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Abstract

Cross-layer optimization based on maximizing the utility of network robot 5G multimedia sensor network is a systematic method for cross-layer design of wireless networks. It abstracts the functional and performance requirements of the layers in the protocol stack into objective functions and constraints in mathematical optimization problems. In this article, the cross-layer optimization problem of wireless Mesh networks using multi-radio interface multi-channel technology is studied. The optimization problem is modelled based on the network utility maximization method, and the corresponding algorithm is proposed. Based on the random network utility maximization method, the cross-layer optimization model of network robot 5G multimedia sensor network is established. Aiming at the time-varying randomness of random data flow and wireless propagation environment in network robot 5G multimedia sensor network, a model of joint congestion control and power control based on chance constrained programming is proposed, and its genetic algorithm is used to verify it. Reforming research will help speed up the practical pace of the field, with certain theoretical forward-looking and practical value.

Keywords

Network robot 5G multimedia sensor cross-layer design optimization algorithm

Introduction

Multimedia sensor networks (MSNs) are distributed sensing networks consisting of a set of multimedia sensing nodes with computing, storage and communication capabilities.^1
–3 It uses the multimedia sensor on the node to sense the various media (audio, video, image, numerical value, etc.) information of the surrounding environment and transmits the data to the information aggregation centre through the multi-hop relay method. The convergence centre analyses the monitoring data to realize comprehensive and effective environmental monitoring.

With the increasing scale of data sets and the increasing demand for real-time data processing, and more reliance on large-scale and long-term data storage,^4
–6 5G technology can play its powerful role only when it is used in conjunction with the next generation of robots equipped with electric servo motors, sensors and other advanced hardware. As robots become more sophisticated and take over more tedious work in factories, the demand for small, efficient motors will increase. Due to the high emphasis on artificial intelligence (AI), machine learning and advanced processing algorithms,^7
–9 4G has been difficult to keep up with this demand. Robots can perform more tasks than monotonous tasks, but sometimes they need to learn new tasks or instructions and make decisions without human intervention.^10
–12 5G technology data return is more efficient. At present, the downlink peak speed of 5G is 20 Gbps, which is 20 times faster than that of Gigabit 4G network, so it will make the robot more efficient and rapid in receiving information and task instructions in the process of using. To know that in general, 5G network delay to 1 ms, for humans to respond to the time will reach 400 ms, so we can see that 5G compared to 4G network, end-to-end delay shortened by five times. After the popularization of 5G, the timeliness of data return will be greatly improved, and people can monitor and manage the robot’s work in real time. At the same time, the characteristics of low latency will add a new form of work to the industrial field: remote operation.^13
–15 In the past, every remote operation command needed data transmission to the manipulating machine, and the results were fed back through video. 5G technology can greatly reduce the transmission delay. The 1–2 ms interval is almost the same as the field operation. Like the recent rise of telemedicine surgery, low latency not only changes the pattern of time but also shortens the distance of space. 5G network is more flexible and end-to-end. In fact, we all know that Wi-Fi communication mode has some shortcomings such as easy interference, switching and coverage. But after 5G appeared, eLTE technology^16,17 based on 5G technology appeared in the process of factory application. It has relatively strong anti-interference ability. At the same time, 5G can also increase the connection of networked production equipment by 10–100 times, which means the coverage is more and more widespread. Widespread, which can help the robot application solutions to get better data analysis, but also to a certain extent to save the cost of network communications. 5G can be said to be the basic technology to realize cloud-based robots, and the emergence of 5G will have the characteristics of high bandwidth and low latency. Importantly, it can also put most of the computing in the cloud, which will be more secure and effective to ensure the computing data.^18,19 It is important to know that when the robot is deployed and applied, the cloud, as a central control management platform, can be remotely controlled to reverse the robot control.

Due to the time-varying wireless channel of the network robot 5G MSN and the broadcast characteristics of the wireless medium,^20

–24 the traditional layer-based network design could not fully exert the performance of the network, so it is not suitable for the design of wireless multi-hop network. In contrast, cross-layer design and optimization improves the performance of wireless networks by allowing different protocol layers to perceive changes in the wireless environment and coordinate and adaptively change protocol parameters. Although the idea of cross-layer design has been widely accepted, and many optimization theories and techniques^25
–27 have also been introduced into cross-layer design, there are still many technical difficulties in specific network design, such as cross-layer interaction. The trade-off with hierarchical structure, complexity and optimal performance, trade-offs between different performance objectives, channel time-varying effects, integration of new technologies (such as network coding), and design of distributed algorithms.

