A Computation Offloading Model over Collaborative Cloud-Edge Networks with Optimal Transport Theory
AA Computation Offloading Model overCollaborative Cloud-Edge Networks with OptimalTransport Theory
Zhuo Li , Xu Zhou , Yang Liu , Congshan Fan , Wei Wang Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China University of Chinese Academy of Sciences, Beijing 100049, China School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China Knet Technologies Co. Ltd., Beijing 100190, China { lizhuo, zhouxu, fcs, wangwei } @cnic.cn, [email protected] Abstract —As novel applications spring up in future networkscenarios, the requirements on network service capabilities fordifferentiated services or burst services are diverse. Aiming at theresearch of collaborative computing and resource allocation inedge scenarios, migrating computing tasks to the edge and cloudfor computing requires a comprehensive consideration of energyconsumption, bandwidth, and delay. Our paper proposes a col-laboration mechanism based on computation offloading, which isflexible and customizable to meet the diversified requirements ofdifferentiated networks. This mechanism handles the terminal’sdifferentiated computing tasks by establishing a collaborativecomputation offloading model between the cloud server and edgeserver. Experiments show that our method has more significantimprovements over regular optimization algorithms, includingreducing the execution time of computing tasks, improving theutilization of server resources, and decreasing the terminal’senergy consumption.
Index Terms —computation offloading, computational optimaltransport, cloud computing, edge computing
I. I
NTRODUCTION
Technological innovation represented by the 5th generationof communication (5G) and Artificial Intelligence (AI) hasbrought about the booming of emerging industries, includingthe Industrial Internet of Things (IIoT), Internet of Vehicles(IoV), and AR/VR. Starting from the traditional PC eradominated by stand-alone applications, the Internet has enteredthe era of mobile web, and it is about to face the era of theInternet of Everything (IoE) [1].With the widespread use of the terminal, mobile data thatneeds to be processed has exploded, while the computingpower, memory scale, and battery capacity of the terminal areminimal. Cloud computing brought about by the developmentof wireless communication technologies such as 3G, 4G, andWi-Fi effectively solves the above challenges by plentifulcomputing resources and more substantial computing capacity.Computation offloading through offloading computationallyintensive tasks to the cloud data center to improve the uti-lization of cloud server resources and reduce the energyconsumption of the terminal [2]. However, the emergenceof new edge applications such as telemedicine, autonomous driving, unmanned aerial vehicle (UAV), and other delay-sensitive tasks put forward higher demands on the responsedelay in the service [3]. With the trend of network servicesmigrating to the edge, edge computing emerges as a criticaltechnology of the 5G network architecture. It satisfies thethree characteristics of high-speed, large-capacity, and low-latency of the 5G network, and distributes resources to provideservices of computing, communication, control, and storage onthe user side or nearby edge devices and systems [4].Because of the mode of cloud computation offloading(CCO) is extended to the edge network, edge computationoffloading (ECO) reduces the significant transmission delayand energy consumption caused by offloading tasks to remotecloud data centers [2], [5]. Existing offloading strategies focuson using cloud computing or edge computing to offloadtasks without considering collaboration between them, whoseoptimization goal is restricted by terminal equipment, energyconsumption, or response delay. With the rapid development ofbattery storage technology, the impact of energy consumptionis gradually decreasing, whereas computing power is playingan increasingly important role in processing tasks.Therefore, the research goal of this paper is to introducethe collaboration between cloud computing and edge com-puting, establish a computation offloading model, and per-form different offloading tasks in combination with offloadingrequirements and the use of server resources. The primarycontributions of this paper are: • We proposed a computation model offloading over a col-laborative cloud-edge network, which takes full accountof offloading requirements and server resource utilization. • We creatively introduced the classic transmission op-timization problem into the design of the offloadingstrategy. The convex optimization problem can get aunique and optimal solution. • We analyzed the system’s total energy consumption, thesuccess rate of offloading, and the server resource usagewhen using the collaborative offloading strategy.We organize the rest of the paper as follows. In the next a r X i v : . [ c s . N I] F e b ection, we review background and related works on cloudcomputing and edge computing and computation offloading.Section III and IV present the system model of computationoffloading and the major algorithms used in the collaborativesystem. It conducts evaluation and analysis of algorithms inSection V, and we conclude the paper in Section VI.II. R ELATED W ORKS
This section provides details of the current work in the cloudand edge computing and computation offloading.
