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@ -40,13 +40,13 @@ Switzerland]{Prof.}{Walter}{Binder}
Switzerland]{Dr.}{Andrea}{Ros\'a} Switzerland]{Dr.}{Andrea}{Ros\'a}
\end{committee} \end{committee}
\abstract{The project aims at comparing two different traces coming from large \abstract{The thesis aims at comparing two different traces coming from large
datacenters, focusing in particular on unsuccessful executions of jobs and datacenters, focusing in particular on unsuccessful executions of jobs and
tasks submitted by users. The objective of this project is to compare the tasks submitted by users. The objective of this thesis is to compare the
resource waste caused by unsuccessful executions, their impact on application resource waste caused by unsuccessful executions, their impact on application
performance, and their root causes. We show the strong negative impact on performance, and their root causes. We show the strong negative impact on
CPU and RAM usage and on task slowdown. We analyze patterns of CPU and RAM usage and on task slowdown. We analyze patterns of
unsuccessful jobs and tasks, particularly focusing on their interdependency. unsuccessful jobs and tasks, focusing on their interdependency.
Moreover, we uncover their root causes by inspecting key workload and Moreover, we uncover their root causes by inspecting key workload and
system attributes such as machine locality and concurrency level.} system attributes such as machine locality and concurrency level.}
@ -56,24 +56,23 @@ system attributes such as machine locality and concurrency level.}
\newpage \newpage
\section{Introduction} In today's world there is an ever growing demand for \section{Introduction} In today's world there is an ever growing demand for
efficient, large scale computations. The rising trend of ``big data'' put the efficient, large scale computations. The rising trend of ``big data'' puts the
need for efficient management of large scaled parallelized computing at an all need for efficient management of large scaled parallelized computing at an all
time high. This fact also increases the demand for research in the field of time high. This fact also increases the demand for research in the field of
distributed systems, in particular in how to schedule computations effectively, distributed systems, in particular in how to schedule computations effectively,
avoid wasting resources and avoid failures. avoid wasting resources and avoid failures.
In 2011 Google released a month long data trace of their own cluster management In 2011 Google released a month long data trace of their own cluster management
system\cite{google-marso-11} \textit{Borg}, containing a lot of data regarding system~\cite{google-marso-11} \textit{Borg}, containing a lot of data regarding
scheduling, priority management, and failures of a real production workload. scheduling, priority management, and failures of a real production workload.
This data was 2009
This data was the foundation of the 2015 Ros\'a et al.\ paper This data was the foundation of the 2015 Ros\'a et al.\ paper
\textit{Understanding the Dark Side of Big Data Clusters: An Analysis beyond \textit{Understanding the Dark Side of Big Data Clusters: An Analysis beyond
Failures}\cite{dsn-paper}, which in its many conclusions highlighted the need Failures}~\cite{dsn-paper}, which in its many conclusions highlighted the need
for better cluster management highlighting the high amount of failures found in for better cluster management highlighting the high amount of failures found in
the traces. the traces.
In 2019 Google released an updated version of the \textit{Borg} cluster In 2019 Google released an updated version of the \textit{Borg} cluster
traces\cite{google-marso-19}, not only containing data from a far bigger traces~\cite{google-marso-19}, not only containing data from a far bigger
workload due to improvements in computational technology, but also providing workload due to improvements in computational technology, but also providing
data from 8 different \textit{Borg} cells from datacenters located all over the data from 8 different \textit{Borg} cells from datacenters located all over the
world. world.
@ -90,8 +89,8 @@ in carrying out non-successful executions, i.e.\ executing programs that would
eventually ``crash'' and potentially not leading to useful results\footnote{This eventually ``crash'' and potentially not leading to useful results\footnote{This
is only a speculation, since both the 2011 and the 2019 traces only provide a is only a speculation, since both the 2011 and the 2019 traces only provide a
``black box'' view of the Borg cluster system. Neither of the accompanying ``black box'' view of the Borg cluster system. Neither of the accompanying
papers for both traces\cite{google-marso-11}\cite{google-marso-19} or the papers for both traces~\cite{google-marso-11}~\cite{google-marso-19} or the
documentation for the 2019 traces\cite{google-drive-marso} ever mention if documentation for the 2019 traces~\cite{google-drive-marso} ever mention if
non-successful tasks produce any useful result.}. The 2019 subplot paints an non-successful tasks produce any useful result.}. The 2019 subplot paints an
even darker picture, with less than 5\% of machine time used for successful even darker picture, with less than 5\% of machine time used for successful
computation. computation.
@ -107,7 +106,7 @@ models to mitigate or erase the resource impact of unsuccessful executions.
%\subsection{Challenges} %\subsection{Challenges}
Given that the new 2019 Google Borg cluster traces are about 100 times larger Given that the new 2019 Google Borg cluster traces are about 100 times larger
than the 2011 ones, and given that the entire compressed traces package has a than the 2011 ones, and given that the entire compressed traces package has a
non-trivial size (weighing approximately 8 TiB\cite{google-drive-marso}), the non-trivial size (weighing approximately 8 TiB~\cite{google-drive-marso}), the
computations required to perform the analysis we illustrate in this report computations required to perform the analysis we illustrate in this report
cannot be performed with classical data science techniques. A cannot be performed with classical data science techniques. A
considerable amount of computational power was needed to carry out the considerable amount of computational power was needed to carry out the
@ -118,7 +117,7 @@ MapReduce-like structure.
%\subsection{Contribution} %\subsection{Contribution}
This project aims to repeat the analysis performed in 2015 DSN Ros\'a et al.\ This project aims to repeat the analysis performed in 2015 DSN Ros\'a et al.\
paper\cite{dsn-paper} to highlight similarities and differences in Google Borg paper~\cite{dsn-paper} to highlight similarities and differences in Google Borg
workload and the behaviour and patterns of executions within it. Thanks to this workload and the behaviour and patterns of executions within it. Thanks to this
analysis, we aim to understand even better the causes of failures and how to analysis, we aim to understand even better the causes of failures and how to
prevent them. Additionally, given the technical challenge this analysis posed, prevent them. Additionally, given the technical challenge this analysis posed,
@ -130,12 +129,12 @@ The report is structured as follows. Section~\ref{sec2} contains information
about the current state of the art for Google Borg cluster traces. about the current state of the art for Google Borg cluster traces.
Section~\ref{sec3} provides an overview including technical background Section~\ref{sec3} provides an overview including technical background
information on the data to analyze and its storage format. Section~\ref{sec4} information on the data to analyze and its storage format. Section~\ref{sec4}
will discuss about the project requirements and the data science methods used to discusses about the project requirements and the data science methods used to
perform the analysis. Section~\ref{sec5}, Section~\ref{sec6} and perform the analysis. Section~\ref{sec5}, Section~\ref{sec6} and
Section~\ref{sec7} show the result obtained while analyzing, respectively the Section~\ref{sec7} show the result obtained while analyzing, respectively the
performance input of unsuccessful executions, the patterns of task and job performance input of unsuccessful executions, the patterns of task and job
events, and the potential causes of unsuccessful executions. Finally, events, and the potential causes of unsuccessful executions. Finally,
Section~\ref{sec8} contains the conclusions. Section~\ref{sec8} concludes.
\section{State of the Art}\label{sec2} \section{State of the Art}\label{sec2}
@ -159,17 +158,17 @@ H & Europe/Brussels \\
timezone of each cluster in the 2019 Google Borg traces.}\label{fig:clusters} timezone of each cluster in the 2019 Google Borg traces.}\label{fig:clusters}
\end{figure} \end{figure}
In 2015, Dr.~Andrea Rosà et al.\ published a In 2015, Rosà et al.\ published a
research paper titled \textit{Understanding the Dark Side of Big Data Clusters: research paper titled \textit{Understanding the Dark Side of Big Data Clusters:
An Analysis beyond Failures}\cite{dsn-paper} in which they performed several An Analysis beyond Failures}~\cite{dsn-paper} in which they performed several
analysis on unsuccessful executions in the Google's 2011 Borg cluster traces analyses on unsuccessful executions in the Google's 2011 Borg cluster traces
with the aim of identifying their resource waste, their impacts on the with the aim of identifying their resource waste, their impacts on the
performance of the application, and any causes that may lie behind such performance of the application, and any causes that may lie behind such
failures. The salient conclusion of that research is that actually lots of failures. The salient conclusion of that research is that actually lots of
computations performed by Google would eventually end in failure, then leading computations performed by Google would eventually end in failure, then leading
to large amounts of computational power being wasted. to large amounts of computational power being wasted.
However, with the release of the new 2019 traces\cite{google-marso-19}, However, with the release of the new 2019 traces~\cite{google-marso-19},
the results and conclusions found by that paper could be potentially outdated the results and conclusions found by that paper could be potentially outdated
in the current large-scale computing world. in the current large-scale computing world.
The new traces not only provide updated data on Borg's The new traces not only provide updated data on Borg's
@ -180,7 +179,7 @@ from now on referred as ``Cluster A'' to ``Cluster H''.
The geographical The geographical
location of each cluster can be consulted in Figure~\ref{fig:clusters}. The location of each cluster can be consulted in Figure~\ref{fig:clusters}. The
information in that table was provided by the 2019 traces information in that table was provided by the 2019 traces
documentation\cite{google-drive-marso}. documentation~\cite{google-drive-marso}.
The new 2019 traces provide richer data even on a cluster by cluster basis. For The new 2019 traces provide richer data even on a cluster by cluster basis. For
example, the amount and variety of server configurations per cluster increased example, the amount and variety of server configurations per cluster increased
@ -191,27 +190,27 @@ Figure~\ref{fig:machineconfigs-csts} on a cluster-by-cluster basis.
