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Policy Optimization for Dynamic Power Management
G. A. Paleologo
L. Benini
A. Bogliolo
G. De Micheli
Universit a di Bologna
Dip. Informatica, Elettronica,
Sistemistica
Bologna, ITALY 30165
Stanford University
Dept. of Engineering-Economic Systems and
Operations Research, Stanford, CA 94305-4023
Stanford University
Computer Systems Laboratory
Stanford, CA 94305-4070
Abstract
tion of this laptop by
10X
would reduce the overall power con-
sumption by less than 19%. Laptop computers are not an isolated
case. Almost all electronic appliances are complex and heteroge-
neous systems containing a wide variety of devices that do not fall
within the scope of the available computer-aided power optimiza-
tion techniques. Nevertheless, designers have reacted promptly to
the new challenges posed by low-cost, low-power portable appli-
ances. Battery lifetime (or time between recharges) is steadily in-
creasing and the physical dimensions of portable devices are pro-
gressively shrinking. These surprising results are achieved thanks
to a well-balanced mix of technological innovation, architectural
design and optimization. One of the most successful techniques em-
ployed by designers at the system level is
dynamic power manage-
ment
[2]. This technique reduces power dissipation by selectively
turning off (or reducing the performance of) system components
when they are idle (or partially unexploited). Building a complex
system that supports dynamic power management is a difficult and
error-prone process. Long trial-and-error iterations cannot be toler-
ated when fast time to market is the main factor deciding the success
of a product. Unfortunately, system-level computer-aided design
environments are still in their infancy, and EDA vendors are lagging
far behind the needs of this segment of the electronic industry. To
compensate for this lack of support, several system developers and
vendors [10, 9] are aggressively pursuing a long-term, wide-scope
strategy to greatly simplify the task of designing large and complex
power-managed systems. The strategy is based on a standardization
initiative known as the
Advanced Configuration and Power Inter-
face
(ACPI). ACPI specifies an abstract and flexible interface be-
tween power-manageable hardware components (VLSI chips, disk
drivers, display drivers, etc.) and the
power manager
(the system
component that controls when and how to turn on and off functional
resources). The ACPI interface specification enormously simplifies
the task of controlling the operating conditions of the system re-
sources but it does not provide any insight on how and when to
power manage them. We call
power management policy
(
policy
for
brevity) an algorithm that takes decisions upon the state of oper-
ation of system components. The most aggressive policy (that we
call
eager
policy) turns off every system component as soon as it be-
comes idle. Whenever the functionality of a component is required
to carry out a system task, the component must be turned on and
restored to its fully functional state. The transition between the in-
active and the functional state requires time and power. As a result,
the eager policy is often unacceptable because it greatly degrades
performance and may not decrease power dissipation. The choice
of the policy that minimizes power under performance constraints
(or maximizes performance under power constraint) is a new kind
Dynamic power management schemes (also called policies) can be
used to control the power consumption levels of electronic systems,
by setting their components in different states, each characterized
by a performance level and a power consumption. In this paper,
we describe power-managed systems using a finite-state, stochas-
tic model. Furthermore, we show that the fundamental problem
of finding an optimal policy which maximizes the average perfor-
mance level of a system, subject to a constraint on the power con-
sumption, can be formulated as a stochastic optimization problem
called policy optimization. Policy optimization can be solved ex-
actly in polynomial time (in the number of states of the model). We
implemented a policy optimization tool and tested the quality of the
optimal policies on a realistic case study.
1
Introduction
Battery-operated portable appliances impose tight constraints on
the power dissipation of their components. Designers struggle to
meet increasingly tight power budgets as complexity and perfor-
mance requirements are pushed forward by user demand. Numer-
ous computer-aided design techniques [11] for low power have been
proposed to help designers reduce time to market and improve the
quality of their products. The vast majority of CAD techniques for
low power targets digital VLSI circuits, i.e. chip-level designs. Un-
fortunately, almost every portable electronic appliance is far more
complex than a single chip. Portable devices such as cellular tele-
phones and laptop computers contain tens or even hundreds of com-
ponents. In most electronic products, digital components are re-
sponsible for only a fraction of the power consumed. Analog, electro-
mechanical and optical components are a significant fraction of
the total, and are often responsible for the largest contributions to
the power budget. For example, the power breakdown for a well-
known laptop computer [14] shows that, on average 36% of the total
power is consumed by the display, 18% by the hard drive, 18% by
the wireless LAN interface, 7% by non-critical components (key-
board, mouse etc.), and only 21% by digital VLSI circuitry (mainly
memory and CPU). Reducing the power in the digital logic por-
1
cameras are a few examples of portable appliances for which power
is a major concern.
