  To identify the causes of performance problems or to predict process
behavior, it is essential to have correct and complete event data. This is
particularly important for distributed systems with shared resources, e.g., one
case can block another case competing for the same machine, leading to
inter-case dependencies in performance. However, due to a variety of reasons,
real-life systems often record only a subset of all events taking place. For
example, to reduce costs, the number of sensors is minimized or parts of the
system are not connected. To understand and analyze the behavior of processes
with shared resources, we aim to reconstruct bounds for timestamps of events
that must have happened but were not recorded. We present a novel approach that
decomposes system runs into entity traces of cases and resources that may need
to synchronize in the presence of many-to-many relationships. Such
relationships occur, for example, in warehouses where packages for N incoming
orders are not handled in a single delivery but in M different deliveries. We
use linear programming over entity traces to derive the timestamps of
unobserved events in an efficient manner. This helps to complete the event logs
and facilitates analysis. We focus on material handling systems like baggage
handling systems in airports to illustrate our approach. However, the approach
can be applied to other settings where recording is incomplete. The ideas have
been implemented in ProM and were evaluated using both synthetic and real-life
event logs.