\input{figures/machine_configs} \input{figures/machine_configs}
There are two main works covering the new data, There are two main works covering the new data, one being the paper
one being the paper \textit{Borg: The Next Generation}\cite{google-marso-19}, \textit{Borg: The Next Generation}~\cite{google-marso-19}, which compares the
which compares the overall features of the trace with the 2011 overall features of the trace with the 2011
one\cite{google-marso-11}\cite{github-marso}, and one covering the features and one~\cite{google-marso-11}~\cite{github-marso}, and one covering the features
performance of and performance of \textit{Autopilot}~\cite{james-muratore}, a software that
\textit{Autopilot}\cite{james-muratore}, a software that provides autoscaling provides autoscaling features in Borg. The new traces have also been analyzed
features in Borg. The new traces have also been analyzed from the execution from the execution priority perspective~\cite{down-under}, as well as from a
priority perspective\cite{down-under}, as well as from a cluster-by-cluster cluster-by-cluster comparison~\cite{golf-course} given the multi-cluster nature
comparison\cite{golf-course} given the multi-cluster nature of the new traces. of the new traces.
Other studies have been performed in similar big-data systems focusing on the Other studies have been performed in similar big-data systems focusing on the
failure of hardware components and software failure of hardware components and software
bugs\cite{9}\cite{10}\cite{11}\cite{12}. bugs~\cite{9}~\cite{10}~\cite{11}~\cite{12}.
However, the community has not yet performed any research on the new Borg However, the community has not yet performed any research on the new Borg
traces analysing unsuccessful executions, their possible causes, and the traces analysing unsuccessful executions, their possible causes, and the
relationships between tasks and jobs. Therefore, the only current research in relationships between tasks and jobs. Therefore, the only current research in
this field (beside this report) is the 2015 Ros\'a et al.\ this field is this very report, providing and update to the the 2015 Ros\'a et
paper\cite{dsn-paper}. al.\ paper~\cite{dsn-paper} focusing on the new trace.
\section{Background information}\label{sec3} \section{Background}\label{sec3}
\textit{Borg} is Google's own cluster management software able to run \textit{Borg} is Google's own cluster management software able to run
thousands of different jobs. Among the various cluster management services it thousands of different jobs. Among the various cluster management services it
@ -227,11 +226,17 @@ paper\cite{dsn-paper}.
consisting of multiple processes, which has to be run on a single machine. consisting of multiple processes, which has to be run on a single machine.
Those tasks may be ran sequentially or in parallel, and the condition for a Those tasks may be ran sequentially or in parallel, and the condition for a
job's successful termination is nontrivial. job's successful termination is nontrivial.
% Both tasks and jobs lifecyles are represented by several events, which are
% encoded and stored in the trace as rows of various tables. Among the Both tasks and jobs lifecyles are represented by several events, which are
% information events provide, the field ``type'' provides information on the encoded and stored in the trace as rows of various tables. Among the
% execution status of the job or task. This field can have several values, information events provide, the field ``type'' provides information on the
% which are illustrated in Figure~\ref{fig:eventtypes}. execution status of the job or task. We focus only on events whose ``types''
indicate a termination, i.e.\ the end of a task or job's execution.
These termination event types are illustrated in Figure~\ref{fig:eventtypes}.
We then define an unsuccessful execution to be an execution characterized by a
termination event of type \texttt{EVICT}, \texttt{FAIL} or \texttt{KILL}.
Conversely, a successful execution is characterized by a \texttt{FINISH}
termination event.
\subsection{Traces} \subsection{Traces}
@ -276,7 +281,7 @@ Google\label{fig:eventTypes}}
\end{figure} \end{figure}
\hypertarget{traces-contents}{% \hypertarget{traces-contents}{%
\subsection{Traces contents}\label{traces-contents}} \subsection{Trace Contents}\label{traces-contents}}
The traces provided by Google contain mainly a collection of job and The traces provided by Google contain mainly a collection of job and
task events spanning a month of execution of the 8 different clusters. task events spanning a month of execution of the 8 different clusters.
@ -301,8 +306,7 @@ used by Google that combines several parameters like number of
processors and cores, clock frequency, and architecture (i.e.~ISA). processors and cores, clock frequency, and architecture (i.e.~ISA).
\hypertarget{overview-of-traces-format}{% \hypertarget{overview-of-traces-format}{%
\subsection{Overview of traces' \subsection{Trace Format}\label{overview-of-traces-format}}
format}\label{overview-of-traces-format}}
The traces have a collective size of approximately 8TiB and are stored The traces have a collective size of approximately 8TiB and are stored
in a Gzip-compressed JSONL (JSON lines) format, which means that each in a Gzip-compressed JSONL (JSON lines) format, which means that each
@ -328,7 +332,7 @@ The scope of this thesis focuses on the tables
\hypertarget{remark-on-traces-size}{% \hypertarget{remark-on-traces-size}{%
\subsection{Remark on traces size}\label{remark-on-traces-size}} \subsection{Remark on Trace Size}\label{remark-on-traces-size}}
While the 2011 Google Borg traces were relatively small, with a total While the 2011 Google Borg traces were relatively small, with a total
size in the order of the tens of gigabytes, the 2019 traces are quite size in the order of the tens of gigabytes, the 2019 traces are quite
@ -361,8 +365,7 @@ parallel Map-Reduce computations. In this section, we discuss the technical
details behind our approach. details behind our approach.
\hypertarget{introduction-on-apache-spark}{% \hypertarget{introduction-on-apache-spark}{%
\subsection{Introduction on Apache \subsection{Apache Spark}\label{introduction-on-apache-spark}}
Spark}\label{introduction-on-apache-spark}}
Apache Spark is a unified analytics engine for large-scale data Apache Spark is a unified analytics engine for large-scale data
processing. In layman's terms, Spark is really useful to parallelize processing. In layman's terms, Spark is really useful to parallelize
@ -386,7 +389,7 @@ Spark has very powerful native Python bindings in the form of the
\emph{PySpark} API, which were used to implement the various queries. \emph{PySpark} API, which were used to implement the various queries.
\hypertarget{query-architecture}{% \hypertarget{query-architecture}{%
\subsection{Query architecture}\label{query-architecture}} \subsection{Query Architecture}\label{query-architecture}}
\subsubsection{Overview} \subsubsection{Overview}
@ -406,13 +409,13 @@ Finally, a reduce operation is applied to either
further aggregate those computed properties or to generate an aggregated data further aggregate those computed properties or to generate an aggregated data
structure for storage purposes. structure for storage purposes.
\subsubsection{Parsing table files} \subsubsection{Parsing Table Files}
As stated before, table ``files'' are composed of several Gzip-compressed As stated before, table ``files'' are composed of several Gzip-compressed
shards of JSONL record data. The specification for the types and constraints shards of JSONL record data. The specification for the types and constraints
of each record is outlined by Google in the form of a protobuffer specification of each record is outlined by Google in the form of a protobuffer specification
file found in the trace release file found in the trace release
package\cite{google-proto-marso}. This file was used as package~\cite{google-proto-marso}. This file was used as
the oracle specification and was a critical reference for writing the query the oracle specification and was a critical reference for writing the query
code that checks, parses and carefully sanitizes the various JSONL records code that checks, parses and carefully sanitizes the various JSONL records
prior to actual computations. prior to actual computations.
@ -424,7 +427,7 @@ these values the key-value pair in the JSON object is outright omitted. When
reading the traces in Apache Spark is therefore necessary to check for this reading the traces in Apache Spark is therefore necessary to check for this
possibility and insert back the omitted record attributes. possibility and insert back the omitted record attributes.
\subsubsection{The queries} \subsubsection{The Queries}
Most queries use only two or three fields in each trace records, while the Most queries use only two or three fields in each trace records, while the
original table records often are made of a couple of dozen fields. In order to original table records often are made of a couple of dozen fields. In order to
@ -452,14 +455,12 @@ and performing the desired computation on the obtained chronological event log.
Sometimes intermediate results are saved in Spark's parquet format in order to Sometimes intermediate results are saved in Spark's parquet format in order to
compute and save intermediate results beforehand. compute and save intermediate results beforehand.
\subsection{Query script design} \subsection{Query Script Design and the \textit{Task Slowdown} Script}
In this section we aim to show the general complexity behind the implementations In this section we aim to show the general complexity behind the implementations
of query scripts by explaining in detail some sampled scripts to better of query scripts by explaining in detail some sampled scripts to better
appreciate their behaviour. appreciate their behaviour.
\subsubsection{The ``task slowdown'' query script}
One example of analysis script with average complexity and a pretty One example of analysis script with average complexity and a pretty
straightforward structure is the pair of scripts \texttt{task\_slowdown.py} and straightforward structure is the pair of scripts \texttt{task\_slowdown.py} and
\texttt{task\_slowdown\_table.py} used to compute the ``task slowdown'' tables \texttt{task\_slowdown\_table.py} used to compute the ``task slowdown'' tables
@ -532,7 +533,7 @@ in the clear and coincise tables found in Figure~\ref{fig:taskslowdown}.
\section{Analysis: Performance Input of Unsuccessful Executions}\label{sec5} \section{Analysis: Performance Input of Unsuccessful Executions}\label{sec5}
Our first investigation focuses on replicating the analysis done by the paper of Our first investigation focuses on replicating the analysis done by the paper of
Ros\'a et al.\ paper\cite{dsn-paper} regarding usage of machine time Ros\'a et al.\ paper~\cite{dsn-paper} regarding usage of machine time
and resources. and resources.