A. Cloud Computing and Edge Computing
Because of the terminal limitations in computation andstorage resources, many applications have reduced the qualityof users’ experience, while cloud computing in a mobileenvironment can provide enhanced computation capabilitiesand reduce computing latency [6]. Cloud computing adoptsthe migration of computing-intensive applications such asvideo and games to a cloud server to solve the problem ofinsufficient device resources and provides many advantagesfor mobile devices by migrating the computation and storagerequirements of tasks from restricted terminal to the free cloudserver. Although many instances under cloud computing canimprove execution speed and reduce the energy consumptionof devices, cloud computing also brings immense latencyproblems that latency-sensitive applications cannot execute.The authors in [7] proposed edge computing and defined itas a model for performing calculations on the network, whereedge refers to any computing and network resource from theterminal to the cloud data center. Therefore, edge computingcan significantly reduce latency and jitter when compared tocloud computing. Table I summarizes the characteristics ofcloud and edge computing in different indicators. Resourcesnear the terminal can no longer be limited by resources whencomputing tasks while using edge computing alone cannotadequately meet users’ massive offloading requests. Edgecomputing should not wholly replace cloud computing, andthe two should complement each other to meet the offloadingrequests of computing tasks better.
B. Computation Offloading
Computation offloading is a technology of assigning asizeable amount of computation to a computation node withsufficient resources for processing and then retrieving thecomputing results from the computation node. As one of thecritical technologies of edge computing, computation offload-ing is mainly divided into offloading decision and resourceallocation. Researchers focus on whether to offload tasks, howmany tasks will offload, and where to offload tasks from theperspective of the offloading decision. From the perspective ofresource allocation, communication and computing resourceswill be allocated after the offloading decision is completed,which needs to consider the transmission delay and terminals’energy consumption caused by task offloading.Aiming at the problem of multi-user computation offload-ing, the authors in [8] formulated the dynamic optimization
TABLE IC
OMPARISON OF C LOUD C OMPUTING AND E DGE C OMPUTING
Indicators Cloud computing Edge computing
Deployment Centralized DistributedServer location Cloud center Edge networkComputing capacity Unlimited RestrictedStorage capacity Unlimited RestrictedNetwork access Wired connections Wireless connectionsProcessing delay Higher LowerDistance Remote NearbyScenario Compute-intensive Latency-intensive problem into an infinite-horizon average-reward continuous-time Markov decision process (CTMDP) model. They pro-posed a joint computation offloading and multi-user schedulingalgorithm that minimizes the long-term average weightedsum of delay and power consumption under stochastic trafficarrival. Kuang et al. [9] studied the problem of multi-usercomputation offloading and divided mobile users into activeand inactive categories. The dynamic offloading decisionprocess of mobile users was regarded as a random game,and an effective multi-agent random learning algorithm wasproposed based on this. However, the above two algorithmsonly consider the edge server’s computing resources and donot pay attention to the more substantial cloud data center.In terms of centralized cloud computation offloading, Guo etal. [10] proposed a location-aware offloading scheme in a two-layer cloud environment. The cloud environment includes edgeservers and a centralized cloud server. It is necessary to choosean offloading strategy for mobile devices that can guaranteethe quality of service and save the energy consumption ofthe equipment, and define it as a constrained optimizationproblem, and minimize the total energy consumption of allmobile devices as the optimization goal, as giving a centralizedapproximate algorithm and distributed collaborative algorithm.Most of the documents, as mentioned above, aim at min-imizing the energy consumption of mobile devices. It onlygives the processing time of computing tasks a threshold. Fewdocuments individually optimize it, but the processing time ofcomputing tasks is a vital indicator of assessing the Qualityof Service (QoS), especially for differentiated services andunexpected services. This article considers the importance oftask processing time and minimizes the total processing timeof all computing tasks as the optimization goal.III. S
YSTEM M ODEL AND P ROBLEM F ORMULATION
We consider an offloading system over collaborative cloud-edge networks, whose model is shown in Fig. 1. The remotecloud server is connected to the base station that provideswireless access points in cellular networks through a wiredconnection. At the same time, numerous edge servers aredeployed near the base stations. When the terminal generates acontinuous stream of computation tasks and can compute somesimple or necessary tasks that cannot be offloading accordingto its own capabilities, the remote cloud servers and edgeservers allocate their own resources to process computing tasksased on the collected offloading requirements from multipleterminal.
Cloud server
Edge serverTask Base Station Edge computingCloud computing Offloading
Core Network ②① ② ③ ③ Computing ResultsData Uploading ④ Fig. 1. Offloading model over collaborative cloud-edge networks.