In this article, the cross-layer optimization problem of wireless Mesh networks using multi-radio interface multi-channel technology is studied. The optimization problem is modelled based on the network utility maximization method, and the corresponding algorithm is proposed. Based on the random network utility maximization method, the cross-layer optimization model of network robot 5G MSN is established. Aiming at the time-varying randomness of random data flow and wireless propagation environment in network robot 5G MSN, a model of joint congestion control and power control based on chance constrained programming is proposed, and its genetic algorithm is used to verify it. Reforming research will help speed up the practical pace of the field, with certain theoretical forward-looking and practical value.

Cross-layer design and optimization algorithm

Network coding^28
–30 has unique advantages in wireless networks. Due to the broadcast characteristics of the intelligent city 5G MSN, the node can detect the receiving node is not its own message; on the other hand, it can also encode a coded message (originated message from multiple different receiving nodes). Broadcast to multiple neighbour nodes is at the same time.

Cross-layer design of network coding in network robot 5G MSN

Integrating network coding into existing network robot 5G MSN architectures is not easy. Network coding cannot be seen as an independent function of a specific network protocol layer. It may have a significant impact on the various functions of the current protocol layer, such as transport layer congestion control, network layer routing and media access layer scheduling. The optimal network control algorithm involves a joint design between network coding and various protocol layer functions.

According to the perspective of network optimization, many existing network protocols can be regarded as a distributed solution to solve some form of network utility maximization problem, which has been fully obtained in the reverse engineering of TCP protocol. Shao et al.³⁰ pointed out that the various congestion control mechanisms and variants of TCP/IP protocol are actually the basic network utility maximization problem of various different forms of utility functions. The various utility functions can be reverse engineered through TCP. TCP protocol for a specific congestion control mechanism. In addition, recent studies have also pointed out that border gateway protocols (BGPs) can be reverse engineered as a stable path problem (in the form of network utility maximization problem),⁷ contention-media access control protocol (contention-based medium access control) can be reverse engineered to maximize the selfish utility function based on game theory.^16,31,32 According to this idea, the existing network protocol can be modelled as a network utility maximization problem, and then mathematical Optimized knowledge is analysed and modified to optimize existing protocols. In fact, network utility maximization is used to improve and analyse transfer control protocol (TCP) congestion control.^33,34 Table 1 lists some optimization goals. Existing network protocol designs are implicitly or explicitly used as one of their design goals. These optimization goals are also key performance indicators when designing protocols.

Table 1.

Example of optimization targets for each layer.

Protocol layer	Optimize the target
Application layer	Minimize reaction time (such as web browsing)
Transport layer	Maximize utility function, congestion control (TCP/AQM)
Network layer	Minimize path overhead (shortest path routing, minimum load path routing, etc.)
Data link layer	Minimize conflicts, conflict times, and so on
Physical layer	Maximize delivery rate, minimize power consumption.

The basic form of basic network utility (Basic NUM) is as follows

\begin{array}{l} maximize \sum_{s} U_{s} (x_{s}) \\ subject, R X \leq C \end{array}

The network design problem that the basic network utility maximization model can express is quite limited, so researchers such as Mung Chiang have proposed a more flexible generalized network utility maximization problem (Generalized NUM), which has the most published network utility. The research papers can be regarded as the result of the instantiation of the generalized network utility maximization model. The expressions are as follows

\begin{array}{l} maximize \sum_{s} U_{s} (x_{s}, p_{s}) + \sum_{j} V_{j} (w_{j}) \\ subject, R X \leq C (W, P) \\ x \in C_{1} (P_{s}), x \in C_{1} (F) \\ R \in R_{1}, F \in F_{1}, w \in W_{1} \end{array}

Considering the fairness of communication nodes, the fairness function has the following expression

U^{a} (x) = {\begin{cases} w_{s} {(1 - a)}^{- 1} x^{1 - a}, a \neq 1 \\ w_{s} log x \end{cases}

Consider a communication network with S source nodes and L links, so the problem of maximizing network utility is expressed as

\begin{array}{l} max \sum_{s} U_{s} (x_{s}) \\ s.t. x_{s} \geq 0, x_{s} \leq c_{l} \forall l \end{array}

In summary, the entire cross-layer design algorithm is given in Table 2.

Table 2.

Cross-layer design algorithm.