In this section we perform several analyses focusing on how machine time and In this section we perform several analyses focusing on how machine time and
@ -638,13 +639,13 @@ Refer to Figure~\ref{fig:taskslowdown} for a comparison between the 2011 and
means are computed on a cluster-by-cluster basis for 2019 data in means are computed on a cluster-by-cluster basis for 2019 data in
Figure~\ref{fig:taskslowdown-csts}. Figure~\ref{fig:taskslowdown-csts}.
In 2015 Ros\'a et al.\cite{dsn-paper} measured mean task slowdown per each task In 2015 Ros\'a et al.~\cite{dsn-paper} measured mean task slowdown per each task
priority value, which at the time were numeric values between 0 and 11. However, priority value, which at the time were numeric values between 0 and 11. However,
in 2019 traces, task priorities are given as a numeric value between 0 and 500. in 2019 traces, task priorities are given as a numeric value between 0 and 500.
Therefore, to allow an easier comparison, mean task slowdown values are computed Therefore, to allow an easier comparison, mean task slowdown values are computed
by task priority tier over the 2019 data. Priority tiers are semantically by task priority tier over the 2019 data. Priority tiers are semantically
relevant priority ranges defined in the Tirmazi et al.\ relevant priority ranges defined by Tirmazi et al.\ in
2020\cite{google-marso-19} that introduced the 2019 traces. Equivalent priority 2020~\cite{google-marso-19} that introduced the 2019 traces. Equivalent priority
tiers are also provided next to the 2011 priority values in the table covering tiers are also provided next to the 2011 priority values in the table covering
the 2015 analysis. the 2015 analysis.
@ -687,7 +688,7 @@ tier respectively, and Cluster D has 12.04 mean slowdown in its ``Free'' tier.
In this analysis we aim to understand how physical resources of machines In this analysis we aim to understand how physical resources of machines
in the Borg cluster are used to complete tasks. In particular, we compare how in the Borg cluster are used to complete tasks. In particular, we compare how
CPU and Memory resource allocation and usage are distributed among tasks based CPU and memory resource allocation and usage are distributed among tasks based
on their termination on their termination
type. type.
@ -739,9 +740,9 @@ traces.
\section{Analysis: Patterns of Task and Job Events}\label{sec6} \section{Analysis: Patterns of Task and Job Events}\label{sec6}
This section aims to use some of the tecniques used in section IV of This section aims to use some of the tecniques used in section IV of
the Ros\'a et al.\ paper\cite{dsn-paper} to find patterns and interpendencies the Ros\'a et al.\ paper~\cite{dsn-paper} to find patterns and interpendencies
between task and job events by gathering event statistics at those events. In between task and job events by gathering event statistics at those events. In
particular, Section~\ref{tabIII-section} explores how tasks of the success of a particular, Section~\ref{tabIII-section} explores how the success of a
task is inter-correlated with its own event patterns, which task is inter-correlated with its own event patterns, which
Section~\ref{figV-section} explores even further by computing task success Section~\ref{figV-section} explores even further by computing task success
probabilities based on the number of task termination events of a specific type. probabilities based on the number of task termination events of a specific type.
@ -765,7 +766,7 @@ traces is shown in Figure~\ref{fig:tableIII}. Additionally, a cluster-by-cluster
breakdown of the same data for the 2019 traces is shown in breakdown of the same data for the 2019 traces is shown in
Figure~\ref{fig:tableIII-csts}. Figure~\ref{fig:tableIII-csts}.
Each table from these figure shows the mean and the 95-th percentile of the Each table from these figures shows the mean and the 95-th percentile of the
number of termination events per task, broke down by task termination. In number of termination events per task, broke down by task termination. In
addition, the table shows the mean number of \texttt{EVICT}, \texttt{FAIL}, addition, the table shows the mean number of \texttt{EVICT}, \texttt{FAIL},
\texttt{FINISH}, and \texttt{KILL} for each task event termination. \texttt{FINISH}, and \texttt{KILL} for each task event termination.
@ -807,10 +808,10 @@ overall data from the 2019 ones, and in Figure~\ref{fig:figureV-csts}, as a
cluster-by-cluster breakdown of the same data for the 2019 traces. cluster-by-cluster breakdown of the same data for the 2019 traces.
In Figure~\ref{fig:figureV} the 2011 and 2019 plots differ in their x-axis: In Figure~\ref{fig:figureV} the 2011 and 2019 plots differ in their x-axis:
for 2011 data conditional probabilities are computed for a maximum event coun for 2011 data conditional probabilities are computed for a maximum event count
t of 30, while for 2019 data are computed for up to 50 events of a specific of 30, while for 2019 data are computed for up to 50 events of a specific kind.
kind. Nevertheless, another quite striking difference between the two plots can Nevertheless, another quite striking difference between the two plots can be
be seen: while 2011 data has relatively smooth decreasing curves for all event seen: while 2011 data has relatively smooth decreasing curves for all event
types, the curves in the 2019 data almost immediately plateau with no types, the curves in the 2019 data almost immediately plateau with no
significant change easily observed after 5 events of any kind. significant change easily observed after 5 events of any kind.
@ -872,8 +873,8 @@ Additionally, it is noteworthy that cluster A has no \texttt{EVICT}ed jobs.
\section{Analysis: Potential Causes of Unsuccessful Executions}\label{sec7} \section{Analysis: Potential Causes of Unsuccessful Executions}\label{sec7}
This section re-applies the tecniques used in section V of the Ros\'a et al.\ This section re-applies the tecniques used in Section V of the Ros\'a et al.\
paper\cite{dsn-paper} to find patterns and interpendencies paper~\cite{dsn-paper} to find patterns and interpendencies
between task and job events by gathering event statistics at those events. In between task and job events by gathering event statistics at those events. In
particular, Section~\ref{tabIII-section} explores how tasks of the success of a particular, Section~\ref{tabIII-section} explores how tasks of the success of a
task is inter-correlated with its own event patterns, which task is inter-correlated with its own event patterns, which
@ -882,109 +883,177 @@ probabilities based on the number of task termination events of a specific type.
Finally, Section~\ref{tabIV-section} aims to find similar correlations, but at Finally, Section~\ref{tabIV-section} aims to find similar correlations, but at
the job level. the job level.
\subsection{Event rates vs.\ task priority, event execution time, and machine \subsection{Task Event Rates vs.\ Task Priority, Event Execution Time, and
concurrency.}\label{fig7-section} Machine Concurrency.}\label{fig7-section} \input{figures/figure_7}
\input{figures/figure_7} This analysis shows event rates (i.e.\ the relative percentage of termination
type events) over different configurations of task-level parameters.
Figure~\ref{fig:figureVII-a} and Figure~\ref{fig:figureVII-a-csts} show the
distribution of event rates over the various task priority tiers.
Figure~\ref{fig:figureVII-b} and Figure~\ref{fig:figureVII-b-csts} show the
distribution of event rates over the total event execution time. Finally,
Figure~\ref{fig:figureVII-c} and Figure~\ref{fig:figureVII-c-csts} show the
distribution of event rates over the metric of machine concurrency, defined as
the number of co-executing tasks on the machine and at the moment the
termination event is recorded.
Refer to figures \ref{fig:figureVII-a}, \ref{fig:figureVII-b}, and From this analysis we can make the following observations:
\ref{fig:figureVII-c}.
\textbf{Observations}:
\begin{itemize} \begin{itemize}
\item \item
No smooth curves in this figure either, unlike 2011 traces The behaviour of the curves in the task priority distributions
(in Figure~\ref{fig:figureVII-a} and Figure~\ref{fig:figureVII-a-csts})
for the 2019 traces is almost the opposite of the
2011 ones, i.e.\ in-between priorities have higher kill rates while
priorities at the extremum have lower kill rates;
\item \item
The behaviour of curves for 7a (priority) is almost the opposite of The event execution time curves (in Figure~\ref{fig:figureVII-b} and
2011, i.e. in-between priorities have higher kill rates while Figure~\ref{fig:figureVII-b-csts}) for the 2019 traces
priorities at the extremum have lower kill rates. This could also be are quite different than 2011 ones, here it
due bt the inherent distribution of job terminations;
\item
Event execution time curves are quite different than 2011, here it
seems there is a good correlation between short task execution times seems there is a good correlation between short task execution times
and finish event rates, instead of the U shape curve in 2015 DSN and finish event rates, instead of the ``U shape'' curve found in the Ros\'a
et al.\ 2015 DSN paper~\cite{dsn-paper};
\item \item
In figure \ref{fig:figureVII-b} cluster behaviour seems quite uniform The behaviour among different clusters for the event execution time
distributions in Figure~\ref{fig:figureVII-b-csts} seem quite uniform;
\item \item
Machine concurrency seems to play little role in the event termination The machine concurrency metric, for which a distribution of event rates is
distribution, as for all concurrency factors the kill rate is at 90\%. computed in Figure~\ref{fig:figureVII-c} and
Figure~\ref{fig:figureVII-c-csts}, seems to play little role in the event
termination distribution, as for all concurrency factors the \texttt{KILL}
event rate is around 90\% with little fluctuation.
\end{itemize} \end{itemize}
\subsection{Event Rates vs. Requested Resources, Resource Reservation, and \subsection{Task Event Rates vs.\ Requested Resources, Resource Reservation, and
Resource Utilization}\label{fig8-section} Resource Utilization}\label{fig8-section}
\input{figures/figure_8} \input{figures/figure_8}
Refer to Figure~\ref{fig:figureVIII-a}, Figure~\ref{fig:figureVIII-a-csts} This analysis is concerned with the distribution of event rates over several
Figure~\ref{fig:figureVIII-b}, Figure~\ref{fig:figureVIII-b-csts} resources related parameters.
