Scheduling drone charging for multi-drone network based on consensus time-stamp and game theory

Computer Communications 149 (2020) 51–61

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Scheduling drone charging for multi-drone network based on consensus time-stamp and game theory Vikas Hassija a , Vikas Saxena a , Vinay Chamola b ,∗ a b

Department of CSE and IT, JIIT, Noida, India Department of Electrical and Electronics Engineering, BITS-Pilani, India

ARTICLE

INFO

Keywords: Directed Acyclic Graph Unmanned Aerial Vehicles Internet of drones Distributed applications Consensus Smart charging Blockchain

ABSTRACT Drones or Unmanned Aerial Vehicles (UAVs) can be highly efficient in various applications like hidden area exploration, delivery, or surveillance and can enhance the quality of experience (QoE) for end-users. However, the number of drone-based applications are not very high due to the constrained flight time. The weights of the drones need to be kept less, and intuitively they cannot be loaded with big batteries. Frequent recharging and battery replacement processes limit the appropriate use of drones in most applications. A peer-to-peer distributed network of drones and charging stations is a highly promising solution to empower drones to be used in multiple applications by increasing their flight time. The charging stations are limited, and therefore, an adequate, fair, and cost-optimal scheduling algorithm is required to serve the most needed drone first. The proposed model allows the drones to enter into the network and request for a charging time slot from the station. The stations are also the part of the same network, this work proposes a scheduling algorithm for drones who compete for charging slots with constraints of optimizing criticality and task deadline. A game-theoretic approach is used to model the energy trading between the drones and charging station in a cost-optimal manner. Numerical results based on simulations show that the proposed model provides a better price for the drones to get charged and better revenue for the charging stations simultaneously.

1. Introduction Technology is advancing as days are passing. The current hot topic of interest for most of the researchers is to automate task using machines. As the discussion is regarding automation, the term that first comes to the mind is UAV (Unmanned Aerial Vehicle). UAV was first used in the early 19th century by the military for getting intelligence update regarding the combat field. Now apart from the military use [1], commercial use of drones is also being promoted for the various applications like Agriculture-Application [2], Infrastructure Management, Data-Sharing, Disaster-Relief [3,4], Delivery Services [5,6], Outdoor– Indoor Navigation, exploration of hazardous area which is not safe for humans [7], use as fireflies to illuminate the areas and on the same hand conserve energy [8] and many more. However, there are various drawbacks in expanding the usage of drones such as a limited battery, limitations in terms of carrying heavy loads, limited flight time, and multiple UAV cooperative timing problems. The largest flight time recorded for a drone is only for 30 min in 2019 [9]. Various factors are pulling back drones to perform a long-duration flight to name a few are fixed-wing size, weather conditions, limited battery, degradation of battery over an extended period, usages of GPS and sensor accuracy. There are various parameters through which these

hurdles can be overcome, such as the use of high-quality equipment such as motor, wing, and battery. Various optimized graph algorithms such as Dijkstra’s Algorithm are also being used to find the shortest possible path for the drone to reach the destination [10]. The focus of this work is to increase the flight time of drones by providing required charging to the drones in a cost-optimal way. A peer-to-peer network of drones and charging stations can be a highly promising solution. The peer-to-peer network can help the drones to reserve a charging slot over the nearest charging station on its way at the best available cost. Fig. 1 shows the motivation of the work in a pictorial manner. The drones are allowed to enter or leave the network as per requirements. Such a facility would enable drones to fly for longs hours, perform monitoring/delivery services and rescue operations. The main hurdle in a peer-to-peer network is to achieve consensus finality among the participating nodes in the network. Message passing is the most common and traditional way to reach consensus finality in such distributed networks. The issue with message passing algorithms is that they are limited with the bandwidth required to pass the votes or messages. Such systems can work only in a closed group where the participants are limited and are already known. Other blockchain-based open networks are able to perform such tasks for more number of nodes

∗ Corresponding author. E-mail addresses: [email protected] (V. Hassija), [email protected] (V. Saxena), [email protected] (V. Chamola).

https://doi.org/10.1016/j.comcom.2019.09.021 Received 8 August 2019; Received in revised form 19 September 2019; Accepted 27 September 2019 Available online 5 October 2019 0140-3664/© 2019 Elsevier B.V. All rights reserved.

V. Hassija, V. Saxena and V. Chamola

Computer Communications 149 (2020) 51–61

Table 1 Related work on charge scheduling. Year

Author

Contributions

2016

Sheng Zang et al. [16]

Optimizing itinerary selection and charging association for mobile chargers

2017

Samer Aldhaher et al. [17]

Light-weight wireless power transfer for the mid-air charging of drones

2018

Chiuk Song et al. [18]

EMI reduction methods in wireless power transfer system for drone electrical charger

2018

Maxim Lu et al. [19]

Wireless charging techniques for UAVs: A review, reconceptualization, and extension.

2018

Jinyong Kim et al. [10]

CBDN: Cloud-based drone navigation for efficient battery charging in drone networks.

2018

Angelo Raciti et al. [18]

Drone charging stations over the building based on a wireless power transfer system

2018

Ali Rohan et al. [20]

Development of drone battery charging system based on wireless power transmission

2019

MyungJae Shin et al. [21]

Auction-based charging scheduling with deep learning framework for multi-drone networks.

2019

V. Sharma et al. [22], [23]

Neural blockchain based assistance for swarm of drones.

Hedera Hashgraph is Atomic, Consistent, Isolated, and Durable, i.e., ACID-compliant database that offers high security. Hashgraph is also resistant to Distributed Denial of Service (DDoS) attack as there is no special priority given to any node to mine the blocks or to calculate the consensus. Hashgraph consensus algorithm is also asynchronous byzantine fault tolerant (ABFT) and can easily overcome the issues related to a set of nodes acting maliciously. These additional advantages of hashgrpah algorithm are the motivating factor behind using hashgraph in the proposed peer-to-peer network above the blockchain. The main contributions of this work are listed as follows: • A peer-to-peer network of drones and charging station is created where drones can securely enter and leave the network and can request for a charging slot. • Hashgraph consensus algorithm is used for calculation of the consensus time-stamp to schedule the charging requests. • The game-theoretic approach is used for allotment of the charging slots to the drones in a cost-optimal manner. • The proposed model is evaluated on a hashgraph simulation, and the numerical results prove the higher efficiency of the model as compared to its counterparts.

