Dynamic Power Management for Systems with Multiple Power Saving States

1. Dynamic Power Management for Systems with Multiple Power Saving States Sandy Irani, Sandeep Shukla, Rajesh Gupta

2. Hardware Resource Power versus Performance Control Knob Power-aware Resource Manager OS/Middleware/Application Canonical Power Management • Observations • Tuning power-performance control knobs often has time and/or energy cost • Decision procedures needed, e.g., transition to a lower power state. • Question: • How effective is a specific power-aware resource management policy in terms of energy saved and timing constraints observed? Latency & Energy

3. Effectiveness of Power Mgmt. • Model • Functionality composed of individual tasks • Each task dissipates power to service requests that arrive over time • Inter-arrival time of requests is unknown • Requests are of different sizes and must be served in the order received • Task can choose to move to power minimizing states • DPM is an on-line problem • Input sequence is received at runtime • Characteristics of the input sequence is not known • Any algorithm to solve the problem can not make static decisions about the input • Competitive analysis provides a framework for understanding online strategies.

4. Competitive Analysis • Strategy S is a c-competitive • if for all input sequence, s, CS(s) <= c. Copt(s) • Competitive ratio (CR) of S is infimum over all c, such that S is c-competitive • Assume an adversary that generates inputs to S knowing only the strategy S • If S has a ratio r against this adversary, then in the worst case it would dissipate as much power as against an optimal offline strategy. • Adversary can be generated automatically through constraint generation and property checking. • DPM bounds are useful in strategy characterization.

5. DPM Bounds • DPM strategies can be non-adaptive or adaptive • Known DPM bounds with one idle state, one power saving state • Non-adaptive strategies • 2 – 1/k where k is discretized `break-even time’ • It is also shown that this bound is tight, i.e., no deterministic strategy has a better CR • Adaptive strategies (shutdown after variable time) • e/(e-1) ~ 1.6 • No adaptive algorithm has a better CR • CR akin to complexity lower bounds • Represent the worst possible scenario • Two limitations: • Worst case is really too pessimistic to be useful • Most interesting devices have multiple states: • Multiple power saving states • Multiple active states • Each state has different power characteristic and transition penalty.

6. Multi-State DPM: CR Bounds • Let there be k+1 states • Let State 0 be the shut-down state and k be the active state • Let I be the power dissipation rate at state I • Let I be the total energy dissipated to move back to State k • States are ordered such that I  I+1 • Let 0 = 0 • Assume • Power down energy cost can be incorporated in the power up cost for analysis • Idle time duration is unknown.

7. Lower Envelope Algorithm State1 State2 State3 State 4 Energy t1 t2 t3 Time

8. Deterministic Algorithm (LEA) • The Lower Envelope Defines an ordering of the states. • Throw out states that do not appear on lower envelope • Given this ordering, only need to determine thresholds: • When to transition from state I to state I+1. • Lower Envelope Algorithm Transitions from one state to the next at the discontinuities of the lower envelope curve. • Theorem: Lower Envelope Algorithm is 2-competitive. • This ratio can be improved by considering input distribution • Which can be learned on-line.

9. Stochastic Modeling in DPM • Using recent history in access patterns, determine the distribution which governs idle period length • An important issue but not covered here. • Formulate an optimization problem which gives the exact timings when the power states should be changed. • This approach works for any distribution over idle period lengths and adapts dynamically to patterns in the input sequence.

10. Probability-based LEA • Use same order of states as determined by lower envelope function. • Two state case can be solved by expressing expected cost as a function of the threshold and minimizing total energy consumption. • Our approach: • Determine threshold for transitioning from state I to state I+1 by solving the optimization problem where I and I+1 are the only states in the system. • THEOREM: PLEA is e/(e-1)-competitive.

11. Experimental Framework • Use trace data to obtain realistic probability distributions governing idle period length. • Simulate algorithms for idle periods generated by these distributions. • Algorithms tested: • Optimal Offline • Lower Envelope Algorithm (LEA) • Probabilistic Lower Envelope Algorithm (PLEA)

12. IBM Mobile Hard Drive Trace data with arrival times of disk accesses from Auspex file server archive.

13. Experimental Evaluation

14. Summary • This paper builds up our earlier work to make the adversary-based approach to characterization of the DPM algorithms: • Extension of results on DPM bounds from 2-state case to multi-state case • Improve DPM bounds by using additional information regarding the input. • Analytical results match bounds for 2-state case. • Experimental results show that probability-based algorithm improves upon deterministic by 25%bringing the strategy to within 23% of optimal.