A Game-Theoretic Drone-as-a-Service Composition for Delivery
AA Game-Theoretic Drone-as-a-Service Composition for Delivery
Babar Shahzaad ∗ , Athman Bouguettaya ∗ , Sajib Mistry †∗ School of Computer Science, The University of Sydney, Australia { babar.shahzaad, athman.bouguettaya } @sydney.edu.au † School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, [email protected]
Abstract —We propose a novel game-theoretic approach fordrone service composition considering recharging constraints.We design a non-cooperative game model for drone services.We propose a non-cooperative game algorithm for the selectionand composition of optimal drone services. We conduct severalexperiments on a real drone dataset to demonstrate theefficiency of our proposed approach.
Keywords -DaaS, Service selection, Service composition,Game-theory, Non-cooperative game, Recharging
I. I
NTRODUCTION
A drone is an aircraft that can fly with no pilot onboard.Drones offer a myriad of new potential applications inseveral domains including agriculture, geographic mapping,healthcare, shipping, and shopping [1]. Drones provide a va-riety of services such as inspection , sensing , and delivery [2].Amazon and other large corporations are making efforts tocommercially use drones for delivery. Drones provide faster and cost-effective delivery services [3]. Delivery dronesdiffer from ground vehicles which are constrained by roadinfrastructure and traffic congestion.The service paradigm [4] provides an elegant mechanismto abstract the functional and non-functional or Quality ofService (QoS) properties of a drone termed as
Drone-as-a-Service (DaaS) [5]. The functional property represents thedelivery of packages in a skyway network. The skywaynetwork is made up of a set of line segments of whichendpoints are nodes of the network. The nodes in theskyway network are the rooftops of high-rise buildings.The nodes are assumed to be delivery targets or rechargingstations . The non-functional properties represent the qualityparameters that distinguish between functionally equivalentdrone services, i.e., flight range, speed, payload, and batterycapacity.The practical utilization of drones for delivery is restrictedby a number of intrinsic and extrinsic factors [6]. The in-trinsic factors include limited battery capacity , limited flightrange , and constrained payload of a drone. The extrinsicfactors are related to the drone service environment such as a highly dynamic operating environment and constraints onrecharging pads at each station. The maximum flight rangeof a delivery drone with full payload weight varies from 3to 33 km [7]. The battery capacity, speed, payload weight, and weather conditions influence the flight range of a drone [8]. The drones may need multiple times of recharging tocover long-distance areas.The drone delivery problem is defined as the time-optimaldelivery of packages from a source to a destination in askyway network. Using the service paradigm, we reformu-late the drone delivery problem as finding an optimal set ofdrone services from a given source (e.g., warehouse rooftop)to a destination (e.g., recipients landing pad). Therefore, thetarget is the selection and composition of the best servicesto minimize the delivery time. DaaS composition is theprocess of selection of the best services that make up askyway path from source to destination. The compositionis constrained by drone payload, range, and availability ofrecharging stations. We assume that no handover of packagestakes place among different drones at intermediate stationsas this would be more realistic.To the best of our knowledge, existing approaches mainlyfocus on routing and scheduling of drones by formulatingthe problem as Travelling Salesman Problem (TSP) [9] andVehicle Routing Problem (VRP) [10]. Most of the studiessolve the TSP and VRP problems for a combination ofground vehicles and drones [11]. In contrast, we focus on theDaaS composition in a dynamic multi-drone environment ,i.e., several drone services operating in the same skywaynetwork. Each drone service has its own delivery plan. Thedrone services act independently and selfishly as they areonly interested in minimizing their own delivery time. There-fore, the drone services may impact each other’s compositionas they share the same network and compete for limitedrecharging pads which leads to congestion. We propose a game-theoretic approach for the selectionand composition of optimal DaaS services . An optimalDaaS service avoids congestion at intermediate stations. Thecomposition will take into account two main constraints: (1)the availability of recharging pads at the recharging stationsand (2) the influence of a drone’s choice of recharging onother drones. It is assumed that the intrinsic features ofeach drone service are deterministic , i.e., the payload, speed,flight range, and battery capacity of each drone are known apriori. In contrast, the extrinsic features such as the serviceenvironment are stochastic , i.e., the availability of rechargingpads is not guaranteed.We predict the availability of recharging pads by con- a r X i v : . [ c s . N I] A ug idering all drone services approaching and leaving certainrecharging stations during a specific time interval. We repeatthe process for all stations within the range of a selecteddrone service. This process continues until the delivery ofthe package to the destination. We summarize the maincontributions of this paper as follows: • A non-cooperative game model for drone services. • A new non-cooperative game algorithm for the selec-tion and composition of drone services. • An evaluation using a real-world dataset to demonstratethe effectiveness of the proposed approach.II. R
ELATED W ORK
Several studies address the routing and scheduling prob-lems for drone delivery services. Most of the existingresearch work focuses on using drones in conjunction withground vehicles for last-mile delivery. A hybrid frameworkfor a traditional delivery truck and a companion drone wasfirst studied in [12]. Two new approaches are proposed toaddress the operational challenges associated with drone-assisted parcel delivery. In one of two approaches, a truckacts as a mobile depot for a drone to make deliveries tocustomers along its route. The drone departs from and landsback on the truck after making a delivery. In the secondapproach, the drone and the truck make deliveries separately.The customers that are close enough to the warehouse areserved directly from the warehouse using drones. The truckmakes deliveries to the customers who are not within themaximum range of the drone. The proposed approaches usea truck to make deliveries which is not suitable for remoteareas where there is no road infrastructure.
