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Aggregation of Spatio-temporal and Event Log Databases for Stochastic Characterization of 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: • Service duration at each customer; • Travel times between customers; Stochastic Data PAIS Spatio- GPS Event Log Temporal

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

The Problem System Stochastic Characterization Real Event Log Occurrences of Process Activities Log time ≠ Real time User

The Problem STOP Drive Sign Up Rest Unload 0 1 2 3 4 5 6 7 8 9 10 Duration [Hours]

Framework 52.02 Data point 52 Spatio- Event Log 51.98 Temporal 51.96 51.94 Latitude [°] 51.92 Trajectory 51.9 51.88 51.86 51.84 51.82 4 4.05 4.1 4.15 4.2 4.25 4.3 4.35 4.4 4.45 Longitude [°]

Framework 52.5 60 Spatio- Event Log 52 Temporal 50 51.5 Trajectory 51 40 Speed [Km/h] Latitude [°] 50.5 Speed 30 Estimation 50 20 49.5 ⎧ Δ t j ≥ δ if ⎪ s j s j = ⎨ 10 49 ⎪ s j − 1 else ⎩ 48.5 2 3 4 5 6 7 8 9 Longitude [°]

Framework Spatio- Event Log Temporal Time-Windows are defined based on speed profiles : Trajectory • Portions of the trajectory where truck was stopped Speed à Used to estimate load & unload activity duration; Estimation • Portions of the trajectory where truck was moving Time- à Used to estimate travel times between locations; Windows

Framework Truck ID Date & Hour Event Activity 1141 2013-05-02 12:57:52 Navigation ETA update - Spatio- 1141 2013-05-02 13:57:55 Contact ON - Event Log Temporal 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 - Activity 1141 2013-05-02 15:21:46 Cancellation of - Trajectory Recognition 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 Speed 1141 2013-05-02 15:23:15 Start of - Estimation … … … … 1141 2013-05-02 18:23:34 Task Busy - 1141 2013-05-02 18:23:55 Cancellation of - Time- 𝐵 = 𝑏 % , 𝑏 ' , … , 𝑏 ) 1141 2013-05-02 18:24:56 Start of Unload Unloading Windows 𝑇 = {𝑡 % , 𝑡 ' , … , 𝑡 ) } 1141 2013-05-02 18:26:29 Contact OFF Unloading 1141 2013-05-02 18:27:31 Driving times state event Unloading 𝐺 = {𝑔 % , 𝑔 ' , … , 𝑔 ) } 1141 2013-05-02 18:27:46 Basic record Unloading 𝐷 = {𝑑 % , 𝑑 ' , … , 𝑑 ) } 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

Framework • Time-windows define the upper and lower boundary of the activity time-line Spatio- Event Log Temporal and serves as estimation interval ; • Activities are assigned to the Activity Trajectory Recognition correspondent time-lines and the activity time-line is built; Speed Estimation • A subset of activities is defined: Time- • 𝑩 ∗ à Set of human logged activities Windows • 𝑩 ∗ ⊂ 𝑩 Activity Time- Line Activity 1 Activity 2 Activity 5 Activity 3 Activity 4 t j t 0,1 t m,1 t 0,2 t m,2 t 0,3 t m,3 t 0,4 t m,4 t 0,5 t m,5 t n

Framework Activity durations are estimated based on Spatio- Event Log the empty time in the neighborhood of Temporal such activities: Activity Trajectory Recognition 𝑏 5 ∉ 𝐵 ∗ 𝑏 5 ∈ 𝐵 ∗ 𝑏 5 ∉ 𝐵 * Speed 𝑢 9 𝑢 ) Estimation Activity Time-line 𝑏 5 ∉ 𝐵 * 𝑏 5 ∈ 𝐵 * 𝑏 5 ∉ 𝐵 * Time- Windows 𝑢 9 𝑢 ) Activity Time-line Activity Time- Line Estimation

Activity Time-Line a k ∉ A * a k ∈ A * a k ∉ A * t j t n ROI Activity Time Line a k ∈ A * a k ∉ A * a k ∈ A * a k ∈ A * a k ∉ A * t j t n ROI Activity Time Line

Single activity case a k ∈ A * a k ∈ A * 0 min 0 min ROI Time Line ROI Time Line t t a k ∈ A * a k ∉ A * a k ∈ A * a k ∉ A * 0 min t ROI Time Line 0 min ROI Time Line t a k ∉ A * a k ∈ A * a k ∉ A * a k ∈ A * 0 min ROI Time Line t 0 min ROI Time Line t a k ∉ A * a k ∈ A * a k ∉ A * a k ∉ A * a k ∈ A * a k ∉ A * 0 min ROI Time Line t 0 min ROI Time Line t

Multiple activities case (ex.) a k ∉ A * a k ∈ A * a k ∈ A * a k ∉ A * a k ∈ A * ROI Time Line t 0 min a k ∉ A * a k ∈ A * a k ∈ A * a k ∈ A * a k ∉ A * t 0 min ROI Time Line activity duration ≤ ɛ Short activity activity duration > ɛ Long activity

Customer Analysis 52.33 Estimated Latitude Longitude Truck ID Activity Duration 52.296 𝛸 1 λ 1 TID 1 a 1 𝚬 d 1 52.32 𝛸 2 λ 2 TID 2 a 2 𝚬 d 2 52.295 … … … … … 𝛸 N λ N TID N a N 𝚬 d N 52.31 52.294 52.33 Latitude [°] Latitude [°] Mean Load Locations 52.3 52.32 52.293 52.31 52.29 Latitude [°] 52.292 52.3 52.29 52.28 52.291 52.28 52.27 4.762 4.72 4.764 4.74 4.766 4.76 4.768 4.78 4.77 4.8 4.772 4.82 52.27 4.72 4.74 4.76 4.78 4.8 4.82 Longitude [°] Longitude [°] Longitude [°]

Original Load Activities Duration 52.304 KLM Cargo Loads 52.3038 Mean = 43.7356 52.3036 Median = 15.9 Standard Deviation = 57.5501 52.3034 Latitude [°] 52.3032 52.303 52.3028 52.3026 52.3024 52.3022 4.75 4.7505 4.751 4.7515 4.752 4.7525 4.753 4.7535 4.754 Longitude [°] 52.33 52.325 52.32 52.315 52.31 Latitude [°] 52.305 52.3 52.295 52.29 52.285 52.28 4.7 4.71 4.72 4.73 4.74 4.75 4.76 4.77 4.78 4.79 Longitude [°]

Estimated Load Activities Duration 52.304 KLM Cargo Loads 52.3038 Mean = 64.6226 52.3036 Median = 54.9056 Standard Deviation = 51.3781 52.3034 Latitude [°] 52.3032 52.303 52.3028 52.3026 52.3024 52.3022 4.75 4.7505 4.751 4.7515 4.752 4.7525 4.753 4.7535 4.754 Longitude [°] 52.33 52.325 52.32 52.315 52.31 Latitude [°] 52.305 52.3 52.295 52.29 52.285 52.28 4.7 4.71 4.72 4.73 4.74 4.75 4.76 4.77 4.78 4.79 Longitude [°]

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 450 400 350 300 Service Time [Min] 52.31 250 52.305 200 150 52.3 100 52.295 50 0 52.29 Latitude [°] 4.73 4.735 4.74 4.745 4.75 4.755 52.285 4.76 4.765 4.77 4.775 4.78 Longitude [°]

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;