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Battery Aware Dynamic Scheduling for Periodic Task Graphs. Venkat Rao # , Nicolas Navet # , Gaurav Singhal *, Anshul Kumar  , GS Visweswaran  # TRIO Group, INRIA-Lorraine /LORIA. * Dept of ECE, UT Austin,  Dept of CSE, IIT Delhi  Dept of EE, IIT Delhi . Introduction.

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battery aware dynamic scheduling for periodic task graphs

Battery Aware Dynamic Scheduling for Periodic Task Graphs

Venkat Rao#, Nicolas Navet #, Gaurav Singhal *, Anshul Kumar, GS Visweswaran

#TRIO Group, INRIA-Lorraine /LORIA.

* Dept of ECE, UT Austin, Dept of CSE, IIT Delhi

Dept of EE, IIT Delhi

introduction
Introduction
  • Battery lifetime is major constraint
  • Slow growth in energy densities not keeping up with increase in power consumption
  • Extension of battery lifetime and not just low energy design the REAL GOAL

Mobile Embedded Systems Design :

Venkat Rao – INRIA Lorraine /LORIA

traditional approaches to energy optimization
CMOS Energy and power

Energy α V2

Power α V2.f

fmaxα V

Dynamic Voltage Scaling (DVS):

busy system => increase Vdd, frequency

idle system => decrease Vdd, frequency

Potential to achieve quadratic energy and cubic power savings.

Traditional approaches to energy optimization

Venkat Rao – INRIA Lorraine /LORIA

variable supply architectures
Variable-supply Architectures
  • High-efficiency adjustable DC-DC converter
  • View from battery side
    • Vbat is constant and depends on battery technology( 1.2 V for NiMh, 3.6-4.2 V for Li ion)
    • High Vdd translates to high Ibat `

SoC

Vsys X Isys = µ X Vbat X Ibat

Power Manager

Clkgen

Vsys

Switching

DCDC

regulator

Battery

Vbat

Isys

WK

to f

f to

Vdd

Ibat

Vset

Venkat Rao – INRIA Lorraine /LORIA

battery basics

Electron Flow

_

Load

+

Cathode

Positive

Ions

Anode

Electrolyte

Battery Basics
  • Battery characterized by Voc and Vcut.
  • Battery lifetime governed by active species concentration at electrode-electrolyte interface.
  • Phenomenon governing battery lifetime:
    • “Rate Capacity Effect”

“high load current implies lower charge delivered.”

    • “Recovery Effect” “charge recovered by giving idle slots”

Venkat Rao – INRIA Lorraine /LORIA

diffusion model rakhmatov vrudula et al
Diffusion Model- Rakhmatov, Vrudula et al.

After a recent discharge

Fully charged battery

Electrode

Electrode

Fully discharged

After Recovery

Electrode

Electrode

Electro-active species

  • Analytically very sound but computationally intensive
  • Cannot be used for online scheduling decisions.

Venkat Rao – INRIA Lorraine /LORIA

battery aware scheduling
Battery Aware Scheduling
  • Guideline 1: For a set of schedulable tasks (t0, t1……tN) having corresponding currents costs (I0, I1……IN) scheduling them in decreasing order of current costs is the optimum battery solution.[Rakhmatov03]

Ibat

time

Venkat Rao – INRIA Lorraine /LORIA

battery aware scheduling8
Battery Aware Scheduling
  • Guideline 2: For a given task t to be executed before a given deadline d its better to lower the frequency and run without giving an idle slot than give an idle slot and run at a higher frequency.[Rakhmatov03]

freq

freq

idle

time

time

d

d

Venkat Rao – INRIA Lorraine /LORIA

problem definition
Problem Definition

To find a battery efficient schedule for a given a set of periodic tasks graphs (T1, T2, ....Tn) which have corresponding deadlines (D1,D2, .....Dn) equal to their periods, where a taskgraph Ti comprises of any m interdependent nodes, each of which are in themselves tasks with given worst case computations (wci1, wci2, ......wcim).

