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Scheduling Method for Network Lifetime Estimation of Wireless Sensor Network.tex

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Mar 24, 2014, 3:36:07 PM (11 years ago)

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dron

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Publications/Wilfried Dron/JOURNAL - Scheduling Method for Network Lifetime Estimation of WSN/Scheduling Method for Network Lifetime Estimation of Wireless Sensor Network.tex (modified) (21 diffs)

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Publications/Wilfried Dron/JOURNAL - Scheduling Method for Network Lifetime Estimation of WSN/Scheduling Method for Network Lifetime Estimation of Wireless Sensor Network.tex

-                      r133
+                      r134
 % *** CITATION PACKAGES ***
+%
 %\usepackage{cite}
+\usepackage{cite}
 % cite.sty was written by Donald Arseneau
 % V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
 …
 \usepackage{balance}
 \usepackage{xspace}
+%\usepackage[caption=false]{subfig}
 \newcommand{\pmsg}{{\textit{PowerMessage}}}
 \newcommand{\imsg}{{\textit{InterfaceMessage}}}
 …
 \begin{abstract}
 %\boldmath
 The network lifetime is a major constraint for the design of WSN's hardware and software.
+The network lifetime is a major requirement for the design of WSN's hardware and software.
 %While several simulation tools are focused on power consumption estimation, the network lifetime has been estimated using an ideal battery model.
 While several simulation tools are focused on estimating power consumption, the lifetime is commonly computed using a simple ideal battery model.
 As a consequence, issues related with the use of a more realistic (non-ideal) battery model are not addressed yet.
 Considering the error that is made in node's lifetime estimation using an ideal battery model (up to 40\%), specifications-based models have been implemented to achieve more reliable predictions.
+As a consequence, issues related to the use of a more realistic (non-ideal) battery model are not addressed yet.
+Considering the error that is made in node's lifetime estimation using an ideal battery model (up to 40\%), specifications-based models were implemented to achieve more reliable predictions.
 In this context, we introduce four scheduling methods to address the challenges relative to such battery models.
 These methods aim to manage energy transactions between the wireless node model and a non-ideal battery model.
+These methods manage energy transactions between the wireless node model and a non-ideal battery model.
 %In this context, we introduce four scheduling methods to manage the energy transactions between the wireless node model and a non-ideal battery model, allowing a more accurate network lifetime estimation to be achieved.
 Each of our methods is analyzed and compared through a typical temperature sensing application case.
 We conducted several simulations considering power consumption estimation, simulation performances, node lifetime estimation and scalability.
 Comparison of the obtained results highlights two methods, one more accurate but, rather slow, whereas the other is strongly scalable but less accurate.
+Comparison of the obtained results highlights two methods, one more accurate, but rather slow, whereas the other is strongly scalable, but less accurate.
 \end{abstract}
 …
 It reflects the time while the network can operate properly according to application-defined constraints.
 %Even if almost every application defines its own constraints, the network lifetime cannot be estimated without being able to estimate the node's lifetime.
 Even if almost every application defines its own constraints, the network lifetime is estimated using the individual node's lifetime information.
+Even if almost every application defines its own constraints, the network lifetime is estimated using the individual nodes' lifetime.
 Since some specific application requires the nodes to have a long lifetime~\cite{outdoor_gplatform} (\eg from several weeks to several years) and/or the network to count several dozen of nodes~\cite{wsn_trends}, it is common to use simulation and modeling tools to design such devices.
 …
 It can be either based on experimental measurements or technical specifications.
 To remain consistent using such a model, electrical laws have to be applied.
 Therefore, it is important to pay attention to the way power transactions between battery and supplied components are acheived.
+Therefore, it is important to pay attention to the way power transactions between battery and supplied components are achieved.
 In other words, the scheduling of the energy transactions trough the simulated time is crucial (\cf Fig.~\ref{archi_methods}).
 %As a consequence, the scheduling of the energy transactions among the battery and the electronic components models is important.
 …
 In this context, we introduce four scheduling methods to schedule the energy transactions in a modeled wireless sensor network node.
 %We show that these methods are influencing the node lifetime estimation.
