Near-Threshold Computing Review of Previous Work
An Optimal Control Policy in a Mobile Cloud Computing System
Based on Stochastic DataXue Lin, Yanzhi Wang, Massoud
PedramUniversity of Southern California1Cloud Computing and Mobile
DevicesCloud Computing ParadigmCloud service providerClientsMobile
Device Computing PlatformCompactness, portability, and
functionalityWeak computing and storageShort battery lifeMobile
Cloud Computing (MCC) paradigmExtend capabilitiesImprove
performanceReduce energy consumption
2Mobile cloud computing (MCC)2Mobile Devices in MCC
ParadigmService RequestLocal processingRemote processing by
offloading to the cloudControl DecisionWhether to offload a service
requestCPU operating frequency for local processingPerformance and
Power ConsumptionHigher performance means higher powerA trade-off
is desirable3Mobile device make use of MCC3OutlineMotivationSystem
ModelMCC systemBattery modelExpected performance sumOptimal Control
PolicyProblem formulationDynamic programming algorithmExperimental
ResultsConclusion44MotivationInter-Charging Interval (ICI)Short ICI
length: high performance modeLong ICI length: low power modeOnly
stochastic data is availablePower and Performance
Trade-OffPerformance sum: the sum of the performance for all
requests processed during an ICIMaximize the expected performance
sum5
System Model: MCC SystemA mobile device in the MCC system :
service request generation rate, Poisson : local processing
probability : local request rate, Poisson : remote request rate,
Poisson
6System Model: Response TimeAverage response time of local
processing
Average response time of remote processing
Average response time
: avg. request processing rate of the CPU
: avg. request sending rate in the RF
: avg. request sending time
: avg. round trip time7
System Model: Power ConsumptionMobile Device Power
ConsumptionCPU: dynamic and static powerRF: dynamic and static
power8
System Model: BatteryBattery is power source during ICI : length
of an ICI, random variable, probability density function (p.d.f) ,
the i-th time interval , ,
The remaining energy in the battery
The operating time of the mobile device, assuming an infinite
long ICI,
9System Model: Expected Performance SumThe performance for
processing a request
The expected value of the performance sum
where
is the indicator function
10
Problem FormulationDerive the optimal control policy for the
mobile device, based on the stochastic data of the ICI length, to
maximize the expected performance sumDerive the optimal and for can
only assume values for the set , where the elements are request
processing rates corresponding to K CPU frequency values.The
stochastic data about ICI length are given in the form of .
11Optimal Control Policy ProblemGiven: (i) the number of
discharging time intervals , and (ii) the amount of remaining
battery energy after the discharging process.Find: the and values
for .Maximize:
Subject to:
This is a general problem i.e., problem.When and , the problem
becomes the Optimal Control Policy (OCP) problem.
12Dynamic Programming AlgorithmThe optimal substructure
property: Suppose that the problem has been optimally solved, and
the the energy stored in the battery at time is in that optimal
solution. This corresponds to the problem. The optimal solution of
the problem contains within it the optimal solution of the
problem.Find the optimal solution of the problem from the optimal
solutions of the problems for , which are stored in matrix
elements
13
Dynamic Programming AlgorithmMaximize the expected performance
of the mobile device during the time intervalGiven: the battery
energy at time is and the battery energy at time is Find: the and
values Maximize: the expected performance
Subject to:The maximum expected performance in time interval is
denoted by
14Dynamic Programming AlgorithmFind the optimal solution of the
problem is then calculated as
The optimal is stored in the matrix entry
The problem is solved as we calculate
15
Dynamic Programming Algorithm
16Dynamic Programming AlgorithmThe average performance value is
a non-increasing function, or equivalently, is a non-decreasing
function, over all the time intervals .Proof: Suppose that function
is not a non-decreasing function. Then there must exist two
consecutive time intervals i and i+1 satisfying . We exchange the
control decisions with , and it will result in the same value but a
higher expected value of the performance sum. This is because .
17Experimental ResultsTwo baseline control policies:Always
chooses the highest CPU operating frequency, and chooses p[i]
values to maximize performance.Always chooses the lowest CPU
operating frequency, and chooses p[i] values to maximize
performance.Three probability density functions of ICI length
1818Experimental ResultsThe optimal control policy outperforms
two baseline control policies with higher expected value of the
performance sum.19
Experimental Results
20ConclustionThe mobile device control decisions should be made
according to the ICI length.We define the expected performance sum
as the objective function, which is a trade-off between performance
and power consumption and accounts for the ICI length uncertainty.A
dynamic programming algorithm is proposed to derive the optimal
control policy.21Thank you !
