Methods and systems for estimating latent service and latent wait times include extracting transition times between activities from a partial event log. Parameters for respective gamma distributions are estimated that characterize latent waiting time and latent service time for each activity. A latent waiting time and latent service time for each activity is estimated based on the estimated parameters using a processor.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for estimating latent service and latent wait times, comprising: extracting transition times between activities from a partial event log; estimating parameters for respective gamma distributions that characterize latent waiting time and latent service time for each activity; and estimating a latent waiting time and latent service time for each activity based on the estimated parameters using a processor. 2. The method of claim 1, further comprising determining a likelihood that the estimated parameters would reproduce the partial event log. 3. The method of claim 2, further comprising iterating the estimation of parameters and the determination of the likelihood until the likelihood converges. 4. The method of claim 3, wherein the iteration ends when a likelihood from a previous iteration is within a threshold value of a likelihood from a current iteration. 5. The method of claim 2, wherein the likelihood is determined by: ∑ ( a , b ) ∈ Trans  ∑ k = 1 n ab  log  e - t α   bk β b Γ  ( l a )  Γ  ( m b )  α a l a  β b m b  f  ( t abk , l a , α a , m b , β b ) wherein a is a source activity, b is a destination activity, nab is a number of observed transition times from a to b, tabk is the kth transition time from a to b, la, αa, mb, and βb are parameters of the gamma function Γ(x), and f  ( t , l , α , m , β ) = ∫ 0 t  z l - 1  ( t - z ) m - 1  e ( 1 β - 1 α )  z  dz . 6. The method of claim 1, wherein the partial event log comprises only one of start-event information and end-event information for each activity. 7. The method of claim 1, wherein extracting transition times between activities comprises: determining a first event at which a source activity is first recorded in the partial event log; and determining a second event at which a destination activity is first recorded in the partial event log, wherein the transition time between the source activity and the destination activity is a difference in time between the first event and the second event. 8. The method of claim 1, wherein the latent service time is estimated as: sa=laαa wherein a is an activity, la is a shape parameter of a gamma distribution for the activity, and αa is a scale parameter of the gamma distribution for the activity. 9. The method of claim 1, wherein the latent waiting time is estimated as: wa=maβa wherein a is an activity, ma is a shape parameter of a gamma distribution for the activity, and βa is a scale parameter of the gamma distribution for the activity. 10. A computer readable storage medium comprising a computer readable program for estimating latent service and latent wait times, wherein the computer readable program when executed on a computer causes the computer to perform the steps of claim 1. 11. A method for estimating latent service and latent wait times, comprising: extracting transition times between activities from a partial event log that comprises only one of start-event information and end-event information for each activity; estimating parameters for respective gamma distributions that characterize latent waiting time and latent service time for each activity, comprising: determining a likelihood that the estimated parameters would reproduce the partial event log; and iterating the estimation of parameters and the determination of the likelihood until the likelihood converges; and estimating a latent waiting time and latent service time for each activity based on the estimated parameters using a processor. 12. A system for estimating latent service and latent wait times, comprising: a transition time module configured to extract transition times between activities from a partial event log; a parameter module configured to estimate parameters for respective gamma distributions that characterize latent waiting time and latent service time for each activity; and a latent time module comprising a processor configured to estimate a latent waiting time and latent service time for each activity based on the estimated parameters. 13. The system of claim 12, wherein the parameter module is further configured to determine a likelihood that the estimated parameters would reproduce the partial event log. 14. The system of claim 13, wherein the parameter module is further configured to iterate the estimation of parameters and the determination of the likelihood until the likelihood converges. 15. The system of claim 14, wherein the parameter module is further configured to halt iteration when a likelihood from a previous iteration is within a threshold value of a likelihood from a current iteration. 16. The system of claim 13, wherein the likelihood is determined by: ∑ ( a , b ) ∈ Trans  ∑ k = 1 n ab  log  e - t α   bk β b Γ  ( l a )  Γ  ( m b )  α a l a  β b m b  f  ( t abk , l a , α a , m b , β b ) wherein a is a source activity, b is a destination activity, nab is a number of observed transition times from a to b, tabk is the kth transition time from a to b, la, αa, mb, and βb are parameters of the gamma function Γ(x), and f  ( t , l , α , m , β ) = ∫ 0 t  z l - 1  ( t - z ) m - 1  e ( 1 β - 1 α )  dz . 17. The system of claim 12, wherein the partial event log comprises only one of start-event information and end-event information for each activity. 18. The system of claim 12, wherein the transition time module is further configured to determine a first event at which a source activity is first recorded in the partial event log and to determine a second event at which a destination activity is first recorded in the partial event log, wherein the transition time between the source activity and the destination activity is a difference in time between the first event and the second event. 19. The system of claim 12, wherein the latent service time is estimated as: sa=laαa wherein a is an activity, la is a shape parameter of a gamma distribution for the activity, and αa is a scale parameter of the gamma distribution for the activity. 20. The system of claim 12, wherein the latent waiting time is estimated as: wa=maβa wherein a is an activity, ma is a shape parameter of a gamma distribution for the activity, and βa is a scale parameter of the gamma distribution for the activity.