Precendence constraint

wci

T3D3

T2 D2

T1 D1

Venkat Rao – INRIA Lorraine /LORIA

our methodology
Our Methodology
  • There are 2 aspects to the problem
      • Global Frequency Setting
      • Local order of execution of nodes

Task Graphs

nodes

WCi’s

Di’s

Ready list

fcurr

Frequency Setting

DVS Algorithm

next node

Priority function for max slack recovery

Local Task Order

Venkat Rao – INRIA Lorraine /LORIA

global frequency setting
Global Frequency Setting
  • To calculate the min frequency that can ensure all subsequent deadlines are met.

upon release( Taskgraph Ti )

1: WCi = åwcij

2: select_frequency( )

upon end_of_node( τij )

1: WCi = WCi + acij − wcij

2: select frequency( )

select_frequency ( )

1: U = åWCi/Di

2: fref = U × Fmax , return fref

Modified ccEDF algorithm from [pillai01]

Venkat Rao – INRIA Lorraine /LORIA

global frequency setting12
Global Frequency Setting
  • Follows EDF so works up to U= 100%
  • Ensures all deadlines are met.
  • Ensures a Non Increasing discharge profile for set of jobs (set of instances of periodic tasks)

re-computing speed

freq

time

d

Venkat Rao – INRIA Lorraine /LORIA

loc al order of execution
Local order of execution
  • Slack Recovery maximization.
    • Worst case seldom arrives leading to dynamic slack
    • Order of execution effects dynamic slack recovery
    • Important to choose the order optimally
    • A priority function needs to be chosen
    • Heuristics like LTF and STF work well in specific cases
    • pUBS : a near optimal priority function from [Gruian02]

Venkat Rao – INRIA Lorraine /LORIA

ready list
Ready List
  • Ready list comprising of nodes from current(EDF) Task graph only.

D3

D2

D1

Ready list

D1 < D2 < D3

Priority function

Execute

Venkat Rao – INRIA Lorraine /LORIA

ready list comprising of nodes from current task graph only
Ready list comprising of nodes from current Task graph only
  • Advantages :
    • Follows EDF so ensures meeting of deadlines
    • Simple to implement
  • Disadvantages :
    • Limited choice for the priority function.
    • Limited slack recovery.

Venkat Rao – INRIA Lorraine /LORIA

ready list16
Ready List
  • Ready list comprising of nodes from all released Task graphs.

D3

D2

D1

Ready list

D1 < D2 < D3

Priority function

Execute

Venkat Rao – INRIA Lorraine /LORIA

ready list comprising of nodes from all released task graphs
Ready list comprising of nodes from all released Task graphs
  • Advantages :
    • More choice for the priority function.
    • Better slack recovery hence lower energy consumption
  • Disadvantages :
    • Out of EDF execution hence deadline can be missed

Need For additional feasibility check

Venkat Rao – INRIA Lorraine /LORIA

ready list18
Ready List
  • Ready list comprising of nodes from all released Task graphs.

D3

D2

D1

Ready list

D1 < D2 < D3

Feasibility check

Priority function

Execute

Venkat Rao – INRIA Lorraine /LORIA

feasibility check
Feasibility check
  • Check to ensure that an out of EDF execution will not cause a deadline miss
  • Or more stringently will not cause the raising of frequency later for meeting deadlines
  • For task belonging to EDF order k, k-1 checks are required.

Feasibility Check ( tij )

flag= 1;

for (k=1 to j-1)

{

if (åWCk +wcij > fcurr X Dk – Tcurr )

Flag =0;

}

return flag

Venkat Rao – INRIA Lorraine /LORIA

simulations
Simulations
  • C simulations were conducted to test our methodology
  • The DVS enabledprocessor simulated supports the following 3 frequency-voltage tuples [(0.5GHz,3 V), (0.75GHz,4V),(1.0GHz,5V)].
  • Task graphs were generated from TGFFwith random dependencies
  • Utilization of the system waskept to 70%
  • Stochastic battery model from [G.Singhal05] was used to estimate battery life for the profiles generated by various scheduling algorithms
  • Simulated for NiMH AAA Panasonic batteries with max capacity of 2000mAh and nominal capacity of 1600mAh

Venkat Rao – INRIA Lorraine /LORIA

simulation results battery lifetime and charge delivered
Simulation Results :Battery lifetime and charge delivered.
  • Results were obtained by averaging performance ofthe various algorithms over 100 random taskgraph sets
  • Battery Aware Schedule 2 delivers maximum battery life amongst the schemes compared

Venkat Rao – INRIA Lorraine /LORIA

conclusion
Conclusion
  • We have presented a Battery-aware SchedulingMethodology that facilitates the combining of a goodDVS algorithm with a heuristic based priority functionfor scheduling of taskgraphs.
  • Simulations suggest that ourmethodology performs up to 47% better than ccEDFand upto 23.3% better than laEDF scheduling schemes in terms of battery lifetime.
  • It can result in up to 100%improvement in battery lifetime over systems with noDVS.