 We show that the way this scheduling is achieved impact significantly the lifetime estimation showing difference in the obtained results that reaches 11.7\%.
+We show that the scheduling has a significant impact on the lifetime estimation, showing differences in the obtained results that reach 11.7\%.
 %Moreover, the simulation's performance is also impacted, bounding the uses of certain methods to small-sized networks or short lifetime modeling.
 As a side effect, the scheduling method also impacts the overall simulation performances, restricting the ability to simulate large scale and/or long time lasting networks.
 This article is structured as follows.
 The second section hold the background of this work.
+The second section holds the background of this work.
 The scheduling methods principles are explained in the section 3.
 The fourth section address the implementation of these methods in OMNeT++ trough a WSN framework that is oriented toward power consumption estimation.
 Finally, the two last sections hold respectively the simulation results and the discussion of these results.
+The fourth section addresses the implementation of these methods in OMNeT++ through a WSN framework that is oriented towards power consumption estimation.
+Finally, the two last sections hold respectively the simulation results and their discussion.
 \begin{figure}
 …
 \section{Background}
 The scheduling method for energy transactions have not been addressed yet, thus there is no previous work on that subject.
 However, there are related works that are dealing with the power consumption estimation issues for the wireless sensor network simulation.
 Since the node lifetime estimation relies on the battery models as well it is important to give a brief introduction to the battery behavior.
 In that purpose, this section holds a short background about the battery behavior before addressing the core-related works.
+Scheduling methods for energy transactions have not been addressed yet, thus there is no previous work on that subject.
+However, there are some related works that deal with the power consumption estimation issues for the wireless sensor network simulation.
+Since the node lifetime estimation relies on the battery models as well, it is important to give a brief introduction to the battery behavior.
+For that purpose, this section holds a short background about the battery behavior before addressing the core-related works.
 \subsection{Battery Behavior and Modeling} \label{sect:battery_desc}
 The batteries are electrochemical power sources.
+The primary batteries are electrochemical power sources.
 In contrast with the wired power sources, the amount of energy that they carry is limited.
 This amount of energy is called \textit{nominal capacity} if the battery is new or \textit{residual capacity} (shorten to \textit{residual}) if it has been partially used.
 Considering a battery under use, its residual varies with the ambient temperature and the instantaneous current draw.
 In other words, the available amount of energy change over the time according to the aforementioned factors.
+In other words, the available amount of energy changes over the time according to the aforementioned factors.
 The battery's \textit{nominal current} (set by the manufacturer) represent the ``normal operation'' current limit under continuous draw.
 The term \textit{effective capacity} stands for the battery's capacity that is really available given a set of condition (\eg specific instantaneous current draw and a temperature).
 Furthermore, their supply voltage varies as well with temperature and instantaneous current draw but also with the residual.
+The term \textit{effective capacity} stands for the battery's capacity that is really available given a set of condition (\eg a specific instantaneous current draw and temperature).
+Furthermore, the supply voltage varies as well with temperature and instantaneous current draw but also with the residual.
 As a consequence, a specific current draw can produce a drift in the battery's supply voltage value.
 According to the ohm law, this drift will change the current draw itself leading to a new drift.
 …
 %All these assumptions were experimentally validated.
 A first study highlights the fact that the way in which the components are drawing the current has a strong influence in the \textsl{effective capacity}~\cite{battery_char}.
+A first study highlights the fact that the way in which the components are drawing the current has a strong influence on the \textsl{effective capacity}~\cite{battery_char}.
 These observations were confirmed by a more recent work that characterized commercial Li-Ion batteries behaviors through real measurements~\cite{battery_char_new}.
+In this work, {K. Mikhaylov} and {J. Tervonen} observed again that the available capacity of the battery depends mainly on the instant current draw under constant temperature.
+Another article that focuses on remaining capacity measurements agrees on the same conclusion~\cite{remaining_capacity_measurement}.
+In this work, {K. Mikhaylov} and {J. Tervonen} observed again that the available capacity of the battery depends mainly on the instantaneous current draw under constant temperature.
+%Another article that focuses on remaining capacity measurements agrees on the same conclusion~\cite{remaining_capacity_measurement}.
+Another article agrees on the same conclusion~\cite{remaining_capacity_measurement}.
