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

Transcription

1 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

2 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 Event Log Spatio- Temporal GPS

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

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

5 The Problem STOP Drive Sign Up Rest Unload Duration [Hours]

6 Framework Data point Latitude [ ] Event Log Spatio- Temporal Trajectory Longitude [ ]

7 Framework Event Log Spatio- Temporal Trajectory Latitude [ ] Speed [Km/h] Speed Estimation Longitude [ ] 10 s j = s j if Δt j δ s j 1 else

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

9 Framework Truck ID Date & Hour Event Activity :57:52 Navigation ETA update :57:55 Contact ON :57:58 Start of Break Break :21:41 Cancellation of Break :21:45 End of Break Break :21:46 Start of :21:46 Cancellation of :22:21 Start of Drive Driving :22:45 Driving times state event Driving :22:45 Basic record Driving :23:15 End of Drive Driving :23:15 Start of :23:34 Task Busy :23:55 Cancellation of :24:56 Start of Unload Unloading :26:29 Contact OFF Unloading :27:31 Driving times state event Unloading :27:46 Basic record Unloading :28:52 Contact ON Unloading :28:53 Task Finished Unloading :30:46 End of Unload Unloading Event Log Activity Recognition A = a %, a ',, a ) S = {s %, s ',, s ) } F = {f %, f ',, f ) } C = {c %, c ',, c ) } Time- Windows Spatio- Temporal Trajectory Speed Estimation

10 Framework Time-windows define the upper and lower boundary of the activity time-line and serves as estimation interval; Event Log Spatio- Temporal 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 A Activity 1 Activity 2 Activity 3 Activity 4 Activity 5 Activity Recognition Activity Time- Line Time- Windows Trajectory Speed Estimation tj t0,1 tm,1 t0,2 tm,2 t0,3 tm,3 t0,4 tm,4 t0,5 tm,5 tn

11 Framework Activity durations are estimated based on the empty time in the neighborhood of such activities: Event Log Activity Recognition Spatio- Temporal Trajectory a 5 A* a 5 A a 5 A t ) t 9 Activity Time-line Speed Estimation a 5 A* a 5 A* a 5 A* t ) t 9 Activity Time-line Time- Windows Activity Time- Line Estimation

12 Activity Time-Line ak A * ak A * ak A * tj ak A * ak A ak A ROI Activity * Time Line * tn tj ROI Activity Time Line tn ak A * ak A * ak A * ak A * ak A * tj ak A * ak A * ak A * ak A ak ROI Activity Time Line * A * tn tj ROI Activity Time Line tn

13 Single activity case ak A * ak A * 0 min ROI Time Line t 0 min ROI Time Line t ak A * ak A * ak A * ak A * 0 min ROI Time Line t 0 min ROI Time Line t ak A * ak A * ak A * ak A * 0 min ROI Time Line t 0 min ROI Time Line t ak A * ak A * ak A * ak A * ak A * ak A * 0 min ROI Time Line t 0 min ROI Time Line t

14 Multiple activities case (ex.) ak A * ak A * ak A * ak A * ak A * 0 min ROI Time Line t 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

15 Customer Analysis Number of Clusters = 38 Latitude Longitude Truck ID Activity Estimated Duration 𝛷1 λ1 TID1 a1 𝚫d1 𝛷2 λ2 TID2 a2 𝚫d2 𝛷N λn TIDN an 𝚫dN Mean Load Locations Latitude [ ] Latitude [ ] Latitude [ ] Longitude [ ] Longitude [ ]

16 Original Load Activities Duration KLM Cargo Loads Mean = Median = 15.9 Standard Deviation = Latitude [ ] Longitude [ ] Latitude [ ] Longitude [ ]

17 Estimated Load Activities Duration KLM Cargo Loads Mean = Median = Standard Deviation = Latitude [ ] Longitude [ ] Latitude [ ] Longitude [ ]

18 Original Service Duration Mean = Median = Standard Deviation =

19 Estimated Service Duration Mean = Median = Standard Deviation =

20 Service times at Amsterdam Airport Service Time [Min] Latitude [ ] Longitude [ ]

21 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.

22 Travel Times

23 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;

24 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;