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

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 Introduction Mobile Embedded Systems Design :

Traditional approaches to energy optimization CMOS Energy and power Energy α V 2 Power α V 2 .f f max α V Dynamic Voltage Scaling (DVS): busy system => increase V dd , frequency idle system => decrease V dd , frequency Potential to achieve quadratic energy and cubic power savings.

Variable-supply Architectures High-efficiency adjustable DC-DC converter View from battery side V bat is constant and depends on battery technology( 1.2 V for NiMh, 3.6-4.2 V for Li ion) High V dd translates to high I bat ` Power Manager WK to f f to Vdd Switching DCDC regulator V set V sys Clkgen SoC Battery V bat I bat I sys V sys X I sys = µ X V b at X I bat

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” Positive Ions Load _ + Electron Flow Anode Cathode Electrolyte

Diffusion Model - Rakhmatov, Vrudula et al. Analytically very sound but computationally intensive Cannot be used for online scheduling decisions. Fully charged battery After Recovery After a recent discharge Fully discharged Electrode Electrode Electrode Electrode Electro-active species

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

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 d d

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 T3D3 T2 D2 wci Precendence constraint

Our Methodology There are 2 aspects to the problem Global Frequency Setting Local order of execution of nodes Task Graphs Frequency Setting Priority function for max slack recovery DVS Algorithm Local Task Order Ready list WCi’s Di’s nodes fcurr next node

Global Frequency Setting To calculate the min frequency that can ensure all subsequent deadlines are met. upon release( Taskgraph T i ) 1: WC i =  wc ij 2: select_frequency( ) upon end_of_node( τ ij ) 1: WC i = WC i + ac ij − wc ij 2: select frequency( ) select_frequency ( ) 1: U =  WC i /D i 2: f ref = U × F max , return f ref Modified ccEDF algorithm from [pillai01] The jth node of the ith task graph whose execution just ended. τ ij Deadline for the ith task graph Di Actual exec time for jth node of the ith task graph at fmax acij WCET of the jth node of the ith task graph at fmax wcij

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) freq time d re-computing speed

Loc al 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 p UBS : a near optimal priority function from [Gruian02]

Ready List Ready list comprising of nodes from current(EDF) Task graph only. Ready list D1 D3 D2 D1 < D2 < D3 Priority function Execute

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.

Ready List Ready list comprising of nodes from all released Task graphs. Ready list D1 D3 D2 D1 < D2 < D3 Priority function Execute

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

Ready List Ready list comprising of nodes from all released Task graphs. Ready list D1 D3 D2 D1 < D2 < D3 Priority function Execute 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 ( 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

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

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

Conclusion W e 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 u p to 100% improvement in battery lifetime over systems with no DVS.

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] G ruian F., Energy-Centric Scheduling for Real-Time Systems, PhD thesis, Lund Institute 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 Voltage Scaling for Embedded Systems. In Proceedings of International Conference on VLSI Design , pages 650–653, January 2004.

Battery Models Still Too computationally intensive for use at runtime Not accurate, elements change value depending conditions Use capacitor and resistors to represent battery Circuit Still in the process of development. Relatively accurate and fast. Stochastic Slow, involves a large number of parameters Accurate PDE (higher forms of KiBaM) Disadvantages Advantages

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. back

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. Elapsed time of discharge Cell Voltage Intermittent Discharge Continuous discharge back

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%

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.

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.

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

Battery Aware Dynamic Scheduling for Periodic Task Graphs

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Battery Aware Dynamic Scheduling for Periodic Task Graphs

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