Known parameters: the utility function of each source node and the capacity of each link.
Initialization: set t = 0, any non-negative value Each source node solves the problem locally and then broadcasts the optimal solution. $x_{s} (λ (t))$ Each link updates $x_{s} (λ (t))$ and broadcasts the result. t1 = tl + 1, check the convergence condition, if it is satisfied, the algorithm ends; if not, jump to 1)

According to the capacity limitation relationship, the sum of the rates of the data flows carried by any link should be less than the capacity of the link, that is, the following relationship is satisfied

\sum_{s, l} x_{s, d} \leq C_{l}, \forall l \in {set}_{l}

Cross-layer design optimization algorithm

A near-optimal distributed algorithm was designed by using the idea of relaxation and approximation first. This is a two-step solution. The first step is to relax the integer variables and constraints to obtain a convex programming problem. The solution to the convex programming problem can be used as an upper bound on the original problem. The second step is to design the approximation algorithm so that the results are as close as possible to the upper bound. To evaluate the effect of the method, this article compares the near-optimal solution obtained by the algorithm with the results obtained by the branch and bound method. The simulation results show that the result of the algorithm is close to the optimal result obtained by the branch and bound method.

To maintain the fairness of the throughput of each session stream, we can express the cross-layer design problem of the network robot 5G MSN using OTIC network coding as the following optimization problem

maximize \sum_{i, d \in N} U_{l}^{d} (x_{l}^{d})

In the queue model used by the cross-layer algorithm, each node maintains a queue for each aggregated stream. In contrast, in the designed queue model, each node maintains multiple queues for each aggregated stream.

Using the sub-gradient projection method to solve the dual problem, we can get

\begin{array}{l} α_{l} (t + 1) = {[α_{l} (t) + h_{l} (t) (\sum_{s \in S} \sum_{d \in D} B_{s, d}^{l} r_{s, d} - \sum_{m = 1}^{M} E_{l}^{m} - c_{l}]}^{l} \\ β_{n} (t + 1) = [β_{n} (t) + h_{2} (t) (\sum_{l} c_{l} - \sum_{j} c_{j}^{max})]^{n} \end{array}

In the actual network robot 5G MSN, we can use the queue length information of the above queue model instead of the dual variable to apply the obtained algorithm. Using the designed queue model in each node, we propose the following back pressure-based cross-layer optimization algorithm (Table 3).

Table 3.

Cross-layer optimization algorithm.

Node n runs the following algorithm locally

First node. Initialize its corresponding with any non-negative value $α_{l} (0), β_{n} (0)$ .

Node. Locally solve the optimization sub-problem to get the transmission rate $r_{s, d} (t)$ .

Node. Get sub-problems locally based on their priority $E_{l}^{n} (t)$ and notify the neighbour node of the result.

According to the iterative update, get $α_{l} (t + 1)$ , and the value of $α_{l} (t + 1)$ is sent to the corresponding source node of each data stream that routes through the link.

Get $β_{n} (t + 1)$ based on iterative update and send $β_{n} (t + 1)$ value to all its neighbours.

t = t + 1, if the convergence condition is met, the algorithm ends: otherwise (2)

If the time average of the sum of the queue lengths satisfies the following conditions

\sum_{d} \sum_{l} Q_{l}^{d} + P_{d l}^{d}

The algorithm is a kind of heuristic stochastic optimization algorithm with excellent performance. The positive feedback mechanism is used to realize distributed global optimization. The pheromone is continuously updated to finally converge on the optimal path, which can be applied to the global optimization of single target and multi-target. The combination of optimal optimization of routing in the communication network, its inherent parallel computing characteristics are conducive to the implementation of decentralized control, can greatly improve the reliability and robustness of the system to enhance the ability of the communication network to adapt to unexpected events such as transmission failures and sudden business. The algorithm does not need to perform a large number of probability calculations or build complex mathematical models for system prediction and does not impose a lot of burden on the network signal system, which is easy to implement. The algorithm does not depend on the mathematical description of the specific problem and has a strong global optimization capabilities.

It can be assumed that the network route has been established by a certain multi-path routing protocol, and the route discovery process may be earlier than the channel allocation. In this case, the route discovery process may be completed by using a common channel or other related technologies, and the entire network includes P aggregated links.

