\documentclass{usiinfbachelorproject}
\usepackage{multirow}
\usepackage{ifthen}
\usepackage{enumitem}
\usepackage{fontawesome5}
\usepackage{pgf}
\usepackage{tikz}
\usetikzlibrary{fit,arrows,calc,positioning}
\usepackage{parskip}
\usepackage{xcolor}
\usepackage{amsmath}
\usepackage{subcaption}
\usepackage{graphicx}
\usepackage[backend=biber,style=numeric,citestyle=ieee]{biblatex}
\usepackage{booktabs}
\usepackage{pgfplots}
\usepackage{array}
\newcolumntype{C}[1]{>{\centering\arraybackslash}p{#1}}
\usepgfplotslibrary{external}
\usepackage{titlesec}

\newcommand{\sectionbreak}{\clearpage}

\addbibresource{references.bib}

\setlength{\parskip}{5pt}
\setlength{\parindent}{0pt}

\captionsetup{labelfont={bf}}

\title{Understanding and Comparing Unsuccessful Executions in Large Datacenters}
%\subtitle{The (optional) subtitle}
\author{Claudio Maggioni}
\versiondate{\today}

\begin{committee}
\advisor[Universit\`a della Svizzera Italiana,
Switzerland]{Prof.}{Walter}{Binder}
\assistant[Universit\`a della Svizzera Italiana,
Switzerland]{Dr.}{Andrea}{Ros\'a}
\end{committee}

\abstract{The project aims at comparing two different traces coming from large
datacenters, focusing in particular on unsuccessful executions of jobs and
tasks submitted by users. The objective of this project is to compare the
resource waste caused by unsuccessful executions, their impact on application
performance, and their root causes. We will show the strong negative impact on
CPU and RAM usage and on task slowdown.  We will analyze patterns of
unsuccessful jobs and tasks, particularly focusing on their interdependency.
Moreover, we will uncover their root causes by inspecting key workload and
system attributes such asmachine locality and concurrency level.}

\begin{document}
\maketitle
\tableofcontents
\newpage

\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
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
distributed systems, in particular in how to schedule computations effectively,
avoid wasting resources and avoid failures.

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
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
\textit{Understanding the Dark Side of Big Data Clusters: An Analysis beyond
Failures}\cite{vino-paper}, which in its many conclusions highlighted the need
for better cluster management highlighting the high amount of failures found in
the traces.

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
workload due to improvements in computational technology, but also providing
data from 8 different \textit{Borg} cells from datacenters located all over the
world. These new traces are therefore about 100 times larger than the old
traces, weighing in terms of storage spaces approximately 8TiB (when compressed
and stored in JSONL format)\cite{google-drive-marso}, requiring a considerable
amount of computational power to analyze them and the implementation of special
data engineering techniques for analysis of the data.

\input{figures/machine_configs}

An overview of the machine configurations in the cluster analyzed with the 2011
traces and in the 8 clusters composing the 2019 traces can be found in
figure~\ref{fig:machineconfigs}. Additionally, in
figure~\ref{fig:machineconfigs-csts}, the same machine configuration data is
provided for the 2019 traces providing a cluster-by-cluster distribution of the
machines.

This project aims to repeat the analysis performed in 2015 to highlight
similarities and differences in workload this decade brought, and expanding the
old analysis to understand even better the causes of failures and how to prevent
them. Additionally, this report will provide an overview on the data engineering
techniques used to perform the queries and analyses on the 2019 traces.

\section{Background information}

  \textit{Borg} is Google's own cluster management software able to run
  thousands of different jobs. Among the various cluster management services it
  provides, the main ones are: job queuing, scheduling, allocation, and
  deallocation due to higher priority computations.

  The core structure of Borg is a cell, a set of
  machines usually all within the same cluster, whose work is allocated by the
  same cluster-management system and hence a cell is handled as a unit. Each
  cell may run large computational workload that is submitted to Borg. Such
  workload is called ``job'', which outlines the computations that a user wants
  to run and is made up of several ``tasks''.  A task is an executable program,
  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
  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
  % information events provide, the field ``type'' provides information on the
  % execution status of the job or task. This field can have several values,
  % which are illustrated in figure~\ref{fig:eventtypes}.