High level of abstraction
. The choice of abstraction level is prob-
ably the most important decision in system-level power modeling.
In order to manage complexity, irrelevant (or marginally relevant)
information should be abstracted. In our formulation, resources are
described by abstract power and performance models.
Non-determinism
. The uncertainty on estimation caused by the
abstraction process (and the consequent information loss) is mapped
to the inherent uncertainty in the estimation of the expected value
of random variables.
In the following we will consider a discrete-time (i.e. slotted time)
setting. Thus, time is described by an infinite series of discrete val-
ues , where is the time resolution (or
period
), .
We model a system with a single user (or service requestor) whose
requests are enqueued in a single queue and serviced by a single
service provider. A power manager controls over time the behavior
of the service provider (Figure 1). In more detail, the components
are described in the following subsections.
A
SERVICE REQUESTOR
(SR). This unit sends requests to the
Service Provider. The SR is modeled as a Markov Chain with tran-
sition matrix , where the observed variable is the number of
requests (with ) sent to the SR during
time interval . We assume that the process and all its relevant pa-
rameters are known.
As a simple example, consider the SR with a maximum of one re-
quest per period (i.e., two states), as shown in the right hand side of
Figure 1.
Observation
Observation
Power Manager
Command
(s_on, s_off)
Service Requestor
Service Provider
Q
ueue
Request
(1, 0)
s_off/0.2
s_on/0.0
Service Provider
0.05
Service Requestor
s_off/0.8
s_on/1.0
s_off/1.0
s_on/0.97
on
off
0.95
0
1
0.88
s_off/0.0
s_on/0.03
0.12
on,1/0.2
off,1/1.0
Queue
on,0/0.2
on,1/1.0
0
1
on,1/0.8
off,1/0.0
on,0/0.8
on,1/0.0
Figure 1:
The abstract system model. Components are modeled as
Markov chains whose state transition graphs are represented for a simple
example situation. The service requestor (SR) has only two states, 0 and
1, representing the number of requests per time period sent to the provider.
The queue of the service provider (SQ) has two states, 0 and 1, representing
the number of requests to be serviced. The service provider (SP) has two
states, on and off, representing its functional state. When on, it serves up to
a request per time period taken from the queue. When off it does not serve
any request. SR evolves independently, while the transition probabilities of
SP depend on the command issued by the power manager (PM) and those
of SQ depend on the state of both SP and SR.
of constrained optimization problem which is of great relevance for
low-power electronic systems. We call this problem
policy opti-
mization
(PO). Several heuristic power management policies have
been investigated in the past [5, 8, 12] but no strong optimality re-
sult has been proved. In this paper we propose a stochastic model
for the rigorous formulation of policy optimization and we describe
a procedure for its
exact
solution. The procedure can be employed
to explore the power vs. performance tradeoff curve. The global op-
timum solution of PO is computed in polynomial time by solving a
linear optimization problem. This strong optimality result critically
depends on the modeling assumptions. We assess the soundness
of our assumptions by constructing the stochastic model for a real-
life device (a disk drive) under a realistic workload. We then apply
our optimization algorithm and compute optimal policies. The per-
formance and power dissipation of the policies are then validated
against simulation. Moreover, the optimal policies are compared
with heuristic solutions.
The paper is organized as follows: in Section 2 we outline our
stochastic model, starting from a qualitative description, then mov-
ing to a more rigorous mathematical formulation. The policy opti-
mization problem is then formulated and a procedure for its solution
is described. In Section 3 we carry out modeling and policy opti-
mization for a realistic case study, namely a commercial disk drive
with advanced power management support under workload condi-
tions obtained from actual usage traces. In Section 4 we summarize
our findings and outline future direction of research.
The example matrix models a “bursty” workload. There is a high
probability (0.88) of receiving a request at time if a request
was received at time , and the mean duration of a stream of re-
quests is equal to periods.
