Battery Aware Dynamic Scheduling for Periodic Task Graphs Venkat Rao #, Nicolas Navet #, Gaurav Singhal *, Anshul Kumar, GS Visweswaran 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 Dept of EE, IIT Delhi

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Battery lifetime is major constraint Battery lifetime is major constraint Slow growth in energy densities not keeping up with increase in power consumption 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 Extension of battery lifetime and not just low energy design the REAL GOAL Introduction Mobile Embedded Systems Design :

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Traditional approaches to energy optimization CMOS Energy and power CMOS Energy and power Energy α V 2 Power α V 2.f f max α V Dynamic Voltage Scaling (DVS): Dynamic Voltage Scaling (DVS): busy system => increase V dd, frequency busy system => increase V dd, frequency idle system => decrease V dd, frequency idle system => decrease V dd, frequency Potential to achieve quadratic energy and cubic power savings. Potential to achieve quadratic energy and cubic power savings.

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Variable-supply Architectures High-efficiency adjustable DC-DC converter High-efficiency adjustable DC-DC converter View from battery side View from battery side V bat is constant and depends on battery technology( 1.2 V for NiMh, V for Li ion) V bat is constant and depends on battery technology( 1.2 V for NiMh, V for Li ion) High V dd translates to high I bat ` High V dd translates to high I bat ` Power Manager WK to f f to Vdd Switching DCDC regulator V set V sy s Clkgen SoC Battery V bat I bat I sy s V sys X I sys = µ X V bat X I bat

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Positive Ions Load_ + Electron Flow AnodeAnode CathodeCathode Electrolyte Battery Basics Battery characterized by V oc and V cut. 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 Recovery Effect

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Diffusion Model - Rakhmatov, Vrudula et al. Analytically very sound but computationally intensive Analytically very sound but computationally intensive Cannot be used for online scheduling decisions. Cannot be used for online scheduling decisions. Fully charged battery After Recovery After a recent discharge Fully discharged Electrode Electro-active species

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Battery Aware Scheduling Guideline 1: For a set of schedulable tasks (t 0, t 1 ……t N ) having corresponding currents costs (I 0, I 1 ……I N ) scheduling them in decreasing order of current costs is the optimum battery solution.[Rakhmatov03] Ibat time

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA 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 time freq time idle dd

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA 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). T1 D1 T3 D3 T2 D2 wci Precendence constraint

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Our Methodology There are 2 aspects to the problem There are 2 aspects to the problem Global Frequency Setting Global Frequency Setting Local order of execution of nodes Local order of execution of nodes Task Graphs Frequency Setting Priority function for max slack recovery DVS Algorithm Local Task Order Ready list WCis Dis nodes fcurr next node

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Global Frequency Setting To calculate the min frequency that can ensure all subsequent deadlines are met. To calculate the min frequency that can ensure all subsequent deadlines are met. upon release( Taskgraph Ti ) 1: WCi = wcij 2: select_frequency( ) upon end_of_node( τij ) 1: WCi = WCi + acij wcij 2: select frequency( ) select_frequency ( ) 1: U = WCi/Di 2: fref = U × Fmax, return fref Modified ccEDF algorithm from [pillai01] wcij wcij WCET of the jth node of the ith task graph at fmax acij acij Actual exec time for jth node of the ith task graph at fmax Di Deadline for the ith task graph τij The jth node of the ith task graph whose execution just ended.

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Global Frequency Setting Follows EDF so works up to U= 100% Follows EDF so works up to U= 100% Ensures all deadlines are met. Ensures all deadlines are met. Ensures a Non Increasing discharge profile for set of jobs (set of instances of periodic tasks) Ensures a Non Increasing discharge profile for set of jobs (set of instances of periodic tasks) freq timed re-computing speed

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Local order of execution Slack Recovery maximization. Slack Recovery maximization. Worst case seldom arrives leading to dynamic slack Worst case seldom arrives leading to dynamic slack Order of execution effects dynamic slack recovery Order of execution effects dynamic slack recovery Important to choose the order optimally Important to choose the order optimally A priority function needs to be chosen A priority function needs to be chosen Heuristics like LTF and STF work well in specific cases Heuristics like LTF and STF work well in specific cases p UBS : a near optimal priority function from [Gruian02] p UBS : a near optimal priority function from [Gruian02]

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Ready List Ready list comprising of nodes from current(EDF) Task graph only. Ready list comprising of nodes from current(EDF) Task graph only. Ready list D1 D3 D2 D1 < D2 < D3 Priority function Execute

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Ready list comprising of nodes from current Task graph only Advantages : Advantages : Follows EDF so ensures meeting of deadlines Follows EDF so ensures meeting of deadlines Simple to implement Simple to implement Disadvantages : Disadvantages : Limited choice for the priority function. Limited choice for the priority function. Limited slack recovery. Limited slack recovery.