Fig. 1. Pictorial representation of proposed drone charging framework.

but are probabilistic in nature and never reach a consensus finality [11– 13]. Most of the recent work in the direction of charge scheduling for drones has been carried out using centralized architectures which have their inbuilt limitation of being a single point of failure. Very few works have been done in the direction of creating a distributed peer-to-peer network of drones and charging stations using blockchain technology [14,15]. To the best of our knowledge, this is the first work to propose the peer-to-peer drone charging model based on hedera hashgraph. Hedera hashgraph is a distributed ledger technology that works on a Directed Acyclic Graph (DAG) data structure. The blockchain distributed ledger architecture has various fundamental defects such as low throughput and low latency as compared to hashgraph [24]. Blockchain consensus is reached using proof of work (POW) algorithm which also requires a high computation power [25–27]. Additionally, the issue of forking and pruning in blockchain makes it less efficient as compared to hashgraph [28]. A number of blocks created in blockchain are redundant and are removed from the main chain in later stages, thereby reducing the overall efficiency [29,30]. In the proposed model, Drones are expected to enter and leave the network at a high frequency, and it is imperative to record all the events efficiently is perfect time-stamp order to avoid conflicts. The charging stations are limited, and the number of drones is high as compared to charging stations. Therefore an accurate optimization and scheduling algorithm is required for such a model. Blockchain does not maintain any time stamp ordering of the received transactions, and therefore such a distributed ledger technology (DLT) is not a good fit for the proposed model.

1.1. Organization The rest of this paper is organized as follows. The recent work related to drone charge scheduling applications is presented in Section 2. Some background information about the hedera hashgraph technology and decentralized system model is presented in Section 3. Network model and some prelims information about Drones and Charging station are discussed in Section 4. Sections 5 and 6 present the best price formulation strategy for the Drones and Charging Stations, respectively. The Ascending-Price progressive auction algorithm among drones is presented in Section 7 (A) and Auctioning among charging stations is carried out in Section 7 (B). In Section 8, the simulation results are presented and are compared with the existing models for drone charging. Section 9 finally concludes the paper. 2. Related work In this section, we present the existing work in academia and industry in the direction of improving the usability of drones in various applications (see Table 1). Various leading companies such as DJI, Kespry, Yuneec [31], Skycatch Inc. and many more are into rapid research and development towards providing optimized results in terms of loadcarrying efficiency, performance in day to day tasks like delivery, 52

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Computer Communications 149 (2020) 51–61

monitoring, etc. Amazon has released a program named Amazon Prime Air that is used to make fast delivery using drones within a radius of 10 miles. They have also patented the beehive-like structure of drones for household delivery of goods weighing less than 2.25 kg [5]. Intel and Disney are also trying to replace their aerial firework shows using drones [32]. Even Zomato has acquired a company named techEagle to start aerial food delivery to deliver fresh food to customers as soon as possible [33]. Millions of dollars are being invested by the governments of various countries to promote the research and development in the direction of using drones in multiple applications [34,35]. All these existing and future drone applications are highly constrained with the limited flight time of drones [36]. Therefore, a secure peer-to-peer open network of drones and charging stations can be a highly promising solution to enhance the usability of drones [37,38]. Sheng Zhang et al. [16] have proposed the use of mobile chargers to extend the overall battery life of energy-seeker drones. The architecture designed by the authors uses the pre-planned charging itineraries that schedules and associates the drones to mobile chargers to minimize the amount of energy loss. The mobile charger approach is centralized and works based on pre-planned itineraries. The model does not cater to the dynamic and real-time charging demands. The authors of [17] have proposed a model that aims at reducing the weight of drones by installing a Wireless power receiver that operates at a very high frequency and generates a very high gravimetric energy density. Chiuk Song et al. [18] have proposed a model that tries to reduce the electromagnetic interference (EMI) and electromagnetic fields (EMF) that are generated during the power transfer from source to battery during wireless charging. This method was however beneficial only for the drones operating at 60 kHz frequency and tries to eliminate the third harmonic and its integer multiples in the output voltage. Maxim Lu et al. [19] have proposed various methods to increase the flight time of drones using wireless as well as the wired medium. They have suggested the use of both the electromagnetic field and nonelectromagnetic field for generation of electricity. Some of the non-emf based methods proposed by them use wind energy and try to uplift the drone by adjusting the airflow [39]. The proposed model is useful only above oceans or in an environment where there are strong winds. Another Wireless method proposed by them was photovoltaic (PV) arrays that use solar energy during flight time and rely on battery power during night or bad weather. This method ends up into incrementing the weight of drones due to the use of solar panels. The authors also proposed a method to charge the drones on the fly using laser beaming. This method is constrained with the issue of having laser fitted vehicles in the vicinity of the drone. Jinyong Kim et al. [10] have proposed a model to reduce the congestion of drones at the charging station. This model utilizes Dijkstra’s Algorithm for scheduling of charging time and queuing time. They have divided the model into three-component, i.e., Traffic Control Center (TCC) that will schedule the drones to Quick Charging Machine (QCM) avoiding the congestion at a QCM. The major weakness of this model is that in this model, TCC acts as the backbone of the entire system. If TCC fails or gets hacked then it may end up into shutting down the entire network. Angelo Raciti et al. [40] have proposed a model where drones could land on the roof of the building and get charged. The authors try to minimize the energy loss due to misalignment between the charging pad and drone. The misalignment mainly arises due to the variability of the coupling factor. The authors of [20] have also proposed a model where charging station consists of multiple power transmitters and a receiver to charge drones. In this method, instead of using sensors for coupling, they have used a hill-climbing algorithm for coupling between transmitter and receiver. Myung Jae Shin et al. [21] have proposed a model to allot charging time slot to the drones using the auctioning process. A second-price auction model is used in which the winner of the auction pays the second-highest bid value. In this model, data required for the distribution of drones was retrieved from the deep learning process. These models do not consider the possibility of