A
SERVICE PROVIDER
(SP). The SP is a device which serves
incoming requests from a workload source. In each time interval, it
can be in only one
state
. Each state is charac-
terized by a performance level and by a power consumption level (to
be defined later). In the simplest example, we could have two states
( ):
on
and
off
. At each period, transitions between power
states are controlled by a
power manager
(PM) through
commands
. For example, we can define two simple
commands: switch on (
s on
) and switch off (
s off
). When a spe-
cific command is issued, the SP will move to a new state in the next
period with a fixed probability dependent only on the command
itself, and on the departure and arrival states. In other terms, af-
ter being given a transition command by the power manager, the SP
can remain in its current state during the next period with a non-zero
probability. This aspect of the model takes into account the uncer-
tainty in the transition time between states caused by the abstraction
of functional information. Our probabilistic model is equivalent to
the assumption that the evolution in time of power states is mod-
eled by a Markov process that depends on the commands issued by
the PM. Thus, we define one transition matrix for each command .
Back to our example with two states and two commands, we could
have the following transition matrices:
2
Stochastic model
We introduce a modeling approach that is aimed at providing sup-
port for system-level optimization of power-managed systems. The
key features of our model are:
Generality
. Any power-managed electronic appliance (not only
computer systems) can be modeled. Cellular phones, pagers, digital
on
off
on
off
on
off
on
off
s on
s off
The Markov chains corresponding to the matrices are pictorially
represented in Figure 1. Note that the transition time from
off
to
on
when the
s on
command has been issued is a geometric random
variable with average equal to periods.
Each power state has a specific
power consumption rate
. It is
a function both of the state and the command performed on the
state: . Dependency on the state is obvious: power dissi-
pation depends on the operational state of the SP (for our example
on off
). Dependence on the command issued is also
essential: referring to our example,
off s on off s off
, be-
cause the activation process of the device requires additional energy
consumption. Data on the power dissipation in various operating
conditions is usually provided in the data-sheets of the SPs, or it
can be directly measured.
A
QUEUE
. When service requests arrive during one period, they
are buffered in a queue of length . In our treatment we
will consider a FIFO discipline, although other disciplines can be
modeled. The request is processed and serviced within the same
period with a probability dependent on the power state of the SP.
In this way we model the non-deterministic service time of a re-
quest as a geometric random variable, similarly to the exponential
service time for the class in queueing theory [6]. It fol-
lows that also the queue length (denoted by , with )
is a Markov process with transition matrix . We refer
again to our example: if
on
and
off
, and the buffer
contains at most one request, we have (on the bottom of Figure 1):
Given our stochastic system model, we can now proceed to the
formulation of the policy optimization problem. Our objectives are:
i) to formally describe the behavior of the PM; ii) to find the partic-
ular behavior that optimally reduces power dissipation under per-
formance constraints (or optimizes performance under power con-
straints). Hence, we need to provide formal definition for power
and performance cost metrics as well.
DECISIONS.
At the beginning of time period , the PM observes
the “history” of the system (i.e., the sequence of states and com-
mands up to ) and controls the Service Provider by taking a
de-
cision
. A
deterministic decision
consists in taking a single action
on the basis of the history of the system. Yet, we will consider the
much broader set of
randomized decisions
: in this case, the Power
Manager assign probabilities to every available command and then
chooses the command to issue, according to this probability distri-
bution. In this way, even if the same decision is taken in different
periods, the actual commands issued could be different. Analyti-
cally, the decision can be represented by a set of real num-
bers, , where each
represents the probability of issuing command given that the
history of the system is . A deterministic decision is the special
case with for some command . The definition of
extends naturally to the case of a randomized decision , and we de-
note the transition matrix . We stress again the generality of such
a class of decisions (randomized and history-dependent). Consider
the example of the previous section. Suppose that the PM observes
the following history:
on
,
off
(states in
period , ), and
s off
(action taken at time ). Then, a
possible decision at time , when state is observed, could consist
in assigning probabilities of performing commands
s on
and
s off
equal to
s on
,
s off
respectively.
POLICIES
. Over an finite time horizon (up to time interval
on
on
), the
decisions taken by the PM are a finite discrete sequence
.
off
off
We call this sequence a
policy
. The policy
is the independent
A
POWER MANAGER
(PM). This component communicates with
the service provider and attempts to set its state at the beginning of
each period, by issuing commands chosen among a finite set .