\subsection{Traces}

The data relative to the events happening while Borg cell
processes the workload is then encoded and stored as rows of several tables that
make up a single usage trace. Such data comes from the information obtained by
the cell's management system and single machines that make up the cell. Each
table is identified by a key, usually a timestamp.

In general events can be of two kinds, there are events that are relative to the
status of the schedule, and there are other events that are relative to the
status of a task itself.

% \subsection{Rosà et al.~2015 DSN paper}

In 2015, Dr.~Andrea Rosà, Lydia Y. Chen and Prof.~Walter Binder published a
research paper titled \textit{Understanding the Dark Side of Big Data Clusters:
An Analysis beyond Failures}\cite{vino-paper} in which they performed several
analysis on unsuccessful executions in the Google's 2011 Borg cluster traces
with the aim of identifying their resource waste, their impacts on the
performance of the application, and any causes that may lie behind such
failures. The salient conclusion of that research is that actually lots of
computations performed by Google would eventually end in failure, then leading
to large amounts of computational power being wasted.

\begin{figure}[h]
\begin{center}
\begin{tabular}{p{3cm}p{12cm}}
\toprule
\textbf{Type code} & \textbf{Description} \\
\midrule
% SUGGERIMENTO, NON CANCELLARE MAI, A MENO CHE NON SONO COSE COMPLETAMENTE
% INUTILI, IN MOLTI CASI VA BENE COMMENTARE, INTANTO NON INFLUISCONO CON LA
% COMPILAZIONE.
% 	\texttt{QUEUE} & The job or task was marked not eligible for scheduling
%   by Borg's scheduler, and thus Borg will move the job/task in a long
%   wait queue\\
% \texttt{SUBMIT}  & The job or task was submitted to Borg for execution\\
% \texttt{ENABLE}  & The job or task became eligible for scheduling\\
% \texttt{SCHEDULE}  & The job or task's execution started\\
\texttt{EVICT}  & The job or task was terminated in order to free
   computational resources for an higher priority job\\
\texttt{FAIL}  & The job or task terminated its execution unsuccesfully
   due to a failure\\
\texttt{FINISH}  & The job or task terminated succesfully\\
\texttt{KILL}  & The job or task terminated its execution because of a
   manual request to stop it\\
% \texttt{LOST}  & It is assumed a job or task is has been terminated, but
%   due to missing data there is insufficent information to identify when
%   or how\\
% \texttt{UPDATE\_PENDING}  & The metadata (scheduling class, resource
%   requirements, \ldots) of the job/task was updated while the job was
%   waiting to be scheduled\\
% \texttt{UPDATE\_RUNNING}  & The metadata (scheduling class, resource
%   requirements, \ldots) of the job/task was updated while the job was in
%   execution\\
\bottomrule
\end{tabular}
\end{center}
  \caption{Overview of job and task event types.}\label{fig:eventtypes}
\end{figure}

Figure~\ref{fig:eventTypes} shows the expected transitions between event
types.

\begin{figure}[h]
\centering
	\resizebox{\textwidth}{!}{%
		\includegraphics{./figures/event_types.png}}
\caption{Typical transitions between task/job event types according to
Google\label{fig:eventTypes}}
\end{figure}

\hypertarget{traces-contents}{%
\subsection{Traces contents}\label{traces-contents}}

The traces provided by Google contain mainly a collection of job and
task events spanning a month of execution of the 8 different clusters.
In addition to this data, some additional data on the machines'
configuration in terms of resources (i.e.~amount of CPU and RAM) and
additional machine-related metadata.

Due to Google's policy, most identification related data (like job/task
IDs, raw resource amounts and other text values) were obfuscated prior
to the release of the traces. One obfuscation that is noteworthy in the
scope of this thesis is related to CPU and RAM amounts, which are
expressed respetively in NCUs (\emph{Normalized Compute Units}) and NMUs
(\emph{Normalized Memory Units}).

