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Voltage Set-up Problem on Embedded Systems with Multiple Voltages∗

Shaoxiong Hua and Gang Qu

Electrical and Computer Engineering Department and

Institute for Advanced Computer Studies

University of Maryland, College Park, MD 20742, USA

{shua, gangqu}@eng.umd.edu

Abstract

Dynamic voltage scaling (DVS), arguably the most effective energy reduction technique, can be

enabled by having multiple voltages physically implemented on the chip and allowing the operating

system to decide which voltage to use at run-time. Indeed, this is predicted as the future low-power

system by International Technology Roadmap for Semiconductors (ITRS). There still exist many

important unsolved problems on how to reduce the system’s dynamic and/or total power by DVS.

One of such problems, which we refer to as the voltage set-up problem, is how many levels and at

which values should voltages be implemented for the system to achieve the maximum energy saving.

It challenges whether DVS technique’s full potential in energy saving can be reached on multiple-

voltage systems. In this paper, (1) we derive analytical solutions for dual-voltage system. (2) For

the general case that does not have analytic solutions, we develop efficient numerical methods that

can take the overhead of voltage switch and leakage into account. (3) We demonstrate how to apply

the proposed algorithms on system design. (4) Interestingly, the experimental results, on both real

life DSP applications and random created applications, suggest that multiple-voltage DVS systems

with only a couple levels of voltages, when set up properly, can be very close to DVS technique’s full

potential in energy saving.

Keywords: System analysis and design, Design automation, Voltage, Energy management.

∗Parts of this manuscript have been published in IEEE/ACM International Conference on Computer Aided Design, pp.

26-29, November 2003.

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1Introduction

Energy consumption has become a major design issue for modern embedded systems especially battery-

operated portable devices. The aggressive push for low-power design has prompted the International

Technology Roadmap for Semiconductors (ITRS) to predict that the future system will feature multiple

supply voltages (Vdd), and multiple threshold voltages (Vth), on the same chip [1]. This enables the

dynamic voltage scaling (DVS) technique that varies the supply voltage and clock frequency according

to workload at run time to save energy. DVS achieves the highest energy efficiency for time-varying

computational loads if voltage can be varied arbitrarily [2, 3]. However, physical constraints of CMOS

circuit limit the applicability of having voltage varying continuously and instantaneously. Instead, it

is more practical to make multiple discrete voltages simultaneously available for the system. Many

commercial high-performance microprocessors, such as Transmeta’s Crusoe [4], AMD’s Athlon 4 [5],

Intel’s XScale [6], and some DSP (digital signal processing) cores developed in Bell Labs all support

voltage scaling for low power.

Most existing work on multiple voltage DVS systems assumes that the voltage set-up, which includes

the number of voltage levels and the voltage value at each level, is given a priori and focuses on developing

the voltage scheduling algorithms to minimize system’s energy consumption [7, 8, 9, 10, 11]. However,

for multiple voltage DVS systems, the energy consumption depends on not only the scheduler but also

the voltage set-up. To the best of our knowledge, how to set up the voltages has been discussed in the

following contexts: Chen and Sarrafzadeh [12, 13] studied the power minimization problem on dual-

voltage system at gate level, where 5.0V was used as the high voltage and different voltages from 2.0V

to 4.2V were used as the low voltage. They suggested that the voltages should be chosen carefully

based on the slack distribution of the circuits. Qu and Potkonjak [9] gave analytical solutions on how to

build energy efficient communication pipelines under latency constraints by voltage scaling and careful

packet fragmentation, where each pipeline stage receives one fixed voltage. Dhar and Maksimovic [14]

considered the design of finite impulse response filters and applied Lagrangian method to find the 2N+1

voltages for power minimization, where N is the order of the filter.

In this paper, we consider the following voltage set-up problem at the application level: how to

determine the number of voltages and each voltage value on a multiple-voltage application specific DVS

system such that the system’s energy consumption is minimized? The differences between our work and

the ones mentioned above are: 1) we do voltage scaling at the application level, not the gate level, 2)

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we determine the voltage values for any number of voltages, not only for dual-voltage or levels tightly

bounded to the applications, and 3) we also find the best number of voltage levels.