Figure~\ref{fig:figureVIII-c}, Figure~\ref{fig:figureVIII-c-csts} Figure~\ref{fig:figureVIII-a} and Figure~\ref{fig:figureVIII-a-csts} show the
Figure~\ref{fig:figureVIII-d}, Figure~\ref{fig:figureVIII-d-csts} distribution of task event rates w.r.t.\ the amount of CPU the task has
Figure~\ref{fig:figureVIII-e}, Figure~\ref{fig:figureVIII-e-csts} requested, while Figure~\ref{fig:figureVIII-b} and
Figure~\ref{fig:figureVIII-f}, and Figure~\ref{fig:figureVIII-f-csts}. Figure~\ref{fig:figureVIII-b-csts} show task events rates vs.\ requested memory.
Figure~\ref{fig:figureVIII-c} and Figure~\ref{fig:figureVIII-c-csts} show the
distribution of task event rates w.r.t.\ the amount of CPU that has collectively
requested on the machine where the task is running, while
Figure~\ref{fig:figureVIII-d} and Figure~\ref{fig:figureVIII-d-csts} show a
similar distribution but for memory. Finally Figure~\ref{fig:figureVIII-e} and
Figure~\ref{fig:figureVIII-e-csts} show the distribution of task event rates
w.r.t.\ the amount of CPU the task has really been utilized, while
Figure~\ref{fig:figureVIII-f} and Figure~\ref{fig:figureVIII-f-csts} show task
events rates vs.\ used memory.
\subsection{Job Rates vs. Job Size, Job Execution Time, and Machine Locality From this analysis we can make the following observations:
}\label{fig9-section}
\begin{itemize}
\item In the 2019 trace, the amount of requested CPU resources seem to play
little effect on the job termination as it can evinced in
Figure~\ref{fig:figureVIII-a} and Figure~\ref{fig:figureVIII-a-csts}.
Instead, the job rate distributions w.r.t.\ the amount of requested memory
(Figure~\ref{fig:figureVIII-b} and Figure~\ref{fig:figureVIII-b-csts}) show
no discernable pattern;
\item
Overall a significant increment in the killed event rate can be observed. They
seem to dominate all event rates measures;
\item
Among all clusters in Figure~\ref{fig:figureVIII-a-csts} there can be noted the
dominance of the killed event rate. In 2011, it was observed a more dominant
behaviour by the success event rate curve;
\item
For each analysed distribution, clusters do not show a common behaviour of the
curves. Some are similar, but they are generally distinguishable;
\item
In Figure~\ref{fig:figureVIII-e} there can be seen that while a drastic decrease
of the killed event rate curve is observed as the CPU utilization increases,
the success event rate does not increase much.
\end{itemize}
\subsection{Job Event Rates vs.\ Job Size, Job Execution Time, and Machine
Locality}\label{fig9-section}
\input{figures/figure_9} \input{figures/figure_9}
Refer to figures \ref{fig:figureIX-a}, \ref{fig:figureIX-b}, and This analysis shows job event rates (i.e.\ the relative percentage of
\ref{fig:figureIX-c}. termination type events) over different configurations of job size, job
execution time and machine locality.
\textbf{Observations}: Figure~\ref{fig:figureIX-a} and Figure~\ref{fig:figureIX-a-csts} provide
the plots of job event rates versus the job
size. Job size is defined as the number of tasks belonging to the job.
Figure~\ref{fig:figureIX-b} and Figure~\ref{fig:figureIX-b-csts} provide
the plots of the job event rates versus
execution time.
Figure~\ref{fig:figureIX-c} and Figure~\ref{fig:figureIX-c-csts} provide
the plots of the job event
rates versus machine locality.
Machine locality is defined as the ratio between the number
of machines used to execute the tasks inside the job and the job size.
By analysing these plots, we can make the following observations:
\begin{itemize} \begin{itemize}
\item \item
Behaviour between cluster varies a lot There can be noted significant variations in the behaviour of the curves
between clusters;
\item \item
There are no ``smooth'' gradients in the various curves unlike in the There are no smooth gradients in the various curves unlike in the
2011 traces 2011 traces;
\item \item
Killed jobs have higher event rates in general, and overall dominate Killed jobs have higher event rates in general, and overall dominate
all event rates measures all event rates measures. As can be seen in Figure~\ref{fig:figureIX-a}, an
higher number of tasks (i.e., an higher job size) seems to be correlated to
an higher killed event rate in 2019 rather than in 2011. In
Figure~\ref{fig:figureIX-b}, we observe the best success event rate for a
job execution time of 4-10 minutes, while in 2011, it seemed that the finish
event rate increases along with the job execution time;
\item \item
There still seems to be a correlation between short execution job There still seems to be a strong correlation between short execution job
times and successfull final termination, and likewise for kills and times and successful final termination, and likewise for kills and
higher job terminations higher job terminations. Especially for these two curves, in most cases also
between the clusters, their behaviour suggests a specular trend;
\item \item
Across all clusters, a machine locality factor of 1 seems to lead to As can be seen in Figure~\ref{fig:figureIX-c}, across all clusters, a machine
the highest success event rate locality factor of 1 seems to lead to the highest success event rate, while
in 2011 the same machine locality factor led to the lowest success event
rate.
\end{itemize} \end{itemize}
\section{Conclusions, Limitations and Future Work}\label{sec8} \section{Conclusions, Limitations and Future Work}\label{sec8}
In this report we analyze the Google Borg 2019 traces and compared them with In this report we analyzed the Google Borg 2019 traces and compared them with
their 2011 counterpart from the perspective of failures, their impact on their 2011 counterpart from the perspective of unsuccessful executions, their
resources and their causes. We discover that the impact of non-successful impact on resources and their causes. We discover that the impact of
executions (especially of \texttt{KILL}ed tasks and jobs) in the new traces is unsuccessful executions (especially of \texttt{KILL}ed tasks and jobs) in the
still very relevant in terms of machine time and resources, even more so than in new traces is still very relevant in terms of machine time and resources, even
2011. We also discover that unsuccessful job and task event patterns still play more so than in 2011. We also discover that unsuccessful job and task event
a major role in the overall execution success of Borg jobs and tasks. We finally patterns still play a major role in the overall execution success of Borg jobs
discover that unsuccessful job and task event rates dominate the overall and tasks. We finally discover that unsuccessful job and task event rates
landscape of Borg's own logs, even when grouping tasks and jobs by parameters dominate the overall landscape of Borg's own logs, even when grouping tasks and
such as priority, resource request, reservation and utilization, and machine jobs by parameters such as priority, resource request, reservation and
locality. utilization, and machine locality.
We then can conclude that the performed analysis show a lot of clear trends We then can conclude that the performed analysis show many clear trends
regarding the correlation of execution success with several parameters and regarding the correlation of execution success with several parameters and
metadata. These trends can potentially be exploited to build better scheduling metadata. These trends can potentially be exploited to build better scheduling
algorithms and new predictive models algorithms and new predictive models that could understand if an execution has
that could understand if an execution has high probability of failure based on high probability of failure based on its own properties and metadata. The
its own properties and metadata. The creation of such models could allow for creation of such models could allow for computational resources to be saved and
computational resources to be saved and used to either increase the throughput used to either increase the throughput of higher priority workloads or to allow
of higher priority workloads or to allow for a larger workload altoghether. for a larger workload altoghether.
The biggest limitation and threat to validity posed to this project is the The biggest limitation and threat to validity posed to this project is the
relative lack of infrormation provided by Google on the true meaning of relative lack of information provided by Google on the true meaning of
unsuccessful terminations. Indeed, given the ``black box'' nature of the traces unsuccessful terminations. Indeed, given the ``black box'' nature of the traces
and the rather scarcity of information in the traces and the rather scarcity of information in the traces
documentation\cite{google-drive-marso}, it is not clear if unsuccessful documentation~\cite{google-drive-marso}, it is not clear if unsuccessful
executions yield any useful computation result or not. Our assumption in this executions yield any useful computation result or not. Our assumption in this
report is that unsuccesful jobs and tasks do not produce any result and are report is that unsuccesful jobs and tasks do not produce any result and are
therefore just burdens on machine time and resources, but should this assumption therefore just burdens on machine time and resources, but should this assumption
be incorrect then the interpretation of the analyses might change significantly. be incorrect then the interpretation of the analyses might change.
Given the significant computational time invested in obtaining the results shown Given the significant computational time invested in obtaining the results shown
in this report and due to time and resource limitations, some of the analysis in this report and due to time and resource limitations, some of the analysis
were not completed. Our future work will focus on finishing these analysis, were not completed on all clusters. Our future work will focus on finishing
namely by computing results for the missing clusters and obtaining a true these analysis, computing results for the missing clusters and obtaining an
overall picture of the 2019 Google Borg cluster traces w.r.t.\ failures and overall picture of the 2019 Google Borg cluster traces w.r.t.\ failures and
their causes. their causes.