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Ready List Ready list comprising of nodes from all released Task graphs. Ready list comprising of nodes from all released Task graphs. Ready list D1 D3 D2 D1 < D2 < D3 Priority function Execute

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Ready list comprising of nodes from all released Task graphs Advantages : Advantages : More choice for the priority function. More choice for the priority function. Better slack recovery hence lower energy consumption Better slack recovery hence lower energy consumption Disadvantages : Disadvantages : Out of EDF execution hence deadline can be missed Out of EDF execution hence deadline can be missed Need For additional feasibility check

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Ready List Ready list comprising of nodes from all released Task graphs. Ready list comprising of nodes from all released Task graphs. Ready list D1 D3 D2 D1 < D2 < D3 Priority function Execute Feasibility check

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Feasibility check Check to ensure that an out of EDF execution will not cause a deadline miss 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 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. For task belonging to EDF order k, k-1 checks are required. Feasibility Check ( t ij ) flag= 1; for (k=1 to j-1) { if ( WC k +wc ij > f curr X D k – T curr ) Flag =0; } return flag

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Simulations C simulations were conducted to test our methodology The DVS enabled processor simulated supports the following 3 frequency-voltage tuples [(0.5GHz,3 V), (0.75GHz,4V), (1.0GHz,5V)]. Task graphs were generated from TGFF with random dependencies Utilization of the system was kept 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

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Simulation Results : Battery lifetime and charge delivered. Results were obtained by averaging performance of the various algorithms over 100 random taskgraph sets Battery Aware Schedule 2 delivers maximum battery life amongst the schemes compared

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Conclusion We have presented a Battery-aware Scheduling Methodology that facilitates the combining of a good DVS algorithm with a heuristic based priority function for scheduling of taskgraphs. Simulations suggest that our methodology performs up to 47% better than ccEDF and 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 no DVS.

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA References and Credits [1] V. Rao and G. Singhal. Integrated power management for embedded systems. Bachelors Thesis, Indian Institute of Technology, Delhi, [2] F.Yao, A Demers and S Shenkers. A Scheduling Model for Reduced CPU energy. IEEE [3] P. Pillai and K. G.Shin. Real time dynamic voltage scaling for low powered embedded systems. Operating Systems Review, 35:89–102, October [4] S. Vrudhula and D. Rakhmatov. Energy management for battery powered embedded systems. ACM Transactions on Embedded Computing Systems, pages 277– 324, August 2003 [4] S. Vrudhula and D. Rakhmatov. Energy management for battery powered embedded systems. ACM Transactions on Embedded Computing Systems, pages 277– 324, August [5] J. Luo and N. K. Jha. Battery-aware static scheduling for distributed real-time embedded systems. In DAC01: Proceedings of the 38th conference on Design automation, 2001 [5] J. Luo and N. K. Jha. Battery-aware static scheduling for distributed real-time embedded systems. In DAC01: Proceedings of the 38th conference on Design automation, [6] Gruian F., Energy-Centric Scheduling for Real-Time Systems, PhD thesis, Lund Institute of Technology, [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 [8] V. Rao, G. Singhal, and A. Kumar. Real Time Dynamic Voltage Scaling for Embedded Systems. In Proceedings of International Conference on VLSI Design, pages 650–653, January 2004.

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Thank You

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Advantages Disadvantages Disadvantages PDE (higher forms of KiBaM) Accurate Slow, involves a large number of parameters Circuit Use capacitor and resistors to represent battery Not accurate, elements change value depending conditions Stochastic Relatively accurate and fast. Still in the process of development. Battery Models Still Too computationally intensive for use at runtime

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA 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. back

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA 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. Elapsed time of discharge Cell Voltage Intermittent Discharge Continuous discharge back

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Simulation Results: Effect of ready list on energy consumption Energy consumption (normalized w.r.t optimal schedule) by various scheduling policies for different number of tasks in a taskgraph At Utilization 70% and actual computation times varying from 20% to 70%

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Simulation Results: Effect of priority function on energy consumption Energy consumption (normalized w.r.t optimal schedule) by various scheduling policies for different number of tasks in a taskgraph At Utilization 70% and actual computation times varying from 20% to 70%. Ready list comprises of most imminent.

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Kinetic Battery Model Simplest PDE model to explain both recovery and rate capacity. Simplest PDE model to explain both recovery and rate capacity. Available and Bound charge wells Available and Bound charge wells Dynamic transfer of charges governed by a rate constant and difference in heights. Dynamic transfer of charges governed by a rate constant and difference in heights.

WDPRTS, Rhode Island Greece 25 th April 2006 Venkat Rao – INRIA Lorraine /LORIA Introduction Introduction Battery Basics Battery Basics 1. Rate Capacity Effect 2. Recovery Effect Related Work : Review of relevant models Related Work : Review of relevant models Scheduling Problem Scheduling Problem Our Methodology. Our Methodology. Simulation and Results Simulation and Results Conclusion Conclusion