 This last work addressed the specific case of determining the remaining battery capacity for a wireless sensor node using a method that consider the effective capacity and the instantaneous current draw instead of the voltage information.
 More battery centered work were achieved to reach a better understanding of the battery properties.
+More battery centered work were conducted to reach a better understanding of the battery properties.
 Among them, another property known as \textit{relaxation effect} is explained in two articles written by L. Feeney and al.~\cite{battery_feeney,battery_model_feeney}.
 As mentioned, when a strong current is drawn from the battery, its \textsl{effective capacity} decrease.
+As mentioned, when a strong current is drawn from the battery, its \textsl{effective capacity} decreases.
 In other words, its actual available energy is lower than the nominal value.
 This assumption is valid for a current draw that remains the same until the end of the battery life.
+If, for instance, the current draw decrease to a value that is beyond the battery's ``nominal current'', the battery will ``recover'' some capacity.
+To summarize, there are strong evidences that explain the limitations of ideal battery model.
+While this model is extremely flexible and fast thanks to the fact that it is not dependent on any phenomena, it is highly inaccurate and does not reproduce the behavior of a real battery.
+For instance, if the current draw decrease to a value that is beyond the battery's ``nominal current'', the battery will ``recover'' some capacity.
+%To summarize, there are strong evidences that explain the limitations of ideal battery model.
+To summarize, the aforementioned evidences clearly established the limitations of the ideal battery model.
+While this model is extremely flexible and fast thanks to the fact that it is not dependent on any electrical or electrochemical effects, it is highly inaccurate and does not reproduce the behavior of a real battery.
 \subsection{Simulation and Modeling Environments}
 …
 The most noticeable are Power-TOSSIM~\cite{powertossim_ws} and mTOSSIM~\cite{mtossim}.
 Power-TOSSIM enables the power consumption to be computed after the simulation ends.
 In contrast, mTOSSIM go further allowing the lifetime to be estimated.
+In contrast, mTOSSIM goes further, allowing the lifetime to be estimated.
 It does so using a super-capacitor to model the power supply of the nodes.
 The super-capacitor behavior is very different from battery behavior (\cf Section~\ref{sect:battery_desc}).
+The super-capacitor behavior is very different from the battery behavior (\cf Section~\ref{sect:battery_desc}).
 As a consequence, this model cannot be used to estimate the lifetime of nodes equipped with batteries.
 …
 Regarding the more general simulation environments, there are several network simulators like NS-2/3~\cite{ns2_ws}, OMNeT++~\cite{omnet_ws}, WSNeT~\cite{wsnet} or IdeaOne~\cite{ideaone}.
 Some of them are able to estimate power consumption thanks to extension called \textit{frameworks}.
+Some of them are able to estimate power consumption thanks to extensions called \textit{frameworks}.
 However, the goal of these environments is to deal with network modeling issues more than network lifetime estimation.
 The OMNeT++ simulator is less concerned than the other environments since its flexibility allows new features to be integrated more easily as described in many surveys \cite{sim_survey_0,sim_survey_1,sim_survey_2,sim_survey_3} or in dedicated report from A. Varga and R. Hornig~\cite{omnet_overview}.
 As a consequence, several~\textit{power-aware} framework were developed over the previous years.
+The OMNeT++ simulator is less concerned than the other environments since its flexibility allows new features to be integrated more easily, as described in many surveys \cite{sim_survey_0,sim_survey_1,sim_survey_2,sim_survey_3} or in dedicated report from A. Varga and R. Hornig~\cite{omnet_overview}.
+As a consequence, several~\textit{power-aware} frameworks were developed over the previous years.
 Energy Model~\cite{modeling_energy}, Pawis~\cite{pawis_fm_2} and Energy Framework~\cite{energy_fm} were thus introduced.
 Unfortunately a common short-coming of these framework is that none of them provides a non-ideal battery model.
 Nevertheless, this short-coming was partially covered in an extension of the Energy Framework.
 In their article, K. Mikhaylov and J. Tervonen were presenting a battery model~\cite{energy_fm_2} that was validated through measurement of real battery.
+Unfortunately, a common short-coming of these frameworks is that none of them provides a non-ideal battery model.