The proposedapproaches do not consider the recharging constraints toserve long-distance areas.
A spatio-temporal service model is proposed for droneservices in [5]. The drone services are selected and com-posed considering QoS properties. The proposed model doesnot take into account the battery capacities of drones andrecharging constraints at stations. The proposed model isextended in [8] by taking into account the recharging con-straints. A deterministic lookahead heuristic-based algorithmis developed to solve the proposed problem. However, thedynamic service environment, the effects of stochastic arrivalof drone services on other drones, and the competition ofservices for the recharging pads are not considered in theproposed approach.Game-theoretical approaches have been applied to modeland analyze competing services in various areas of servicecomputing [13]. A non-cooperative game model is proposedto solve QoS-aware service selection and composition prob-lem in [14]. The game depicts a competitive relationship be-tween concurrent tasks for multiple users. An iterative algo-rithm is proposed to obtain Nash equilibrium for maximizingthe utility of each user by selecting a suitable service. The computational complexity for the iteration process is veryhigh which limits the potential of the proposed approach.A non-cooperative game is proposed to solve the recharg-ing assignment problem of multiple robots to recharging sta-tions in [15]. An allocation algorithm is proposed to achievethe pure strategy Nash equilibrium. Multirobot rechargingstrategies are presented based on the proposed algorithmto reduce the total cost with mobile recharging stations.The efficiency of the strategies is evaluated by using theconcept of the price of anarchy. The proposed approach doesnot consider dynamic congestion conditions at rechargingstations.
To our knowledge, this paper is the first attemptto model the drone delivery problem as a non-cooperativegame considering the congestion conditions at rechargingstations .III. N ON -C OOPERATIVE G AME M ODEL FOR D RONE S ERVICES
A. Problem Statement
We model the drone service selection and compositionproblem as a non-cooperative game problem. Let P = { p , p , . . . , p n } be a finite set of n players, each corre-sponding to a drone. Each player is selfish and rationaland tries to maximize its own payoff which depends onits strategy (in this case is the service selection). Eachselected service leads to a recharging station or a deliverytarget. We assume that each player knows the locationinformation of other players without explicit communication.Let R = { r , r , . . . , r m } be a finite set of m resources(in this case are the recharging stations located in thenetwork, each having a finite set of recharging pads). Weassume that the recharging stations are stationary and theirpositions are known to the players. Each player makes adecision of recharging station selection in a non-cooperativesetting. Let t p i jk be the travelling time of a player p i fromthe recharging station r j to r k (i.e., there exists a skywaysegment drone service from r j to r k ). Let rt p i k and wt p i k denote the recharging and waiting times of a player p i at the recharging station k . As the game observes FCFS property, therefore the waiting time wt of any player mayvary depending on the recharging station selection by otherplayers. We define the payoff (i.e., total time) T pik of a player p i for selecting a recharging station k as follows. T pik = t p i jk + rt p i k + wt p i k ( j, k ∈ N, p i ∈ P ) The objective is to find an optimal set of payoffs for aplayer p i from a source to a destination, defined as follows. T pi = min u (cid:88) k =1 T pik ( u ∈ N, p i ∈ P ) where u represents the total number of recharging stationswhere a player competes for resources and T pi denotes thesum of payoffs of player p i . . Non-Cooperative Game with Complete Information A non-cooperative game with complete information(NCG-CI) is used to solve the scheduling problems [16].We use NCG-CI as the baseline approach to finding anoptimal DaaS composition plan. In this approach, there isno uncertainty involved during the composition process, i.e.,the actual information about the arrival of drone servicesis known beforehand. The NCG-CI computes all possiblecompositions of drone services taking into account the actualarrival time of other drone services. We select an optimalDaaS composition considering the best QoS in terms ofdelivery time. Finding and evaluating all possible DaaScompositions in the baseline approach is computationallyexpensive which reduces its performance significantly.