With the above settings, the optimization model is constructed according to the characteristics of the network. Each wireless link in the network obviously can occupy at most one channel at any time, so there are

\sum_{k = 1}^{K} z_{l, p}^{k} \leq 1, \forall (l, p)

The out-degree and in-degree of a node, that is, the number of transmitting links and receiving links and the number of wireless interfaces that cannot exceed the node, are for any node i

\sum_{p} | A L_{p} | \leq f_{l}, \forall l

In summary, the following forms of convex optimization problems can be obtained

max \sum_{s = 1}^{S} U_{s} \sum_{g} r_{s g} - θ_{s} {(r_{s g} - y_{s g})}^{2} - \sum_{p} w_{p} x_{p}^{2}

Since the Lagrangian function L is a separable form, the problem can be solved by calculating the respective optimization problems at the respective source nodes and the transmitting ends of the respective aggregated links. At each source node, solve the corresponding problem

\begin{array}{l} max \sum_{s = 1}^{S} U_{s} \sum_{g} r_{s g} - θ_{s} {(r_{s g} - y_{s g})}^{2} - \sum_{p} β_{s g}^{p} α_{p} \\ s.t. m_{s} \leq \sum_{g = 1}^{G} r_{s g} \leq M_{s} \end{array}

The node cost size order is prioritized, the node with the larger node cost preferentially selects the available channel, and then the node with the second largest node cost selects the available channel, and then continues until all nodes are selected. To achieve this goal, each node needs to know the node cost of other nodes in the network, which can be achieved through broadcasts throughout the network, but this will incur a large amount of communication overhead, especially when the network size is large. On the other hand, if each node only needs to know the information of its neighbour nodes, the communication overhead will be greatly reduced. Of course, after such processing, the corresponding channel allocation result may not be optimal because global information is not obtained. In many cases, it is often worthwhile to lose a small amount of performance in exchange for a significant reduction in overhead.

Expectation value modelling is the most natural idea in random programming, which replaces the mathematical expectation of random variables with the random variables themselves. Since the mathematical expectation of random variables is a common variable, stochastic programming becomes a deterministic plan with integrals after processing the expected values.

The network robot 5G MSN can provide a variety of network applications. The network carries a variety of service flows, and the characteristics of various network flows are also different. For some TCP data streams that require long-term high-traffic connections, such as file transfer, the controllability is good, and the congestion control mechanism can be used to adjust the network injection rate. The third chapter combines the congestion control mechanism of this type of data stream with the power control of network robot 5G MSN. However, there are some uncontrollable data streams in the network robot 5G MSN, such as multimedia data streams based on user datagram protocol (UDP) protocol and some short-lived data streams (such as web mice data stream), bursts caused by application layer protocols. The process is of arriving at the sex package and so on. Such data streams do not need to be controlled due to short time or service characteristics, so that in addition to the controllable data stream, there are some uncontrollable data streams in the network, and their traffic is randomly changed.

Adding two random factors in the cross-layer optimization will more accurately reflect the network state. The first point is to add the unmeasured traffic in the network to the model, that is, how to determine the optimal injection rate when there is random traffic, which can be regarded as the second level is to add environmental noise random variables, and the wireless channel capacity is more realistically modelled, so that the calculation model of optimal power allocation is closer to reality, which can be regarded as channel-level random. The goal of optimization is to maximize the utility of the entire network, that is, to solve the optimization problem.

Simulation

The simulation experiment is carried out in a network robot 5G MSN consisting of nine communication nodes. The network is a tree structure. The spanning tree construction algorithm is similar to the IEEE 802.1 D spanning tree algorithm. The gateway node of the network is generated. The root is of the tree. Each node uses an uplink NIC to connect its parent node and multiple downlink NICs to connect its child nodes. For a given node, the channel used by its uplink NIC is specified by the parent node. Let the experimental network have four orthogonal channels a, b, c, d. In addition, there are three random data streams in the network (as shown in Table 4), which are subject to the uniform distribution in the interval,^2,3,6 the exponential distribution with the parameter of 0.4, and the normal distribution of N(2, 0.4). The confidence intervals for each link are set to 0.7, 0.8 and 0.9 respectively.

Table 4.

Simulation data flow.

