Bus Arrival Time Prediction with LSTM Neural Network A. Agafonov, A. - - PowerPoint PPT Presentation

Bus Arrival Time Prediction with LSTM Neural Network

• A. Agafonov, A. Yumaganov

Samara National Research University

• A. Agafonov, A. Yumaganov

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Task definition

Public transport arrival time prediction to stops Take into account different factors that characterize the traffic state Develop a distributed prediction model Task Real-time processing High accuracy

• A. Agafonov, A. Yumaganov

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Initial data. Preprocessing

GPS coordinates are obtained every 30 seconds Coordinates are fitted using information about the road network geometry and transport routes Travel times for each road link are calculated

• A. Agafonov, A. Yumaganov

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Problem formulation

S is the set of stops; R is the set of routes; N is the maximum number of route links; tdep

i

the departure time from stop i ∈ S;

tarr

j

is the arrival time at stop j ∈ S;

Ttravel

ij

the travel time between stops i and j.

tarr

j

= tdep

i

+ Ttravel

ij

• A. Agafonov, A. Yumaganov

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Feature vector: base factors

To estimate the travel time Ttravel

ij

we used the following factors:

day, time vi−1,i - travel speed on the previous route link hr - time headway to the preceding vehicle with the same route Tm,r

ij

travel time of the preceding vehicle m with the same route r

˜ Tr

ij - weighted travel time of preceding vehicles with the same route:

˜ Tr

ij =

• k∈Nr ω
• t − tdep,k

i

• Ttravel,k

ij

• k∈Nr ω
• t − tdep,k

i

• A. Agafonov, A. Yumaganov

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Feature vector

hany - time headway to the preceding vehicle with any route Tm,any

ij

• travel time of the preceding vehicle with any route

˜ Tany

ij

• weighted travel time of preceding vehicles with any route

Thist

ij (t) - historical average travel time

Tflow

ij

(t) - historical average travel time by traffic flow data cij - number of vehicles on the targeted route link Xi,j =

• day, time, vi−1,i, hr, Tm,r

ij , ˜

Tr

ij, hany, Tm,any ij

, ˜

Tany

ij , Thist ij

, Tflow, cij

• A. Agafonov, A. Yumaganov

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Long short-term memory (LSTM) cell

forget gate input gate

• utput gate

x + x

tanh tanh

x Ct-1 ht-1 xt ft it

• t

ht Ct ht-1 xt ht-1 xt ht-1 xt ht-1 xt ht-1 xt

t

C

• ht
• A. Agafonov, A. Yumaganov

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LSTM network

. . . . . . . . .

...

x0,1 x1,2 xt-1,t

...

. . .

xt,t+1

... ...

. . .

xN-1,N

Output Output

, 1 travel t t

T

• 1,

travel N N

T

• LSTM

cell LSTM cell LSTM cell LSTM cell LSTM cell

• A. Agafonov, A. Yumaganov

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Long short-term memory (LSTM) neural network

Route Links Feature Vector Batch

Input data

Route Links Batch

Output data

1 ... ... 1 1 1 1 1 1 1 1 ... ....

Route Links Batch

Mask

• A. Agafonov, A. Yumaganov

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Model analysis

Comparison: Proposed / Base LSTM models ANN, 1 hidden layer Linear Regression MAE = 1

n

n

• t=1

|Vt − ˆ Vt|,

MAPE = 1

n

n

• t=1

|Vt − ˆ Vt| Vt × 100%

Data set: Five bus routes Average route length is 16 km Travel time observations in 30 days

• A. Agafonov, A. Yumaganov

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Model analysis. MAE / MAPE

Table: Algorithms Comparison

MAE MAPE LSTM 22.12 19.78 Base LSTM 23.64 21.24 ANN 25.54 23.25 Regression 26.89 25.19

300 600 900 1200 1500 1800 300 600 900 1200 1500 1800

Predicted travel time, sec

Real travel time, sec

• A. Agafonov, A. Yumaganov

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Model analysis. MAE / MAPE for routes

5 10 15 20 25 30 35

route 12 route 50 route 181 route 265 route 330 MAE, sec

LSTM Linear Regression ANN Base LSTM

5 10 15 20 25 30 35

route 12 route 50 route 181 route 265 route 330 MAPE, %

LSTM Linear Regression ANN Base LSTM

• A. Agafonov, A. Yumaganov

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Model analysis. MAE / MAPE

20 40 60 80 100 120 140 160 180 200 5 10 15 20 25 30

MAE, s Accumulated travel time, minutes

MAE, seconds

LSTM Linear Regression ANN Base LSTM

10 20 30 40 50 60 5 10 15 20 25 30

MAPE, % Accumulated travel time, minutes

MAPE, %

LSTM Linear Regression ANN Base LSTM

• A. Agafonov, A. Yumaganov

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Model analysis. Execution time

Intel Core i5-3740 3.20 GHz, 8 GB RAM / Nvidia GeForce GTX 1080 Ti

100 200 300 400 500 600 700 800 128 256 384 512

Computation time, ms Batch size CPU GeForce1080Ti

10 12 14 16 18 20 22 24 128 256 384 512

Computation time, ms Batch size GeForce1080Ti

• A. Agafonov, A. Yumaganov

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Conclusion

The proposed LSTM based arrival time prediction model has the following advantages: Combines different factors describing the traffic situation. It has high prediction accuracy. It has a low computation time.

• A. Agafonov, A. Yumaganov

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Thank you!

Anton Agafonov ant.agafonov@gmail.com

The work was supported by the Ministry of Science and Higher Education

• f the Russian Federation (project no. RFMEFI57518X0177)
• A. Agafonov, A. Yumaganov

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