=Paper= {{Paper |id=Vol-3310/paper2 |storemode=property |title=A framework for encoding the multi-location load state of a business process |pdfUrl=https://ceur-ws.org/Vol-3310/paper2.pdf |volume=Vol-3310 |authors=Björn Rafn Gunnarsson,Jochen De Weerdt,Seppe Vanden Broucke |dblpUrl=https://dblp.org/rec/conf/ijcai/GunnarssonWB22 }} ==A framework for encoding the multi-location load state of a business process== https://ceur-ws.org/Vol-3310/paper2.pdf

A framework for encoding the multi-location load
state of a business process
Björn Rafn Gunnarsson1 , Jochen De Weerdt1 and Seppe vanden Broucke2,1
1
Research Center for Information Systems Engineering (LIRIS), KU Leuven, Naamsestraat 69, Leuven 3000, Belgium
2
Department of Business Informatics and Operations Management, UGent, Tweekerkenstraat 2, Ghent 9000, Belgium

Abstract
Predictive process monitoring techniques proposed in the literature have in general relied on intra-case
features in order to make predictions. Consequently, these techniques do not incorporate inter-case
information, e.g. reflecting the overall state of the process. In this work, a novel framework for encoding
inter-case features is proposed. This framework enriches events with a representation of the multi-
location load state of a business process. The framework solely relies on deriving the load state at
relevant locations in the process and therefore provides users with a straightforward approach for
incorporating the status of a business process. The framework was evaluated using a typical predictive
process monitoring setup over a number of real-life event logs where predictive process monitoring
techniques were developed for predicting the remaining processing time of ongoing cases. A general
performance gain was observed for models that use inter-case features encoded using the proposed
multi-location load state framework compared to models that only consider intra-case features in order
to make predictions. This opens up interesting avenues for future research including expanding the
proposed framework so that it additionally incorporates forecasts for the future multi-location load state
of a process under investigation.

Keywords
Predictive process monitoring, Inter-case features, Process mining, Remaining time prediction

1. Introduction
Modern businesses rely on process-aware information systems to support their business pro-
cesses. Consequently, detailed information can be extracted from these systems in the form
of event logs containing information on the actual execution of the business processes [1].
Predictive process monitoring (PPM) is a domain of research which concerns itself with devel-
oping predictive models based on historical process executions [2]. These methods can provide
organizations with valuable insights in order to improve business operations, e.g. by providing
predictions for future process violations and/or delays for ongoing cases. This in turn allows
businesses to carry out preventive measures in order to mitigate the loss resulting from such
deviations [3, 4]. Consequently, a variety of predictive process monitoring techniques have been
proposed for different prediction tasks such as remaining time prediction [5, 6, 7], outcome-
oriented prediction [8, 9, 10], next event prediction [11, 12, 13] and trace prediction [14, 15, 16].