C. Drone Service Selection Game Model
We model the drone service selection game as follows.Each player can select any service leading to the rechargingstations in its range within the skyway network. The servicesand recharging stations are assumed to have a one-to-onecorrespondence. If M out of total m recharging stations arein the range of the player p i , then player p i has M possiblestrategies. Each strategy has a distinct payoff. Each playerselects an optimal delivery service. An optimal deliveryservice leads to the destination faster by minimizing thetravel, waiting, and recharging times of a drone.The proposed non-cooperative game model has someflavour of a sequential game. The players’ decisions aremade sequentially which may influence the payoffs. Theplayers have information about the service selections ofprevious players but their arrival times are not guaranteed.The service selection of a new player may potentiallyinfluence the previous players. As a result, the decisionsmade previously may be invalidated by future changes. Theproposed game is not a pure sequential game because thestrategy (i.e., selection decision) of one player may causemultiple players to change their strategies.In general, the optimal service selection and compositionin a resource-constrained environment is an NP-hard prob-lem [17]. We define some reasonable assumptions to solvethe problem in polynomial time. We assume that a desiredplayer p i has the following information about rechargingstations in its range for decision-making at a particularstation. Statically, the desired player p i is given that (1) Howmany drones are being recharged at each particular station,(2) How long each drone still needs to get recharged, (3)How many other drones are waiting to be recharged, and(4) How many drones are expected to reach each particularstation.IV. S OLUTION A LGORITHM FOR N ON -C OOPERATIVE G AME
In a non-cooperative game, the objective of each playeris simply to maximize its reward. The players present
DaaS Source DaaS Destination Node
Node ConnectionNodes in Range
Range of Competing Players
Figure 1. Local skyway network for reducing search space myopic behaviour to minimize the total delivery time, i.e.,each player makes a greedy decision based on the currentinformation. The greedy approach may not provide the bestoutcome due to the congestion at certain nodes and the lackof real-time communication with other players.We present a prediction-based non-cooperative game(NCG-PB) theory approach to deal with the congestion atcertain nodes. Most of the existing approaches focus onfinding the shortest path to the destination. The travel timefor the shortest path may not guarantee the overall shortesttime to the destination due to the congestion conditions atintermediate recharging stations. We, therefore, consider thesummation of the shortest travel time, waiting time, andrecharging time to select a particular service.The search space becomes huge if we compute strategiesfor all players in the skyway network. The desired player canreach a limited number of recharging stations. We reducethe search space by only considering players that can arriveat stations in the range of the desired player, termed aslocal skyway network. For example, a desired player p i can reach a recharging station r j at 10:00 am. We consideronly those players that are expected to reach the station r j between 09:50 am to 10:10 am. We assume this threshold toincorporate the variations in arrival times of other players.Fig. 1 illustrates the local skyway network for reducingsearch space. A. Algorithm
We present a new non-cooperative game algorithm fordrone service selection. The service selection at eachrecharging station leads to the composition of drone servicesfrom source to destination. The details of the proposedalgorithm are presented in Algorithm 1. In Algorithm 1, theoutput is a composition delivery plan from a given sourceto a destination. It takes as input a skyway network givenby Graph G , the source src , the destination dst , a set ofresources (recharging stations) R , a set of players P , theweight of package w , the time window tw for choosingthe competing players. We create empty lists for the outputcomposition plan Comp , the total delivery time
T ime , andthe recharging stations in the range of the desired player lgorithm 1
Non-Cooperative Game Algorithm
Input: G , src , dst , R , P , w , tw Output:
Comp Comp ← φ T ime ← φ St range ← φ p i ← P [ i ] curLoc ← src St range ← get stations in range of player p i from curLoc while St range is not empty do if dst is in St range then compute T ime to dst from curLoc DaaS ← a segment from curLoc to dst Comp .append (
DaaS ) return Comp else get list of scheduled players from P at each st in St range in time tw compute travel, wait, and recharge times to each st from curLoc compute distance to dst from each st select st with minimum T ime from curLoc and time to dst
DaaS ← a segment from curLoc to st Comp .append(