NCUs and NMUs are defined based on the raw machine resource
distributions of the machines within the 8 clusters. A machine having 1
NCU CPU power and 1 NMU memory size has the maximum amount of raw CPU
power and raw RAM size found in the clusters. While RAM size is measured
in bytes for normalization purposes, CPU power was measured in GCU
(\emph{Google Compute Units}), a proprietary CPU power measurement unit
used by Google that combines several parameters like number of
processors and cores, clock frequency, and architecture (i.e.~ISA).

\hypertarget{overview-of-traces-format}{%
\subsection{Overview of traces'
format}\label{overview-of-traces-format}}

The traces have a collective size of approximately 8TiB and are stored
in a Gzip-compressed JSONL (JSON lines) format, which means that each
table is represented by a single logical ``file'' (stored in several
file segments) where each carriage return separated line represents a
single record for that table.

There are namely 5 different table ``files'':
\begin{description}
\item[\texttt{machine\_configs},] which is a table containing each physical
  machine's configuration and its evolution over time;
\item[\texttt{instance\_events},] which is a table of task events;
\item[\texttt{collection\_events},] which is a table of job events;
\item[\texttt{machine\_attributes},] which is a table containing (obfuscated)
  metadata about each physical machine and its evolution over time;
\item[\texttt{instance\_usage},] which contains resource (CPU/RAM) measures
  of jobs and tasks running on the single machines.
\end{description}

The scope of this thesis focuses on the tables
\texttt{machine\_configs}, \texttt{instance\_events} and
\texttt{collection\_events}.

\hypertarget{remark-on-traces-size}{%
\subsection{Remark on traces size}\label{remark-on-traces-size}}

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
challenging to analyze due to their sheer size. As stated before, the
traces have a total size of 8 TiB when stored in the format provided by
Google. Even when broken down to table ``files'', unitary sizes still
reach the single tebibyte mark (namely for \texttt{machine\_configs},
the largest table in the trace).

Due to this constraints, a careful data engineering based approach was
used when reproducing the 2015 DSN paper analysis. Bleeding edge data
science technologies like Apache Spark were used to achieve efficient
and parallelized computations. This approach is discussed with further
detail in the following section.

\hypertarget{project-requirements-and-analysis}{%
\section{Project requirements and
analysis}\label{project-requirements-and-analysis}}

\textbf{TBD} (describe our objective with this analysis in detail)
The aim of this thesis is to repeat the analysis performed in 2015 on the
dataset Google has released in 2019 in order to find similarities and
differences with the previous analysis, and ultimately find whether
computational power is indeed wasted in this new workload as well. The 2019 data
comes from 8 Borg cells spanning 8 different datacenters located in different
geographical positions, all focused on computational oriented workloads. The
data collection time span matches the entire month of May 2019.


\hypertarget{analysis-methodology}{%
\section{Analysis methodology}\label{analysis-methodology}}

Due to the inherent complexity in analyzing traces of this size, novel
bleeding-edge data engineering tecniques were adopted to performed the required
computations. We used the framework Apache Spark to perform efficient and
parallel Map-Reduce computations. In this section, we discuss the technical
details behind our approach.

\hypertarget{introduction-on-apache-spark}{%
\subsection{Introduction on Apache
Spark}\label{introduction-on-apache-spark}}

Apache Spark is a unified analytics engine for large-scale data
processing. In layman's terms, Spark is really useful to parallelize
computations in a fast and streamlined way.

In the scope of this thesis, Spark was used essentially as a Map-Reduce
framework for computing aggregated results on the various tables. Due to
the sharded nature of table ``files'', Spark is able to spawn a thread
per file and run computations using all processors on the server
machines used to run the analysis.

Spark is also quite powerful since it provides automated thread pooling
services, and it is able to efficiently store and cache intermediate
computation on secondary storage without any additional effort required
from the data engineer. This feature was especially useful due to the
sheer size of the analyzed data, since the computations required to
store up to 1TiB of intermediate data on disk.