	Source node	Destination node	Routing
Data stream 1	1	9	1-3-7-9
Data stream 2	2	9	2-4-7-9
Data stream 3	5	9	5-7-9
Data stream 4	3	9	6-8-9
Random data stream 1	2	9	3-7-9
Random data stream 2	4	9	5-7-9
Random data stream 3	8	9	8-9

Because the form of the problem is more complicated, it is difficult to transform into a deterministic plan, so the cross-layer design optimization algorithm is used to solve it. Figure 1 is an iterative convergence process of the algorithm when the link confidence level is 0.7. The horizontal axis in the figure represents the iterative step, and each point represents the best fitness in all chromosomes of an iterative step. As can be seen from the figure, the whole process gradually converges to the optimal value. Figure 1 is the group distance of each chromosome of each algorithm when the link confidence level is 0.7. When the initial population is selected, it needs to be universal and representative, so its group distance is large. With the iteration, the chromosomes are more the closer to the optimal solution, the smaller the group distance is until it approaches zero. Similarly, Figure 2 show the iterative convergence process and group distance of the algorithm when the link confidence level is 0.8; Figure 3 shows the iterative convergence process and group distance of the algorithm when the link confidence level is 0.98.

Figure 1.

Cross-layer optimization process and distance with link confidence level of 0.7.

Figure 2.

Cross-layer optimization process and distance with link confidence level of 0.8.

Figure 3.

Cross-layer optimization process and distance with link confidence level of 0.98.

When the confidence level is increased, that is, when the transmission reliability requirement is increased, the data stream will be appropriately reduced in rate to ensure smooth link. Obviously, the low rate is more likely to be supported by the link under the influence of random noise (including the randomness of wireless propagation and network flow), which is consistent with the intuitive imagination. The network injection rate is at the high link confidence level. It should be more conservative, and the network throughput will drop. Antisense, when the link confidence level is low, the data rate increases, causing the network throughput to rise (as shown in Table 5). Correspondingly, the transmit power of each node will also be adjusted accordingly to adapt to the change of data rate (as shown in Table 6).

Table 5.

Optimal rate.

Link confidence level	X1	X2	X3	X4
0.7	13.90	11.45	6.52	74.00
0.8	2.98	7.95	23.71	12.97
0.9	2.65	1.83	12.63	3.42

Table 6.

Optimal transmit power.

Link confidence level	P5	P6	P7	P8	P9	P10	P11	P12
0.7	8.56	9.73	9.29	9.92	0.33	9.39	5.65	8.95
0.8	4.17	7.22	2.77	3.91	2.99	5.41	6.79	7.35
0.9	4.19	2.23	9.72	4.43	0.81	2.89	9.75	9.82

Based on the opportunity constrained programming, the cross-layer optimization model of the network robot 5G multimedia network is established by using the random network utility maximization. Firstly, a brief introduction to the maximization of random network utility is given. Then the theory and application of stochastic optimization, especially opportunity constrained optimization, are expounded. This kind of optimization problem can be transformed into deterministic programming solution according to structural characteristics, or it can be solved by evolutionary algorithm such as design optimization algorithm. Aiming at the random factors of random data flow in the network robot 5G multimedia network and the time-varying nature of the wireless propagation environment, some uncontrollable data streams and time-varying characteristics of the wireless propagation environment in the network robot 5G multimedia network are modelled as random variables. A model of joint congestion control and power control based on chance constrained programming is simulated and verified. The results are analysed. The calculation results reflect the quantitative constraint relationship between network throughput and link confidence level.

Conclusion

5G not only enables it to design robots that can communicate with other robots or human employees in real time but also enables some of them to learn new tasks through direct observation or computer programs. 5G will also help reduce the cost of robots in the workplace and at home and make them cheaper.

The cross-layer optimization problem of multi-radio interface multi-channel intelligent city 5G multimedia network is considered. The problem is modelled by using network utility maximization, and the corresponding solution algorithm is proposed. It mainly includes three major parts: multi-channel intelligent city 5G multimedia network cross-layer optimization combined with rate control and power allocation, and cross-layer optimization of wireless network random factors. It provides power control, channel allocation and wireless for network robot 5G multimedia network. Joint optimization modelling of interface allocation and wireless link scheduling has been studied.

The cross-layer optimization problem of joint congestion control and channel allocation is modelled as a mixed integer nonlinear programming problem. Firstly, the cross-layer optimization problem of joint congestion control and channel allocation in multi-radio multi-channel network robot 5G multimedia network with single routing is modelled as a mixed integer nonlinear programming problem, which is solved by Lagrangian dual decomposition technique. Decomposed into multiple sub-problems, and finally solved the sub-problems to obtain the corresponding near-optimal distributed algorithm. The simulation experiment proves that the distributed algorithm can achieve good approximation effect, and the corresponding communication overhead is also small.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) received no financial support for the research,authorship,and/or publication of this article.

ORCID iD

Yongqiang He

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