Venkat Rao – INRIA Lorraine /LORIA

references and credits
References and Credits

[1] V. Rao and G. Singhal. Integrated power management for embedded systems. Bachelors Thesis, Indian Institute of Technology, Delhi, 2005.

[2] F.Yao,A Demers and S Shenkers. A Scheduling Model for Reduced CPU energy. IEEE 1995.

[3] P. Pillai and K. G.Shin. Real time dynamic voltage scaling for low powered embedded systems. Operating Systems Review, 35:89–102, October 2001.

[4] S. Vrudhula and D. Rakhmatov. Energy management for battery powered embedded systems. ACM Transactions on Embedded Computing Systems, pages 277– 324, August 2003.

[5] J. Luo and N. K. Jha. Battery-aware static scheduling for distributed real-time embedded systems. In DAC’01: Proceedings of the 38th conference on Design automation, 2001.

[6] Gruian F., Energy-Centric Scheduling for Real-Time Systems, PhDthesis, LundInstitute of Technology, 2002.

[7] V. Rao, G. Singhal, A. Kumar, and N. Navet. Battery model for embedded systems. In Proceedings of International Conference on VLSI Design, pages 105–110, January 2005.

[8] V. Rao, G. Singhal, and A. Kumar. Real Time Dynamic VoltageScaling for Embedded Systems. InProceedings of InternationalConference on VLSI Design, pages 650–653, January2004.

Venkat Rao – INRIA Lorraine /LORIA

thank you
Thank You

Venkat Rao – INRIA Lorraine /LORIA

battery models
Battery Models

Still Too computationally intensive for use at runtime

Venkat Rao – INRIA Lorraine /LORIA

rate capacity effect
Rate Capacity Effect
  • Total charge delivered by the battery goes down with the increase in load current.
  • Concentration of active species at interface falls rapidly with increasing load current.
  • Battery seems discharged when the concentration at interface becomes zero.

Rate Capacity Effect

back

Venkat Rao – INRIA Lorraine /LORIA

recovery effect
Recovery Effect
  • Battery recovers capacity if given idle slots in between discharges.
  • Diffusion process compensates for the low concentration near the electrode.
  • Battery can support further discharge.

Intermittent Discharge

Cell Voltage

Continuous discharge

Elapsed time of discharge

Recovery Effect

back

Venkat Rao – INRIA Lorraine /LORIA

simulation results effect of ready list on energy consumption
Simulation Results:Effect of ready list on energy consumption

At Utilization 70% and actual computation times varying from 20% to 70%

Energy consumption (normalizedw.r.t optimal schedule) byvarious schedulingpolicies for different number of tasks ina taskgraph

Venkat Rao – INRIA Lorraine /LORIA

simulation results effect of priority function on energy consumption
Simulation Results:Effect of priority function on energy consumption

At Utilization 70% and actual computation times varying from 20% to 70%. Ready list comprises of most imminent.

Energy consumption (normalizedw.r.t optimal schedule) byvarious schedulingpolicies for different number of tasks ina taskgraph

Venkat Rao – INRIA Lorraine /LORIA

kinetic battery model
Kinetic Battery Model
  • Simplest PDE model to explain both recovery and rate capacity.
  • Available and Bound charge wells
  • Dynamic transfer of charges governed by a rate constant and difference in heights.

Venkat Rao – INRIA Lorraine /LORIA

slide31
Introduction
  • Battery Basics
    • Rate Capacity Effect
    • Recovery Effect
  • Related Work : Review of relevant models
  • Scheduling Problem
  • Our Methodology.
  • Simulation and Results
  • Conclusion

Venkat Rao – INRIA Lorraine /LORIA