Distributed optimization via primal and dual decompositions for delay-constrained FANETs
Introduction
Unmanned Aerial Vehicle (UAV) can be treated as sensors to collect environmental data e.g., temperature, humidity and wind speed, and transmit these collected data to ground bases (GB) [1], [2]. The single-UAV system provides various advantages including flexibility, expansibility to be used for decades [3]. Nevertheless, the simple functions and limited coverage of single-UAV systems restrict their further applications. Hence multi-UAV systems are built to improve operational performances through the cooperation of UAVs. However, the limited communication radius in multi-UAV systems may cause the link between a UAV and GB to be disconnected, which is need to be solved immediately. An alternative is to establish ad hoc networks among the UAVs in flying ad hoc networks (FANETs). The UAVs in FANETs can communicate with each other in peer-to-peer mode. In recent years, FANET applications have been extended to other networks [4] to support immediate communication in a hostile and noisy environment. Although FANETs can be used in many potential application domains, the high mobility of UAVs gives rise to unreliable link, and the difficulty of distributed optimization.
As pointed out in [5], FANETs can be characterized by a higher degree of mobility as a special case of mobile ad hoc networks (MANETs). In it, real-time routing is one of the most challenging and crucial issues, since successful mission completion severely depends on real-time and reliable transmission of critical information. The existing routing algorithms designed for MANETs [2] fail to match with environmental variations, because these algorithms cannot keep up with the fast evolution of link states, while resulting in a predefined path to be out of service. Moreover, the algorithms proposed for Delay Tolerant Networks (DTNs) [6], such as EPIDEMIC [7], BUBBLE [8], GDTN [9], and PROPHET [10], are destined to handle the recurrent disconnections of the links due to the high degree of nodes’ mobility. This category of routing methods uses the technique of store-carry-and-forward when the senders lose connectivity with their neighbors to deliver the packets to destination. Although these routing methods can perform well for the dynamic network topology of FANETs, they create more delays in completing the transmission for each flow due to the lack of delay control mechanism. In addition, the routing methods for DTN mainly focus on the best-effort delivery with less consideration of the various channel statuses, which are unsuitable for real-time applications because of increasing delay consumption for single-hop transmission. The high mobility of UAVs causes the transmission over a link to be more sensitive to interference. Further, it is still a challenging issue to select a power level to reduce the co-channel interference [11] among different transmissions. Since the interference level at each receiver directly determines the transmission reliability, which means that the higher interference level creates more delays for single-hop transmission. In summary, it is necessary to propose an optimization method with routing and power control to match dynamic network topology and meet the delay-constrained requirement.
As mentioned above, due to the presence of the unpredictable channel states at any time in FANETs, traditional centralized optimization methods hardly handle such dynamic environment. This work proposes a distributed optimization method based on the fact that global knowledge of the network topology is unnecessary for each UAV. To this end, we use a decomposition method [12] to decompose the global optimization problem into several sub-problems, including path selection and primal-dual parameter updates. The former is to select a path for each flow to satisfy the delay constraint, while the latter aims to optimize the network parameters at intermediate nodes. Finally, we analyse the performances of the proposed optimization method and its convergence.
To the best of our knowledge, few previous work jointly consider delay-constrained routing, rate allocation and power control optimization problems in FANETs. In addition, there are some differences between this paper and our previous work in [13], mainly include the following contents: 1) this paper aims to maximize the single-hop transmission rate over the links rather than the end-to-end generation rate at the sources in [13]; 2) the work in [13] is devoted to process delay constraint with end-to-end link state, which is different from the local operations considered in this paper. In this paper, our contributions are two-fold as follows:
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We formulate a utility maximization framework to model the joint optimization problem for delay-constrained FANETs. To match with the dynamic network topology, the dual and primal decomposition methods are exploited to decouple the link-layer and end-to-end delay constraints in FANETs. Then the centralized optimization problem is divided into three sub-problems: rate allocation, delay-constrained routing, and power control, which allow the senders to use only local information from their neighbors to update the primal and dual parameters.
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We propose a distributed optimization algorithm that incorporates local channel information from neighbors to achieve the optimal solution of sub-problems. To maximize the network utility and reduce the transmission delay in distributed manner, each sender estimates the single-hop delay by considering the packets’ progress to the destination and the current remaining time for transmission. The algorithm allows the parameter update operations to be performed at each node. We also use the sub-gradient method to update the dual parameter, and the one-order derivative method to obtain the primal solution at the current moment to accelerate the convergence of the algorithm. Finally, we analyse the performances of the optimization method and prove its convergence.
