Traffic Graph Convolutional Network for Dynamic Urban Travel Speed Estimation

Abstract

The dynamic urban link travel speed estimation (DU-LSE) problem has been studied extensively with approaches ranging from model to data driven since it benefits multiple applications in transport mobility, especially in dense cities. However, with drawbacks such as heavy assumption in model-driven and not being capable for big city network in data-driven, there has not been a consensus on the most effective method. This study aims to develop a Sequential Three Step framework to solve the DU-LSE problem using only the passively collected taxi trip data. The framework makes use of two deep learning models namely Traffic Graph Convolution (TGCN) and its recurrent variant TGCN_lstm to capture both spatial and temporal correlation between road segments. The proposed framework has three advantages over similar approaches: (1) it uses only the affordable taxi data and overcomes the data’s incompleteness both in spatial (full GPS trajectory is not available) and temporal (incomplete historic time-series) domain, (2) it is specifically designed to preserve the directionality nature of traffic flow, and (3) it is capable for large networks. The model results and validations suggest the framework can achieve high enough accuracy and will provide valuable mobility data for cities especially those without traffic sensing infrastructure already in place.

Appendices

Appendix A. Sets, Parameters, and Decision Variables used in the paper

1.1 Sets

N :

Set of nodes

A :

Set of links

F :

Set of node features or directions

K :

Set of layers

I :

Set of taxi trips

T :

Set of time periods

1.2 Parameters

η:

Total number of trips selected for subset S in the TTS model of step 2

L :

Total number of links included in subset S in the TTS model of step 2

P _i :

[$\mathrm{A}\times 1$] vector representing links comprising the travel path of taxi trip i

β :

Hyperparameter in the TTS model of step 2

length _a :

Length of link $a$

$t_i^{pred}$ :

Predicted travel time for taxi trip i

$t_i^{obs}$ :

Observed travel time for taxi trip i

Δ _i :

Intersection delay of trip i

$\alpha_a^{link}$ :

North-bearing angle of link a

A :

Modified directional adjacency matrix with dimension [$N\times N\times F$]

a ^f :

Subset of $A$ at $f$ with dimension [$N\times F$]

$H_k^u$ :

Feature representation of a node u at k^th hidden layer

$H_k^t$ :

$\lbrack N\times F\rbrack$ matrix contains information of all nodes in the network at k^th hidden layer and time period t

for _t :

Forget value for TGCN_lstm at time period t

inp _t :

Input value for TGCN_lstm at time period t

Out _t :

Output value for TGCN_lstm at time period t

act _t :

Activation value for TGCN_lstm at time period t

s _t :

Internal State value for TGCN_lstm at time period t

Loss :

Overall loss value for the deep learning model in step 3

1.3 Decision Variables

x_i={0,1}:

1 if trip $i$ is selected for subset S in the TTS model of step 2, and 0 otherwise

tt :

[A $\times 1$] vector representing link travel time from PLTT model

W ^t :

[$N\times N$] weight matrix in TGCN for passing information between neighbors at time period t

W^for, W^inp, W^act, W^out:

[$N\times 2N$] weight matrices for passing information and calculating internal state values in TGCN_lstm cell

B^for, B^inp, B^act, B^out:

[$N\times F$] Bias matrices in TGCN_lstm cell

1.4 Models and Operations

PCP:

Path Choice Prediction. The first step in the framework

PLTT:

Partial Link Travel Time Prediction. The second step in the framework

TTS:

Taxi Trip Subsetting. An inner preprocessing model within step 2

TGCN:

Traffic Graph Convolution Network. An operation for passing message between host node and its neighbor, specifically design to capture directional traffic flow

TGCN_lstm:

Traffic Graph Convolution Network with Long-Short Term Memory. An operation for passing message between host node’s historical data as well as its neighbor’s

Appendix B