Construction of energy consumption minimization problem

Based on the data transmission model in the previous section, if the transmission power of the mobile terminal is P, then the energy consumption of one data transmission using m is P·t. Assuming that the number of times for one round of channel detection using m is N, then one round of channel bandwidth detection The total energy consumption for measurement and data transmission is: Emx=N·E, P – t.

If the mobile terminal repeatedly uses the given rule RMB round for application m, then the stop time number sequence {N, N,,…,N,,…,Ny| and the total energy consumption sequence {Ex, Ex,…, generated by the RMB round) ,Ex ,… ,Exy}.where,N. Indicates the stop time number of the main wheel. E is the total energy consumption when the main wheel stops at N. When the m-th wheel stops at N, the total time spent by the mobile terminal is the detection time ATx, =T·N, and transmission time t, which is ATx. t. The amount of data to be transmitted is Q1). Then the amount of data not to be transmitted in this round Lmx is:

If the mobile terminal obtains the minimum average energy consumption per unit of data after continuously observing the channel N times, then N is the optimal stop time. Because the mobile terminal detects at least one

sub-channel bandwidth, so the optimal stop time N≥1. The maximum transmission delay of the data to be transmitted is Dm. Define Z=LDm/T”, then 1≤n≤N≤Z.

According to the theorem of large numbers, equation (7) converges to ME[E,]/E[Q 1)-Ly]. Therefore, we construct a stopping time 1≤N≤Z to minimize ME[Ex]/EL[Q *1)-L]. This rule is derived from the channel transmission rate r detected during the interval T, and the detection time sequence AT, and generates the energy consumption sequence Ex, the data volume sequence to be transmitted O, and the data that cannot be transmitted Quantity sequence L. These sequence values can be obtained by measurement.

4.2 Solution of energy consumption minimization secretary problem

Our goal is to minimize the average energy consumption during the data transmission process from the mobile terminal to the cloud, that is, to select the moment when the transmission rate is the largest to transmit data. In this section, we will carry out the rule of letting k candidates go and then accepting the best ones. Solve to obtain the optimal k value and prove that the obtained k value is the optimal value.

This article defines V as the absolute ranking of the candidates selected according to the rule of letting go of k applicants and then accepting the best candidates; The probability that the selected candidate’s absolute ranking is r and the step size is s. PN =P(V=r) is the probability that the selected candidate’s absolute ranking is r when the decision-making process ends.

Lemma 1. When 1≤k≤N-1 and k 1≤s≤N, there is:

The mobile terminal performs channel detection every period T. After k detections, when it detects that the rate r at the current moment is greater than any previous rate value, the mobile terminal stops detection and sends data to the cloud. Otherwise, Continue to detect. If the mobile terminal does not transmit data for the first Z-1 detections, it must send data when the detection time reaches the maximum number of detections Z. The mobile terminal continues channel detection and data transmission according to this strategy , thereby reducing energy consumption during data transmission. 5 Simulation results and analysis

In this section, we conduct simulation experiments to compare the proposed strategy with related literature strategies in three aspects: average energy consumption per unit data, energy efficiency and detection efficiency, to prove the applicability of our proposed strategy.

The fading of data during wireless channel transmission is small-scale fading, and its fading model is usually simulated as Rayleigh distribution and Rician distribution. In the experiment, we conducted simulation experiments in the simulation environment of the two fading models, and the experimental parameter values are shown in the table 1.

This paper proposes the Optimal Transmission Strategy based on Secretary Problem (OTSSP) based on the optimal stopping theory of the secretarial problem, which is to let k candidates go and then accept the best candidates, and compares it with two other related literature strategies. Among them ,The other two comparison strategies are:

1) The Sooner The Better (TSTB) mechanism: the mobile terminal sends data after detecting the channel for the first time;

2) Random Transmission Strategy (RTS): The mobile terminal randomly selects a certain time for data transmission from Z clocks with a maximum transmission delay Dm with an equal probability 1/Z.

In order to take into account factors such as average energy consumption and maximum transmission delay, according to the literature [3], in the experiment, we set the maximum number of mobile terminal applications M to be s; the data generation rate c to be 10×103bps; and the data detection period T to be The value is 1s; the data transmission time r takes the value 0.9s; the data transmission delay is D. The value is 10s; the data detection energy consumption E is 1×10J. In this experiment, we consider the maximum number of applications M, the data generation rate c and the data transmission delay D. The impact on the average energy consumption per unit data, energy consumption efficiency and detection efficiency when changing. The changing factor M has a value range of 1~10; c has a value range of 1×103~15 x 10’bps; D has a value range of 1~15s .

5.1 Average energy consumption

The average energy consumption reflects the energy consumed by each bit of data in successfully transmitted data (including channel detection energy consumption Ep and data transmission energy consumption Pt).

Figure 2 shows the comparison results of the average energy consumption of the three strategies under different M changes under the Rayleigh distribution and the Rician distribution. It is observed from Figure 2 that the average energy consumption of each strategy of the Rician distribution is less than the average energy consumption of the corresponding strategy of the Rayleigh distribution. As As the M value increases, the average energy consumption of the OTSSP strategy is the smallest compared to the other two strategies at the same M value, the energy efficiency is optimal, and the average energy consumption growth rate is the slowest; the TSTB strategy does not consider energy consumption The factor transmits data directly, so the average energy consumption value is the largest and the energy efficiency is the worst.