A. Communication Model
The edge base station for wireless access can be a wirelessnetwork access point or a base station in a cellular network,which can be used to manage the mobile device’s upload ordownload communication link. Let S n = { , } denote theoffloading decision of mobile user, S n = 0 indicates thatmobile user chooses to offload tasks to the edge server througha wireless channel, and S n = 1 indicates that mobile usern chooses cloud server to offload tasks [11]. Given that thedecision set a = { a , a , a , · · · , a N } of all users, N is thenumber of users. According to Shannon’s law, the transmissiondata rate R of mobile user can be calculated as: R = W log (1 + P n H n ω n + (cid:80) Nm =1 P m H m ) , (1)among them, W is the channel bandwidth, P i ( i = m, n ) is the transmission powers, H m and Y m are the channelgains between the mobile device users n and m and thebase station respectively, and ω is the background interfer-ence power consumption, including noise power consumption ω n = ω n + ω n and the interference power consumption ofwireless transmission from other mobile devices ω n . It can beseen from the above formula (1) that if multiple mobile devicessimultaneously perform calculation and offloading through thewireless access channel, serious interference and a decrease indata transmission rate will result.According to the communication model, the offloadingdecisions among mobile users are interrelated. If too manymobile users simultaneously offload tasks to the cloud throughwireless channel computing, it will inevitably lead to low datatransmission rates. When mobile users’ data rate is lower, thebackhaul link will bring higher energy consumption and longertransmission time when offloading tasks. It is more helpful in computing tasks on edge servers, which can avoid the longtransmission delay of cloud computing. B. Computation Model
For the computing tasks generated by the terminal equip-ment, the network requirements are the amount of calculation M i , the required CPU clock cycle C i and the maximumallowable delay D i , and the maximum allowable energyconsumption E i . T ask i = { M i , C i , D i , E i } . (2)The computing model can divide into local computing, edgecomputing, and cloud computing, the computation capabili-ties of mobile devices, edge servers, and cloud services are CA locali , CA meci , and CA mcci respectively [10], and energyconsumption and transmission power of mobile device is CP i and T P i . a) Local Computing: In local computing, the processingtime and energy consumption calculated locally are T locali and E locali . T locali = C i CA locali , (3) E locali = CP i × T locali . (4) b) Edge Computing: In edge computing, the terminal’scomputing task is offloaded to the edge server near the basestation, increasing the wireless channel transmission time ofthe task offloading from the terminal to the edge server. Theprocessing time and energy consumption are T meci and E meci . T meci = C i CA meci + M i R , (5) E meci = T P i × T meci . (6) c) Cloud Computing: In cloud computing, the computingtasks of the terminal are offloaded to a remote cloud datacenter, and usually have sufficient computing resources tohandle the terminal’s computing tasks. The upload time ofdata from the base station to the cloud data center is theuplink transmission delay t uplinki , and cloud computing timeand energy consumption are T mcci and E mcci . T mcci = C i CA mcci + M i R × N + t uplinki , (7) E mcci = T P i × T mcci . (8)The computing time and energy consumption generated bythe edge computing model and cloud computing model as thebasis for offloading are combined with the computing amountof each task. The maximum tolerable delay, the required num-ber of clock cycles and the maximum energy consumption aretolerated for each task. The calculation model is classified, andthe calculation method of the task classification’s comparisonweight ∆ is as follows: ∆ = γ × T mec,mcci + (1 − γ ) × E mec,mcci , (9)here γ is the weight value of delay energy consumption,representing the weight value of the several variables in theunloading decision index, and its initial value is 0.5. Incalculating the offload, the size can be adjusted accordingto the computing task’s actual situation, with the computingamount and the maximum tolerable delay as indicators. Takingcomputationally intensive tasks as an example, when thecalculation of a task is astronomical, the weight of delayenergy consumption can be increased. When the computingtask is a delay-sensitive task, the weight of delay energyconsumption can be reduced.IV. O PTIMAL T RANSPORT C OMPUTATION O FFLOADING
A. Computation Optimal Transport
After getting the offloading request of the task, it is nec-essary to determine the computation node determined byeach computation task. The computation optimal transport isintroduced, whose purpose is to find the transmission schemewith the least overall cost [12]. For the set of tasks ϕ thatshould be offloaded, setting a discrete probability measureof ϕ so that the cost of a discrete measure corresponding tothe computing task ϕ that should be performed is minimized,where the computation task that should be allocated is equalto the computing task that should be performed: ϕ = (cid:88) ni =1 α i δ x i = (cid:88) ni =1 β i δ y i = φ. (10)With reference to the transport optimization problem, theabove task allocation model can be described as a taskallocation problem: min (cid:90) M × M C ( x, F ( x )) dψ ( x, y ) , (11)where C ( x, F ( x )) is the transmission delay here, and ψ ( x, y ) is the computation power of the terminal. The Kantorovichoptimal transport problem is a special linear programmingproblem, so advanced linear programming algorithm can beused to solve it. When faced with large-scale offloading, timecomplexity is a crucial factor, and the linear programmingalgorithm based on the interior point method has great limi-tations in execution time. B. L1 Regularization and SinkHorn Algorithm