+Nevertheless, this short-coming was partially covered in an extension of the Energy Framework~\cite{energy_fm_2}.
+In their article, K. Mikhaylov and J. Tervonen presented a battery model that was validated through measurements of real batteries~\cite{battery_char_new}.
 Unfortunately, this validation does not consider battery supply voltage variations due to the current draw.
 Furthermore, it neglects the internal resistance of the battery and the relaxation effect.
 …
 %Moreover, the simulation case that was chosen was limited to a simple resistive model in which the supply voltage drifts were not considered.
 %As a result, it is difficult to re-use this work as a base for the network lifetime estimation.
 A last power-aware framework for OMNeT++ was introduced~\cite{newcas}.
+The battery model that is provided by the authors was build following technical specifications.
+Finally, the conclusion of their work states on the fact that using of the event driven technique together with their battery model results in erroneous battery lifetime estimations.
+To address this issue, they introduced a periodical scheduling method called \textit{Fixed Frequency Sampling} method.
+The battery model that is provided by the authors was built following technical specifications.
+%Finally, the conclusion of their work states on the fact that using of the event driven technique together with their battery model results in erroneous battery lifetime estimations.
+Finally, the conclusion of their work states that the formal event driven technique used together with their battery model results in erroneous battery lifetime estimations.
+%To address this issue, they introduced a periodical scheduling method called \textit{Fixed Frequency Sampling} method.
 %This latest framework was selected to implement the scheduling method because of its unique component oriented architecture and the several proposed models.
 …
 \section{Scheduling Methods} \label{sec:schedul_meth}
+Our scheduling methods can be used in any structure that model one to N battery-supplied components.
+Modeling of the supply voltage and the instantaneous current draw is the only requirement that could limit their application.
+The architecture that is considered here is composed of one to N components model and a battery that supply them (\cf Fig.\ref{archi_methods}).
+A concrete application case is added as example after the general descriptions.
+In this context, we introduce four scheduling methods to address the challenges relative to non-ideal battery models.
+All along this section we are assuming the statement that the wireless sensor nodes are described using a model for each of the hardware component that they embeds.
+In other words, the architecture that is considered here is composed of one to N components models and a battery that supply them (\cf Fig.\ref{archi_methods}).
+Each component's model is assumed to have as many power modes as the modeled component has (\eg ON, OFF, POWER DOWN or SLEEP).
+A specific instantaneous current draw is associated to each power mode.
+Consequently, each power mode change results in a new instantaneous current draw.
+Considering these statements, modeling of the supply voltage and the instantaneous current draw are mandatory to apply the following scheduling methods.
+The ``end-of-life'' of the battery can be expressed in two ways: the total depletion of the battery (which is unlikely to happen in real experimental case) or reaching the cut-off voltage threshold.
+The cut-off voltage threshold is the most robust approach.
+Actually, the cut-off voltage is the voltage value under which the electronic components operation are not guaranteed.
+However, the above descriptions are applicable in both cases.
+%Our scheduling methods can be used in any structure that model one to N battery-supplied components.
+%Modeling of the supply voltage and the instantaneous current draw is the only requirement that could limit their application.
+This sections holds the description of our scheduling methods.
+A concrete application case is added as an example after the general descriptions.
 % in order to expose the differences between every scheduling method.
 Integration of these scheduling algorithms is explained as the conclusion of the section.
 …
 \textbf{Fixed frequency sampling method states graphic:}
 This graph shows the principle of the \ffs\xspace method.
 It appears that the battery update are triggered periodically (each \textit{T} second) after the step~5.
+The battery update are triggered periodically (each \textit{T} second) after the step~5.
+}
 \end{center}
 …
 The \textit{Fixed Frequency Sampling} method (shorten to \ffs) was introduced into prior work~\cite{newcas}.
 This method relies on a periodic update of the battery's parameters and the current drawn by the components.
 Figure~\ref{figure1} is a state chart that describe its algorithm.
+Figure~\ref{figure1} is a state chart that describes its scheduling algorithm.
 First of all, the battery initiates the simulation by sending its supply voltage value to the component.
 This allow the components to turn into ON mode.