Fig. 2. Event in hashgraph.

enhancing the revenue of the charging station and the possibility of providing charge to the drones at lower prices. Although there are several works in this direction, they are centralized and are more or less based on predictive analysis or sensor data. Sensor data-based approaches are quite expensive, and prediction based approaches are probabilistic. There is no peer-to-peer network of drones and charging stations where the nodes can securely enter or leave the network and can request for charging in a secure and cost-optimal way. This calls the need for a distributed framework for drone charging that is cost-optimal, fair, secure, and accurate. This paper proposes an end-to-end distributed drone charging application that aims at maximizing the flight time for drones in minimum cost and the revenue of the charging station owners simultaneously. 3. Proposed model for multiple-drone charging system 3.1. Digital identity for drones The proposed model is deployed on the hedera hashgraph network, and a smart contract is deployed on the hashgraph to schedule charging of drones. Hashgraph can be considered as an advanced version of blockchain that provides all the inherent features of generic blockchain and removes its fundamental limitations as discussed in Section 1. Smart contract is a self-executing lines of code that is deployed on a distributed ledger to enhance the level of security and trust among the nodes. Currency used for the exchange of energy between drones and charging station would be Hbar, the native currency for hedera platform. Drones can enter or leave the distributed network at any time. The network would have its own genesis address book that will be used to store the information about the public key of all the nodes in the network and stakes they are holding. To interact with the network, Drones need to generate the key pair using ED25519 algorithm. Hence when drone tries to enter into the network, they have to provide information about their public key and stakes they are holding. Ones drones are successfully registered into the network after identity verification using KYC (Know-Your-Customer) through Escrowed Identity System [41]; they can initiate a request for charging in the hash graph network. The charging request is spread into the network using gossip the gossip protocol. 3.2. Event creation for drone charging Charging stations and drones represent the nodes in the hashgraph. The gossip protocol is used to exponentially spread any transaction issued by any node on the network. In the gossip protocol, a node 53

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randomly selects another node and shares all its information with that node. The information is shared in the form of event. Fig. 2 shows the structure of an event stored in hashgraph. An Event consists of transactions, a hash of both the parents of the event, the time-stamp of event creation and a digital signature of the creator [42]. Information such as the energy required by drones, the energy available with the charging station, criticality of charge required by drones, price of charge sold by charging station, etc. is stored in the form of transactions inside the events. The hashgraph is divided into rounds, where each round indicates that a particular event has been gossiped with at least 2∕3rd of the nodes in the entire network. Fig. 3 shows the process of round creation and message gossip as the hashgraph grows with time. The different nodes, i.e., A, B, C, D, are the number of participants in the network. These participants can either be drones or charging stations. Each participant is sending the information that it has to all the other participants that do that have that particular information. This way, each information is shared with all nodes in the network in very less time. The process of this information sharing uses the protocol named as ‘‘gossip the gossip’’ protocol. Hashgraph is a Directed Acyclic Graph that grows in only one direction. The hashgraph consensus algorithm assures that the transactions are processed in timestamp order with a complete agreement of all the nodes in the network. This increases the overall fairness in the framework. Hashgraph plays an important role in the proposed model by avoiding any conflicts between the nodes and thereby enhancing the overall performance of the network. 3.3. Consensus algorithm In hashgraph, virtual voting is used to get the consensus time-stamp. Virtual voting does not involve any message passing to calculate the vote of other nodes. All the nodes share the copy of the hashgraph being generated. The votes are calculated by each node individually based on the graph. Since all the copies of hashgraphs are same, the nodes eventually end up into calculating the same vote. The first event for every node in each round is considered as the witness for that round. Every node decides on the witnesses to be famous or not-famous based on the fact that the witnesses in next round are able to strongly see the witnesses of the current round or not. If more than 2∕3rd of the witnesses in next round vote in favor of the current witness, then it is decided that the witness is a famous witness. Once fame of all the witnesses is decided then the consensus time-stamp of any event 𝑥 can be calculated by taking the median of the time-stamp at which the famous witnesses of that round encountered the event 𝑥. Please note that the median is the value that is nearest to the middle of all timestamp and is not changed or affected due to the extreme values. We take the median and not the mean because if some time-stamp is too far from the middle value due to some reason, it will be discounted and will not affect the median value or the consensus time-stamp for that event. Therefore, if a node tries to change its clock, it will not be able to change the consensus timestamp for the transactions [43].

Fig. 3. Pictorial representation of hashgraph.

4. Network model and prelims We design a network model with a multiple number of drones and charging stations. Table 2 gives the meaning of all the mathematical notations used in this paper. Let  = {1, 2, 3, … , 𝑑} denote the set of the drones in the community and || represent the total number of drones in the community that needs to get charged. Similarly,  = {1, 2, 3, … , 𝑐} denote the set of the charging station and || represents the total number of charging station in the community that are readily available to charge the drones. We have divided the total working time of network into an equal time slot for the fair working of p2p network. After the end of each slot, the algorithm would be run for allotment of charging slots. We have considered divided time slot of 1 h for calculation, which can be changed as per requirement. Let  = {1, 2, 3, … , 𝑡} denote the set of working time of network with 𝑡 ∈ 𝑇 and | | represents the total number of working time slots.