In our example, the commands can be
s on
, and
s off
. It contains
all proper specifications and collects all relevant information (by
observing SR and PM) needed for implementing a power manage-
ment policy. The consumption of the power manager is assumed to
be much smaller than the consumption of the subsystems it controls
and it is not a concern here. The state of the system composed of
the SP, the SR and the queue is then a triple . Being
the composition of three Markov chains, will be a Markov chain
(with states), whose transition matrix
depends on the command issued to the SP by the PM. Hence, the
system is fully described by a set of
variable of our optimization problem. If a policy
is adopted, we define ; this is simply the
transition matrix from period to period under policy . Among
all policies the
stationary policies
play an important role: in this
case does not depend on the entire history . For stationary
policies, decisions are a function of the current state of the system
and the function does not change over time (other-
wise, stationarity would be lost). A generic randomized stationary
policy can be represented as a
matrix
.
An element
of
is the probability of issuing command
given that the
state of the system is .
COST METRICS
. It is now possible to define the metrics of rel-
evance in the PO problem. In their most general form, they are
function both of the state and of , i.e., the decision we take
when we are in state . An early example of cost metric is the
ex-
pected power consumption level
per unit time, introduced
earlier in this section, which represents the expected consumption
per period when the SP is in state and decision is taken. A
second parameter of interest is the
performance penalty
per unit
time which depends on the queue length (number of jobs in
the queue). A natural way to define the performance penalty is the
queue length:
transition matrices, one for
each command.
In the above description no mention is made of the energy source
(i.e., the battery). In this paper our goal is to minimize (or bound)
the average power consumption of the SP, and not to maximize the
expected battery life. This choice has several advantages: it allows
us not to consider the details of the power source (path-dependent
discharge characteristics, possible recharge “on the run”), while still
retaining the primary feature of minimizing (or constraining) the
consumption level. A second desirable feature of the model is that
in this it can be used to independently maximize policies in the
case of multiple SPs, and consider the average aggregate consump-
tion rate as the only relevant quantity for dimensioning the power
source.
. Finally, we consider the
request loss
per
period
. It takes value
when a request arrives (
)
and is forced to balk because the queue buffer is full (
); oth-
erwise it is
. For notational convenience, define the consumption,
State
active
performance penalty and request loss vectors
NA
idle
idleLP
standby
sleep
.
.
.
For example the element of each vector is the expected value
of the consumption rate (or performance penalty, or request loss)
when the system is in state and decision is taken. Analogous
considerations apply to the other vectors. Using the above vectors,
we can express the expected value of a cost metric in period
Table 1:
State, transition time to active and power dissipation for a hard
disk driver
, when
decision
is taken, given that the system is in state
in period
:
PM is the following: i) observe the state of the system (SP, SR
and queue) at time , and ii) select the command to be issued with
probabilities given by the row of matrix . For instance,
the optimum policy for the system in Figure 1 is represented by a
matrix . Assume that the row of corresponding to
state
on
is . If the system is in state
, the PM will issue the
s on
command with probability or the
s off
command with probability . Concluding the section, we
want to stress the fundamental assumptions that allows us to com-
pute optimal policies in polynomial time. First, both SR and SP
must be modeled by Markov chains with known parameters; also
the cost metrics must be known. Second, the time horizon (i.e.,
the number of time intervals over which the policy is valid) must
be long enough to be a good approximation of an infinite horizon.
These assumptions will be checked in the next section for a realistic
case study.
it is given by the element of the vector .
When performing policy optimization, we want to maximize the av-
erage performance level over a long time period while keeping the
average consumption and request loss below some levels specified
by the user. This can be formally expressed as follows:
PO :
s.t.
the objective function is an -dimensional vector. Its element
is the average (over time periods) of the expected performance
level per period, given that the system starts in state in period
, and and are the maximum expected consumption per
period and the maximum expected request loss per period respec-
tively (as specified by the user). Strictly speaking, we should solve
optimization problems [4], one for each initial state. Moreover,
the optimization is carried the set of
all
possible policies. Hence,
solving PO appears to be a formidable task. Fortunately, the this is
not the case, thanks to the following result of general validity.
Theorem
[4, 7] When the constraints in PO are active and the
Markov process is unichain (i.e., for each policy there is a single
communicating class), there exists a unique optimal policy for all
the optimization problems of PO, which is stationary, Markovian
(and possibly randomized). Furthermore, if constraints are inac-
tive, the policy is deterministic
.