24
report/figures/figure_8.tex
View file

@ -11,7 +11,7 @@
\begin{figure}[p] \begin{figure}[p]
\figureVIII[0.49\textwidth]{rcpu-2011} \figureVIII[0.49\textwidth]{rcpu-2011}
\figureVIII[0.49\textwidth]{rcpu-all} \figureVIII[0.49\textwidth]{rcpu-all}
\caption{Task event rates vs.\ requested CPU (expressed in \textit{Normalized compute units}), \caption{Task event rates vs.\ requested CPU (expressed in \textit{NCUs}),
w.r.t.\ task termination for 2011 and 2019 (all cluster aggregated) traces.}\label{fig:figureVIII-a} w.r.t.\ task termination for 2011 and 2019 (all cluster aggregated) traces.}\label{fig:figureVIII-a}
\end{figure} \end{figure}
@ -24,7 +24,7 @@
\figureVIII{rcpu-f} \figureVIII{rcpu-f}
\figureVIII{rcpu-g} \figureVIII{rcpu-g}
\figureVIII{rcpu-h} \figureVIII{rcpu-h}
\caption{Task event rates vs.\ requested CPU (expressed in \textit{Normalized compute units}), \caption{Task event rates vs.\ requested CPU (expressed in \textit{NCUs}),
w.r.t.\ task termination for each cluster in the 2019 traces.}\label{fig:figureVIII-a-csts} w.r.t.\ task termination for each cluster in the 2019 traces.}\label{fig:figureVIII-a-csts}
\end{figure} \end{figure}
@ -33,7 +33,7 @@
\begin{figure}[p] \begin{figure}[p]
\figureVIII[0.49\textwidth]{rram-2011} \figureVIII[0.49\textwidth]{rram-2011}
\figureVIII[0.49\textwidth]{rram-all} \figureVIII[0.49\textwidth]{rram-all}
\caption{Task event rates vs.\ requested memory (expressed in \textit{Normalized memory units}), \caption{Task event rates vs.\ requested memory (expressed in \textit{NMUs}),
w.r.t.\ task termination for 2011 and 2019 (all cluster aggregated) traces.}\label{fig:figureVIII-b} w.r.t.\ task termination for 2011 and 2019 (all cluster aggregated) traces.}\label{fig:figureVIII-b}
\end{figure} \end{figure}
@ -46,7 +46,7 @@
\figureVIII{rram-f} \figureVIII{rram-f}
\figureVIII{rram-g} \figureVIII{rram-g}
\figureVIII{rram-h} \figureVIII{rram-h}
\caption{Task event rates vs.\ requested memory (expressed in \textit{Normalized memory units}), \caption{Task event rates vs.\ requested memory (expressed in \textit{NMUs}),
w.r.t.\ task termination for each cluster in the 2019 traces.}\label{fig:figureVIII-b-csts} w.r.t.\ task termination for each cluster in the 2019 traces.}\label{fig:figureVIII-b-csts}
\end{figure} \end{figure}
@ -55,7 +55,7 @@
\begin{figure}[p] \begin{figure}[p]
\figureVIII[0.49\textwidth]{rscpu-2011} \figureVIII[0.49\textwidth]{rscpu-2011}
\figureVIII[0.49\textwidth]{rscpu-all} \figureVIII[0.49\textwidth]{rscpu-all}
\caption{Task event rates vs.\ reserved CPU (expressed in \textit{Normalized compute units}), \caption{Task event rates vs.\ reserved CPU (expressed in \textit{NCUs}),
w.r.t.\ task termination for 2011 and 2019 (clusters A,B,E,F aggregated) traces.}\label{fig:figureVIII-c} w.r.t.\ task termination for 2011 and 2019 (clusters A,B,E,F aggregated) traces.}\label{fig:figureVIII-c}
\end{figure} \end{figure}
@ -65,7 +65,7 @@
\figureVIII[0.49\textwidth]{rscpu-e} \figureVIII[0.49\textwidth]{rscpu-e}
\hfill \hfill
\figureVIII[0.49\textwidth]{rscpu-f} \figureVIII[0.49\textwidth]{rscpu-f}
\caption{Task event rates vs.\ reserved CPU (expressed in \textit{Normalized compute units}), \caption{Task event rates vs.\ reserved CPU (expressed in \textit{NCUs}),
w.r.t.\ task termination for clusters A,B,E,F in the 2019 traces.}\label{fig:figureVIII-c-csts} w.r.t.\ task termination for clusters A,B,E,F in the 2019 traces.}\label{fig:figureVIII-c-csts}
\end{figure} \end{figure}
@ -74,7 +74,7 @@
\begin{figure}[p] \begin{figure}[p]
\figureVIII[0.49\textwidth]{rsram-2011} \figureVIII[0.49\textwidth]{rsram-2011}
\figureVIII[0.49\textwidth]{rsram-all} \figureVIII[0.49\textwidth]{rsram-all}
\caption{Task event rates vs.\ reserved memory (expressed in \textit{Normalized memory units}), \caption{Task event rates vs.\ reserved memory (expressed in \textit{NMUs}),
w.r.t.\ task termination for 2011 and 2019 (clusters A,B,E,F aggregated) traces.}\label{fig:figureVIII-d} w.r.t.\ task termination for 2011 and 2019 (clusters A,B,E,F aggregated) traces.}\label{fig:figureVIII-d}
\end{figure} \end{figure}
@ -84,7 +84,7 @@
\figureVIII[0.49\textwidth]{rsram-e} \figureVIII[0.49\textwidth]{rsram-e}
\hfill \hfill
\figureVIII[0.49\textwidth]{rsram-f} \figureVIII[0.49\textwidth]{rsram-f}
\caption{Task event rates vs.\ reserved memory (expressed in \textit{Normalized memory units}), \caption{Task event rates vs.\ reserved memory (expressed in \textit{NMUs}),
w.r.t.\ task termination for clusters A,B,E,F in the 2019 traces.}\label{fig:figureVIII-d-csts} w.r.t.\ task termination for clusters A,B,E,F in the 2019 traces.}\label{fig:figureVIII-d-csts}
\end{figure} \end{figure}
@ -93,7 +93,7 @@
\begin{figure}[p] \begin{figure}[p]
\figureVIII[0.49\textwidth]{ucpu-2011} \figureVIII[0.49\textwidth]{ucpu-2011}
\figureVIII[0.49\textwidth]{ucpu-all} \figureVIII[0.49\textwidth]{ucpu-all}
\caption{Task event rates vs.\ used CPU (expressed in \textit{Normalized compute units}), \caption{Task event rates vs.\ used CPU (expressed in \textit{NCUs}),
w.r.t.\ task termination for 2011 and 2019 (clusters A-D aggregated) traces.}\label{fig:figureVIII-e} w.r.t.\ task termination for 2011 and 2019 (clusters A-D aggregated) traces.}\label{fig:figureVIII-e}
\end{figure} \end{figure}
@ -103,7 +103,7 @@
\figureVIII[0.49\textwidth]{ucpu-c} \figureVIII[0.49\textwidth]{ucpu-c}
\hfill \hfill
\figureVIII[0.49\textwidth]{ucpu-d} \figureVIII[0.49\textwidth]{ucpu-d}
\caption{Task event rates vs.\ used CPU (expressed in \textit{Normalized memory units}), \caption{Task event rates vs.\ used CPU (expressed in \textit{NMUs}),
w.r.t.\ task termination for clusters A-D in the 2019 traces.}\label{fig:figureVIII-e-csts} w.r.t.\ task termination for clusters A-D in the 2019 traces.}\label{fig:figureVIII-e-csts}
\end{figure} \end{figure}
@ -112,7 +112,7 @@
\begin{figure}[p] \begin{figure}[p]
\figureVIII[0.49\textwidth]{uram-2011} \figureVIII[0.49\textwidth]{uram-2011}
\figureVIII[0.49\textwidth]{uram-all} \figureVIII[0.49\textwidth]{uram-all}
\caption{Task event rates vs.\ used memory (expressed in \textit{Normalized memory units}), \caption{Task event rates vs.\ used memory (expressed in \textit{NMUs}),
w.r.t.\ task termination for 2011 and 2019 (clusters A-D aggregated) traces.}\label{fig:figureVIII-f} w.r.t.\ task termination for 2011 and 2019 (clusters A-D aggregated) traces.}\label{fig:figureVIII-f}
\end{figure} \end{figure}
@ -122,7 +122,7 @@
\figureVIII[0.49\textwidth]{uram-c} \figureVIII[0.49\textwidth]{uram-c}
\hfill \hfill
\figureVIII[0.49\textwidth]{uram-d} \figureVIII[0.49\textwidth]{uram-d}