The remainder of this paper is organized as follows. In Section 2, we introduce some previous work by other researchers. In Section 3, we presents some preliminary concepts used in the proposed method. In Section 4, we introduces the specific implementation process of the proposed dsitributed optimization algorithm and in Section 5, we show some experimental results for the proposed algorithm. Finally, we conclude the paper and discuss future work in Section 6.
Section snippets
Related work
There are many researchers focusing on the routing problems for FANETs. For example, Oubbati et al. [14] proposed a classification and a taxonomy of position-based routing protocols, including a detailed description of the routing schemes. Then, they proposed a comparative study for these protocols, and presented some new challenges in future research. Differing from the consideration of position-based routing protocols in [14], Arafat et al. [15] investigated cluster-based routing protocols
Network model
In this paper, we focus on FANETs composed of multiple UAVs that are independently and uniformly distributed in the deployed area, and a GB serves as the destination of data flows. Assume that the coordination of the ground base is unchangeable, and all UAVs communicate with the GB in single-hop or multi-hop mode, as shown in Fig. 1. Specifically, each UAV can serve as a source to initiate a flow or a relay node to forward the packet for other UAVs, and a GB is only used to terminate flows
Problem formulation
In this study, we mainly focus on the distributed optimization for delay-constrained FANETs. To improve the performance of the proposed optimization algorithm, we optimize three network metrics: the throughput, end-to-end delay, and power consumption. Because the cost of the acknowledgment (ACK) is small compared with the data packet, the effect of the ACK on the link reliability can be ignored [34].
Before formulating the optimization problem, two objective functions have to be defined: the
Analysis of the simulation results
In this paper, we use OMNET++ 5.0 to simulate the network scenario and collect relevant results. In the initialization phase, the nodes spread randomly and uniformly in an area of 1000 m * 1000 m * 100m and move with a random way-point mobility model [41]. Random Way-point model allows nodes to begin by staying in one location for a certain period of time (i.e. a pause time), once the period expires, the nodes choose a random destination in the simulation area. In Random Walk model, each node
Conclusion
This work presents a distributed optimization algorithm for FANETs by jointly using primal and dual decompositions, which can improve network throughput, reduce co-channel interference, and limit the end-to-end delay to a given threshold. Specifically, the original optimization problem is formulated and transformed as three sub-problems by considering both primal and dual decomposition techniques. Further, the single-hop delay is estimated to decouple the end-to-end delay constraint, which is
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This work is supported by the National Science Foundation of China (Nos. 61772385, 61572370).
Shaojie Wen received the B.Sc. degree from Henan Normal University, Henan, China, in 2011 and M.Sc degree from Xinjiang University, Xinjiang, China, in 20 14. He was a Ph.D. student at Wuhan University in 2019 He is currently a researcher at Zhuhai Da Hengqin Science and Technology Development Co., Ltd. Ltd., Zhuhai. His research interests include Mobile ad hoc networks and Adaptive routing. Email: [email protected]
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Shaojie Wen received the B.Sc. degree from Henan Normal University, Henan, China, in 2011 and M.Sc degree from Xinjiang University, Xinjiang, China, in 20 14. He was a Ph.D. student at Wuhan University in 2019 He is currently a researcher at Zhuhai Da Hengqin Science and Technology Development Co., Ltd. Ltd., Zhuhai. His research interests include Mobile ad hoc networks and Adaptive routing. Email: [email protected]
Lianbing Dengis the director general manager of Zhuhai Da Hengqin Science and Technology Development Co., Ltd. And he is also the director of Post doctoral Programme of China (Hengqin) Pilot Free Trade Zone and the director of Information Centre of Hengqin New Area. He has received his doctor degree in Huazhong University of Science and Technology. His researches are in the field of big data, project management, and economic research. He is the vice chairman of China Big Data Council of MIIT of the People’s Republic of China. Email: [email protected]
Yuhang Liuwas born in Hubei, China, in 1989. He is currently pursuing the Ph.D. degree with the School of Computer Science, Wuhan University. He was a joint training Ph.D. student at Australian Institute for Machine Learning, The University of Adelaide, in 2018. Hi s current research interests include Bayesian learning, deep learning and their applications in image processing, computer vision and signal processing. Email: liuyuhang @whu.edu.cn