IEEE Transactions on Consumer Electronics, Vol. 55, No. 2, MAY 2009
656
Hybrid Model for Dynamic Power Management Wai-Kong Lee, Sze-Wei Lee, and Wee-Ong Siew Abstract — Dynamic Power Management (DPM) is a system level power management technique that selectively shut down idle electrical components to save power. Previous works are mainly focused on certain types of prediction technique which assume that the idle period is long range dependent (heuristic prediction based on past history), random process (Markov Process) or short range dependent (Autoregressive) characteristic. However, the user behavior is highly variable and single assumption might not hold for all conditions. Thus, techniques based on the above assumptions will only be effective in certain condition only. Hence, we propose here a Hybrid Model DPM system that combines Moving Average (MA), Time Delay Neural Network (TDNN) and random walk model to perform idle period prediction. The Hybrid Model will first analyze the Long Range Dependency and central tendency of the past idle period time series, and choose the most appropriate strategy for future idle period prediction. Simulation results show that the Hybrid Model achieves higher power saving in most of the scenarios compared to the other methods. 1 Index Terms - Dynamic Power Management, Time Delay Neural Network, Hurst Exponent.
I. INTRODUCTION Power consumption has become the major concern in many portable designs (laptop, PDA, cell-phone, etc) nowadays, due to the fact that power consumed by these devices increase faster than the capacity advancement in battery. One of the popular strategies to tackle this problem is by adopting Dynamic Power Management technique to monitor the power consumption at the system level. DPM is based on the observation that many portable systems are idle most of the time and only active for very short period when the user uses it. If these devices are to remain active all the time, it will cause huge power loses. DPM is achieved by selectively putting the portable system into power saving mode during its idle period. To achieve power saving, the actual idle period need to be more than the breakeven time (Tbe), which is defined as
Tbe = Ttr +
Elatency Psaved
(1)
1 Wai-Kong Lee is with the Faculty of Engineering, Multimedia University, 63100 Cyberjaya, Selangor, Malaysia. (e-mail:
[email protected]). Sze-Wei Lee is with the Institute of Postgraduate Studies & Research, University Tunku Abdul Rahman, (e-mail:
[email protected]). Wee-Ong Siew is with the Faculty of Engineering, Multimedia University, 63100 Cyberjaya, Selangor, Malaysia. (e-mail:
[email protected]).
Contributed Paper Manuscript received January 3, 2009
= Ttr +
( Ew + Es ) Psaved .
Ttr is the time for state transition (wakeup or shutdown), Ew and Es are wakeup energy and shutdown energy respectively, and Psaved is the power consumption for the system to transit into sleep state. Since power-down and power-up processes introduce power latency, turning off the device immediately when idle state is detected (Greedy) is not a wise choice, as the actual idle period is most likely to be shorter than Tbe. Hence, choosing the best prediction method to accurately predict next user idle period and make decision for power state transition, remain the main challenge in DPM design. Previous approaches for the implementation of DPM at system level can be classified into three major categories: a)
Timeout: Timeout [1] is the most widely used technique due to its simplicity. Fixed timeout technique forces the system to enter low power state after a fixed idle period is detected. In [2], the author proposed to set the timeout to breakeven time, Tbe. This method is named Competitive Analysis (CA) and has been proven to achieve power saving within a factor of 2 from the optimal power can be saved (competitive-2). The Adaptive timeout technique [3], [4] changes the timeout period adaptively based on the accuracy of prediction. The timeout method is not optimized to save power as it needs to wait for the timeout period to elapse before entering low power state.
b) Stochastic Model: This strategy models the device and user request as stochastic processes. Discrete Time Markov Decision (DM) [5] process assumes stationary geometric distribution for request arrivals and the Markov model is known in advance. This is particularly not true for many event-driven portable systems. Hence it is further extended to deal with non-stationary requests by using sliding window [6]. Another model like Continuous Time Markov Process (CM) [7] is asynchronous and thus enables the power manager to change state as long as an event occurs. Both DM and CM approaches model request arrivals and the power state transitions using memory-less distributions, which is not always true in real systems. In SemiMarkov model (SM) [8] the transition time between power states is assumed to have uniform distributions. Time-Indexed Semi Markov (TISM) [9] models further generalize it by using Pareto distributions.