3.4. Security model Peer-to-peer systems pose unique challenges from a computer security perspective. Various vulnerabilities related to such distributed networks include DDoS attacks, 51% attack, malicious partitioning attack, Sybil attacks, etc. If the decentralization is not sufficient, and the majority of the nodes in the network can collude to form a cluster, then the security of the network can be easily compromised. A sufficient degree of decentralization and governance is required to prevent such attempts. The proposed model is based on aBFT consensus and can easily prevent the occurrence of such attempts. There are various other security mechanisms and algorithms in the hashgraph consensus that tend to prevent such attacks [43].

4.1. System overview Fig. 4 shows the detailed step by step overview of the proposed system. Once the drones successfully join the network, a transaction 54

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Computer Communications 149 (2020) 51–61

Fig. 4. Work-flow of system model. Table 2 Notation summary. Notations

Meaning

𝑑 𝑐 𝑃𝑐ℎ,𝑐 𝑃𝑑𝑐ℎ,𝑐 𝑜𝑐 𝑜𝑑 𝜂 𝜈  𝑇 .𝐸  𝜌     𝜆 𝑁𝑇   𝛾 𝜓 𝜁 𝑥, 𝑦 𝜔 𝜉

Energy in battery of 𝑑th drone Energy in battery of 𝑐th charging station Charging power of 𝑐th charging station Discharging power of 𝑐th charging station Efficiency of 𝑐th charging station Efficiency of 𝑑th drone Normalization factor Timestamp Mileage Total energy Criticality Price per unit given by drone Normalized timestamp Normalized mileage Normalized criticality Normalized price Priority of drones Normalized time Distance among drone and charging station Energy rate offered by charging station Normalized distance Normalized energy rate Priority for charging station Index of Winners for both auction respectively Budget of drone Maximum energy rate

3. Ones the requests are added, consensus time-stamp is calculated using hashgraph consensus algorithm, and the charge scheduling priority is calculated. 4. Next, the auction process is carried out amongst the drones and drones iteratively change their parameters to get a charging slot. The priority is recalculated based on the updated parameters. 5. An auction mechanism takes place among the charging stations to attract more drones. 6. Finally, the association of drones to charging stations is done in a cost-optimal way. 4.2. Drones battery energy storage system Let 𝑡−𝛥𝑡 and 𝑡𝑑 denotes energy in battery of 𝑑th drone at the 𝑑 𝑡 beginning and completion of time slot t [44]. Let 𝑐ℎ,𝑑 denote the 𝑡 charging power of 𝑑th drone at time slot t, and 𝑑𝑐ℎ,𝑑 denote the discharging power for 𝑑th drone at time slot t. Let 𝑜𝑡𝑐ℎ,𝑑 and 𝑜𝑡𝑑𝑐ℎ,𝑑 denotes the efficiency of charging and discharging of battery of 𝑑th drone at t time slot. ( ) 𝑡 𝛽𝑑𝑡 𝑃dch,𝑑 𝑡 𝑡𝑑 = 𝛥𝑡 × 𝛼𝑑𝑡 𝑃ch,𝑑 𝑜𝑡ch,𝑑 − 𝑡 + 𝐵𝑑𝑡−𝛥𝑡 (1) 𝑜dch,𝑑 𝑝𝑑 ≤ 𝑑 ≤ 𝑞𝑑 𝑝𝑑

(2) 𝑞𝑑

Here, and represents the minimum energy and maximum energy respectively required by the 𝑑th drone to continue to function properly

is flooded in the network requesting a charging slot. Please note that here transaction is not referring to any financial transaction of cryptocurrency. The transaction referred here is a message request from the drones to the charging stations. The following steps clearly explain the system overview through Fig. 4.

𝛼𝑑𝑡 + 𝛽𝑑𝑡 = 1, 𝛼𝑑𝑡

𝛼𝑑𝑡 , 𝛽𝑑𝑡 ∈ {0, 1}

(3) 𝛽𝑑𝑡

where is the charging constant and is discharging constant for 𝑑th drone at time t. In practical implementation simultaneous charging and discharging is avoided by (3).

1. The first box in the figure shows the first step where the charging request is gossiped in the network of drones and charging stations. 2. The messages from the drones or charging stations are securely stored in the form of hashes in a hashgraph distributed ledger as shown in the second box in the figure.

4.3. Charging stations battery energy storage system Let 𝑡−𝛥𝑡 and 𝑡𝑐 denotes energy in battery of 𝑐th charging station 𝑐 𝑡 at the start and completion of time slot t [44]. Let 𝑐ℎ,𝑐 denote the 𝑡 charging power of 𝑐th charging station at time slot t, and 𝑑𝑐ℎ,𝑐 denote 55

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the discharging power for 𝑐th charging station at time slot t. Let 𝑡𝑐ℎ,𝑐 and 𝑡𝑑𝑐ℎ,𝑐 denotes the efficiency of charging and discharging of battery of 𝑐th charging station at t time slot. ( ) 𝑡 𝛽𝑐𝑡 𝑃dch,𝑐 𝑡 𝑡 𝑡 𝑡 𝑐 = 𝛥𝑡 × 𝛼𝑐 𝑃ch,𝑐 𝑜ch,𝑐 − 𝑡 + 𝐵𝑐𝑡−𝛥𝑡 (4) 𝑜dch,𝑐

5.0.3. Criticality of charge requirement The third information drone has to share is the criticality of charge requirement, i.e., how much battery is available with the drone with respect to the total capacity of the drone. Let 𝐶𝑑 represent the Criticality of 𝑑th drone.

𝑝𝑐

𝐶𝑑 = 1 −

≤ 𝑐 ≤

𝑞𝑐

(5)

Here, 𝑝𝑐 and 𝑞𝑐 represents the minimum energy and maximum energy respectively required by the 𝑐th charging station to continue to function properly 𝛼𝑐𝑡 + 𝛽𝑐𝑡 = 1,

𝛼𝑐𝑡 , 𝛽𝑐𝑡 ∈ {0, 1}

𝛼𝑐𝑡

𝐵𝑑𝑡 𝑇 .𝐸𝑑

(9)

where 𝐵𝑑𝑡 represents the available energy and 𝑇 .𝐸𝑑 represents the total battery capacity of the 𝑑𝑡ℎ drone. [ ] (𝑑 − 𝑝 ) = × 𝜂, 𝑝 ≤ 𝑑 ≤ 𝑞 (10) (𝑞 − 𝑝 )

(6)

where  represents the normalized value of criticality and 𝑝 , 𝑞 represent the minimum and maximum value of criticality respectively. The minimum and maximum value of criticality can range from 0 to 1. Criticality 0 refers to the drone that is fully charged and criticality 1 refers to the drone with no balance energy.