We first use an example to show multiple-voltage system’s energy efficiency and the importance of

the voltage set-up. Suppose that a system periodically executes one application with period equals to 8.

The application’s possible execution times, at the reference voltage 3.3V, are 6, 4, 3, and 2 that occur

with probabilities 0.05, 0.20, 0.45, and 0.30 respectively. The application has a deadline that equals

to its period. Table 1 gives the average energy consumption per iteration when this application is

executed by systems with different voltage set-ups, where the energy is computed based on the optimal

voltage scaling strategies reported in [3] and [7] and is normalized to the average energy consumption

per iteration at supply voltage Vdd(ref) = 3.3V and threshold voltage Vth= 0.5V

1.

Table 1: The average energy consumption per iteration on different systems. (1: the reference fixed

voltage system; 2: the best fixed voltage system; 3-6: dual-voltage systems with different voltage set-ups.

Set-up

Vhigh

Vlow

Energy

123456

3.3

–

1

2.7

–

0.67

3.3

1.0

0.83

3.0

1.0

0.70

3.0

2.0

0.43

2.7

1.8

0.38

1We describe how Table 1 is built.

The average energy consumption per iteration for this application can be expressed as?4

probability that the application requests an execution time (workload) ei and Ei is the minimal energy consumption that

the system completes such workload based on the optimal voltage scaling strategies as we will explain below [3, 7].

First, at the reference voltage Vdd(ref) = 3.3V , the average energy consumption per iteration is EVhigh=3.3V = P(ref)·

?4

iteration. Note that we assume the system shuts down to conserve energy when the current iteration is complete. Otherwise,

the energy consumption becomes 8P(ref) for the always-on system.

Second, the worst case execution time (WCET) 6 is actually less than the deadline 8, we can then utilize this slack to

reduce energy by scaling voltage down. Based on Equation (1) on page 8, one can compute that the lowest voltage to

complete the workload that requires execution time 6 at the reference voltage at time 8 is roughly 2.7V . At this supply

voltage, the average energy consumption per iteration will be 0.67EVhigh=3.3V. Note that system with voltage lower than

2.7V will miss the deadline should the WCET occurs. Therefore, this gives us the minimal energy for fixed-voltage systems.

The rest of Table 1 gives energy consumption of dual-voltage systems. On such system, if the low voltage Vlow provides

sufficient fast speed to complete the application by deadline, the system will operate at Vlowand shut down upon completion.

Otherwise, the system will use Vlowfor some time to complete the workload that requires execution time ti at the reference

voltage before scales up to Vhigh so the computation can be completed on the deadline. ti can be conveniently calculated

i=1pi · Ei, where pi is the

i=1pi · ei = 3.05P(ref), where P(ref) is the power consumption and the sum gives the average execution time per

from the following equation

Vhigh

(Vhigh−0.5)2

(3.3−0.5)2

3.3

(ei− ti) +

Vlow

(Vlow−0.5)2

(3.3−0.5)2

3.3

ti = 8, where ei is the execution time of

the application. This allows us to compute the time that the system is on Vlow and Vhigh and eventually the energy

consumption (see, for example, [3] and [7]).

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We have two interesting observations from Table 1:

• Multiple-voltage systems in general save more energy over fixed-voltage systems. For example, the

voltage set-ups (Vhigh=3.0V, Vlow=2.0V) and (Vhigh=2.7V, Vlow=1.8V) save more than 35% and

43% energy respectively over the best fixed-voltage system with the lowest voltage 2.7V without

any deadline missing.

• Different voltage set-ups result in significantly different energy reduction as we can see from

the last four columns. Moreover, if not set properly, set-ups 3 (Vhigh=3.3V, Vlow=1.0V) and 4

(Vhigh=3.0V, Vlow=1.0V) for example, the multiple-voltage system may consume more energy

than the best fixed-voltage system, the one with a fixed 2.7V supply voltage in this case.