The chosen programming language for writing analysis scripts was Python.
Spark has very powerful native Python bindings in the form of the
\emph{PySpark} API, which were used to implement the various queries.


\hypertarget{query-architecture}{%
\subsection{Query architecture}\label{query-architecture}}

\subsubsection{Overview}

In general, each query written to execute the analysis
follows a general Map-Reduce template.

Traces are first read, then parsed, and then filtered by performing selections,
projections and computing new derived fields. After this preparation phase, the
trace records are often passed through a \texttt{groupby()} operation, which by
choosing one or many record fields sorts all the records into several ``bins''
containing records with matching values for the selected fields. Then, a map
operation is applied to each bin in order to derive some aggregated property
value for each grouping. Finally, a reduce operation is applied to either
further aggregate those computed properties or to generate an aggregated data
structure for storage purposes.

\subsubsection{Parsing table files}

As stated before, table ``files'' are composed of several Gzip-compressed
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
file found in the trace release
package\cite{google-proto-marso}. This file was used as
the oracle specification and was a critical reference for writing the query
code that checks, parses and carefully sanitizes the various JSONL records
prior to actual computations.

The JSONL encoding of traces records is often performed with non-trivial rules
that required careful attention. One of these involved fields that have a
logically-wise ``zero'' value (i.e.~values like ``0'' or the empty string). For
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
possibility and insert back the omitted record attributes.

\subsubsection{The queries}

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 save
memory during the query, a projection is often applied to the data by the means
of a \texttt{.map()} operation over the entire trace set, performed using
Spark's RDD API.

Another operation that is often necessary to perform prior to the Map-Reduce
core of each query is a record filtering process, which is often motivated by
the presence of incomplete data (i.e.~records which contain fields whose values
is unknown). This filtering is performed using the \texttt{.filter()} operation
of Spark's RDD API.

The core of each query is often a \texttt{groupby()} followed by a
\texttt{map()} operation on the aggregated data. The \texttt{groupby()} groups
the set of all records into several subsets of records each having something in
common. Then, each of this small clusters is reduced with a \texttt{map()}
operation to a single record. The motivation behind this way of computing data
is that for the analysis in this thesis it is often necessary to analyze the
behaviour w.r.t. time of either task or jobs by looking at their events. These
queries are therefore implemented by \texttt{groupby()}-ing records by task or
job, and then \texttt{map()}-ing each set of event records sorting them by time
and performing the desired computation on the obtained chronological event log.

Sometimes intermediate results are saved in Spark's parquet format in order to
compute and save intermediate results beforehand.

\subsection{Query script design}

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
appreciate their behaviour.

\subsubsection{The ``task slowdown'' query script}

One example of analysis script with average complexity and a pretty
straightforward structure is the pair of scripts \texttt{task\_slowdown.py} and
\texttt{task\_slowdown\_table.py} used to compute the ``task slowdown'' tables
(namely the tables in figure~\ref{fig:taskslowdown}).

``Slowdown'' is a task-wise measure of wasted execution time for tasks with a
\texttt{FINISH} termination type. It is computed as the total execution time of
the task divided by the execution time actually needed to complete the task
(i.e. the total time of the last execution attempt, successful by definition).

The analysis requires to compute the mean task slowdown for each task priority
value, and additionally compute the percentage of tasks with successful
terminations per priority. The query therefore needs to compute the execution
time of each execution attempt for each task, determine if each task has
successful termination or not, and finally combine this data to compute
slowdown, mean slowdown and ultimately the final table found in
figure~\ref{fig:taskslowdown}.

\begin{figure}[h]
\centering
\includegraphics[width=.75\textwidth]{figures/task_slowdown_query.png}
\caption{Diagram of the script used for the ``task slowdown''
  query.}\label{fig:taskslowdownquery}
\end{figure}

Figure~\ref{fig:taskslowdownquery} shows a schematic representation of the query
structure.

The query first starts reading the \texttt{instance\_events} table, which
contains (among other data) all task event logs containing properties, event
types and timestamps. As already explained in the previous section, the logical
table file is actually stored as several Gzip-compressed JSONL shards. This is
very useful for processing purposes, since Spark is able to parse and load in
memory each shard in parallel, i.e. using all processing cores on the server
used to run the queries.