𝛽𝑐𝑡

where is the charging constant and is the discharging constant for 𝑐th charging station at time t. In practical implementation simultaneous charging and discharging is avoided by (6). 5. Optimal drone scheduling

5.0.4. Price that drone is willing to pay The fourth information shared by the drone is the price that the drone is willing to pay in exchange for energy. The model allows the drones to offer dynamic prices within a set range to get a higher probability of getting charged earlier. Let 𝜌𝑑 represent the price offered by 𝑑th drone. [ ] (𝜌𝑑 − 𝜌𝑝 ) = × 𝜂, 𝜌𝑝 ≤ 𝜌𝑑 ≤ 𝜌𝑞 (11) (𝜌𝑞 − 𝜌𝑝 )

When the drones request the energy from the network, they have to provide a various parameter to become eligible for participation. The major parameters include the time-stamp of entrance into the network, Mileage of the drone, Criticality of the charge requirement, and the price that the drone is ready to pay for getting charged. In this section, we begin with normalizing all these parameters to bring them to the same range and to allot the best suitable charging station to each drone finally. Please note that to get appropriate normalized values of these parameters and to easily compare the values of these parameters, we use the normalization factor 𝜂 in the following equations. Now, the above-discussed parameters related to drones and their normalized values are discussed in detail.

where  represents the normalized value of price and 𝜌𝑝 , 𝜌𝑞 represent the minimum and maximum value of price, respectively. Price would always be greater than a fixed positive quantity set up by the network and will be within the range of energy charges set by the regulatory bodies in a particular area. The minimum price is referred to as the base price, and the price offered by drone should always be greater than the base price to allow the drone to participate in the charge scheduling algorithm. The price range in the network is taken to be [20, 50] cent in Singapore Dollar based on the actual energy prices in Singapore.

5.0.1. Time-stamp of entrance into the network As all the events or charging requests are recorded on the hashgraph and a consensus time-stamp is calculated. We fetch this consensus time-stamp value for each charging request from the hashgraph network. Once the corresponding information about time-stamp is fetched, the normalized value of time-stamp is calculated as follows. Let 𝜈𝑑 represent the consensus timestamp of 𝑑th drone. [ ] (𝜈𝑞 − 𝜈𝑑 ) = × 𝜂, 𝜈𝑝 ≤ 𝜈𝑑 ≤ 𝜈𝑞 (7) (𝜈𝑞 − 𝜈𝑝 )

𝜌 ≥ 𝜌𝑏

(12)

where 𝜌𝑏 represents the base price for per unit charge. Once we have the normalized values of time-stamp, mileage, criticality, and price, we can calculate the charging priority of drones with the help of the below-mentioned equation. The drone having the maximum value of priority will be allotted the charging station first, and so on. √ (13) 𝜆𝑑 =  2 +  2 +  2 + 2

where  represents the normalized value of timestamp. 𝜈𝑝 , 𝜈𝑞 represent the minimum and maximum value of timestamp respectively. As discussed above, the minimum value of timestamp will be the beginning timestamp of each time slot and its maximum value will be the ending timestamp of each time slot.

where 𝜆𝑑 represent the priority for the 𝑑th drone and , , ,  represent the normalized values of timestamp, mileage, criticality and price. The calculated priorities for each drone in the network are further used to assign charging time to each drone. Suppose 𝑖th drone win the auction with 𝜆𝑤 priority, so the winner would be assigned 1 h, and corresponding drones would be assigned time proportionate to the time allotted to the winner. 𝜆 𝜇𝑖 = 𝑖 , 𝑖 ∈ 𝐷 (14) 𝜆𝑤

5.0.2. Mileage of the drone The second information drone has to share is mileage, i.e., the distance traveled by the drone per unit charge. Please note that the value of the mileage that a particular drone provides is taken from the drone manufacturer. The model uses the value provided by the manufacturers to calculate the normalized value of mileage. The normalized value of mileage is calculated as follows. Let 𝑑 represent the Mileage of 𝑑th drone. [ ] (𝑞 − 𝑑 ) = × 𝜂, 𝑝 ≤ 𝑑 ≤ 𝑞 (8) (𝑞 − 𝑝 )

where 𝜆𝑤 is the priority value of the winner of auction, 𝜆𝑖 is the priority value of the 𝑖th drone and 𝜇𝑖 is allotted time for 𝑖th drone. The allotment of the charging station to the drones is done based on the possibility of the drone to reach the respective charging station. If the battery capacity of the drone is not enough to reach a particular charging station, then that charging station is not kept under algorithm consideration. The distance that the drones can travel depends on their current battery capacity and mileage. The following equation is used

where  represents the normalized value of mileage and 𝑝 , 𝑞 represent the minimum and maximum value of mileage respectively. The minimum and maximum values can be set based on the variety of drones available to participate in the network. For the purpose of simulation, the values of 𝑝 and 𝑞 assumed in this paper are [0.2, 3] m/mAh. 56

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Computer Communications 149 (2020) 51–61 Table 3 Distance matrix for 𝑐th charging station and 𝑑th drone.