We formulate and provide practical solutions to the voltage set-up problem that seeks the most

energy efficient voltage setting for the design of multiple-voltage DVS systems. This work is a novel

extension under the DVS research framework. Our main contributions include: (1) analytical solutions

and a linear search algorithm for dual-voltage DVS systems; and (2) an iterative approach and an

approximation method for the general multiple-voltage DVS systems. These results can be used to

guide system design as we show by simulation. Surprisingly, our results show that the 3- or 4-voltage

system can actually be (almost) as energy-efficient as the ideal system that varies voltage arbitrarily.

Finally, we mention that although we restrict most of our discussion to dynamic power reduction (we

do so for the simplicity to explain our approaches and also because that dynamic power still dominates

in embedded system design such as DSP systems), our problem formulation and proposed approaches

can integrate both leakage power/energy model and the overhead on voltage scaling.

The remainder of this paper is organized as follows. In the next section, we survey the related work

on DVS for low power. We then formulate the voltage set-up problem and present the solutions in

Section 3 and Section 4 respectively. Validation of our solutions and experimental results are reported

in Section 5. We conclude the paper in Section 6.

2Related Work

We restrict our survey to the study of multiple-voltage DVS systems. For the discussion on ideal voltage

scaling systems and design/implementation issues on DVS systems, one can find excellent surveys in

[2, 3, 15, 16, 17].

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Early research on multiple-voltage DVS systems focused on voltage scheduling at behavioral level,

typically on data flow graphs to exploit the parallelism among all of the operations. Specifically, op-

erations on the critical path are operated at the reference voltage to keep the required throughput,

but operations off the critical path will be executed at reduced voltages to save power and energy

[12, 18, 19, 20, 21]. Raje and Sarrafzadeh [21] first proposed a multiple voltage scheduling algorithm

to assign voltage level to each operation in a data flow graph to minimize power consumption with a

given computation time constraint. Dual-voltage (5.0V and 3.0V) and three-voltage (5.0V, 3.0V, and

2.4V) were used for experimental purpose. Chang and Pedram [18] presented a dynamic programming

based algorithm extending this to more general cases (such as cyclic graphs, throughput constraints).

Four voltages (5.0V, 3.3V, 2.4V, and 1.5V) were used in the simulation for no specific reasons. Johnson

and Roy [19] proposed a datapath scheduling algorithm that iteratively reduces the operating voltage

until no schedule slack remains. Chen and Sarrafzadeh [12] related the voltage scaling (VS) power

minimization problem on dual-voltage system to the maximal weighted independent set problem, which

is polynomial solvable on transitive graph. They then developed a provably good algorithm to reduce

system’s power consumption. In their simulation, 5.0V was used as the high voltage while different

voltages from 2.0V to 4.2V were used as the low voltage.

The study of multiple-voltage DVS system at high level focused on how to assign voltage to individual

task in order to reduce energy consumption. Ishihara and Yasuura [7] showed that energy is minimized

only when at most two voltages are applied to a single task. They formulated the voltage scheduling

problem as an integer linear programming problem and relied on solving such problem to obtain the

voltage for each task. Quan and Hu [10] studied the problem of determining the optimal voltage

schedule for a real-time system with fixed-priority jobs implemented on multiple VS systems. Their

approach was based on an integer programming formulation, which can be efficiently solved. Manzak and

Chakrabarti [22] proposed periodic and aperiodic task scheduling algorithms for energy minimization

on VS systems. Pillai and Shin [23] presented a class of algorithms that modify the operating system’s

real-time scheduler and task management service to provide significant energy savings while maintaining

real-time deadline guarantee. Most recently, Hua et al. [24] have proposed some scheduling strategies

for a multiple-voltage system in order to reduce the system’s energy consumption while providing non-

perfect completion ratio guarantee statistically. Some tasks are intentionally dropped according to their

on-line scheduling algorithm to conserve energy.

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