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W.-K. Lee et al.: Hybrid Model for Dynamic Power Management
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Heuristic: Heuristic method uses the past history of idle periods to predict the next idle period. This is based on the assumption that the user will most likely repeat the usage pattern in future, or the past usage pattern is influencing the future usage pattern. In [10], the authors suggested to use non-linear regression formula to model the idle period. They also proposed that if the buzy period is smaller than Tthr, the idle period is assumed to be greater than Tbe, based on the observation that the plot of busy period versus idle period is L-shape. C.H. Hwang, C. Allen and H. Wu [11] proposed to predict the next idle period using a simple Exponential Average (EA) equation:
Tn +1 = β Tnn + (1 − β )Tn −1
(2)
Under-prediction is solved by periodically reevaluate the Tn+1 predicted, and over-prediction is tackled by employing a saturation condition where Tn+1 Hthreshold, the idle period series exhibit strong long term dependency, TDNN will be used as predictor to predict next idle period. TDNN training will be performed to update the weights. If the H < Hthreshold, the idle period series is near random walk or mean reverting, random walk model is used as predictor.
Predictor = Moving Average
R/S Analysis Yes
(3)
If a time series has large value for COEFF, it is deviating from the mean with large degree. In contrary, small value of COEFF means the time series is very near to its mean value. Long range dependency is estimated by using R/S analysis. The proposed Hybrid Model work flow is described as below: 1.
The values of Nh and Nw are determined by observing the nature of the workload, which is explained in details in Section IV. Hthreshold is determined using Monte Carlo simulation which is explained in Section III. According to random walk model [20], the best prediction for next value of a random process will be equal to current value. X t +1 = X t + ϕ (4)
H > Hthreshold
Predictor = TDNN
No Predictor = Last Value
Use Selected Predictor for Next Idle Period Prediction
Nw Reached times of prediction?
Yes
No Fig. 1. Work flow for the proposed Hybrid Method
Timeout method is also incorporated into this hybrid design to improve the overall power saving ability. If the predicted value is lower than threshold value, timeout method will be
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used; where the device will be entering low power state if it is idle for a pre-defined time.
6.
Rescaled range for each sub-period is calculated by dividing Ra/ Sa. In step 1, the length of the sub-period is n, so the average R/S value for length is defined as:
III. RESCALED RANGE ANALYSIS Rescaled (R/S) range analysis is used to estimate the Hurst exponent of idle period time series. Studies show that there is no definite method to accurately estimate Hurst exponent [21] in all conditions. However, we are only interested in knowing whether a time series is LRD or not, so it is still possible to use R/S analysis to estimate the long range dependency in this scenario. R/S analysis is developed by a hydrologist H. E. Hurst, in his study on the overflow pattern of Nile River over 847 years (AD 647 – 1469) [22]. He developed a new statistical method to measure the “memory component” in time series based on the work of Einstein’s on Brownian motion. Einstein found that the distance that a random particle covers increases with the square root of time used to measure it:
R = T 0.5
(5)
Hurst used this property to measure the randomness of Nile River and developed the R/S analysis. Since this equation only applies to Brownian motion, Hurst generalized it by taking into account the case if the time series is not Brownian. The general form of equation (1) is expressed as below:
R ( ) n = cn H S
2.
A long time series named N is divided to a few subperiods of length n, such that A*n = N. This forms A sub-periods with length n, and each element in these sub-periods is named Nk,a. For each sub-periods, the average value is taken: n
Ea = ∑ N k , a
(7)
k =1
3.
The time series of accumulated departures (Xk,a) from the mean for each sub-periods is defined as: n
X k ,a = ∑ ( N k ,a − Ea )
(8)
k =1
4.
The range is defined as the maximum minus the minimum of Xk,a within each sub-period:
Ra = max( X k ,a ) − min( X k , a )
(9)
with 1 ≤ k ≤ n. 5.
The standard deviation of each sub-period is calculated:
Sa =
1 n ( N k ,a − Ea ) 2 ∑ n k =1
7.
(10)
(11)
The sub-period length n is increased to the next higher value where (N/n) is an integer. Repeat step 1 – 6 until n = N/2.
8. From (6), (R/S)n = c*nH. By plotting graph of log [(R/S)n] Vs log (n), and solve for the slope through linear regression, we get Hurst Exponent, H.
R log( ) n = log c + H log n S
(12)
Through the derivation of (6) from (5), we understand that a random walk process will have H = 0.5. For time series with 0.5