Algorithm 1 Auctioning Algorithm among the Drones [ ] Input: Timestamp Vector  = 1 , 2 , … , 𝑑 from drones. ] [ Mileage Vector  = 1 , 2 , … , 𝑑 from drones. [ ] Criticality Vector  = 1 , 2 , … , 𝑑 from drones. [ ] Price Vector 𝜌 = 𝜌1 , 𝜌2 , … , 𝜌𝑑 from drones. [ ] Output: Priority Vector 𝜆 = 𝜆1 , 𝜆2 , … , 𝜆𝑑 for drones. 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24:

Charging stations

Drones

Normalize the Timestamp vector according to (7) Normalize the Mileage Vector according to (8) Normalize the Criticality Vector according to (10) Normalize the Price Vector according to (11) Compute priority according to (12) and store in previousPriorityVector 𝐾←0 repeat if 𝐾 ≠ 0 then previousPriorityVector← newPriorityVector end if 𝑥 ← arg max𝜆𝑑 , 𝑖, 𝑑 ∈ 𝐷 𝐾 ← 𝐾 + 1; for all 𝑖 ∈ 𝐷 do if i == x then continue; end if Update price according to (14) if 𝜌 (𝐾 + 1) > 𝜔𝑖 then Update price according to (15) end if end for Normalize the Updated Price Vector according to (11) Compute priority according to (12) and store in

⋯ ⋯ ⋯ ⋯

1𝑘 2𝑘 ⋯ 𝑖𝑘

where 𝛾 represent the normalized distance, 𝑑,𝑐 represent the distance of 𝑑th drone from 𝑐th charging station and 𝑝 , 𝑞 represent the minimum and maximum allowed distance of the drone from the charging station respectively. Algorithm 2 Algorithm for calculation of Energy Rate Input: Distance Matrix similar to Table 3 between the drones and charging stations. Output: Output Matrix similar to Table 4. for all 𝑖 ∈ 𝐷 do Calculate Possible Distance a drone can travel according to (17) and store the result in feasibleChargingStation matrix with the distance. Normalize the Distance according to (16) Initialize Energy Vector with base energy rate 𝑏 Normalize the Energy Vector according to (18) Compute priority according to (19) and store in previousPriorityVector 𝐿←0 repeat if 𝐿 ≠ 0 then previousPriorityVector← newPriorityVector end if 𝑦 = arg max𝜁𝑑,𝑐 , 𝑗, 𝑐 ∈ , 𝑑 ∈ 𝐷 𝐿 ← 𝐿 + 1; for all 𝑗 ∈ feasibleChargingStation do if j == y then continue; end if Update Energy according to (23) if  (𝐾 + 1) > 𝜉 then  (𝐾 + 1) ← 𝜉 end if end for Normalize the Updated Energy Vector according to (11) Compute priority according to (12) and store in

to calculate the set of charging stations that can be considered by a particular drone for getting charged. 𝑖∈𝐷

12 22 ⋯ 𝑖2

more preferred by the charging station. The charging stations would intuitively prefer to avoid idle hours as much as possible. ] [ (𝑞 − 𝑑,𝑐 ) × 𝜂, 𝑝 ≤ 𝑑,𝑐 ≤ 𝑞 (16) 𝛾= (𝑞 − 𝑝 )

25: newPriorityVector 26: until 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠𝑃 𝑟𝑖𝑜𝑟𝑖𝑡𝑦𝑉 𝑒𝑐𝑡𝑜𝑟 ≠ 𝑛𝑒𝑤𝑃 𝑟𝑖𝑜𝑟𝑖𝑡𝑦𝑉 𝑒𝑐𝑡𝑜𝑟

𝛷𝑖 = 𝑖 × 𝐵𝑖 ,

11 21 ⋯ 𝑖1

(15)

where 𝛷𝑖 represents the possible distance that the 𝑖th drone can travel to get charged and 𝑖 , 𝐵𝑖 represent the mileage and the current battery capacity of the 𝑖th drone. 6. Optimal charging station scheduling The proposed model not only considers the optimal scheduling for the drones but also considers the scheduling of the charging stations to maximize their revenue. The charging stations are also allowed to choose the drones that are ready to pay high, and that can allow the charging station to maintain minimum idle time. To achieve these goals, the charging stations are allowed to vary the rate at which they would sell the energy to the drones. The rate variation is allowed only within the regulatory range of a particular geographical zone. This Section discusses the parameters that the charging stations can set and their normalized values.

newPriorityVector until 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠𝑃 𝑟𝑖𝑜𝑟𝑖𝑡𝑦𝑉 𝑒𝑐𝑡𝑜𝑟 ≠ 𝑛𝑒𝑤𝑃 𝑟𝑖𝑜𝑟𝑖𝑡𝑦𝑉 𝑒𝑐𝑡𝑜𝑟 end for 6.0.2. Energy rate offered by charging station to drones In order to attract more drones during non-peak hours and to maximize the revenue during peak hours, the charging stations are allowed to offer different energy rates to the drones dynamically. As discussed above, the energy rates offered are within the regulated range of energy rate decided by the regulating authorities of the particular geographic zone. [ ] (𝑐 − 𝑝 ) 𝜓= × 𝜂, 𝑝 ≤ 𝑐 ≤ 𝑞 (17) (𝑞 − 𝑝 )

6.0.1. Distance of the drone from charging station The distance of the drone requesting to get charged from the charging station is a major point of consideration. First of all, the drones that cannot travel to a particular charging station with their available battery are eliminated from consideration based on the values entered in Table 3. Among the drones that are in the range of a charging station, the drones that are closer to a particular charging station are

where 𝜓 represent the normalized energy rate, 𝑐 represent the energy offered by 𝑐th charging station and 𝑝 , 𝑞 represent the minimum and 57

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Table 4 Output matrix for algorithm. Charging stations 𝐶ℎ𝑎𝑟𝑔𝑖𝑛𝑔 − 𝑆𝑡𝑎𝑡𝑖𝑜𝑛1 𝐶ℎ𝑎𝑟𝑔𝑖𝑛𝑔 − 𝑆𝑡𝑎𝑡𝑖𝑜𝑛2 ... 𝐶ℎ𝑎𝑟𝑔𝑖𝑛𝑔 − 𝑆𝑡𝑎𝑡𝑖𝑜𝑛𝑐