After loading the data, a selection and a projection operation are performed in
the preparation phase so as to ``clean up'' the records and fields that are not
needed, leaving only useful information to feed in the ``group by'' phase. In
this query, the selection phase removes all records that do not represent task
events or that contain an unknown task ID or a null event timestamp. In the 2019
traces it is quite common to find incomplete records, since the log process is
unable to capture the sheer amount of events generated by all jobs in a exact
and deterministic fashion.

Then, after the preparation stage is complete, the task event records are
grouped in several bins, one per task ID\@. Performing this operation the
collection of unsorted task event types is rearranged to form groups of task
events all relating to a single task.

These obtained collections of task events are then sorted by timestamp and
processed to compute intermediate data relating to execution attempt times and
task termination counts. After the task events are sorted, the script iterates
over the events in chronological order, storing each execution attempt time and
registering all execution termination types by checking the event type field.
The task termination is then equal to the last execution termination type,
following the definition originally given in the 2015 Ros\'a et al. DSN paper.

If the task termination is determined to be unsuccessful, the tally counter of
task terminations for the matching task property is increased. Otherwise, all
the task termination attempt time deltas are returned. Tallies and time deltas
are saved in an intermediate time file for fine-grained processing.

Finally, the \texttt{task\_slowdown\_table.py} processes this intermediate
results to compute the percentage of successful tasks per execution and
computing slowdown values given the previously computed execution attempt time
deltas. Finally, the mean of the computed slowdown values is computed resulting
in the clear and coincise tables found in figure~\ref{fig:taskslowdown}.

\section{Analysis: Performance Input of Unsuccessful Executions}

Our first investigation focuses on replicating the methodologies used in the
2015 DSN Ros\'a et al.\ paper\cite{vino-paper} regarding usage of machine time
and resources.

In this section we perform several analyses focusing on how machine time and
resources are wasted, by means of a temporal vs. spatial resource analysis from
the perspective of single tasks as well as jobs. We then compare the results
from the 2019 traces to the ones that were obtained in 2015 to understand the
workload evolution inside Borg between 2011 and 2019.

\subsection{Temporal Impact: Machine Time Waste}
\input{figures/machine_time_waste}

This analysis explores how machine time is distributed over task events and
submissions. By partitioning the collection of all terminating tasks by their
termination event, the analysis aims to measure the total time spent by tasks in
3 different execution phases:

\begin{description}
\item[resubmission time:] the total of all time deltas between every task
  termination event and the immediately succeding task submission event, i.e.
    the total time spent by tasks waiting to be resubmitted in Borg after a
    termination;
\item[queue time:] the total of all time deltas between every task submission
  event and the following task scheduling event, i.e. the total time spent by
    tasks queuing before execution;
\item[running time:] the total of all time deltas between every task scheduling
  event and the following task termination event, i.e. the total time spent by
    tasks ``executing'' (i.e. performing useful computations) in the clusters.
\end{description}

In the 2019 traces, an additional ``Unknown'' measure is counted. This measure
collects all the times in which the event transitions between the register
events do not allow to safely assume in which execution phase a task may be.
Unknown measures are mostly caused by faults and missed event writes in the task
event log that was used to generate the traces.

The analysis results are depicted in figure~\ref{fig:machinetimewaste-rel} as a
comparison between the 2011 and 2019 traces, aggregating the data from all
clusters. Additionally, in figure~\ref{fig:machinetimewaste-rel-csts}
cluster-by-cluster breakdown result is provided for the 2019 traces.

The striking difference between 2011 and 2019 data is in the machine time
distribution per task termination type. In the 2019 traces, 94.38\% of global
machine time is spent on tasks that are eventually \texttt{KILL}ed.
\texttt{FINISH}, \texttt{EVICT} and \texttt{FAIL} tasks respectively register
totals of 4.20\%, 1.18\% and 0.25\% machine time, maintaining a analogous
distribution between them to their distribution in the 2011 traces.