Figure 3 shows the comparison results of the average energy consumption of the three strategies under different c changes under the Rayleigh distribution and the Rician distribution. The average energy consumption value of the OTSSP strategy and the RTS strategy is displayed on the left side of the ￥ axis, and the average energy consumption value of the TSTB strategy is on the ￥ axis. Shown on the right. It is observed from Figure 3 that in the Rayleigh and Rician distributions, as the value of c increases, the average energy consumption values of the OTSSP strategy and the RTS strategy are not too large respectively.

**IoT gateway**

Since data is transmitted when the channel condition is good, the data transmission rate is greater than the data generation rate, and no large amount of data is lost due to timeout transmission, so the average energy consumption per unit data gradually decreases. The energy consumption efficiency of the TSTB strategy is significantly worse than the other two strategies because , The TSTB strategy transmits data at the first transmittable moment. The channel state at this moment is often not ideal, and the amount of data transmitted is small. When the amount of transmitted data is equal to the other two data amounts, more energy must be consumed.

Figure 4 shows different D under Rayleigh distribution and Rician distribution. Comparison results of the average energy consumption of the three strategies when changing. It is observed from Figure 4 that among the two distributions, the OTSSP strategy has the lowest average energy consumption and the best energy efficiency. And the OTSSP strategy and the RTS strategy are different from each other due to the data transmission time. Relatedly, the average energy consumption value shows a decreasing trend as Dm increases. This is because when Dm increases, the generated data has more opportunities to be transmitted to the cloud before the maximum delay, and the energy consumed per unit data decreases, so the average Energy consumption shows a decreasing trend. When the delay D is greater than 25s, the energy consumption per bit of data is infinitely close to 0, but will not be equal to 0. At this time, although the average energy consumption is low, the user experience is not good.

5.2 Energy efficiency

Energy efficiency? Reflects the energy consumed per unit time during data transmission (including detection channel time T and data transmission time t). The smaller the energy consumption efficiency is, the less energy the strategy consumes per unit time.

Figure 5 shows the comparison results of the energy efficiency n value of the three strategies when M changes under Rayleigh distribution and Rician distribution. From Figure 5, it is observed that in the two distributions, the maximum number of applications of the three strategies M and? The values show a linear growth relationship. The OTSSP strategy has the lowest n value, and the TSTB strategy has the largest n value because it does not consider energy factors. At the same time, as the M value increases, the OTSSP strategy value grows the slowest. This shows that when a large amount of data is transmitted to the cloud at the same time , the OTSSP strategy energy consumption rate increases slowly, has better experimental results, and lays the foundation for the rapid development of mobile cloud computing.

Figure 6 shows the comparison results of the energy efficiency n of the three strategies when c changes under the Rayleigh distribution and the Rician distribution. Because the three strategies cannot clearly express the change amplitude in one picture, the OTSSP strategy is displayed as a separate picture; and ( In pictures b) and (d), the energy consumption efficiency value of the TSTB strategy is displayed on the left side of the Y￥ axis, and the energy consumption efficiency value of the RTS strategy is displayed on the right side of the Y￥ axis. Observed from Figure 6

It can be seen that the energy efficiency values of the three strategies in the Rician distribution are better than those in the Rayleigh distribution. As the data generation rate c increases, in the Rayleigh distribution, what is the energy efficiency value of the OTSSP strategy? Values are concentrated in 0.0497 ~ 0. 05, n values of TSTB strategy are concentrated in 0.328 ~ 0.332, values of RTS strategy are concentrated in 0.078 ~ 0.0784; in Rician distribution, values of OTSSP strategy are concentrated in 0.0462 ~ 0.0465; n values of TSTB strategy are concentrated in In 0.1842 ~0.1846; the n value of the RTS strategy is concentrated in 0.0780 ~0.0784. That is, the OTSSP strategy proposed in this article has the lowest energy consumption efficiency, consumes the least energy per unit time, and has the best energy saving effect. The orSSP strategy detects the channel rate for the first k times , starting from the k 1st detection, when the channel rate is greater than the previous k times, the detection will be stopped and data will be sent, thereby greatly improving the data transmission rate and energy utilization.

6 Conclusion

With the rapid development of mobile networks and mobile cloud computing, how to reduce the energy consumption of mobile terminals and clouds, improve energy utilization and enhance user experience is one of the urgent problems that green cloud computing needs to solve. Currently, a small part of the research work is in The network layer of the data transmission process is studied to reduce the energy consumption of mobile cloud computing. This paper will be dedicated to researching the energy consumption optimization problem of mobile terminals during the data transmission process of mobile cloud computing. During the data transmission process between the mobile terminal and the cloud, due to the mobile user’s Affected by factors such as mobility, weather changes, and unstable network bandwidth, if the mobile terminal chooses to send data to the cloud at a time when the channel status is good and the transmission rate is high, it can reduce a large amount of energy consumption and improve energy utilization. The optimal stopping theory is as It is an effective tool to solve the problem of maximum stop time and provides a basis for optimizing the data transmission energy consumption of mobile terminals. Based on the secretarial problem in which the average absolute ranking of the selected candidates is the smallest, this paper proposes to let k candidates go and then accept the best candidates. Energy consumption optimization strategy. This paper considers the case where data transmission has a certain delay. In the Rayleigh distribution and Rician distribution, assuming a constant data generation rate, a data transmission queue model with multiple applications and a minimization model of the average energy consumption per unit of data are constructed. , and use the improved secretarial problem (the rule of letting k candidates go and accepting the ones with the best results) to solve the problem to achieve the purpose of minimizing the average energy consumption per unit data. In the simulation experiment, the OTSSP strategy and TSTB strategy proposed in this article are Comparing with the RTS strategy, it is found that the OTSSP strategy has lower average energy consumption.

Keywords: Internet of Things gateway