DaaS ) curLoc ← st select St range from curLoc end if end while St range (Lines 1-3). We choose a player p i from a given setof players P in the skyway network (Line 4). We assumethat the following attributes for each player in P are given:the speed, the flight range, and the recharging time. Weget all stations in the range of player p i depending on thepackage weight w (Line 6). If the player p i can reach thedestination without requiring recharging, then there is nocompetition with other players. It directly moves from sourceto destination, returning a segment from the given source todestination (Lines 8-12). If the player p i requires rechargingto reach the destination, we compute the competing playersand their scheduled arrival times schedP ls at each stationin the range of player p i . We consider only players arrivingat any particular station of player p i within a certain timewindow tw (Line 14). The travel time, waiting time, andrecharging time are computed for each station in the rangeof player p i (Line 15). We compute the distances from allthe nearby stations to the given destination dst of player p i (Line 16). We select an adjacent station from the currentlocation of player p i which takes the overall shortest traveltime (Line 17). On each iteration, we simply add the selectedskyway segment service to the composition plan Comp (Lines 18-19). We update the current location and thensearch for the nearby recharging stations of the player p i which in turn updates its neighbour services (Lines 20-21).This process continues till the destination node is discoveredor nearby stations list is empty (i.e., no service compositionplan found). Table IE
XPERIMENT V ARIABLES
Simulation Parameter ValueDrone name DJI M200 V2Payload 1.45 KgFlight time 24 minFlight range 32.4 kmMax speed 81 km/hRecharging time 60 minBattery capacity 4280 mAhNumber of nodes 300Experiment run (% times the total nodes) 50
V. E
XPERIMENTS AND R ESULTS
We perform several experiments to investigate the perfor-mance of the proposed game-theoretic approach. We com-pare the proposed prediction-based non-cooperative game(NCG-PB) theory approach with a non-cooperative gamewith complete information (NCG-CI) [16] approach. Wefocus on the run-time complexity and average delivery timefor evaluating the proposed solution approach.
A. Experimental Settings
In this section, we explain the setup of the simulationenvironment. We use NetworkX python library to build thetopology of the skyway network. We model the deliverydrones operating in the skyway network. We evaluate theproposed NCG-PB approach using a real drone dataset[18]. The dataset contains the trajectories of drones, whichinclude data for coordinates, altitude, and timestamps. TableI summarizes the simulation parameters and values. Weconduct experiments for an average of 50 percent times thetotal nodes. For example, an experiment is performed 50times for 100 nodes. Each experiment starts with a randomsource and a destination point.
B. Results and Discussion
The proposed game-theoretic approach performs the com-position of selective drone services considering the con-gestion conditions at intermediate recharging stations. Thetarget is to reach the destination faster.
1) Run-time Complexity:
The run-time complexity of theNCG-CI approach is very high compared to our proposedNCG-PB approach. The computation time increases due tothe increasing number of possible compositions for droneservices. The difference in run-time complexity for NCG-CIand NCG-PB approaches is shown in Fig. 2. As expected,the average computation time for the increasing number ofnodes is much higher for the NCG-CI approach than ourproposed approach. It is impractical to use the baselineapproach in real-world scenarios as it is exhausted for largescale problems.
2) Average Delivery Time:
The delivery time is highlyuncertain for composite drone services. The competingdrone services can occupy recharging pads for long timeperiods. The delivery time includes the flight time, waiting
Avg. Computation Time (ms)
N u m b e r o f N o d e s
N C G - C I
N C G - P B
Figure 2. Average computation time
Avg. Delivery Time (min)
N u m b e r o f N o d e s
N C G - P B
N C G - C I
Figure 3. Average delivery time time, and recharging time at each station. The selection of a right drone service guarantees the availability of rechargingpads ahead of time which minimizes the overall deliverytime. Fig. 3 shows the efficiency of the proposed NCG-PB approach compared to NCG-CI baseline approach. TheNCG-CI approach provides the exact solution as it findsall possible compositions. Our proposed NCG-PB approachprovides computationally fast and near-optimal solutions fordelivering the packages compared to the NCG-CI approach.VI. C
ONCLUSION
We propose a game-theoretic approach for drone servicecomposition considering recharging constraints. The pro-posed NCG-PB algorithm significantly reduces the searchspace of candidate drone service compositions. It enablesa fast online composition plan which is essential for time-constrained drone-based delivery requirements. Experimen-tal results illustrate that the proposed approach producesnear-optimal DaaS compositions compared to the NCG-CIbaseline approach. In future, we plan to consider handoversat intermediate stations and uncertain wind effects on thebattery consumption of drones. A
CKNOWLEDGMENT
This research was partly made possible by DP160103595and LE180100158 grants from the Australian ResearchCouncil. The statements made herein are solely the respon-sibility of the authors. R
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