Drone d

𝐸𝑛𝑒𝑟𝑔𝑦 − 𝑅𝑎𝑡𝑒1 𝐸𝑛𝑒𝑟𝑔𝑦 − 𝑅𝑎𝑡𝑒2 ... 𝐸𝑛𝑒𝑟𝑔𝑦 − 𝑅𝑎𝑡𝑒𝑐

maximum rate of energy offered to the drones by the charging station respectively. For simulation purpose the values of 𝑝 and 𝑞 to attract drone are assumed as [4, 11] mAh per unit price respectively. Once we have the normalized values of distance and energy rate, the priority of the drone to select a particular charging station can be calculated as follows. √ (18) 𝜁𝑑,𝑐 = 𝛾 2 + 𝜓 2

Fig. 5. Variation of normalized value of charging time with iterations.

where 𝜁𝑑,𝑐 represent the priority given to 𝑐th charging station by 𝑑th drone. The charging stations can keep on changing the above-discussed parameters to increase their probability of being selected by drones.

price to attract more drones. Winner of auction between the charging station in each iteration is calculated as follows.

7. Double auctioning model

𝑦𝑐 = arg max𝜁𝑑,𝑐 ,

𝑗, 𝑐 ∈ ,

(22)

𝑑∈𝐷 𝑐 𝑡ℎ

where 𝑦𝑐 represent the index of winner corresponding to charging station. Once Winner is decided, the rest of bidder increase the energy per unit price, trying to attract the drones in the next iteration based on the following equation.

The proposed model allows both the drones and the charging stations to iteratively change the respective parameters to find out the best suitable options eventually. The drones can find out the bestsuited charging station at a minimum price, and charging stations can vary the prices offered to drones to maximize charging requests and revenue. In this Section, the iterative auctioning among the drones and the charging stations is discussed.

 (𝑘 + 1) =  (𝑘) + 𝑗,

Once the priorities for charging slot allocation and the winner for a particular round is announced by the network, each drone except winner gradually increases the price to win the auction eventually. The complete process of auctioning among the drones is shown in Algorithm 1. The winner in each round or iteration is calculated based on the following equation. 𝑖, 𝑑 ∈ 𝐷

8. Numerical analysis

(19) In this Section, simulation is conducted to show the performance and efficiency of the proposed algorithm for drone charge scheduling.

where 𝑥𝑖 represents index corresponding to winner. Ones the winner is decided, the rest of the drones are allowed to increase their price value. Each drone has its own fixed budget, which would be a value that is secret to the drone. The drones would eventually go on increasing the price value until they reach their secret budget and would stop increasing the value after that. Hence price update is controlled by the following constraint. 𝜌 (𝑘 + 1) = 𝜌 (𝑘) + 𝑗,

𝑗 ∈ {0, 1, 2, 3}

8.1. Simulation settings Consider a decentralized network use case consisting of multiple drones and charging station. For the evaluation purpose, we have considering the drone that has entered the network between 10:00 am to 11:00 am on 22nd June 2019. The battery limits of the drones while entering or leaving the network is assumed to be in the range of [2500, 6500] mAh. The corresponding mileage of the drones is considered to be in the range of [0.2, 3] m/mAh. The price range in the network is taken to be [20, 50] cent in Singapore Dollar based on the actual energy prices in Singapore. A set of 4 drones and 3 charging station is considered to carry out the experiments. In each iteration except the winner, all the rest participants are given equal chance to increase their bidding price. Once the point of saturation is reached, the next auctioning process start which is carried out among charging station to attract drone within the energy bounded by the network as [4, 11] mAh per unit price. At last, each drone is allocated to the appropriate charging station as calculated by the model. It is assumed that the charging stations can handle more than 1 drone at a single point, hence if multiple drones are assigned to a single charging station all can get charged simultaneously.

(20)

Restriction : if 𝜌 (𝑘 + 1) > 𝜔 then price is 𝜌 (𝑘 + 1) = 𝜔𝑖

(23)

The value of energy per unit price can go a maximum up to 𝜉, i.e., the maximum energy charging station can offer to the drones. The value of 𝜉 is kept confidential to each charging station and depends on the total amount of energy generated and distributed throughout the day by the charging station. The output of Algorithm 2 is represented by Table 4, where each row represents a drone. The columns represent the different energy rates provided by different charging stations to that particular drone. Different charging stations win the bid for different set of drones.

7.1. Auction among the drones

𝑥𝑖 = arg max𝜆𝑑 ,

𝑗 ∈ {0, 1, 2, 3}

(21)

where 𝜔𝑖 is fixed budget corresponding to 𝑖th drone. Eventually, all the drones reach their own true budget value and stop increasing the price after that. At this moment, the drone having the highest priority value is selected and is declared as the final winner, and the algorithm is terminated. 7.2. Auction among the charging station to attract drones Once charging time is allocated to drones, the next step is to perform auctioning among the charging stations to attract more drones. Charging stations iteratively try to increase the energy offered per unit 58

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Computer Communications 149 (2020) 51–61

Fig. 6. Variation of energy rate with iterations.