\caption{Task event rates vs.\ used memory (expressed in \textit{Normalized memory units}), \caption{Task event rates vs.\ used memory (expressed in \textit{NMUs}),
w.r.t.\ task termination for clusters A-D in the 2019 traces.}\label{fig:figureVIII-f-csts} w.r.t.\ task termination for clusters A-D in the 2019 traces.}\label{fig:figureVIII-f-csts}
\end{figure} \end{figure}

2
report/figures/figure_9.tex
View file

@ -9,7 +9,7 @@
\begin{figure}[p] \begin{figure}[p]
\figureIX[0.49\textwidth]{taskcount-2011.pgf} \figureIX[0.49\textwidth]{taskcount-2011.pgf}
\figureIX[0.49\textwidth]{taskcount-all.pgf} \figureIX[0.49\textwidth]{taskcount-all.pgf}
\caption{Job event rates vs.\ job size and final job termination in 2011 and 2019 (all clusters aggregated) traces. The job size is equivalent to the number of tasks belonging to the job.}\label{fig:figureIX-a} \caption{Job event rates vs.\ job size and final job termination in 2011 and 2019 (all clusters aggregated) traces. The job size is defined as the number of tasks belonging to the job.}\label{fig:figureIX-a}
\end{figure} \end{figure}
\begin{figure}[p] \begin{figure}[p]

4
report/figures/machine_configs.tex
View file

@ -103,7 +103,7 @@ Unknown & Unknown & 8729 & 1.639218\% \\
0.479492 & 0.500000 & 2 & 0.000376\% \\ 0.479492 & 0.500000 & 2 & 0.000376\% \\
\bottomrule \bottomrule
\end{tabular}}{2019 data} \end{tabular}}{2019 data}
\caption{Overview of machine configurations in term of CPU and Memory power in 2011 and 2019 (all clusters aggregated) traces. In the 2019 traces NCU stands for ``Normalized Compute Unit'' and NMU stands for ``Normalized Compute Unit'': both are $[0,1]$ normalizations of resource values. While memory was measured in terms of capacity, CPU power was measured in ``Google Compute Units'' (GCUs), an opaque umbrella metric used by Google that factors in CPU clock, number of cores/processors, and CPU ISA architecture.}\label{fig:machineconfigs} \caption{Overview of machine configurations in term of CPU and Memory power in 2011 and 2019 (all clusters aggregated) traces. In the 2019 traces NCU stands for ``Normalized Compute Unit'' and NMU stands for ``Normalized Memory Unit'': both are $[0,1]$ normalizations of resource values. While memory was measured in terms of capacity, CPU power was measured in ``Google Compute Units'' (GCUs), an opaque umbrella metric used by Google that factors in CPU clock, number of cores/processors, and CPU ISA architecture.}\label{fig:machineconfigs}
\end{figure} \end{figure}
\begin{figure}[p] \begin{figure}[p]
@ -231,5 +231,5 @@ Unknown & Unknown & 1720 & 2.933251\% \\
0.591797 & 0.666992 & 500 & 0.852689\% \\ 0.591797 & 0.666992 & 500 & 0.852689\% \\
0.958984 & 1.000000 & 200 & 0.341076\% \\ 0.958984 & 1.000000 & 200 & 0.341076\% \\
}{\\\\\\\\\\} }{\\\\\\\\\\}
\caption{Overview of machine configurations in terms of CPU and RAM resources for each cluster in the 2019 traces. Refer to figure~\ref{fig:machineconfigs} for a column legend.}\label{fig:machineconfigs-csts} \caption{Overview of machine configurations in terms of CPU and RAM resources for each cluster in the 2019 traces. Refer to Figure~\ref{fig:machineconfigs} for a column legend.}\label{fig:machineconfigs-csts}
\end{figure} \end{figure}

3
report/figures/machine_time_waste.tex
View file

@ -10,8 +10,7 @@
\machinetimewaste[1]{2011 data}{cluster_2011.pgf} \machinetimewaste[1]{2011 data}{cluster_2011.pgf}
\machinetimewaste[1]{2019 data}{cluster_all.pgf} \machinetimewaste[1]{2019 data}{cluster_all.pgf}
\caption{Relative task time spent in each execution phase \caption{Relative task time spent in each execution phase
w.r.t.\ task termination in 2011 and 2019 (all clusters aggregated) traces. The x-axis shows task termination type, w.r.t.\ task termination in 2011 and 2019 (all clusters aggregated) traces. The x-axis shows task termination type, while the y-axis shows total time \% spent. Colors break down the time in execution phases. ``Unknown'' execution times are
Y axis shows total time \% spent. Colors break down the time in execution phases. ``Unknown'' execution times are
2019 specific and correspond to event time transitions that are not consider ``typical'' by Google.}\label{fig:machinetimewaste-rel} 2019 specific and correspond to event time transitions that are not consider ``typical'' by Google.}\label{fig:machinetimewaste-rel}
\end{figure} \end{figure}

32
report/figures/table_iii.tex
View file

@ -50,7 +50,7 @@ EVICT & FAIL & FINISH & KILL \\}
\toprule \toprule
\tableIIIh \tableIIIh
\midrule \midrule
EVICT & 78.710 (342) & 52.242 & 0.673 & 0.000 & 25.795 \\ EVICT & 78.710 (342) & 52.242 & 0.673 & 0 & 25.795 \\
FAIL & 24.962 (26) & 0.290 & 23.635 & 0.348 & 0.691 \\ FAIL & 24.962 (26) & 0.290 & 23.635 & 0.348 & 0.691 \\
FINISH & 2.962 (2) & 0.022 & 0.012 & 2.915 & 0.013 \\ FINISH & 2.962 (2) & 0.022 & 0.012 & 2.915 & 0.013 \\
KILL & 8.763 (16) & 1.876 & 0.143 & 0.003 & 6.741 \\ KILL & 8.763 (16) & 1.876 & 0.143 & 0.003 & 6.741 \\
@ -68,52 +68,52 @@ FINISH & 2.962 (2) & 0.022 & 0.012 & 2.915 & 0.013 \\
\begin{figure}[p] \begin{figure}[p]
\tableIII{A}{% \tableIII{A}{%
EVICT & 103.228 (719) & 73.694 & 0.769 & 0.000 & 28.766 \\ EVICT & 103.228 (719) & 73.694 & 0.769 & 0 & 28.766 \\
FAIL & 11.819 (26) & 0.288 & 11.062 & 0.002 & 0.468 \\ FAIL & 11.819 (26) & 0.288 & 11.062 & 0.002 & 0.468 \\
FINISH & 2.185 (1) & 0.019 & 0.004 & 2.153 & 0.008 \\ FINISH & 2.185 (1) & 0.019 & 0.004 & 2.153 & 0.008 \\
KILL & 5.963 (11) & 2.350 & 0.214 & 0.003 & 3.396 \\ KILL & 5.963 (11) & 2.350 & 0.214 & 0.003 & 3.396 \\
} }
\tableIII{B}{% \tableIII{B}{%
EVICT & 83.018 (394) & 64.817 & 0.240 & 0.000 & 17.962 \\ EVICT & 83.018 (394) & 64.817 & 0.240 & 0 & 17.962 \\
FAIL & 20.851 (62) & 0.518 & 19.657 & 0.001 & 0.675 \\ FAIL & 20.851 (62) & 0.518 & 19.657 & 0.001 & 0.675 \\
FINISH & 2.995 (4) & 0.020 & 0.021 & 2.943 & 0.012 \\ FINISH & 2.995 (4) & 0.020 & 0.021 & 2.943 & 0.012 \\
KILL & 9.173 (12) & 3.351 & 0.276 & 0.004 & 5.541 \\ KILL & 9.173 (12) & 3.351 & 0.276 & 0.004 & 5.541 \\
} }
\tableIII{C}{% \tableIII{C}{%
EVICT & 98.437 (444) & 73.716 & 1.813 & 0.000 & 22.908 \\ EVICT & 98.437 (444) & 73.716 & 1.813 & 0 & 22.908 \\
FAIL & 52.010 (30) & 0.773 & 48.446 & 2.035 & 0.756 \\ FAIL & 52.010 (30) & 0.773 & 48.446 & 2.035 & 0.756 \\
FINISH & 2.507 (2) & 0.018 & 0.013 & 2.471 & 0.006 \\ FINISH & 2.507 (2) & 0.018 & 0.013 & 2.471 & 0.006 \\
KILL & 5.452 (6) & 1.533 & 0.116 & 0.004 & 3.799 \\ KILL & 5.452 (6) & 1.533 & 0.116 & 0.004 & 3.799 \\
} }
\tableIII{D}{% \tableIII{D}{%
EVICT & 76.759 (366) & 62.001 & 0.700 & 0.000 & 14.058 \\ EVICT & 76.759 (366) & 62.001 & 0.700 & 0 & 14.058 \\