PMAI@IJCAI22: International IJCAI Workshop on Process Management in the AI era, July 23, 2022, Vienna, Austria
Envelope-Open bjornrafn.gunnarsson@kuleuven.be (B. R. Gunnarsson); jochen.deweerdt@kuleuven.be (J. De Weerdt);
seppe.vandenbroucke@ugent.be (S. vanden Broucke)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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In general, PPM techniques proposed in the literature rely on encoding schemes where
intra-case features, i.e. providing information about the execution history of a specific ongoing
case of interest, are constructed and utilized in order to make predictions. Therefore, these
techniques assume that the processing of a case solely depends on the attributes of the case itself.
However, cases are not processed in isolation and their processing can potentially be influenced
by other cases processed in the system [17]. Recently, techniques have been proposed in order
to extract relevant inter-case features from event logs [18, 19, 20]. The motivation for this
development is to allow PPM techniques to additionally incorporate information on the overall
status of the process under investigation in order to make improved predictions for an ongoing
case of interest.
In this work, we propose a framework for generating inter-case features enriching events
with information on the multi-location load state of the process. A pivotal advantage of this
framework is that it solely relies on encoding the load state at relevant locations in the process
where locations are defined based on control-flow information. It therefore provides practition-
ers with a straightforward approach for incorporating the relevant status of a business process
in order to make improved predictions when developing PPM techniques. Two configurations of
the suggested framework are considered. On the one hand, a general system based encoding is
proposed, containing a representation of the load state at a fixed set of important locations in the
system. On the other hand, a case based encoding is introduced, providing a representation of
the status of a process in close proximity to a case of interest. Additionally, two approaches for
deriving the load state for a single location in a business process are considered and compared.
The first counts the number of active cases in a location and therefore provides a snapshot view
of the current status at a given location. The second identifies an optimal time window and
counts the number of cases which have been processed at the location during this optimal time
window.
The remainder of this paper is structured as follows. An overview of the relevant literature is
provided in Section 2. The following section provides relevant background information. The
framework for encoding the multi-location load state of a business process is introduced and
discussed in Section 4. Section 5 provides details on the considered experimental setup and the
results of the experimental evaluation of the proposed framework. This is followed by a more
detailed discussion on the obtained results in Section 6. The last section of this paper provides
concluding remarks and opportunities for future work.

2. Literature review
The development of accurate PPM methods has been extensively studied in the current literature.
However, the lion’s share of research in PPM has solely considered intra-case information, i.e.
information originating from the execution history of the case of interest, in order to make
predictions for that case. These studies therefore assume that cases are processed in isolation
and therefore are not affected by the processing of other cases. However, this assumption
seems unrealistic for many processes, e.g. where cases compete for a limited number of
resources [18, 21].
Nonetheless, a few papers have incorporated a limited number of inter-case features when
developing PPM techniques. In [8], the authors considered the total number of active cases
at the time of execution of a given event as a feature when predicting the outcome of cases.
Similarly, [22] considered the number of active cases when predicting the remaining processing
time of cases. Additionally, a few studies (see e.g. [20, 23, 24]) have considered using the so
called performance spectrum [17] in order to extract a number of performance related inter-case
features which in turn can be utilized for predictive performance monitoring tasks.
Previous research most related our work is proposed in [18] and [25]. In [18] the authors
propose a general encoding framework for deriving inter-case features. This framework relies
on the general notion of case-types which can be used to partition an event log into groups of
cases that share a common characteristic (i.e. case type). Then, a derivation function is used
to obtain representations of inter-case dependencies. The authors evaluate this framework by
considering different definitions of case-types and compare the performance of models which
are allowed to use inter-case features to models that solely rely on intra-case features in order to
make predictions. The best performing model is obtained when case-types are defined based on
a prefix consisting of the last three observed events of active cases and the derivation function
set to count the number of active cases of each case-type. In [19], the authors extend on the
work presented in [18] by considering a data-driven approach for obtaining a representation of
inter-case dependencies where proximity measures are used to identify relevant concurrently
running cases when making predictions for a case of interest. Similarly, [25] proposes a general
framework for deriving inter-case features. This framework relies on considering a number
of process perspectives, i.e. control-flow, resource, time and attribute, compared to the very
general notion of case-types. The authors then derive inter-case features for each perspective,
e.g. the number of cases associated with a specific resource in a user specified time window.
In this paper we extend on the current body of PPM research by proposing a system load
based framework for developing inter-case features. To their benefit, previously proposed
frameworks for constructing inter-case features are general and multiple different features can
be considered and constructed within the proposed frameworks. The framework proposed
in [18] for example relies on the very general notion of case types and derivation functions in
order to derive inter-case features. Similarly, the framework proposed in [25] relies on a number
of process perspectives and multiple inter-case features can be considered and constructed for
each of these perspectives. However, the very general nature of these frameworks makes them
not straightforward to implement. In comparison, the framework for encoding a multi-location
load state proposed here is straightforward to implement for event logs in general. The proposed
framework relies on computing system loads at relevant locations in the business process under
investigation in order to enrich events with a representation of the multi-location load state
of a business process. Two alternative configurations are considered in order to derive the
status at relevant locations in a business process. Firstly, a global system based configuration is
considered where each event is enriched with information on the status at multiple important
locations in the system. Secondly, a case specific configuration is considered where events
are enriched with information on the status of the system in close proximity to the case of
interest. In order to derive the status of the system in a specific location two derivation functions
are considered and compared. The first computes the number of active cases and has been
previously considered for deriving inter-case features (see e.g. [8, 18]). The second relies on
computing the number of cases which have recently visited the location for which we want
to derive the status of. A similar function was considered in [25] where the authors utilize
a user specified time window in order to derive inter-case features. However, we extend on
this approach by proposing a method for automatically identifying an optimal time window
(duration) for the different locations considered.