The above theorem has three implications. First, and most impor-
tantly, under our modeling assumptions the optimal policies are sta-
tionary. This result rules out policies based on statistics taken in pe-
riods before the period during which the decision is taken. Second,
a stationary policy can be described and implemented in a compact
fashion, because no time dependence must be taken into account,
and decisions at any time can be taken only by observing the
current state of the system. Third, the optimal policy can be ef-
ficiently computed. Several algorithms are available to solve PO
when no constraint is active. For constrained problems, it is possi-
ble to solve PO by solving a linear programming problem, which
is solvable in polynomial time in the number of states. Hordijk and
Kallenberg [7], and references therein, describe a solution proce-
dure. The solution procedure is not outlined here because of space
limitation. It is however important to mention that the matrix
describing the optimum policy that solves PO can be extracted from
the solution of the optimization problem in a straightforward fash-
ion. If
3
Case Study
We tested the validity of our approach by calculating optimal poli-
cies for a commercially-available hard disk drive [13] and contrast-
ing them against heuristic policies. The hard disk drive can be op-
erated in 5 different energy states, as shown in Table 1. In four of
the five states, the device cannot perform data reads or writes, hence
they are all
inactive
states. The inactive states span the tradeoff be-
tween power consumption and time required to return to the fully
operational
active
state.
More in detail, in the
idle
state the disk is spinning, but some of
the electronic components of the drive are turned off. The transi-
tion from
idle
to
active
is extremely fast, but only marginal power
is saved in the
idle
state. The
low-power idle
state is similar to
the
idle
state, but it has decreased power dissipation (and increased
transition time to the
active
state). In the
standby
and
sleep
state,
the disk is spun down, hence the transition to the
active
state is not
only slow, but it causes additional power consumption (the addi-
tional current absorbed by the motor to accelerate the disk). It is
important to mention that the transition times of Table 1 are explic-
itly declared as
typical
in the data sheets. In other works, they can
be interpreted as expected values of random variables. The sim-
plified transition graph of the service provider that models the disk
drive is shown in Figure 2 (a). Several transitions between inactive
states (and a few transient states) have been omitted for the sake of
readability. The figure shows only the transitions from and to the
active
state, which have a major impact on power and performance.
Assume that the disk is in one of the inactive states and a file read
or write request is received. The request must be enqueued (in our
model, the queue has length two) because the SP is inactive and
cannot serve it right away. The PM observes the state of the system
is available, the decision procedure implemented by the
service because the drive’s response is very slow. The tool for pol-
icy optimization is built around an advanced LP solver based on an
interior point algorithm [3]. We implemented an optimization shell
that can compute trade-off curves between performance and power.
Each point on the curve is a solution of a PO problem with different
constraints (i.e., a
Pareto-efficient point
). Additionally, we imple-
mented a simulation tool for validation of the PO results. The sim-
ulator can compute the power consumption, performance degrada-
tion and request loss of the system by simulating actual usage traces
as they are processed by the SP controlled by the policy computed
by the policy optimization tool. The cost metrics obtained by sim-
ulation should match the values computed by the optimizer. It is
important to remember that the policies computed by the optimizer
are global optimum ones. In other words, the only sources of error
in our procedure come from the modeling process. Simulation is
important to assess the quality of the modeling assumptions, and
not the quality of the optimization. We tested the two fundamental
modeling assumptions, namely the infinite-horizon assumption and
the Markov assumption for the SR. Moreover, we compared the op-
timal policies with heuristic ones. The results of our experiments
are shown in Figure 3(a).
The continuous line is the trade-off curve spanned by the opti-
mal policies computed by the optimizer. Its computation took less
than 1 minute on a SUN UltraSPARC workstation. The curve is ob-
tained by maximizing performance with varying power constraint
and fixed request loss (smaller than 50%). Notice how performance
is traded off for power up to a minimum point where power cannot
be reduced further because the constraint on request loss is violated.
The circles in Figure 3(a) represent the results of simulation of the
policies computed by the optimizer with the actual trace and for a
finite time ( time slots). The distance of the circles from the
curve is a measure of the inaccuracies of the modeling process. It
is visually obvious that the inaccuracies are very small, and that the
simulated points lie almost perfectly on the tradeoff curve.
