*2.3.2 Low-complexity operation*

that the arrival process is not controllable (i.i.d. random events); thus, it can be ignored. Then, the final form of the dynamic decision-making algorithm can be

In order to check whether the derived Eq. (18) is correct or not, two example

½ �¼ �*b*ð Þ *<sup>α</sup>*½ �*<sup>t</sup>* arg max *<sup>α</sup>*½ �*<sup>t</sup>* <sup>∈</sup> <sup>A</sup>

Thus, less cores should be allocated for energy consumption minimization which is our main objective. This is semantically true because the given main objective

The proposed dynamic super-resolution model selection algorithm is beneficial

Suppose that this proposed algorithm is implemented in supercomputer-like high-performance computing machines. In this case, the processing should be fast; thus, the queue-backlog is always low. Therefore, the system has more chances to focus on our main objective, i.e., penalty function minimization or utility function maximization. On the other hand, if the hardware itself is performance/resource limited (e.g., mobile devices), then the processing speed is also limited due to the low specifications in processors. Thus, the queue-backlog can be frequently busy because it may not be able to process many data with the queue even though it utilizes the fastest model. Therefore, it can be finally observed that the proposed algorithm is self-adaptive which can adapt depending on the given hardware/ system specifications. It automatically adapts the models based on the given hardware/system; thus, it does not require system engineer's trial-and-error tuning.

As discussed with examples, the proposed Lyapunov optimization-based

Thus, the departure process should be accelerated, i.e., more cores should be allocated. This is semantically true because the fast processing events from the

½ � *V* � *E*ð Þ� *α*½ �*t Q t*½�� *b*ð Þ *α*½ �*t :* (18)

½ � *V* � *E*ð Þ� *α*½ �*t Q t*½�� *b*ð Þ *α*½ �*t* , (19)

½ � *V* � *E*ð Þ� *α*½ �*t Q t*½�� *b*ð Þ *α*½ �*t* , (21)

*V* � *E*ð Þ *α*½ �*t* , (22)

*b*ð Þ *α*½ �*t* , (20)

*<sup>α</sup>*<sup>∗</sup> ½ � *<sup>t</sup>* <sup>þ</sup> <sup>1</sup> arg min *<sup>α</sup>*½ �*<sup>t</sup>* <sup>∈</sup> <sup>A</sup>

cases can be considered, i.e., (i) *Q t*½ �≈ ∞, and (ii) *Q t*½�¼ 0:

*<sup>α</sup>*<sup>∗</sup> ½ � *<sup>t</sup>* <sup>þ</sup> <sup>1</sup> arg min *<sup>α</sup>*½ �*<sup>t</sup>* <sup>∈</sup> <sup>A</sup>

<sup>¼</sup> arg min *<sup>α</sup>*½ �*<sup>t</sup>* <sup>∈</sup> <sup>A</sup>

*<sup>α</sup>*<sup>∗</sup> ½ � *<sup>t</sup>* <sup>þ</sup> <sup>1</sup> arg min *<sup>α</sup>*½ �*<sup>t</sup>* <sup>∈</sup> <sup>A</sup>

should be desired if the system is stable, i.e., *Q t*½�¼ 0.

*2.3.1 Hardware/system-independent self-adaptation*

**2.3 Discussions in stabilized control**

in various aspects, as follows.

**102**

<sup>¼</sup> arg min *<sup>α</sup>*½ �*<sup>t</sup>* <sup>∈</sup> <sup>A</sup>

dynamic core allocation decision-making algorithm works as desired.

• *Busy queue case* (*Q t*½ �≈ ∞): in this case

*Advances and Applications in Deep Learning*

queue is desired if overflow situations happen.

• *Busy queue case* (*Q t*½�¼ 0): In this case

defined as follows:

As shown in Algorithm 1, the computation procedure is iterative for solving closed-form equation, i.e., (11) and (16). Thus, the computational complexity of the proposed algorithm is polynomial time, i.e., *O N*ð Þ, where *N* is the number of the given control actions. Thus, it guarantees low-complexity operations.