Considering instead the distribution between execution phase times, the
comparison shows very similar behaviour between the two traces, having the
``Running'' time being dominant (at a total of 16.63\% across task terminations
in 2019) over the queue and resubmission phases (with respective totals in 2019
of 3.26\% and 0.004\%).

However, another noteworthy difference between 2011 and 2019 data lies in the new
``Unknown'' trace dataset present only in the latter traces, registering a total
80.12\% of global machine time across al terminations. This data can be
interpreted as a strong indication of the ``poor quality'' of the 2019 traces
w.r.t.\ of accuracy of task event logging.

Considering instead the behaviour of each single cluster in the 2019 traces, no
significant difference beween them can be observed. The only notable difference
lies between the ``Running time``-``Unknown time'' ratio in \texttt{KILL}ed
tasks, which is at its highest in cluster A (at 30.78\% by 58.71\% of global
machine time) and at its lowest in cluster H (at 8.06\% by 84.77\% of global
machine time).

\subsection{Average Slowdown per Task}
\input{figures/task_slowdown}

This analysis aims to measure the figure of ``slowdown'', which is defined as
the ratio between the response time (i.e\. queue time and running time) of the
last execution of a given task and the total response time across all
executions of said task. This metric is especially useful to analyze the impact
of unsuccesful executions on each task total execution time w.r.t.\ the intrinsic
workload (i.e.\ computational time) of tasks.

Refer to figure~\ref{fig:taskslowdown} for a comparison between the 2011 and
2019 mean task slowdown measures broke down by task priority. Additionally, said
means are computed on a cluster-by-cluster basis for 2019 data in
figure~\ref{fig:taskslowdown-csts}.

In 2015 Ros\'a et al.\cite{vino-paper} measured mean task slowdown per each task
priority value, which at the time were $[0,11]$ numeric values. However,
in 2019 traces, task priorities are given as a $[0,500]$ numeric value.
Therefore, to allow for an easier comparison, mean task slowdown values are
computed by task priority tier over the 2019 data. Priority tiers are
semantically relevant priority ranges defined in the Tirmazi et al.
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
the 2015 analysis.

In the given tables, the \textbf{\% finished} column corresponds to the
percentage of \texttt{FINISH}ed tasks for that priority or tier. \textbf{Mean
response [s] (last execution)} instead shows the mean response time of the last
task execution of each task in that priority/tier.
\textbf{Mean response [s] (all executions)} provides a very similar figure,
though this column shows the mean response time across all executions.
\textbf{Mean slowdown} instead provides the mean slowdown value for each task
priority/tier.

Comparing the tables in figure~\ref{fig:taskslowdown} we observe that the
maximum mean slowdown measure for 2019 data (i.e.\ 7.84, for the BEB tier) is almost
double of the maximum measure in 2011 data (i.e.\ 3.39, for priority $3$
corresponding to the BEB tier). The ``Best effort batch'' tier, as the name
suggest, is a lower priority tier where failures are more tolerated. Therefore,
due to the increased concurrency in the 2019 clusters compared to 2011 and the
higher machine time spent for unsuccesful executions (as observed in the
previous analysis) and increase slowdown rate for this class is not particularly
surprising.

The amount of non-successful task terminations in the 2019 traces is also rather
high when compared to 2011 data, as it can evinced by the low percentage of
\texttt{FINISH}ed tasks across priority tiers.

Another noteworthy difference is in the mean response times for all and last
executions: while the mean response is overall shorter in time in the 2019
traces by an order of magnitude, the new traces show an overall significantly
higher mean response time than in the 2011 data.

Across 2019 single clusters (as in figure~\ref{fig:taskslowdown-csts}), the data
shows a mostly uniform behaviour, other than for some noteworthy mean slowdown
spikes. Indeed, cluster A has 82.97 mean slowdown in the ``Free'' tier,
cluster G has 19.06 and 14.57 mean slowdown in the ``BEB'' and ``Production''
tier respectively, and Cluster D has 12.04 mean slowdown in its ``Free'' tier.