 Then, they sends back their averaged instantaneous current consumption over the previous period (which is null for the very first period).
+This allows the components to turn into ON mode.
+Then, they send back their averaged instantaneous current consumption over the previous period (which is null for the very first period).
 The battery residual and the supply voltage are then updated according to the received current draw value.
+Finally, if there is enough energy in the battery, the next update is scheduled at $t+T$ time (\textit{T} being the ``sampling period'' expressed in second).
+If the battery is depleted, it sends a $0.0$V supply voltage that turns the components into OFF mode.
+Finally, if there is enough energy in the battery, the next update is scheduled at $t+T$ time (\textit{T} being the ``sampling period'' expressed in seconds).
+If the battery is depleted, the simulation stops (\eg by sending a $0.0$V supply voltage that force the components to turn into OFF mode).
+%If the battery is depleted, it sends a $0.0$V supply voltage that turns the components into OFF mode.
 \subsection{Self Updating Event Driven method (SUED)}
 In contrast with the \ffs\xspace method, the \textit{Self Updating Event Driven} method takes into account every current draw changes instantaneously.
 The \sued\xspace scheduling method uses the same state chart as the \ffs\xspace method (\cf Fig.\ref{figure1}) except that it triggers additional battery updates as explained in the following.
+In contrast with the \ffs\xspace method, the \textit{Self Updating Event Driven} method takes into account every current draw change instantaneously.
+The \sued\xspace scheduling method uses the same state chart as the \ffs\xspace method (\cf Fig.\ref{figure1}), except that it triggers additional battery updates as explained in the following.
 When the simulation starts, the battery sends its supply voltage value to the components.
 The components send back their instantaneous current draw.
 …
 When a component changes its power mode (\eg ON $\rightarrow$ POWER DOWN), the corresponding instantaneous current draw value is sent to the battery.
 Then, the regular updating process is interrupted.
 The battery residual and the supply voltage are updated for the time elapsed from the last battery's update using the latest stored current draw value.
 Finally, the just received instantaneous current draw value is stored and the regular updating process starts again by scheduling the next update at $t+T$.
+The battery residual and the supply voltage are updated for the time elapsed from the last battery's update using the latest stored instantaneous current draw value.
+Finally, this latest current draw value is replaced by the just received one and the regular updating process starts again by scheduling the next update at $t+T$ ($t$ being the actual simulated time expressed in seconds).
 \begin{figure}
 …
 \textbf{Fast event driven method state graphic:}
 This graph shows the principle of the \fed\xspace method.
 In this method, the battery update are triggered by each changes in the operating state of the components.
+In this method, the battery update are triggered by each components' power mode change.
+}
 \end{center}
 …
 \subsection{Fast Event Driven method (FED)}
 The \textit{Fast Event Driven} method is derived from the ``formal'' event driven simulation technique.
 As a consequence, the battery updates are triggered by each current draw changes.
 The sate chart depicted Figure~\ref{figure3} represent the behavior of this scheduling method.
+As a consequence, the battery updates are triggered by each instantaneous current draw changes.
+The state chart depicted in the Figure~\ref{figure3} represents the behavior of this scheduling method.
 The battery initiates the simulation by sending its supply voltage value.
 As a consequence, the components change their state from OFF to ON and send back their associated instantaneous current draw value.
 Alike the \sued\xspace method, this value is stored in the battery model.
 When the component changes its state again, this value will be updated.
 Before storing the just received value, a battery update is processed.
+As a consequence, the components change their power modes (\ie from OFF to ON) and send back their associated instantaneous current draw value.
+In the same way as the \sued\xspace method, this current draw value is stored by the battery model.
+When a component changes its power mode again, this value is updated.
+Before storing the just received value, a battery update is performed.
 %Actually, it will estimate and check its new residual value considering the time elapsed from the previous update.
 This update consist of checking and computing the new battery's residual considering the time elapsed from the previous update.
 Battery's supply voltage value is also updated but using the new instantaneous current draw value and the residual that has just been estimated.
+This update consists of checking and computing the new battery's residual considering the time elapsed since the previous update.
+Battery's supply voltage value is also updated, but using the new instantaneous current draw value and the residual that has just been estimated.
