08-09-2014, 11:18 AM
Energy-Optimal Mobile Cloud Computing under Stochastic Wireless Channel
Optimal Mobile Cloud.pdf (Size: 656.67 KB / Downloads: 31)
INTRODUCTION
T HE tension between resource-hungry applications and
resource-poor mobile devices is considered as one of
the driving forces for the evolution of mobile platforms. Due
to the limited physical size, mobile devices are inherently
resource-constrained [1], equipped with a limited supply of
resources in computation, energy, bandwidth and storage. In
particular, the energy supply from the limited battery capacity
[2] has been one of the most challenging design issues for
mobile devices. The limited battery life has been found by
market research as the biggest complaint for smart phonesTherefore, resource limitations in the mobile devices should
be considered for the design of the mobile applications
Mobile Execution Energy Model
When the application is executed on the mobile device, the
energy consumption is determined by the CPU workload. The
workload is measured by the number of CPU cycles required
by the application, denoted as W, which depends on the
input data size and the complexity of the algorithm in the
application. Typically, W is modeled as a random variable,
which we elaborate in Section IV.
As stated in [19], the CPU power consists of the dynamic
power, the short circuit power and leakage power, in which the
dynamic power dominates. As a result, we only consider the
dynamic power for the mobile execution. In CMOS circuits
[20], the energy per operation Ew is proportional to V 2, where
V is the supply voltage to the chip. Moreover, it has been
observed that, when operating at low voltage limits, the clock
frequency of the chip, f, is approximately linear proportional
to the voltage supply, V [20]. As a result, the energy per
operation can be expressed as
Cloud Execution Energy Model
In this research, we make some assumptions for the cloud
execution. First, we assume the binary executable file for the
application has been replicated on the cloud clone initially.
As such, it does not incur additional energy cost. Second
Optimal Application Execution Policy
The decision for energy-optimal application execution, is
to choose where to execute the application, with an objective
to minimize the total energy consumed on the mobile device.
Specifically, the optimal policy is determined by the following
decision rule,
Mobile Execution if E∗
m ≤ E∗
c
Cloud Execution if E∗
m > E∗
c . (5)
As shown in Eq. (1) and Eq. (3), E∗
m is proportional to κ
and E∗
c is proportional to λ. Hence, the absolute values of κ
and λ are not critical, but the ratio between these two constant
energy coefficients, κ/λ, could affect the determination of the
optimal execution policy.
OPTIMAL COMPUTATION ENERGY UNDER MOBILE EXECUTION
In this section, we investigate the problem of minimizing
the energy consumption for executing an application in the
mobile device. Since the energy consumed by CPU is much
larger than the energy consumed by memory and screen,
we only consider the computation energy of executing the
application on mobile device. As such, the problem is to
optimally set the clock frequency of the chip for the minimal
energy. First, we build a probabilistic framework for mobile
execution. Then, we formulate the problem as how to schedule
the clock frequency in each CPU cycle for the application.
Finally, we derive the clock-frequency configuration for the
minimum energy consumption on the mobile device.
Probabilistic Application Execution in Mobile Device
Let W indicate the number of CPU cycles needed for an
application. For a given input data size, L, it can be derived
from [2], [26] as
W = LX, (6)
where X has been shown to be a random variable with an
empirical distribution [26]. The estimation of this distribution,
depending on the nature of the application, e.g., the complexity
of the algorithm, has been treated in [27], [19], [28], and is
thus beyond the scope of this paper. In this paper, we assume
that the probability distribution function (PDF) of X is P(x),
and its cumulative distribution function (CDF) is defined as
Wireless Channel Model
As shown in Fig. 2, we consider the scheduling of L bits of
input data with a deadline in T discrete time slots. The channel
state at time slot t is denoted as gt, which is determined by a
discrete state space Markov model.
We adopt Gilbert-Elliott channel model as a stochastic
model for the practical circumstances in the cloud execution.
This model has been widely used by a number of researchers
on wireless networks [23], [29]. In the Gilbert-Elliott (GE)
channel model, there are two states: “good” and “bad” channel
conditions, denoted as G and B, respectively. The two states
correspond to a two-level quantization of the channel gain. If
the measured channel gain is above some value, the channel
is labeled as good. Otherwise, the channel is labeled as bad.
Let the (average) channel gains of the good and bad states be
gG and gB, respectively
Comparison of Minimum Energy Consumption between
Mobile Execution and Cloud Execution
As proved previously in Section IV and Section V, there
are scaling laws that can be derived between the energy
consumption and the application profile (i.e., data size and
deadline delay): E∗
m ∼ L3 and E∗
m ∼ T −2 for the mobile
execution, and E∗
c ∼ Ln and E∗
c ∼ T −(n−1) for the cloud
execution, respectively. Thus, when n < 3, the cloud execution
consumes less energy for large data, while when n > 3, it is
also encouraged to offload the application to the cloud for
relatively long delay deadline