3. Preliminaries
PPM techniques are developed using previously recorded events representing executions of
activities in a business process [8]. An event is a tuple 𝑒 = (𝑐, 𝑡, 𝑎, 𝑑1 , ..., 𝑑𝑚 ) with 𝑐 a case identifier,
𝑡 a timestamp, 𝑎 an activity label and 𝑑1 , ..., 𝑑𝑚 a number of additional attributes with 𝑚 ≥ 0.
A labeling function maps an event to the value of one of its attributes. Let Case ∶ 𝑒 → 𝑐,
Activity ∶ 𝑒 → 𝑎, Time ∶ 𝑒 → 𝑡 and Attribute𝑚 ∶ 𝑒 → 𝑑𝑚 be labeling functions that return the
case identifier, activity label, timestamp and the attribute(s) for a given event. Given these
attributes, events can be grouped into traces which are ordered sequences of events for each
case where each event refers to a task. More formally, a trace can be defined as 𝜎 = ⟨𝑒1 , ..., 𝑒𝑛 ⟩,
where 𝑛 is the length of the trace and 𝑒𝑖 ∈ 𝜎 is the event at position 𝑖 in trace 𝜎. It holds that
∀𝑒𝑖 , 𝑒𝑗 ∈ 𝜎 , 𝑖 < 𝑗 ∶ Time(𝑒𝑖 ) < Time(𝑒𝑗 ) ∧ Case(𝑒𝑖 ) = Case(𝑒𝑗 ), i.e. the events in the trace are ordered
w.r.t. time and all events in the trace share the same case identifier. An event log can then be
defined as a set of traces 𝐿 = {𝜎 1 , ..., 𝜎 𝐾 } where 𝐾 is the total number of traces and 𝜎 𝑚 ∈ 𝐿 is the
𝑚th trace in the event log 𝐿.
In order to make prediction about the future of an ongoing case, PPM techniques extract
information from the execution of historical cases. Since, predictions should be made at any
point in a case’s development these techniques rely on partitioning traces into a set of pre-
fixes. Given a trace 𝜎 = ⟨𝑒1 , ..., 𝑒𝑛 ⟩ and two positive integer 𝑘 < 𝑛 and 𝑤 < 𝑛, we define
Prefix(𝜎, 𝑘, 𝑤) = ⟨𝑒𝑘−𝑤+1 , ..., 𝑒𝑘 ⟩ which returns a prefix consisting of 𝑤 number of events. Typ-
ically, PPM techniques rely on labeling functions to derive a relevant feature encoding from
obtained prefixes, i.e. in order to extract the activity labels and other relevant attributes of
events. Additionally, other functions are often defined to engineer features from the raw event
attributes, e.g. a function that extracts the hour of the day from the timestamp of an event or
the time which has elapsed since the last activity was executed for that case.

