g1
g6
Spatial Closeness
g7
– 𝑄. 𝑑 in 𝑔2
– 𝑡𝑐𝑢𝑟 + 𝑡𝑗2 ≤ 𝑄. 𝑤𝑑. 𝑙
O
𝑔9
gn
furthest
gm
furthest
g7
earliest g7
g7 2
earliestTaxi
earliest
Taxi7
2
Taxi
Taxi72
Taxi7
Taxix
latest
Taxix
latest
Taxi
x
latest
g3
earliest g3
g3 5
earliestTaxi
earliest
Taxi8
5
Taxi
Taxi85
Taxi8
Taxiy
latest
Taxiy
latest
Taxi
y
latest
g9
earliest g9
g97
earliestTaxi
earliest
Taxi
Taxi107
Taxi
7
Taxi17
10
Taxi10
Taxi17
latest Taxi
Taxi17
z
latest Taxi
z
latest Taxi
z
g7 g3
tcur gg77 gg33
So
tcur
tcur
So
Q.wp.l
So
Q.wp.l
Q.wp.l
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g
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Taxi
2
Taxi
Taxi72
Taxi72
Taxi
Taxi7
g2 g6
g2 g6
gTaxi
2 g6
g2
g2
g
Taxi
23
tcur
tcur
tcur
3
Sd
Taxi
Taxi113
Taxi3 Sd Q.wd.l
Taxi10
11 Sd
Taxi11
Taxi10
Step 1: So ∩ Sd =Taxi
{}10
Q.wd.l
Q.wd.l
B)
earliest
earliest
Taxi
Taxi113 earliest
Taxi
Taxi113
Taxi11
Taxim
latest
Taxim
Taxim latest
g6 latest
A)
Step 1: So ∩ Sd = {}
A)
B)
g9 1:g5So ∩ Sdg=2 {}g6
A) g7 g3 Step
B)
g
g6 earliest
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t
cur
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Taxi
3
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Taxi
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earliest
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t
cur
Taxi
tcur
So Taxi7
Taxi3 Sd
Taxi
earliest
21
Taxi
10
10
tcur
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tcur
Taxi113
Taxi
Taxi
Taxi
10
Taxi
21
2
7
S
S
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17
Taxi
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tcur g77 gg33
tcur
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tcur
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Taxi85
Taxi21
Taxi82: So ∩ Sd = {}17
Step
Taxi17
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Q.wd.l-t
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Step 2: So ∩ Sd = {}
g9 2:g5So ∩ Sd g=2 {}g6
Step
g9 2 g5
g2 g6
Taxi
3
g
g
gTaxi
9 7 5
2 g6
Taxi
Taxi
11
Taxi
Taxi3 Sd
Taxi52
Taxi
10
Taxi
72
Taxi113
Taxi
Taxi8
Taxi
21 Sd
Taxi57
Taxi
Taxi
11
10
Taxi
17 Sd
Taxi10
85
Taxi10
Taxi17
21
97
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17
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∩
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=
{Taxi
,
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d
10 17Taxi17}
E) 97
Taxi17
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E)
E)
Step 3: So ∩ Sd = {Taxi10 , Taxi17}
Step 3: So ∩ Sd = {Taxi10 , Taxi17}
D)
D)
F)
F)
F)
Taxin latest
Taxin latest
Scheduling Module
