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Aggregation of Spatio-temporal and Event Log Databases for Stochastic Characterization

• f Process Activities

Rodrigo M. T. Gonçalves, Rui Jorge Almeida, João M. C. Sousa

Planning and Scheduling

In logistic domains, transportation planning and scheduling are made based on a-priori knowledge about processes:

Stochastic Data

• Travel times between customers;
• Service duration at each customer;

Event Log Spatio- Temporal

PAIS GPS

Partially human generated event logs leads to uncertainty related to the time at which events are logged.

The Problem

Event Log Real Occurrences System User

Log time ≠ Real time Stochastic Characterization

• f Process

Activities

The Problem

Duration [Hours]

1 2 3 4 5 6 7 8 9 10

STOP Drive Sign Up Rest Unload

The Problem

Event Log Spatio- Temporal Trajectory

Framework

Longitude [°]

4 4.05 4.1 4.15 4.2 4.25 4.3 4.35 4.4 4.45

Latitude [°]

51.82 51.84 51.86 51.88 51.9 51.92 51.94 51.96 51.98 52 52.02

Data point

Event Log Spatio- Temporal Trajectory Speed Estimation

Longitude [°]

2 3 4 5 6 7 8 9

Latitude [°]

48.5 49 49.5 50 50.5 51 51.5 52 52.5

Speed [Km/h] 10 20 30 40 50 60

sj = sj if Δt j ≥ δ sj−1 else ⎧ ⎨ ⎪ ⎩ ⎪

Framework

Event Log Spatio- Temporal Trajectory Time- Windows Speed Estimation

Time-Windows are defined based on speed profiles:

• Portions of the trajectory where truck was stopped

à Used to estimate load & unload activity duration;

• Portions of the trajectory where truck was moving

à Used to estimate travel times between locations;

Framework

Event Log Spatio- Temporal Activity Recognition Trajectory Time- Windows Speed Estimation

Truck ID Date & Hour Event Activity 1141 2013-05-02 12:57:52 Navigation ETA update

• 1141

2013-05-02 13:57:55 Contact ON

• 1141

2013-05-02 14:57:58 Start of Break Break 1141 2013-05-02 15:21:41 Cancellation of Break 1141 2013-05-02 15:21:45 End of Break Break 1141 2013-05-02 15:21:46 Start of

• 1141

2013-05-02 15:21:46 Cancellation of

• 1141

2013-05-02 15:22:21 Start of Drive Driving 1141 2013-05-02 15:22:45 Driving times state event Driving 1141 2013-05-02 15:22:45 Basic record Driving 1141 2013-05-02 15:23:15 End of Drive Driving 1141 2013-05-02 15:23:15 Start of

• …

… … … 1141 2013-05-02 18:23:34 Task Busy

• 1141

2013-05-02 18:23:55 Cancellation of

• 1141

2013-05-02 18:24:56 Start of Unload Unloading 1141 2013-05-02 18:26:29 Contact OFF Unloading 1141 2013-05-02 18:27:31 Driving times state event Unloading 1141 2013-05-02 18:27:46 Basic record Unloading 1141 2013-05-02 18:28:52 Contact ON Unloading 1141 2013-05-02 18:28:53 Task Finished Unloading 1141 2013-05-02 18:30:46 End of Unload Unloading

𝐵 = 𝑏%, 𝑏', … , 𝑏) 𝑇 = {𝑡%, 𝑡', … , 𝑡)} 𝐺 = {𝑔

%, 𝑔 ', … , 𝑔 )}

𝐷 = {𝑑%, 𝑑', … , 𝑑

)}

Framework

Activity 1 Activity 5 Activity 2 Activity 3 Activity 4

tj tn

t0,1 tm,1 t0,2 t0,3 t0,4 t0,5 tm,2 tm,3 tm,4 tm,5

Framework

Event Log Spatio- Temporal Activity Recognition Trajectory Time- Windows Activity Time- Line Speed Estimation

• Time-windows define the upper and

lower boundary of the activity time-line and serves as estimation interval;

• Activities are assigned to the

correspondent time-lines and the activity time-line is built;

• A subset of activities is defined:
• 𝑩∗ à Set of human logged activities
• 𝑩∗ ⊂ 𝑩

𝑏5 ∉ 𝐵* 𝑏5 ∉ 𝐵∗ 𝑏5 ∈ 𝐵∗

𝑢) 𝑢9 Activity Time-line

𝑏5 ∉ 𝐵* 𝑏5 ∉ 𝐵* 𝑏5 ∈ 𝐵*

𝑢) 𝑢9 Activity Time-line

Framework

Activity durations are estimated based on the empty time in the neighborhood of such activities:

Event Log Spatio- Temporal Activity Recognition Trajectory Time- Windows Activity Time- Line Speed Estimation Estimation

ak ∉ A* ak ∉ A* ak ∈ A*

ROI Activity Time Line

tj tn

ak ∈ A* ak ∈ A* ak ∉ A* ak ∉ A* ak ∈ A*

ROI Activity Time Line

tj tn

Activity Time-Line

0 min 0 min ROI Time Line ROI Time Line t t

ak ∈ A* ak ∈ A* ak ∈ A* ak ∉ A* ak ∈ A* ak ∉ A*

0 min 0 min ROI Time Line ROI Time Line t t

ak ∉ A* ak ∉ A* ak ∈ A* ak ∈ A*

0 min 0 min ROI Time Line ROI Time Line t t

ak ∈ A* ak ∈ A* ak ∉ A* ak ∉ A* ak ∉ A* ak ∉ A*

0 min 0 min ROI Time Line ROI Time Line t t

Single activity case

0 min ROI Time Line t

ak ∈ A* ak ∉ A*

ak ∈ A*

ak ∈ A* ak ∉ A* ak ∈ A* ak ∉ A* ak ∈ A* ak ∉ A* ak ∈ A*

0 min ROI Time Line t

activity duration ≤ ɛ activity duration > ɛ Short activity Long activity

Multiple activities case (ex.)

Longitude [°]

4.762 4.764 4.766 4.768 4.77 4.772

Latitude [°]

52.291 52.292 52.293 52.294 52.295 52.296

Longitude [°]

4.72 4.74 4.76 4.78 4.8 4.82

Latitude [°]

52.27 52.28 52.29 52.3 52.31 52.32 52.33

Longitude [°]

4.72 4.74 4.76 4.78 4.8 4.82

Latitude [°]

52.27 52.28 52.29 52.3 52.31 52.32 52.33

Mean Load Locations

Customer Analysis

Latitude Longitude Truck ID Activity Estimated Duration 𝛸1 λ1 TID1 a1 𝚬d1 𝛸2 λ2 TID2 a2 𝚬d2 … … … … … 𝛸N λN TIDN aN 𝚬dN

Original Load Activities Duration

Longitude [°]

4.75 4.7505 4.751 4.7515 4.752 4.7525 4.753 4.7535 4.754

Latitude [°]

52.3022 52.3024 52.3026 52.3028 52.303 52.3032 52.3034 52.3036 52.3038 52.304

KLM Cargo Loads

Longitude [°]

4.7 4.71 4.72 4.73 4.74 4.75 4.76 4.77 4.78 4.79

Latitude [°]

52.28 52.285 52.29 52.295 52.3 52.305 52.31 52.315 52.32 52.325 52.33

Mean = 43.7356 Median = 15.9 Standard Deviation = 57.5501

Estimated Load Activities Duration

Longitude [°]

4.75 4.7505 4.751 4.7515 4.752 4.7525 4.753 4.7535 4.754

Latitude [°]

52.3022 52.3024 52.3026 52.3028 52.303 52.3032 52.3034 52.3036 52.3038 52.304

KLM Cargo Loads

Longitude [°]

4.7 4.71 4.72 4.73 4.74 4.75 4.76 4.77 4.78 4.79

Latitude [°]

52.28 52.285 52.29 52.295 52.3 52.305 52.31 52.315 52.32 52.325 52.33

Mean = 64.6226 Median = 54.9056 Standard Deviation = 51.3781

Original Service Duration

Mean = 47.8381 Median = 40.4833 Standard Deviation = 45.4885

Estimated Service Duration

Mean = 65.6914 Median = 56.9917 Standard Deviation = 44.2425

Service times at Amsterdam Airport

52.31 52.305

Latitude [°]

52.3 52.295 52.29 52.285 4.78 4.775 4.77

Longitude [°]

4.765 4.76 4.755 4.75 4.745 4.74 4.735 4.73 200 250 300 350 400 450 150 100 50

Service Time [Min]

Travel Times

Analyse time-windows corresponding to moving portions of the trajectory

• Time-windows are now related to the moving portions of trajectories:
• Start of TW = Start of Trip;
• End of TW = End of Trip;
• To each trip is assigned a TRIP_ID;
• Preform clustering on “start” and “end” locations of trips and intersect clusters

results;

• The intersection between a “start” and an “end” cluster gives the IDs from all

similar trips.

Travel Times

Conclusions and Future Work

• The aggregation of different types of databases leads to the

reduction of uncertainty when preforming stochastic characterization of process activities;

• Enable the prediction of service times at each customer as

well as travel times between customers;

• Estimation constrains applied by time-windows and other

activities create a well conditioned problem;

Future Work

• Use fuzzy systems for the classification of the trajectory

links from spatio-temporal databases to achieve a higher level of detail in event logs. Use additional parameters such as the average link acceleration and link length;