 Finally, this supply voltage value is sent to the component.
 Since the \fed\xspace scheduling method do not update the battery periodically, using this method can lead to node operating without energy.
 If there is no event that makes the current draw change such as power mode changing, the simulation can run even if the battery is totally depleted at a certain point.
+Since the \fed\xspace scheduling method does not trigger updates of the battery periodically, using this method can lead to nodes operating without energy.
+If there is no event that makes the current draw change (\ie power mode changes), the simulation can run even if the battery is totally depleted at a certain point.
 %As a consequence, another mechanism is required.
+A way to avoid this issue is to ``plan'' the end of the battery life assuming that there will be no more event.
+To be consistent, this end of life forecast has to be re-evaluated each time the current draw value changes.
+%A way to avoid this issue is to ``plan'' the end of the battery life assuming that there will be no more event.
+%The end of life of the battery has to be forecast
+A way to avoid this issue is to forecast the battery's end-of-life (being either the full discharge of the battery or the discharge until the cut-off voltage value) assuming that there will be no more event.
+To be consistent, this end-of-life forecast has to be re-evaluated each time the current draw value changes.
 In other words, the battery's end of life has to be re-planned each time that a battery update is triggered.
 \subsection{Self Adaptive method (SA)}
 The \textit{Self Adaptive} method is based on both a periodical update schedule and a event-driven like schedule.
+The \textit{Self Adaptive} method is based on both a periodical update schedule and an event-driven like schedule.
 %Actually, the previously introduced method are sensitive to the time and/or to the current draw changes events.
 In addition, the \sa\xspace method is sensitive to the current draw value.
 Battery behavior observations allow us to make the following assumption: The discharge curve can be separated in two areas, a pseudo-linear area (before the \textit{nominal current} value) and a non-linear area (after the \textit{nominal current} value).
+Battery behavior observations allow us to make the following assumption: the discharge curve can be separated in two areas, a pseudo-linear area (\ie before the \textit{nominal current} value) and a non-linear area (\ie after the \textit{nominal current} value).
 The border between these two areas is the \textit{nominal current draw} (\cf Sec.~\ref{sect:battery_desc}).
 As a consequence, the \sa\xspace scheduling method changes the way it triggers battery's and components updates according to the instantaneous current draw value.
 …
 In the opposite case (the current draw is under the \textit{nominal current} value), these updates are triggered as if the \ffs\xspace scheduling method were used.
 On the one hand, this scheduling algorithm is able to enhance the accuracy of the estimation when it is necessary (when the battery model is strongly non-linear) and on the other hand, it is able to run the simulation faster when there is no need to (when the battery model is almost linear).
+On the one hand, this scheduling algorithm is able to enhance the accuracy of the estimation when it is necessary (\ie in the strongly non-linear part of the battery's discharge curve) and on the other hand, it is able to run the simulation faster when there is no need to (\ie in the ``almost'' linear part of the battery's discharge curve).
 \subsection{Application example}
 The chosen application example is a single component that is supplied by a battery.
 The functional behavior of this component is not discussed here since the meaningful information is its current draw consumption.
 As a consequence, the power mode states are the only information that are considered.
+The functional behavior of this component is not discussed here since the meaningful information is its instantaneous current draw consumption.
+As a consequence, the power mode is the only information that is considered.
 The following mode sequence was arbitrarily chosen:
 \begin{itemize}
 …
 All the graph are time aligned making the difference between each scheduling method easier to understand.
+%\begin{figure}
+%\begin{center}
+%\includegraphics[scale=0.45]{method_global.pdf}
+%\caption{\label{time}
+%\textbf{Application example of the scheduling methods:}
+%This figure is a time graph that shows the application of each scheduling method to our application example.
+%The \ffs\xspace method trigger battery update according to its sampling period \textit{T}.
+%The \sued\xspace method trigger as well the update of the battery each \textit{T} seconds but also when a component changes its operating state.
+%The \fed\xspace method only triggers battery updates on the components change.
+%The \sa\xspace method use periodic update when precision is required and event driven updates when less precision is needed.