\subsection{Spatial Impact: Resource Waste}
\input{figures/spatial_resource_waste}

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
CPU and Memory resource allocation and usage are distributed among tasks based
on their termination
type.

Due to limited computational resources w.r.t.\ the data analysis process, the
resource usage for clusters E to H in the 2019 traces is missing. However, a
comparison between 2011 resource usage and the aggregated resource usage of
clusters A to D in the 2019 traces can be found in
figure~\ref{fig:spatialresourcewaste-actual}. Additionally, a
cluster-by-cluster breakdown for the 2019 data can be found in
figure~\ref{fig:spatialresourcewaste-actual-csts}.

From these figures it is clear that, compared to the relatively even
distribution of used resources in the 2011 traces, the distribution of resources
in the 2019 Borg clusters became strikingly uneven, registering a combined
86.29\% of
CPU resource usage and 84.86\% memory usage for \texttt{KILL}ed tasks. Instead,
all other task termination types have a significantly lower resource usage:
\texttt{EVICT}ed, \texttt{FAIL}ed and \texttt{FINISH}ed tasks register respectively
8.53\%, 3.17\% and 2.02\% CPU usage and 9.03\%, 4.45\%, and 1.66\% memory usage.
This resource distribution can also be found in the data from individual
clusters in figure~\ref{fig:spatialresourcewaste-actual-csts}, with always more
than 80\% of resources devoted to \texttt{KILL}ed tasks.

Considering now requested resources instead of used ones, a comparison between
2011 and the aggregation of all A-H clusters of the 2019 traces can be found in
figure~\ref{fig:spatialresourcewaste-requested}. Additionally, a
cluster-by-cluster breakdown for single 2019 clusters can be found in
figure~\ref{fig:spatialresourcewaste-requested-csts}.

Here \texttt{KILL}ed jobs dominate even more the distribution of resources,
reaching a global 97.21\% of CPU allocation and a global 96.89\% of memory
allocation. Even in allocations, the \texttt{KILL} lead is followed by (in
order) \texttt{EVICT}ed, \texttt{FAIL}ed and \texttt{FINISH}ed jobs, with
respective CPU allocation figures of 2.73\%, 0.06\% and 0.0012\% and memory
allocation figures of 3.04\%, 0.06\% and 0.012\%.

Behaviour across clusters (as
evinced in figure~\ref{fig:spatialresourcewaste-requested-csts}) in terms of
requested resources is pretty homogeneous, with the exception of cluster A
having a relatively high 2.85\% CPU and 3.42\% memory resource requests from
\texttt{EVICT}ed tasks and cluster E having a noteworthy 1.67\% CPU and 1.31\%
memory resource resquests from \texttt{FINISH}ed tasks.

With more than 98\% of both CPU and memory resources used by
(and more than 99.99\% of both CPU and memory resources requested by)
non-successful tasks, it is clear the spatial resource waste is high in the 2019
traces.

\section{Analysis: Pattern and Models for Task and Job Events}

\subsection{Unsuccessful Task Event Patterns}
\input{figures/table_iii} % has table III and table IV in it

Refer to figure \ref{fig:tableIII}.

\textbf{Observations}:

\begin{itemize}
\item
  The mean number of events per task is an order of magnitude higher
  than in the 2011 traces
\item
  Generally speaking, the event type with higher mean is the termination
  event for the task
\item
  The \# evts mean is higher than the sum of all other event type means,
  since it appears there are a lot more non-termination events in the
  2019 traces.
\end{itemize}

\subsection{Unsuccessful Job Event Patterns}

\textbf{Observations}:

\begin{itemize}
\item
  Again the mean number of tasks is significantly higher than the 2011
  traces, indicating a higher complexity of workloads
\item
  Cluster A has no evicted jobs
\item
  The number of events is however lower than the event means in the 2011
  traces
\end{itemize}

\hypertarget{probability-of-task-successful-termination-given-its-unsuccesful-events}{%
\subsection{Probability of task successful termination given its
unsuccesful
events}\label{probability-of-task-successful-termination-given-its-unsuccesful-events}}

\subsection{Conditional Probability of Task Success}
\input{figures/figure_5}

Refer to figure \ref{fig:figureV}.