4. A framework for encoding the multi-location load state of a
business process
By focusing on intra-case features, a large majority of PPM techniques ignore inter-case dynam-
ics when making predictions for ongoing cases. Consequently, these approaches unrealistically
assume that cases are processed in isolation from other cases and that the processing of cases
is independent of the status of the business process where they are being processed. This
limitation has been recognized in [18] and [25] where two general frameworks for constructing
inter-case features are proposed. Due to their general nature, almost any type of inter-case
feature can be considered and constructed within these frameworks. The framework proposed
here solely relies on enriching events with a multi-location load state of relevant locations in a
Figure 1: A graphical representation of the approach used to count active number of cases in a
considered location for time point 𝑡 derived for an event of interest (i.e. 𝑡 = 𝑇 𝑖𝑚𝑒(𝑒𝑡𝑚 )). In the figure three
cases (in blue) are considered active in a location (𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛) at a given time-point (𝑡), e.g. 𝑒𝑖3 (𝑇 𝑖𝑚𝑒(𝑒𝑖3 ) <
𝑡, 𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦(𝑒𝑖3 ) = 𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛) and 𝑒𝑖+1
3 3
(𝑇 𝑖𝑚𝑒(𝑒𝑖+1 3
) > 𝑡, 𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦(𝑒𝑖+1 ) ≠ 𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛). Additionally, two examples
(in red) are given of cases which are not considered active in location at the given time-point. One where
1
the processing of an event occurs before the given time-point, i.e. 𝑇 𝑖𝑚𝑒(𝑒𝑖+1 ) < 𝑡, and another where the
5
processing of an event occurs after the given time-point, i.e. 𝑇 𝑖𝑚𝑒(𝑒𝑖 ) > 𝑡.

business process where locations are defined based on control-flow information obtained from
the process under investigation.

4.1. Deriving the load state for a single location in a business process
Two approaches are considered and compared in order to obtain a representation of the load
state at a relevant location in a process. Both approaches rely on computing the loads at relevant
locations of processes. However, they differ with respect to specifying the duration considered
when computing the load for a given location.

Number of active cases in a location. The first approach considered for deriving the status
at a specific location provides a snapshot view of the number of cases currently being processed
at the location under investigation. It therefore, relies on counting the number of active cases at
a given location for a given time-point. Hereto, we simply count all currently active cases which
most recent event’s activity label matches the location for which a load will be computed (i.e.
𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦(𝑒𝑖𝑚 ) = 𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛) and were executed before this specific time-point (i.e. 𝑇 𝑖𝑚𝑒(𝑒𝑖𝑚 ) < 𝑡).
This is visualized in Figure 1. In the figure, three cases (given in blue) match the conditions
outlined above, i.e. their most recently observed activity label matches the load location of
interest and are currently being processed at that location.

Number of cases in an optimized time window. The second approach considered for
deriving the status at a specific location counts the number of cases which have recently passed
through a specific location of interest. In order to count the number of cases which have recently
been processed at a location a duration needs to be specified for each location. To specify this
duration we first compute both the median throughput time and the 95th percentile throughput
time value for the location of interest. Then a search is carried out for an optimal duration value
in a range defined by the median and 95th percentile value for each location. To find the optimal
Figure 2: A graphical representation illustrating the approach used to count number of recently observed
cases in a location of interest. Given an event (i.e. 𝑒𝑚𝑖 ) an optimal duration (given in green) for location of
interest is identified (i.e. 𝑑𝑢𝑟 = 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛(𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛, 𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦(𝑒𝑚𝑖 ))). The endpoints of the considered time
window are then defined by the timestamp of the event of interest (i.e. 𝑡 = 𝑇 𝑖𝑚𝑒(𝑒𝑚𝑖 )) and the starting
point is defined by the considered duration, (i.e. 𝑡 − 𝑑𝑢𝑟).

duration for each load location we utilize a random forest trained to predict the remaining
runtime of events based on the loads obtained for a specific location using each candidate
duration. This optimization is carried out separately for all activity labels of events in order to
identify the optimal duration for each combination of load location and activity label. Then, in
order to compute the load at a specific location for a given event we simply extract the time
stamp of that event and its activity label and identify the optimal duration for that combination
of load location and activity label (i.e. 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛(𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛, 𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦(𝑒𝑖𝑚 )). In order to compute the
load for an event of interest we simply count all events which event’s activity label matches
the location for which a load will be computed (i.e. 𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦(𝑒𝑖𝑚 ) = 𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛) and fall in a time
window which endpoints are determined by the time stamp of the event and the optimal duration
for that location and activity label (i.e. [𝑇 𝑖𝑚𝑒(𝑒𝑖𝑚 ) − 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛(𝐿𝑜𝑐𝑎𝑡𝑖𝑜𝑛, 𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦(𝑒𝑖𝑚 )), 𝑇 𝑖𝑚𝑒(𝑒𝑖𝑚 )]).

4.2. System based multi-location load state
As mentioned here above cases are not processed in isolation and their processing can be
influenced by the status at important locations in a business process. As an example one can
think of a recently created loan application which needs to be evaluated. The time it will
take to process this application might be affected by the current or recent number of other
loan applications that have been evaluated in the this loan application process. Additionally,
the case might be affected by the number of cases at a later process step, e.g. the number of
loan applications that have already been approved but for which an loan offer has yet to be
created. Therefore, the processing of this loan application is not solely affected by intra-case
attributes (e.g. previous activities carried out for that case) but also the current or recent status
at important locations in the process. The system based inter-case encoding enriches events
with information on the status at important locations in a process under investigation. In order
to identify important locations we first compute the throughput time of different locations in
the process and discard automatic locations. Additionally, infrequent locations (i.e. activities
which are carried out for < 1% of the total number of events) are discarded. All events are then
enriched with a multi-location load state containing the load state at important locations in the
system.
4.3. Case based multi-location load state
The system based inter-case encoding discussed here above provides a representation of the
general status at important locations in the system. However, a case might mainly be affected
by the load state at locations in the process which are in close proximity to the current location
of the case. In order to obtain a representation of the status of the process in close proximity to
a case of interest a multi-location load state is derived for locations which are connected to the
current location of a case. Firstly, the processing of a case at a given location might be affected
by the status at other locations that the case has previously visited. Therefore, we consider the
load state at the last location where a case was processed. Secondly, the processing of a case
might be affected by the load state at the location where the case is currently being processed.
Lastly, the processing of a case of interest might be affected by the status at the locations which
the case is most likely to visit next given its current location. In order to derive the load state at
likely next locations we therefore compute the state for the five most likely next location given
the current location of a cases where e.g. the most likely next location is the location which is
most frequently visited next by cases which are processed at the current location of that case.
All events are therefore enriched with a multi-location load state containing the load state of
the last location where the case was processed, the load state of the current location of that
case and the load state of the five location where the case is most likely to be processed next.

5. Experimental evaluation
5.1. Event logs
A number of event logs were considered when evaluating the multi-perspective framework
proposed here. An overview of the considered event logs is given in Table 1. Two of event logs
have been made available in relation to the BPI Challange (BPIC), i.e. the BPIC121 and BPIC172 .
The BPIC12-Sub event log is a filtered version of the BPIC12 event log where repetitive events
(i.e. sharing the same activity label as the previously observed event) are removed. The BAG
event log was was retrieved from the the luggage system of a Brussels Airport. Information
on the characteristics of the different event logs is provided in the table. As can be seen the
considered event logs are quite varied in terms of the number of available cases (Cases), average
trace length (Avg. TL), processing times (Avg. Duration) and number of possible activities
executed (Numb. Locations). We also report on the number of important locations (Numb.
Imp. Locations), i.e. where non-automatic frequent activities are executed. The system based
inter-case encoding scheme discussed here above enriches events with the multi-location load
state at these important locations. Time independent data splits between training and test set
were utilized when evaluating the performance of the considered models. Hereto, cases in the
event logs were order based on their timestamps. Then, the last occurring quarter of cases was
considered a test set. The remaining cases which had been processed when the first case in the
test set started its process execution were then chosen as a training set.

1
10.4121/uuid:3926db30-f712-4394-aebc-75976070e91f
2
10.4121/uuid:5f3067df-f10b-45da-b98b-86ae4c7a310b
Table 1
Considered event logs
Avg. Numb. Numb. Imp.
Event log Sector Cases Avg. TL Duration Locations Locations
BPIC17 Finance 31509 18 31646 (min) 28 14
BPIC12 Finance 13087 20 12037 (min) 26 5
BPIC12-Sub Finance 13087 12 12037 (min) 26 5
BAG Operations 432357 5 1187 (sec) 60 9

5.2. Implementation
The proposed framework for encoding a multi-location load state was evaluated using a con-
ventional PPM setup. Here, multiple prefixes were extracted from all traces in each event log
using a window length of 3 and left padded where necessary (i.e. 𝑃𝑟𝑒𝑓 𝑖𝑥(𝜎 , 𝑘, 3) for 𝑘 in
⟨1, ..., 𝑛⟩). Then, a feature vector was extracted from the obtained prefix and propagated to a
random forest regressor [26] trained to predict the remaining processing time of a case given a
feature vector. Four versions of feature vectors were considered.

• Intra-case vector solely contains intra-case information. In order to construct this feature
vector, activity labels for all events in the obtained prefixes were extracted and one-hot
encoded. Time related information (i.e. the day of the week and hour of the day) was
additionally extract and included in this feature vector.
• System based multi-location load state vector contains a multi-location load state at impor-
tant locations in the system obtained using the system based inter-case encoding scheme
described here above in addition to the considered intra-case features.
• Case based multi-location load state vector was constructed using the case based inter-case
feature encoding described here above. It therefore contains the multi-location load state
of locations in close proximity to a case of interest in addition to the considered intra-case
features.
• System and case based multi-location load state vector was additionally considered which
includes all intra and inter-case features described here above.

The two approaches for deriving the load state at a location, i.e. counting the active number
of cases and counting the number of cases in a optimal time window, were both considered
and compared for all models which utilize inter-case features when predicting the remaining
processing time of cases.

5.3. Results
The results are summarized in Table 2. Our proposed encodings are compared to the baseline
scenario of only relying on intra-case features. The mean absolute error (MAE) was used to
measure the performance of models. We report on the prediction error in minutes for all event
logs with one exception, namely the BAG event log, where we report on the error in seconds
since the cases in that event log in general take considerably shorter time to process (as can be
seen from Table 1).
Table 2
Prediction results for remaining time prediction evaluated using MAE. Models which outperform the
baseline intra-case feature model are given in bold. Additionally, an underscore is used to indicate the
overall best performing model for each event log.

Feature vector BPIC17 BPIC12-Sub BPIC12 BAG
Intra-case vector 10567 7988 8591 707
System based multi-location load state vector
Number of active cases 10788 8562 8573 704
Number of cases in optimized time window 10548 7910 8387 703
Case based multi-location load state vector
Number of active cases 10527 7849 9041 691
Number of cases in optimized time window 10520 7947 8396 690
System and case based multi-location load state vector
Number of active cases 10822 8076 9076 704
Number of cases in optimized time window 10520 7885 8361 699

A general performance gain can be observed for models that use inter-case features compared
to models that solely rely on using intra-case features when predicting the remaining processing
time of cases. As can be seen from the table, models that utilize a feature vector which contains
some version of the multi-location load state encoding proposed here is the best performing
model on all event logs considered. More specifically, a model that uses a case based multi-
location load state vector, containing information on the load states of locations connected to
the current location of a case of interest in addition to intra-case features, is the best performing
model on all considered event logs, with one exception being the BPIC12 event log where a
model that uses both system and case based multi-location load state vector in order to make
predictions performs best.
When the two approaches for deriving the load state at a given location are compared, one can
see that counting the number of recently observed cases in a time window which is optimized
for all combinations of locations for which a load is computed and activity labels of events in
general leads to a better performance compared to counting the number of active cases in a load
location. This is the case for all event logs and versions of the multi-location load state vectors
considered here with one exception, namely a model trained using a case based multi-location
load state vector on the BPIC12-Sub event log. Here, considering the number of active cases
leads to better performance for predicting the remaining processing time of cases compared to
considering the number of cases in a optimized time window.

6. Discussion
A general performance increase was observed for models that are allowed to utilize inter-case
features, developed using the proposed framework for encoding a multi-location load state,
when predicting the remaining processing times of cases compared to models that solely rely
on using intra-case features for this prediction task. From Table 1 it can be observed that
the average processing time for cases in the BAG event log is considerably shorter then for
other event logs. This event log was obtained from the luggage system at a large international
airport. The system is almost fully automated, with bags being scanned at each location when
moving through the system. From the results, we can observe a relatively large performance
gain for this event log when models are allowed to utilize inter-case features obtained using
the framework proposed here. Additionally, it can be observed that all considered versions of
multi-location load state vectors and approaches for deriving the load state at a location lead to
an improved performance compared to solely relying on intra-case features when predicting
the remaining processing time for cases in this event log. To some extent this is to be expected
given the nature of this process, i.e. it seems reasonable that the processing of bags in a luggage
handling system is largely affected by the load state at relevant parts of the system in addition to
intra-case features. Other event logs considered were extracted from loan application processes
of banks. As can be seen the best performing model for all of these event logs was obtained
using a version of a multi-location load state vector. Therefore, incorporating load state at
relevant locations in the considered loan application processes has a beneficial impact. However,
the processing time of loan applications is also largely influenced by external factors which
cannot be represented by typical intra-case features nor inter-case features. The processing of a
loan application will for example to some extent depend on the willingness of the loan applicant
to participate in the process, e.g. by correctly filling out his loan application and responding
to a loan offer. Therefore, the processing does not solely depend on typical intra-case features
or inter-case features but also other contextual information which is not incorporated by the
multi-location load state encoding framework proposed here.

7. Conclusion
The framework proposed in this paper encodes a multi-location load state representation at
relevant locations in a business process. This framework solely relies on deriving the load
state at relevant locations and therefore provides users with a straightforward approach for
incorporating the status of a business process in order to make improved predictions when
developing PPM techniques. This framework was evaluated using a conventional PPM setup
where random forest regression models were trained to predict the remaining processing times
of cases. The models were constructed using three different feature vectors obtained using
the proposed framework and their performance compared to a model which solely relies on
intra-case features in order to make prediction. This comparison was carried out over four
real-life event logs. A general performance gain was observed for models that use inter-case
features encoded using the multi-location load state framework proposed here. More specifically,
models that used a case based multi-location load state vector in addition to intra-case features
performed best on all considered event logs with one exception where a model that uses both
system and case based multi-location load state performed best.
The proposed framework relies on encoding the current or recent load state at relevant
locations in a process under investigation. However, the future status of a process might also
have an impact on the processing of cases. It would therefore be of interest to expand on the
framework proposed here by incorporating predictions for the future multi-location load state
of a process under investigation. Additionally, LSTMs [27] have been shown to perform well
for a number of PPM tasks including predicting the remaining processing time of cases. It
would therefore be of interest to investigate the additional value of incorporating inter-case
features encoded using the multi-location load state framework proposed here in a PPM setup
which uses an LSTM for this prediction task. Lastly, this paper evaluated the additional value
of inter-case features obtained using the proposed framework for predicting the remaining
processing time of cases. It would be of interest to expand on this by evaluating the additional
value of incorporating information encoded using the proposed framework for other prediction
tasks.

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