+%}
+%\end{center}
+%\end{figure}
 \begin{figure}
+\begin{center}
+\includegraphics[scale=0.45]{method_global.pdf}
+%\begin{center}
+\centering
+\subfigure[Fixed Frequency Sampling]{
+        \includegraphics[scale=0.45]{time_FFS.pdf}
+        \label{time_ffs}
+}
+\subfigure[Self-Updating Event-Driven]{
+        \includegraphics[scale=0.45]{time_FFS.pdf}
+        \label{time_sued}
+}
+\subfigure[Fast Event-Driven]{
+        \includegraphics[scale=0.45]{time_FFS.pdf}
+        \label{time_fed}
+}
+\subfigure[Self Adaptative]{
+        \includegraphics[scale=0.45]{time_FFS.pdf}
+        \label{time_sa}
+}
+%\includegraphics[scale=0.45]{method_global.pdf}
 \caption{\label{time}
 \textbf{Application example of the scheduling methods:}
 This figure is a time graph that shows the application of each scheduling method to our application example.
 The \ffs\xspace method trigger battery update according to its sampling period \textit{T}.
 The \sued\xspace method trigger as well the update of the battery each \textit{T} seconds but also when a component changes its operating state.
+The \ffs\xspace method triggers battery update according to its sampling period \textit{T}.
+The \sued\xspace method triggers as well the update of the battery each \textit{T} seconds but also when a component changes its power mode.
 The \fed\xspace method only triggers battery updates on the components change.
 The \sa\xspace method use periodic update when precision is required and event driven updates when less precision is needed.
+}
 \end{center}
+The \sa\xspace method uses periodic update when precision is required and event driven updates when less precision is needed.
+}
+%\end{center}
 \end{figure}
 Figure~\ref{time}a is the graph that represent the \ffs\xspace method application.
+Figure~\ref{time_ffs} is the graph that represent the \ffs\xspace method application.
 The updates of the battery and the component's current draw changes are asynchronous.
 Moreover, the supply voltage updates are delayed by one period in comparison with the current draw updates.
 In other words, the supply voltage value that is used by the component to compute its draw is the one that has been estimated the previous period by the battery model.
 Figure~\ref{time}b represent the application of the \sued\xspace method.
+Figure~\ref{time_sued} represent the application of the \sued\xspace method.
 In contrast with the \ffs\xspace method, it appears that the battery's updates are synchronized with the current draw changes.
 The periodical update is also observable while the component is in LOW POWER mode.
 Alike the \ffs\xspace method, the supply voltage updates are also delayed.
 The application of the \fed\xspace method is plotted in the graph Figure~\ref{time}c.
+The application of the \fed\xspace method is plotted in the graph Figure~\ref{time_fed}.
 %The fact that the battery updates happen only in synchronization with the component's power mode changes is highlighted.
 The graph highlight that the battery updates happen only in synchronization with the component's power mode changes.
 The Figure~\ref{time}d illustrates the application of the \sa\xspace method.
+The Figure~\ref{time_sa} illustrates the application of the \sa\xspace method.
 This method is sensitive to the current draw value in respect with the battery characteristics.
 The current drawn in ON mode is assumed as being over the \textit{nominal current} value and the current drawn in the POWER DOWN mode is assumed as being under.
 …
 %Even if this abstraction of the real battery behavior is not perfect, it has the advantage of modeling both the \textit{effective capacity} and the \textit{relaxation} effects as well.
 The equation that is used to estimate the battery's residual $R$ at the $t+\Delta t$ instant is the following one:
+The equation that is used to estimate the battery's residual $R$ at the $t+\Delta t$ time is the following one:
 \begin{equation}
 R(t+\Delta t) = R(t) -  i_{eq}(t) \times \frac{\Delta t}{3600}
 …
 The sampling mechanism of the \sa\xspace method allows the battery model to react almost instantly to every current draw variation.
 Finally, while the average voltage obtained using the \ffs\xspace, \sued\xspace and \sa\xspace methods are quite close, the supply voltage value obtained using the \fed\xspace method is higher (\cf Tab.~\ref{voltage_results}).
 This highlights once again the fact that updates are driven by the components' power state changes.
+This highlights once again the fact that updates are driven by the components' power mode changes.
 \subsection{Simulation performance} \label{sim_perfs}

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