FAIL & 62.314 (62) & 0.496 & 58.968 & 0.810 & 2.040 \\ FAIL & 62.314 (62) & 0.496 & 58.968 & 0.810 & 2.040 \\
FINISH & 3.877 (2) & 0.059 & 0.019 & 3.789 & 0.010 \\ FINISH & 3.877 (2) & 0.059 & 0.019 & 3.789 & 0.010 \\
KILL & 6.795 (6) & 1.960 & 0.151 & 0.002 & 4.682 \\ KILL & 6.795 (6) & 1.960 & 0.151 & 0.002 & 4.682 \\
} }
\tableIII{E}{% \tableIII{E}{%
EVICT & 17.678 (72) & 11.781 & 0.106 & 0.000 & 5.791 \\ EVICT & 17.678 (72) & 11.781 & 0.106 & 0 & 5.791 \\
FAIL & 112.384 (28) & 0.458 & 111.471 & 0.000 & 0.456 \\ FAIL & 112.384 (28) & 0.458 & 111.471 & 0 & 0.456 \\
FINISH & 2.029 (2) & 0.014 & 0.008 & 1.999 & 0.008 \\ FINISH & 2.029 (2) & 0.014 & 0.008 & 1.999 & 0.008 \\
KILL & 13.505 (64) & 1.288 & 0.057 & 0.000 & 12.160 \\ KILL & 13.505 (64) & 1.288 & 0.057 & 0 & 12.160 \\
} }
\tableIII{F}{% \tableIII{F}{%
EVICT & 70.146 (114) & 23.974 & 0.192 & 0.000 & 45.980 \\ EVICT & 70.146 (114) & 23.974 & 0.192 & 0 & 45.980 \\
FAIL & 41.087 (54) & 0.279 & 39.257 & 0.000 & 1.550 \\ FAIL & 41.087 (54) & 0.279 & 39.257 & 0 & 1.550 \\
FINISH & 3.129 (4) & 0.019 & 0.004 & 3.008 & 0.098 \\ FINISH & 3.129 (4) & 0.019 & 0.004 & 3.008 & 0.098 \\
KILL & 10.288 (38) & 0.384 & 0.098 & 0.001 & 9.804 \\ KILL & 10.288 (38) & 0.384 & 0.098 & 0.001 & 9.804 \\
} }
\tableIII{G}{% \tableIII{G}{%
EVICT & 136.032 (490) & 77.429 & 0.303 & 0.000 & 58.299 \\ EVICT & 136.032 (490) & 77.429 & 0.303 & 0 & 58.299 \\
FAIL & 8.948 (8) & 0.016 & 8.593 & 0.000 & 0.339 \\ FAIL & 8.948 (8) & 0.016 & 8.593 & 0 & 0.339 \\
FINISH & 14.176 (2) & 0.015 & 0.002 & 14.154 & 0.005 \\ FINISH & 14.176 (2) & 0.015 & 0.002 & 14.154 & 0.005 \\
KILL & 32.320 (164) & 6.909 & 0.135 & 0.000 & 25.276 \\ KILL & 32.320 (164) & 6.909 & 0.135 & 0 & 25.276 \\
} }
\tableIII{H}{% \tableIII{H}{%
EVICT & 14.734 (40) & 6.733 & 0.837 & 0.000 & 7.165 \\ EVICT & 14.734 (40) & 6.733 & 0.837 & 0 & 7.165 \\
FAIL & 41.067 (120) & 0.600 & 37.600 & 0.000 & 2.867 \\ FAIL & 41.067 (120) & 0.600 & 37.600 & 0 & 2.867 \\
FINISH & 3.681 (2) & 0.024 & 0.014 & 3.633 & 0.011 \\ FINISH & 3.681 (2) & 0.024 & 0.014 & 3.633 & 0.011 \\
KILL & 17.976 (98) & 0.633 & 0.170 & 0.000 & 17.173 \\ KILL & 17.976 (98) & 0.633 & 0.170 & 0 & 17.173 \\
} }
\caption{Mean number of termination events and their distributions per \caption{Mean number of termination events and their distributions per
task type for each cluster in the 2019 traces. The tables show an task type for each cluster in the 2019 traces. The tables show an

16
report/figures/table_iv.tex
View file

@ -20,7 +20,7 @@ KILL & 86.8 (400) & $13.3$ & $20.9$ & $26.9$ & $62.7$ \\
\toprule \toprule
\tableIVh% \tableIVh%
\midrule \midrule
EVICT & 1.000 (1) & 1.000 & 0.000 & 0.000 & 0.000 \\ EVICT & 1.000 (1) & 1.000 & 0 & 0 & 0 \\
FAIL & 43.126 (200) & 0.114 & 2.300 & 0.981 & 12.833 \\ FAIL & 43.126 (200) & 0.114 & 2.300 & 0.981 & 12.833 \\
FINISH & 3.074 (2) & 0.005 & 0.153 & 1.778 & 0.014 \\ FINISH & 3.074 (2) & 0.005 & 0.153 & 1.778 & 0.014 \\
KILL & 53.919 (178) & 0.235 & 0.103 & 0.288 & 11.337 \\ KILL & 53.919 (178) & 0.235 & 0.103 & 0.288 & 11.337 \\
@ -42,43 +42,43 @@ FINISH & 1.187 (1) & 0.005 & 0.001 & 1.073 & 0.024 \\
KILL & 16.533 (10) & 1.045 & 0.074 & 0.461 & 1.189 \\ KILL & 16.533 (10) & 1.045 & 0.074 & 0.461 & 1.189 \\
} }
\tableIV{B}{ \tableIV{B}{
EVICT & 1.000 (1) & 1.000 & 0.000 & 0.000 & 0.000 \\ EVICT & 1.000 (1) & 1.000 & 0 & 0 & 0 \\
FAIL & 74.368 (374) & 2.003 & 1.994 & 0.267 & 4.944 \\ FAIL & 74.368 (374) & 2.003 & 1.994 & 0.267 & 4.944 \\
FINISH & 6.304 (10) & 0.022 & 0.008 & 2.349 & 0.013 \\ FINISH & 6.304 (10) & 0.022 & 0.008 & 2.349 & 0.013 \\
KILL & 69.853 (234) & 1.696 & 0.158 & 0.614 & 3.009 \\ KILL & 69.853 (234) & 1.696 & 0.158 & 0.614 & 3.009 \\
} }
\tableIV{C}{ \tableIV{C}{
EVICT & 1.000 (1) & 1.001 & 0.000 & 0.000 & 0.000 \\ EVICT & 1.000 (1) & 1.001 & 0 & 0 & 0 \\
FAIL & 41.982 (200) & 3.484 & 0.998 & 0.376 & 3.998 \\ FAIL & 41.982 (200) & 3.484 & 0.998 & 0.376 & 3.998 \\
FINISH & 1.991 (1) & 0.022 & 0.017 & 1.565 & 0.017 \\ FINISH & 1.991 (1) & 0.022 & 0.017 & 1.565 & 0.017 \\
KILL & 110.681 (652) & 0.627 & 0.059 & 0.656 & 2.267 \\ KILL & 110.681 (652) & 0.627 & 0.059 & 0.656 & 2.267 \\
} }
\tableIV{D}{ \tableIV{D}{
EVICT & 1.000 (1) & 1.000 & 0.000 & 0.000 & 0.000 \\ EVICT & 1.000 (1) & 1.000 & 0 & 0 & 0 \\
FAIL & 43.356 (250) & 6.112 & 0.949 & 0.531 & 6.498 \\ FAIL & 43.356 (250) & 6.112 & 0.949 & 0.531 & 6.498 \\
FINISH & 2.109 (2) & 0.268 & 0.013 & 1.723 & 0.019 \\ FINISH & 2.109 (2) & 0.268 & 0.013 & 1.723 & 0.019 \\
KILL & 89.648 (283) & 1.013 & 0.054 & 0.283 & 3.256 \\ KILL & 89.648 (283) & 1.013 & 0.054 & 0.283 & 3.256 \\
} }
\tableIV{E}{ \tableIV{E}{
EVICT & 1.000 (1) & 1.000 & 0.000 & 0.000 & 0.000 \\ EVICT & 1.000 (1) & 1.000 & 0 & 0 & 0 \\
FAIL & 23.081 (25) & 0.247 & 0.666 & 0.717 & 1.588 \\ FAIL & 23.081 (25) & 0.247 & 0.666 & 0.717 & 1.588 \\
FINISH & 7.776 (2) & 0.019 & 0.029 & 1.934 & 0.021 \\ FINISH & 7.776 (2) & 0.019 & 0.029 & 1.934 & 0.021 \\
KILL & 88.790 (309) & 0.706 & 0.029 & 0.461 & 7.572 \\ KILL & 88.790 (309) & 0.706 & 0.029 & 0.461 & 7.572 \\
} }
\tableIV{F}{ \tableIV{F}{
EVICT & 1.000 (1) & 1.000 & 0.000 & 0.000 & 0.000 \\ EVICT & 1.000 (1) & 1.000 & 0 & 0 & 0 \\
FAIL & 17.161 (8) & 0.621 & 0.546 & 0.426 & 7.559 \\ FAIL & 17.161 (8) & 0.621 & 0.546 & 0.426 & 7.559 \\
FINISH & 2.941 (2) & 0.015 & 0.051 & 1.670 & 0.162 \\ FINISH & 2.941 (2) & 0.015 & 0.051 & 1.670 & 0.162 \\
KILL & 103.889 (361) & 0.183 & 0.064 & 0.417 & 5.824 \\ KILL & 103.889 (361) & 0.183 & 0.064 & 0.417 & 5.824 \\
} }
\tableIV{G}{ \tableIV{G}{
EVICT & 1.000 (1) & 1.000 & 0.000 & 0.000 & 0.000 \\ EVICT & 1.000 (1) & 1.000 & 0 & 0 & 0 \\
FAIL & 51.835 (250) & 0.556 & 3.335 & 0.608 & 20.352 \\ FAIL & 51.835 (250) & 0.556 & 3.335 & 0.608 & 20.352 \\
FINISH & 8.519 (36) & 0.002 & 0.630 & 1.760 & 0.005 \\ FINISH & 8.519 (36) & 0.002 & 0.630 & 1.760 & 0.005 \\
KILL & 37.055 (100) & 5.687 & 0.065 & 0.080 & 19.166 \\ KILL & 37.055 (100) & 5.687 & 0.065 & 0.080 & 19.166 \\
} }
\tableIV{H}{ \tableIV{H}{
EVICT & 1.000 (1) & 1.000 & 0.000 & 0.000 & 0.000 \\ EVICT & 1.000 (1) & 1.000 & 0 & 0 & 0 \\
FAIL & 20.504 (1) & 0.114 & 2.300 & 0.981 & 12.833 \\ FAIL & 20.504 (1) & 0.114 & 2.300 & 0.981 & 12.833 \\
FINISH & 4.278 (14) & 0.005 & 0.153 & 1.778 & 0.014 \\ FINISH & 4.278 (14) & 0.005 & 0.153 & 1.778 & 0.014 \\
KILL & 11.023 (3) & 0.235 & 0.103 & 0.288 & 11.337 \\ KILL & 11.023 (3) & 0.235 & 0.103 & 0.288 & 11.337 \\

39
report/figures/task_slowdown.tex
View file

@ -42,21 +42,22 @@
\toprule \toprule
\taskslowdownheader \taskslowdownheader
\midrule \midrule
Best effort batch & 11.06\% & 4139 & 113 & 7.84\\
Free & 42.85\% & 1374 & 8 & 1.15\\ Free & 42.85\% & 1374 & 8 & 1.15\\