• Calculate schedule for each candidate taxi
Scheduling
Index Updating
Rv
{Taxis}
R
{V}
Taxi Searching
Ru
Spatio-Temporal
index of taxis
Q
Communication Interface
Q
Rv
Service providing data flow
Q=<t, o, wp , d, wd>;
R=Ru || Rv;
V
Rv
V
Taxi status updating flow
V=real time pos
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(𝑛2 ) possible ways of insertion
Q.o
Q1.o
Q.o
Q2.o
Q.o
Q.o
Q1.d
Q.o
Q2.d
Scheduling Module
• Feasibility check (using 𝑄. 𝑜 as an example)
– 𝑡𝑑 = 𝑄2 . 𝑜 → 𝑄. 𝑜 + 𝑄. 𝑜 → 𝑄1 . 𝑑 + 𝑡𝑤 − 𝑄2 . 𝑜 → 𝑄1 . 𝑑
– 𝑡𝑤 : the time spent on waiting for the passenger
– (𝑄. 𝑜)𝑠𝑡 = 𝑄. 𝑤𝑝. 𝑙 − 𝑎𝑝
– (𝑄. 𝑑)𝑠𝑡 = 𝑄. 𝑤𝑑. 𝑙 − 𝑎𝑑
– If 𝒕𝒅 ≥ 𝑴𝒊𝒏{ 𝑸𝟏 . 𝒅 𝒔𝒕 , 𝑸𝟐 . 𝒅
Original schedule
leg1
Q.o
leg2
𝒔𝒕 },
fail
One possible way to insert a new
query Q into the original schedule
Q2.d
Q2.o
Points for time window check
Q1.d
leg3
Q.d
leg4
Points for slack time check
Scheduling Module
• Lazy Shortest Path Calculation
– Find a lower bounder of travel time between two points
– 𝑡𝑂𝐷 ≥ 𝑡𝑖𝑗 − (𝑐𝑖 → 𝑂) − (𝐷 → 𝑐𝑗 )
1. 𝑐𝑖 → 𝑂 + 𝑡𝑂𝐷 ≥ (𝑐𝑖 → 𝐷)
3. 𝑐𝑖 → 𝑂 + 𝑡𝑂𝐷 ≥ 𝑡𝑖𝑗 − (𝐷 → 𝑐𝑗 )
g1
gj
gn

D01
D0j
D0n
D10 
D1j
D1n
gi
Di0 Di1
Dij
Din
gn
Dn0 Dn1
Dnj

g0
cj
2. (𝑐𝑖 → 𝐷)+(𝐷 → 𝑐𝑗 ) ≥ 𝑡𝑖𝑗
(𝑐𝑖 → 𝐷) ≥ 𝑡𝑖𝑗 - (𝐷 → 𝑐𝑗 )
g0
D gj
ci
O gi
g1
M=
Dij = ( tij , dij )
A) Grid-partitioned map
B) Grid distance matrix
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(𝑑1 +∑𝑐𝑚=2 𝛼 + 1 ∗ 𝑑𝑚 𝑚)
𝑇𝑜𝑡𝑎𝑙_𝑃𝑟𝑜𝑓𝑖𝑡 = 𝑝(𝐷𝑛 + 1 + 𝛼 ∗ 𝐷𝑟 )
Evaluation
• Settings
– 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)
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
𝒓𝟏
𝒓𝒊
𝒑𝒊𝟐
#. Of queries
𝒓𝟐
50K
40K
# Query
𝒑𝒊𝟏
extracted
2-inflated
60K
30K
20K
10K
0K
0
5
10
15
hour of day
20
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
5 minute
The # of time bins in a frame
12
Number of queries
27,000
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)
Results
• Effectiveness
SF
SB
DF
DB
NR
50%
40%
Relative Distance Rate
Satisfaction Rate
60%
30%
20%
10%
1
2
3
delta
4
5
6
104%
102%
100%
98%
96%
94%
92%
90%
88%
SF
SB
DF
DB
NR
1
2
3
delta
4
5
6
Results
# Road Nodes Accessed Per Query
90
75
SF
SB
DF
DB
60
45
30
1
2
3
delta
4
5
SF
SB
DF
DB
20
15
10
5
SF
SB
DF
DB
60K
50K
40K
30K
20K
10K
6
1
# Road Nodes Accessed Per Query
#Taxi Accessed Per Query
# Grid Cells Accessed Per Query
• Efficiency
2
3
delta
4
5
6
200K
w/o lazy strategy
with lazy strategy
150K
100K
50K
0K
1
2
3
delta
4
5
6
15*15
20*20
25*25
Grid Size
30*30
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
Thanks!
Yu Zheng
yuzheng@microsoft.com
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