The triangles in Figure 3(a) represent heuristic solutions to the
PO problem. The downwards triangles represent deterministic poli-
cies based on timeouts. Timeout-based policies are widely used for
disk power management [5]. They are based on a simple heuristic
that shuts down the disk when it has been inactive for a time longer
than the timeout . The choice of is based on simulations and
on designer’s experience. The upwards triangles are randomized
policies where the timeout value and the inactive state are chosen
randomly with a given probability distribution. The randomized
policies are the heuristic version of the optimal policies computed
by our tool.
Although we cannot claim that our heuristic policies are the best
that any experienced designer can formulate, some of our policies
perform nearly as well as the optimum ones. The important point
to notice is that it is much more difficult to control the power and
performance produced by the heuristic policies. For example, we
could not generate valid policies in the leftmost part of the power
vs. performance plane, because the constraint on request loss was
always violated. Moreover, it is possible to produce heuristic poli-
cies that produce “reasonable” results (such as those around power
dissipation of ), but there is no way for the designer to esti-
mate if the results can be improved.
In Figure 3(b) we study the dependency of the policies by the work-
load statistics. The tradeoff curve computed with the Markov model
of our usage trace is shown in continuous line. A new tradeoff curve
computed with another SR model (i.e., a Markov chain with differ-
Active
Idle
Rq(1)
Norq(0)
LPidle
Sdby
Sleep
(a)
(b)
Figure 2:
(a) Simplified transition graph for the disk drive. (b) Transition
graph for the workload model
and issues a command for transitioning the resource to the active
state.
The exit from the inactive states upon assertion of a command
from the PM is not instantaneous. Our Markov model has been
set up so that the expected exit time from an inactive state when
a wakeup command has been issued is equal to the (experimental)
average exit time from that inactive state (Table 1). Hence, the self-
loops of the idle states have widely varying conditional proabilities.
For example the conditional probability of the self-loop from
idle
when a wakeup command has been issued is much smaller than the
conditional probability of the self-loop from
sleep
when the same
command has been issued. The probabilities on the self-loops of
the inactive states model the “inertia” of the system in waking up.
Similarly, the self-loop on the active state models the inertia of the
system in going to the inactive states. Its conditional probability
depends on the command issued by the PM.
The model of the workload source can be automatically ex-
tracted from traces of disk accesses (we used the traces provided
in [1]). The Markov model of the SR is extracted from usage traces
with a modeling procedure that will be only briefly described be-
cause of space limitations. Given a time resolution (proportional
to the shortest wakeup time of the SP), the arrival times of the disk
access requests are discretized (i.e., the trace is converted into a bi-
nary stream that has value 1 in position if a request is received
between time and time , zero otherwise). For the
time resolution and the usage traces of this case, a Markov chain
with two states as shown in Figure 2 (b) was sufficient to charac-
terize the system. stream. At any time, the PM can issue a com-
mand to the SP. In our case study, the manager can chose among
5 commands:
GO ACTIVE
,
GO IDLE
,
GO IDLELP
,
GO STBY
,
GO SLEEP
. The final product of the policy optimization is a ma-
trix with five columns (one for each command) and as many rows
as the number of states of the SP, SR and queue system. The com-
plete model of the system (which is slightly more complex than
the simplified version described here) has a total of 48 states. The
power cost metric is obtained from the data sheets of the disk drive
(summarized in Table 1). The performance metric is defined by as-
signing a cost to each state of the system where the SP is inactive
and the queue is full. Roughly speaking, our metric represents a
performance
penalty
which is negative and worsens as the average
waiting time for a request increases. Finally the request loss met-
ric is defined by assigning a cost to the state of the system where
the queue is full and a new request arrives. Notice that request loss
in our abstract models does not imply that a read or write request
is actually lost (i.e., the system malfunctions). It simply represents
an undesirable operating condition where the operating system con-
trolling the drive is required to do extra work to guarantee correct
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Analysis of the PASR Standard and its usability in Handheld Operating Systems such as Linux.pdf
(84 KB)
Compiler-controlled and Compiler-hinted Voltage Scaling Approaches.pdf
(144 KB)
Dynamic and Aggressive Scheduling Techniques for Power Aware RTS.pdf
(181 KB)
CRC.Press.The.Compiler.Design.Handbook.2nd.Edition.Dec.2007.pdr
(0 KB)
Evaluation and Modeling of Power Consumption of a Heterogeneous Dual-Core Processor.pdf
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