Fig. 8. Variation of prices with iterations. Fig. 7. Deviation between first and final price offered by the drones.

tie between the charging station 1 and charging station 3. Charging station 3 has won auction because priority of charging station 3, which was calculated earlier is highest among others. Lastly, for drone 4 in Fig. 6d charging station 1 again attracts the drone by offering energy of 8 units. As an improvement over the generic algorithms, we cater to the possibility of varying energy rates. The proposed model allows the charging stations to vary their energy rate to attract more drones. As the energy rate by a charging station increases more drones are attracted towards it. Fig. 7 shows the comparison of the prices offered by the drones in the proposed model and the normal first-price bidding algorithms. As the drones are greedy in nature and to save money, they will not quote the secret valuation in the first iteration; therefore, the first price bidding algorithm will not be efficient in this particular scenario. It can be observed that due to the iterative auctioning the drones are eventually bidding their true values, thereby enhancing the overall revenue of the charging stations. On the other hand, the charging stations are also charging based on the market competition, thereby enhancing the quality of experience for the drones. Fig. 8 illustrates the variation of the price for four different drones which are increasing the price over each iteration to be announced

8.2. Performance evaluation Fig. 5 shows the efficiency of iterative auction mechanism in terms of efficiently assigning the time for each drone. It can be seen that as the iterations are progressing the normalized time for each drone is also changing. Moreover, the normalized time is relative, i.e., time does not depend only on single drone change in the parameters, but also depends on the change in the parameter of the other drones as well. As compared to the traditional allocation algorithms, where the allocation is done based on the first input, the proposed model shows an improved assignment strategy. Fig. 6 Illustrates the efforts made by charging station to attract the drones in their vicinity by offering the maximum energy. For drone 1 in Fig. 6a it can be seen all the charging station are increasing the energy to attract drone 1 but charging station 1 win over other by offering energy of 8 units. Similarly, in case of Drone 2 in Fig. 6b charging station 3 is not in the vicinity of drone 2 hence not participating in the auction and charging station 1 wins the auction by offering 8 unit energy to drone 2. In the case of drone 3 in Fig. 6c there is a 59

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Computer Communications 149 (2020) 51–61

Fig. 9. Deviation between first energy rate and final energy rate.

as the winner. Drones cannot increase the price beyond their budget which is kept secret. It can be observed that most of the drones are giving a low price in the initial iterations and are gradually increasing the prices to win the auction. Drone 3 stops increasing the price after iteration three due to attaining the secret valuation point. Auctioning model is not biassed towards any particular parameter of algorithm; hence, the winner is declared based on the cumulative result of all the above-discussed parameters. It is important to consider that in the auction mechanism, initially, all the parties tend to win the auction at the lowest possible bid. Therefore the iterative auction model proposed in this paper tends to bring the drones closer to their true budget value. Fig. 9 shows the difference between the first energy and final energy offered by the charging station. Due to our auctioning model, the benefit of each drone has increased as they are now being offered energy greater than five mAh per unit price. To attract Drone 1, it is shown in Fig. 9a that all charging station increase per unit energy price. In case of Drone 3 Fig. 9c shows both charging station 1 and 3 have increased up to 7 units to attract the drone, but due to other factors mentioned above charging station 3 has won the auctioning process. For Drone 4 Fig. 9d shows each charging station has increase per unit energy price as per their capacity but again charging station 1 has won the auction by offering 8 units of energy.

the profit of the charging stations and the drones. The drone and charging station allocation is done based on the cumulative outcome of multiple parameters and not only based on the price. The simulation results prove the proposed algorithm to maximize the profit of both the nodes of the network, i.e., drones and charging station compared to its counterparts. 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. Acknowledgments We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan Xp and Quadro GPU used for this research. We also thank Akash Goel for his support in the completion of the project as an intern at BITS, Pilani. References [1] Z.R. Bogdanowicz, Flying swarm of drones over circulant digraph, IEEE Trans. Aerosp. Electron. Syst. 53 (6) (2017) 2662–2670. [2] P.W. Khan, G. Xu, M.A. Latif, K. Abbas, A. Yasin, Uav’s agricultural image segmentation predicated by clifford geometric algebra, IEEE Access 7 (2019) 38442–38450. [3] M. Erdelj, E. Natalizio, K.R. Chowdhury, I.F. Akyildiz, Help from the sky: Leveraging uavs for disaster management, IEEE Pervasive Comput. 16 (1) (2017) 24–32. [4] X. Liu, N. Ansari, Resource allocation in uav-assisted m2m communications for disaster rescue, IEEE Wirel. Commun. Lett. (2018). [5] Amazon prime AIR, https://www.amazon.com/Amazon-Prime-Air/b?ie=UTF8& node=8037720011, online; accessed 01 2019.

9. Conclusion In this paper, we have proposed an iterative auction based algorithm for optimal charge scheduling among drones. Hashgraph consensus algorithm is used to calculate the consensus time-stamp for the charging request by the drones. The task deadline and the criticality of the task is also considered to schedule the drone along with the arrival timestamp. The double auctioning mechanism is used to simultaneously increase 60

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Vikas Hassija is currently an Assistant Professor at Jaypee Institute of technology and science, Noida. He received his B.tech degree from M.D.U University, Rohtak, India, 2010 and M.S. degree in Telecommunications and Software engineering from Birla Institute of Technology and Science (BITS), Pilani, India in 2014. He is currently pursuing Ph.D. from Jaypee in IoT security and blockchain. He had been working in telecommunication industry since 2011 with Tech Mahindra, India and has worked closely with various mobile network deployments. His research interests include IoT security, Network security, Blockchain and distributed computing.

Vikas Saxena is currently Professor at Jaypee Institute of Information and Technology, Noida, India. He received his B.tech degree IET, MJP Rohilkhand university, Breilly, india in 2000, the M.E degree from VJTI, Mumbai, India, in 2002, and the Ph.D. degree in CSE from Jaypee Institute of Information and Technology, in 2009. His research interests include image processing, blockchain, computer vision‘ and multimedia. Dr. Vikas served as Publicity Co-Chair in the International Conference IC3-2008, India conducted by JIITU and University of Florida, USA.

Vinay Chamola received the B.E. degree in electrical and electronics engineering and master’s degree in communication engineering from the Birla Institute of Technology and Science, Pilani, India, in 2010 and 2013, respectively, and the Ph.D. degree in electrical and computer engineering from the National University of Singapore, Singapore, in 2016. In 2015, he was a Visiting Researcher with the Autonomous Networks Research Group, University of Southern California, USA. He is currently an Assistant Professor in the Department of Electrical and Electronics Engineering, BITS-Pilani, Pilani Campus. His research interests include solar powered cellular networks, energy efficiency in cellular networks, internet of things, and networking issues in cyber–physical systems.

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