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

Aggregation of Spatio-temporal and Event Log

Databases for Stochastic Characterization

of Process Activities

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

Partially human generated event logs leads

to uncertainty related to the time at which

events are logged.

Event Log

Real

Occurrences

System

User

Log time

≠

Real time

Stochastic

Characterization

of Process

Activities

Duration [Hours]

0 1 2 3 4 5 6 7 8 9 10

STOP Drive Sign Up Rest Unload

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

s

_j

=

s

j

if

Δ

t

j

≥

δ

s

_j−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;

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

𝐴 = 𝑎

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, 𝑎

_'

, … , 𝑎

₎

𝑆 = {𝑠

_%

, 𝑠

_'

, … , 𝑠

₎

}

𝐹 = {𝑓

_%

, 𝑓

_'

, … , 𝑓

₎

}

𝐶 = {𝑐

_%

, 𝑐

_'

, … , 𝑐

₎

}

Framework

Activity 1 Activity 2 Activity 3 Activity 4 Activity 5

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

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:

•

𝑨

∗

à

Set of human logged activities

𝑎

₅

∉ 𝐴

*

𝑎

5

∈ 𝐴

∗

𝑎

5

∉ 𝐴

∗

𝑡

₎

_{Activity Time-line}

𝑡

9

𝑎

₅

∉ 𝐴

*

𝑎

₅

∈ 𝐴

*

𝑎

₅

∉ 𝐴

*

𝑡

₎

_{Activity Time-line}

𝑡

9

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

a

k

∉

A

*

a

k

∈

A

*

a

k

∉

A

*

ROI Activity Time Line

t

j

t

n

a

k

∉

A

*

a

k

∈

A

*

a

k

∉

A

*

ROI Activity Time Line

t

j

t

n

a

k

∈

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*

a

k

∈

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*

ak

∉

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*

ak

∈

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ak

∉

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*

ROI Activity Time Line

t

j

t

n

ak

∉

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*

ak

∈

A

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ak

∉

A

*

ROI Activity Time Line

t

j

t

n

ak

∈

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ak

∈

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*

0 min

0 min ROI Time Line t ROI Time Line _t

a

k

∈

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∈

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k

∈

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*

a

k

∉

A

*

a

k

∈

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a

k

∉

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*

0 min

0 min ROI Time Line t ROI Time Line _t

a

k

∉

A

*

a

k

∈

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a

k

∉

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*

a

k

∈

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0 min

0 min ROI Time Line t ROI Time Line _t

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k

∈

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a

k

∉

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0 min

0 min ROI Time Line t ROI Time Line _t

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ROI Time Line

t

a

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∈

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a

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∈

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a

k

∉

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 Number of Clusters = 38 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

𝛷

₁

λ

1

TID

1

a

1

𝚫

d

1

𝛷

₂

λ

2

TID

2

a

2

𝚫

d

2

…

…

…

…

…

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

Estimated Service Duration

Mean = 65.6914

Median = 56.9917

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 0 50

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}

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}

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;