Best effort batch & 11.06\% & 4139 & 113 & 7.84\\
Mid & 2.71\% & 18187 & 157 & 2.55\\ Mid & 2.71\% & 18187 & 157 & 2.55\\
Monitoring & 2.74\% & 834226 & 130 & 2.05\\ Monitoring & 2.74\% & 834226 & 130 & 2.05\\
Production & 13.54\% & 54789 & 24 & 6.68\\ Production & 13.54\% & 54789 & 24 & 6.68\\
\bottomrule \bottomrule
\end{tabular}} \end{tabular}}
\caption{Mean task slowdown for each cluster and each priority ``tier'' for 2011 and \caption{Mean task slowdown for each cluster and each priority ``tier'' for 2011
2019 data. \textbf{\% finished} is the percentage of tasks with and 2019 data. \textbf{\% finished} is the percentage of tasks with
\texttt{FINISH} termination w.r.t.\ priority, \textbf{Mean response [s] (last \texttt{FINISH} termination w.r.t.\ priority, \textbf{mean response [s]
execution)} is the mean response time (queue+execution time, in seconds) for (last execution)} is the mean response time (queue+execution time, in
the last task execution w.r.t.\ priority, \textbf{Mean response [s] (all seconds) for the last task execution w.r.t.\ priority, \textbf{mean
executions)} is the response time (in seconds) of all executions, response [s] (all executions)} is the response time (in seconds) of all
\textbf{Mean slowdown} is the mean slowdown measure w.r.t.\ priority. executions, \textbf{mean slowdown} is the mean slowdown measure w.r.t.\
Priorities with no successfully terminated jobs have been omitted.}\label{fig:taskslowdown} priority. Priorities with no successfully terminated jobs have been
omitted.}\label{fig:taskslowdown}
\end{figure} \end{figure}
\begin{figure}[p] \begin{figure}[p]
@ -65,8 +66,8 @@
\toprule \toprule
\taskslowdownheader \taskslowdownheader
\midrule \midrule
Best effort batch & 212.62\% & 71108 & 14201 & 5.17 \\
Free & 0.33\% & 5769 & 1203 & 82.97 \\ Free & 0.33\% & 5769 & 1203 & 82.97 \\
Best effort batch & 212.62\% & 71108 & 14201 & 5.17 \\
Mid & 46.22\% & 8510 & 9135 & 1.16 \\ Mid & 46.22\% & 8510 & 9135 & 1.16 \\
Monitoring & 2.82\% & 1200998 & 1054458 & 2.86 \\ Monitoring & 2.82\% & 1200998 & 1054458 & 2.86 \\
Production & 27.21\% & 4546 & 16845 & 4.12 \\ Production & 27.21\% & 4546 & 16845 & 4.12 \\
@ -78,8 +79,8 @@
\toprule \toprule
\taskslowdownheader \taskslowdownheader
\midrule \midrule
Best effort batch & 71.84\% & 1018454 & 550288 & 8.47 \\
Free & 45.21\% & 12047 & 5588 & 1.18 \\ Free & 45.21\% & 12047 & 5588 & 1.18 \\
Best effort batch & 71.84\% & 1018454 & 550288 & 8.47 \\
Mid & 8.82\% & 225147 & 336262 & 1.11 \\ Mid & 8.82\% & 225147 & 336262 & 1.11 \\
Monitoring & 4.12\% & 2627612 & 2024679 & 1.51 \\ Monitoring & 4.12\% & 2627612 & 2024679 & 1.51 \\
Production & 30.92\% & 182604 & 466329 & 9.71 \\ Production & 30.92\% & 182604 & 466329 & 9.71 \\
@ -91,8 +92,8 @@
\toprule \toprule
\taskslowdownheader \taskslowdownheader
\midrule \midrule
Best effort batch & 52.96\% & 1236666 & 997117 & 7.40 \\
Free & 73.36\% & 172214 & 5553 & 1.12 \\ Free & 73.36\% & 172214 & 5553 & 1.12 \\
Best effort batch & 52.96\% & 1236666 & 997117 & 7.40 \\
Mid & 95.4\% & 579844 & 248553 & 2.04 \\ Mid & 95.4\% & 579844 & 248553 & 2.04 \\
Monitoring & 5.88\% & 2159459 & 1761833 & 1.74 \\ Monitoring & 5.88\% & 2159459 & 1761833 & 1.74 \\
Production & 3.61\% & 352603 & 357993 & 4.14 \\ Production & 3.61\% & 352603 & 357993 & 4.14 \\
@ -105,8 +106,8 @@
\toprule \toprule
\taskslowdownheader \taskslowdownheader
\midrule \midrule
Best effort batch & 50.56\% & 1154060 & 1135023 & 12.04 \\
Free & 42.82\% & 22831 & 5506 & 1.15 \\ Free & 42.82\% & 22831 & 5506 & 1.15 \\
Best effort batch & 50.56\% & 1154060 & 1135023 & 12.04 \\
Mid & 86.34\% & 228762 & 225269 & 2.56 \\ Mid & 86.34\% & 228762 & 225269 & 2.56 \\
Monitoring & 2.21\% & 1588844 & 913816 & 2.16 \\ Monitoring & 2.21\% & 1588844 & 913816 & 2.16 \\
Production & 6.53\% & 279565 & 349364 & 5.51 \\ Production & 6.53\% & 279565 & 349364 & 5.51 \\
@ -119,8 +120,8 @@
\toprule \toprule
\taskslowdownheader \taskslowdownheader
\midrule \midrule
Best effort batch & 0.47\% & 280811 & 205838 & 8.06 \\
Free & 48.15\% & 33050 & 40073 & 1.44 \\ Free & 48.15\% & 33050 & 40073 & 1.44 \\
Best effort batch & 0.47\% & 280811 & 205838 & 8.06 \\
Mid & 0.46\% & 62123 & 83322 & 10.31 \\ Mid & 0.46\% & 62123 & 83322 & 10.31 \\
Monitoring & 37.71\% & 1415296 & 1263746 & 2.82 \\ Monitoring & 37.71\% & 1415296 & 1263746 & 2.82 \\
Production & 1.96\% & 231639 & 414149 & 8.54 \\ Production & 1.96\% & 231639 & 414149 & 8.54 \\
@ -133,8 +134,8 @@
\toprule \toprule
\taskslowdownheader \taskslowdownheader
\midrule \midrule
Best effort batch & 44.29\% & 1368306 & 1563086 & 6.14 \\
Free & 45.86\% & 187447 & 37069 & 1.09 \\ Free & 45.86\% & 187447 & 37069 & 1.09 \\
Best effort batch & 44.29\% & 1368306 & 1563086 & 6.14 \\
Mid & 31.36\% & 200116 & 110201 & 7.60 \\ Mid & 31.36\% & 200116 & 110201 & 7.60 \\
Monitoring & 8.42\% & 2079134 & 1682711 & 2.08 \\ Monitoring & 8.42\% & 2079134 & 1682711 & 2.08 \\
Production & 3.65\% & 297168 & 492372 & 5.94 \\ Production & 3.65\% & 297168 & 492372 & 5.94 \\
@ -146,8 +147,8 @@
\toprule \toprule
\taskslowdownheader \taskslowdownheader
\midrule \midrule
Best effort batch & 104.33\% & 294959 & 184724 & 19.06 \\
Free & 33.85\% & 64718 & 15473 & 1.14 \\ Free & 33.85\% & 64718 & 15473 & 1.14 \\
Best effort batch & 104.33\% & 294959 & 184724 & 19.06 \\
Mid & 49.06\% & 732532 & 706124 & 3.86 \\ Mid & 49.06\% & 732532 & 706124 & 3.86 \\
Monitoring & 4.36\% & 1991341 & 1676276 & 1.72 \\ Monitoring & 4.36\% & 1991341 & 1676276 & 1.72 \\
Production & 26.75\% & 115953 & 399050 & 14.57 \\ Production & 26.75\% & 115953 & 399050 & 14.57 \\
@ -159,8 +160,8 @@
\toprule \toprule
\taskslowdownheader \taskslowdownheader
\midrule \midrule
Best effort batch & 107.03\% & 947368 & 527812 & 7.33 \\
Free & 28.79\% & 310534 & 290058 & 1.12 \\ Free & 28.79\% & 310534 & 290058 & 1.12 \\
Best effort batch & 107.03\% & 947368 & 527812 & 7.33 \\
Mid & 2.18\% & 338883 & 197440 & 6.49 \\ Mid & 2.18\% & 338883 & 197440 & 6.49 \\
Monitoring & 4.96\% & 2309296 & 1808698 & 1.94 \\ Monitoring & 4.96\% & 2309296 & 1808698 & 1.94 \\
Production & 2.7\% & 298799 & 470783 & 5.80 \\ Production & 2.7\% & 298799 & 470783 & 5.80 \\
@ -168,6 +169,6 @@
\end{tabular} \end{tabular}
} }
\caption{Mean task slowdown for each cluster and each task priority for single \caption{Mean task slowdown for each cluster and each task priority for single
clusters in the 2019 traces. Refer to \ref{fig:taskslowdown} for a legend of the clusters in the 2019 traces. Refer to Figure~\ref{fig:taskslowdown} for a legend
columns}\label{fig:taskslowdown-csts} of the columns.}\label{fig:taskslowdown-csts}
\end{figure} \end{figure}