\textbf{Observations}:

\begin{itemize}
\item
  Behaviour is very different from cluster to cluster
\item
  There is no easy conclusion, unlike in 2011, on the correlation
  between succesful probability and \# of events of a specific type.
\item
  Clusters B, C and D in particular have very unsmooth lines that vary a
  lot for small \# evts differences. This may be due to an uneven
  distribution of \# evts in the traces.
\end{itemize}
\hypertarget{correlation-between-task-events-metadata-and-task-termination}{%
\subsection{Correlation between task events' metadata and task
termination}\label{correlation-between-task-events-metadata-and-task-termination}}

\section{Analysis: Potential Causes of Unsuccessful Executions}

\subsection{Event rates vs. task priority, event execution time, and machine
concurrency.}

\input{figures/figure_7}

Refer to figures \ref{fig:figureVII-a}, \ref{fig:figureVII-b}, and
\ref{fig:figureVII-c}.

\textbf{Observations}:

\begin{itemize}
\item
  No smooth curves in this figure either, unlike 2011 traces
\item
  The behaviour of curves for 7a (priority) is almost the opposite of
  2011, i.e. in-between priorities have higher kill rates while
  priorities at the extremum have lower kill rates. This could also be
  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
  and finish event rates, instead of the U shape curve in 2015 DSN
\item
  In figure \ref{fig:figureVII-b} cluster behaviour seems quite uniform
\item
  Machine concurrency seems to play little role in the event termination
  distribution, as for all concurrency factors the kill rate is at 90\%.
\end{itemize}

\subsection{Event Rates vs. Requested Resources, Resource Reservation, and
Resource Utilization}

\subsection{Figure 8 tbd}
\input{figures/figure_8}

\subsection{Job Rates vs. Job Size, Job Execution Time, and Machine Locality}
\input{figures/figure_9}

Refer to figures \ref{fig:figureIX-a}, \ref{fig:figureIX-b}, and
\ref{fig:figureIX-c}.

\textbf{Observations}:

\begin{itemize}
\item
  Behaviour between cluster varies a lot
\item
  There are no ``smooth'' gradients in the various curves unlike in the
  2011 traces
\item
  Killed jobs have higher event rates in general, and overall dominate
  all event rates measures
\item
  There still seems to be a correlation between short execution job
  times and successfull final termination, and likewise for kills and
  higher job terminations
\item
  Across all clusters, a machine locality factor of 1 seems to lead to
  the highest success event rate
\end{itemize}

\hypertarget{mean-number-of-tasks-and-event-distribution-per-task-type}{%
\subsection{Mean number of tasks and event distribution per task
type}\label{mean-number-of-tasks-and-event-distribution-per-task-type}}


\hypertarget{potential-causes-of-unsuccesful-executions}{%
\subsection{Potential causes of unsuccesful
executions}\label{potential-causes-of-unsuccesful-executions}}

\textbf{TBD}

\hypertarget{implementation-issues-analysis-limitations}{%
\section{Implementation issues -- Analysis
limitations}\label{implementation-issues-analysis-limitations}}

\hypertarget{discussion-on-unknown-fields}{%
\subsection{Discussion on unknown
fields}\label{discussion-on-unknown-fields}}

\textbf{TBD}

\hypertarget{limitation-on-computation-resources-required-for-the-analysis}{%
\subsection{Limitation on computation resources required for the
analysis}\label{limitation-on-computation-resources-required-for-the-analysis}}

\textbf{TBD}

\hypertarget{other-limitations}{%
\subsection{Other limitations \ldots{}}\label{other-limitations}}

\textbf{TBD}

\hypertarget{conclusions-and-future-work-or-possible-developments}{%
\section{Conclusions and future work or possible
developments}\label{conclusions-and-future-work-or-possible-developments}}

\textbf{TBD}

\printbibliography

\end{document}
% vim: set ts=2 sw=2 et tw=80:
