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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>A Tool for Visualizing Costs of Process Variants through Directed Rooted Trees</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Ignacio Velásquez</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Marcos Sepúlveda</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Computer Science, Pontificia Universidad Católica de Chile</institution>
        </aff>
      </contrib-group>
      <abstract>
        <p>Models depicting the behavior and performance of processes can be discovered through Process Mining. These models often facilitate visualizing alternate paths and rework through control-flow logic, but identifying all process variants in such models can become a complex endeavor. To address this, a tool that allows visualizing all process variants within a single model is proposed, in the form of Directed Rooted Trees whose leaves are the end states of variants. The generated trees are also decorated with cost information for quickly comparing the cost performance of variants. The tool is expected to be useful for performing exploratory analyses.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Process Mining</kwd>
        <kwd>Process Discovery</kwd>
        <kwd>Performance Analysis</kwd>
        <kwd>Cost Dimension</kwd>
        <kwd>Directed Rooted Tree</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>the two without applying filters or analyzing the data within the event log.</p>
      <p>
        To address the above, this work proposes a tool that allows the visualization of all process
variants within a single process model. Specifically, the proposed process model is in the form
of a transition system constructed as a Directed Rooted Tree (DRT). In transition systems, the
events of the process are the transitions that imply the flow from one state of the system to
another [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. A DRT, or arborescence, is an acyclic graph that has exactly one path from its root
to each vertex [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. Based on this definition, every bifurcating behavior observed in the event
log generates a separate set of transitions within the proposed DRT visualization. Thus, every
leaf of the resulting model corresponds to the end state of a process variant. Using the same
minimal example as above, Figure 1 (b) shows the DRT generated by the tool. This DRT allows
observing that the actual traces of the event log are "AA" and "AB".
      </p>
      <p>
        Transition systems can be extended to include additional information [
        <xref ref-type="bibr" rid="ref5 ref6">5, 6</xref>
        ]. To provide
additional value with the proposed tool, the use of cost-annotated event logs is supported [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ].
By uploading such a log, the average total, accumulated, and remaining costs of cases flowing
through every state can be observed, as well as the average, minimum, and maximum costs of
every transition. States are also colored based on the average total cost of flowing cases. Using
the decorated information, the visualization provided by the tool allows quickly comparing the
cost performance of process variants, such as identifying the most expensive ones. Figure 1 (c)
shows the DRT of the cost-annotated minimal example generated by the tool.
      </p>
      <p>
        The DRT generated by the proposed tool possess similarities with context trees [
        <xref ref-type="bibr" rid="ref7 ref8">7, 8</xref>
        ]. Both
DRT and context trees allow visualizing the bifurcating behavior of event logs. On one hand, the
nodes in context trees indicate the activity executed in a given path, and its frequency, which
has facilitated the use of these trees for trace clustering. On the other hand, while the proposed
DRT maintain the same activity information in their transitions, the focus is on visualizing the
performance behavior of variants through the annotated aggregation metrics.
      </p>
      <p>The remainder of this work is structured as follows. Section 2 describes the main features of
the tool, as well as its interface. In Section 3, the maturity of the tool is discussed. Section 4
provides links for the demonstration of the tool in the form of a tutorial document and video.
Finally, the conclusions of this work are presented in Section 5.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Tool Features</title>
      <p>
        The proposed tool is available at https://bit.ly/drt-variant-costs. It has been developed as a
web application using the Angular framework [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. For generating the DRT, the Mermaid
diagramming and charting tool [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ] is utilized. Figure 2 shows the interface visualized when
accessing the tool. This interface can be split into three areas: (1) the buttons enabling the
distinct features of the tool, (2) the diagram area, which will contain the Directed Rooted Trees
(DRT) generated by the tool, and (3) the format requirements for the event logs to load.
      </p>
      <p>The buttons in area (1) enable the distinct features of the tool. The "Load Event Log" button
visualizes a modal for loading an event log to the tool. Once loaded, the tool automatically
generates the resulting DRT. The "Filter Event Log" button visualizes a modal containing three
types of filters: “Activities to Include”, which filters the diagram to only visualize events of
selected activities; “Start Activities”, which filters the diagram to only include cases that start
with selected activities; and “End Activities”, which filters the diagram to only include cases
that end with selected activities. The "Configuration" button visualizes a modal that allows
changing the displayed currency, and the visualization of additional metrics in every state and
transition of the DRT. Finally, the "Download Diagram (PNG)" and "Download Diagram (SVG)"
buttons allow the download of a *.png or a *.svg file, respectively, containing the generated DRT.</p>
      <p>By default, the states (nodes) of the transition system of the generated DRT contain the
average case cost of executions flowing through them, whereas transitions (arcs) contain the
activities executed between every state, and their frequency. States are colored using a trafic
light color range (from green, to yellow, to red). The closer to green, the cheaper the average cost
of executions flowing through the state. Conversely, the closer to red, the more expensive the
average cost of flowing executions. The line width of transitions relates to the case frequency,
i.e., a wider transition line corresponds to one with a higher occurrence frequency.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Tool Maturity</title>
      <p>The tool is currently in a stable version. That is, no major bugs are known and all the features
described in this work are implemented. Nevertheless, the maturity of the tool can be described
in relation to its current limitations.</p>
      <p>
        First, as any transition system, the generated DRT has problems expressing parallelism.
Parallelism occurs when two activities of a case overlap [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. As future work, it is desirable to
devise a tool with similar features, but that generates models using a notation that supports
parallelism, such as BPMN [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]. Such a notation could also be used to consider the existence of
process variants in relation to case or activity attributes, rather than solely control-flow.
      </p>
      <p>Second, only visualization of cost performance is currently supported. As future work, the
possibility of extending the tool to also support waiting times between activities is considered.
The visualization of any metric that can be aggregated is also foreseen.</p>
      <p>
        Third, the tool has been designed for processing any event log that complies with the required
format. However, loading event logs containing large numbers of cases (e.g., over 10,000) will
result in long processing times. Moreover, the utility of the tool is reduced when loading event
logs with excessive numbers of variants (e.g, over 100), as their comparison would be dificult
without applying filters. To facilitate the analysis of processes with several variants, the trace
clustering techniques used for context trees [
        <xref ref-type="bibr" rid="ref7 ref8">7, 8</xref>
        ] could be evaluated as future work. Regarding
the performance of the tool, a revision of the source code is considered.
      </p>
      <p>Fourth, design limitations, such as the currently required event log format, could be addressed
through future work. Namely, through input boxes for users to indicate column names of the
event log or the format of timestamps. The possibility of downloading the DRT in editable
formats, such as JSON, or the notation of the used diagramming library, is also considered.</p>
      <p>
        The tool has not been used for real case studies yet. However, it was tested with the road
trafic fine management event log, which contains real-life records of an information system
from an Italian city [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ]. The DRT for this process was generated correctly.
      </p>
    </sec>
    <sec id="sec-4">
      <title>4. Tool Demonstration</title>
      <p>A tutorial document containing step-by-step instructions on how to utilize the tool has been
constructed. This document can be found at https://bit.ly/drt-tutorial-document. A video
summarizing this tutorial can be found at https://bit.ly/drt-video-tutorial.</p>
      <p>
        In the tutorial, an example is used for illustrative purposes. The example is based on the
blasting process of a Chilean copper mine. A model with the activities of this process is publicly
available in Appendix 4 of [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]. Blasting is one of the main methods used in the mining industry
to fragment hard rock minerals [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ]. It is a complex process that requires coordination of
various activities between the blasting crew and other employees [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ]. A detailed description of
this process is included in the tutorial document.
      </p>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion</title>
      <p>This work proposes a tool for the visualization of process variants within a single process model,
in the form of a Directed Rooted Tree. Every leaf of the DRT is the end state of a variant, which
facilitates their side-to-side comparison. The above is enhanced by the inclusion of cost metrics,
which are supported by a color range for the identification of cheaper and more expensive
process variants.</p>
      <p>The proposed tool is expected to serve as a complementary visualization of discovered
processes when performing exploratory analyses of event logs.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>This work was funded by the Agencia Nacional de Investigación y Desarrollo de Chile. Grant
numbers ANID FONDECYT 1230697 and ANID-Subdirección de Capital Humano/Doctorado
Nacional/2021-21210022.</p>
    </sec>
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