In the original definition of the Monge-Kantorovich Prob-lem [12], its constraint requires that for each element in it,it corresponds to an element of equal quality in it. Sincethis constraint is not linear, the problem is challenging tosolve. The introduction of Kantorovich relaxation relaxes thefundamental requirements and allows the mass of each elementto be distributed to multiple elements in the target distributioninstead of one-to-one transportation in the Monge-KantorovichProblem [13], [14]. The simplified constraint condition be-comes linear, which greatly reduces the difficulty of solving.Construct the optimal transmission cost L c ( a, b ) as follows: L c ( a, b ) = min P ∈ U ( a,b ) (cid:104) C, P (cid:105) = (cid:88) i,j C i,j P i,j . (12) Here, P i,j is the decision matrix, a is the computing task tobe uninstalled, b is the computing task that is offloaded to thecomputing node, and C i,j is the delay matrix spent processingthe task. Sparsity regularization includes L0 regularization, L1regularization and L2 regularization [15]. The optimizationproblem of L0 regularization is an NP hard problem, andthere is a theoretically proven that L1 norm is the optimal ofL0 norm convex approximation, so L1 norm is usually usedinstead of L0 norm. L εC ( a, b ) = min P ∈ U ( a,b ) (cid:104) P, C (cid:105) − εH ( P ) , (13) H ( P ) = (cid:88) i,j | P i,j | . (14)After a round of regularization, the solution of Moge-Kantorovich Problem can be written in the following form: P i,j = µ i K i,j ν j , ∀ ( i, j ) ∈ [ n ] × [ m ] (15)The vector µ and ν are the variables required by theSinkHorn algorithm [16]. When µ and ν obtained, the dualproblem f and g of Kantorovich’s solution is obtained, andthe solution of the optimal transport is completed. At each step,update µ to satisfy the equation on the left, and then update ν to satisfy the equation on the right. C. Optimal Solution for Computation Offloading
In most cases, it is not necessary to find the standardKantorovich solution [17]. An approximate algorithm basedon entropy can be used to find the approximate solution. Thenthe computation cost of optimal transport will be significantlyreduced. Therefore, when solving the optimal transmissionof a task, the computation node formula for extension andunloading is: C ( x, F ( x )) = || x − F ( x ) || (16)Here, C(x,F(x)) is the optimal transmission delay that can beachieved by performing ECO or CCO in the current state.It can be proved that the offloading optimization function L c ( a, b ) in (9) is strictly convex, its optimal solution must beunique, that is, the solution space contains only one element,so the offloading decision is the optimal solution.V. S IMULATION AND A NALYSIS
In this section, we will set up a variable simulation experi-ment and select three typical algorithms to compare and verifythe proposed computational offloading model.
A. Simulation Parameter Settings
The algorithms are all implemented in the Matlab language[18], and the running platform is Matlab r2019a. In theexperiment, the wireless channel bandwidth is set to 50MHz,the number of channels is 50, and the number of mobiledevices is 100, and they are randomly distributed within thecoverage of multiple base stations. The fibers’ upload rate isset to 1Gbps, the computing capabilities of mobile devices,edge servers, and cloud servers are set to 1GHz, 10GHz, and100GHz, respectively, the computation power of the mobileevice is set to 0.5W, the background noise power is -100dBm.The data size of computing tasks follows a uniform distributionof [1,500]. The number of CPU cycles required by edgeservers and cloud servers is 200 cycles/bit and 50 cycles/bit.The following Table II shows the main experimental parametersettings [10], [19].
TABLE IIE
XPERIMENTAL P ARAMETER S ETTINGS
Devices Parameter Value
Mobile device Computation capability 1(GHZ)Clock cycles 1000 cycles/bitComputation power 0.5(W)Data upload power 0.1(W)Data download power 0.15(W)Number of devices 100Edge Server Computation capability 10(GHZ)Clock cycles 200 cycles/bitData upload power 0.2(W)Data download power 0.3(W)Cloud Server Computation capability 100(GHZ)Clock cycles 50 cycles/bitNetwork Wireless channels 50Wireless channel bandwidth 50MHzUpload rate 1Gbps
B. Simulation Results and Analysis
Take the three latest task offloading strategy work as theanalysis object. The algorithm based on the Markov modelto optimize the task delay is referred to as ”Markov” [8].The algorithm based on game theory to solve how to selectpartial tasks for offloading in multi-user scenarios is called”Game” [9]. By constructing a Lyapunov-optimized offloadingframework, the algorithm that comprehensively considers thecost of transmission, execution time, and task failure is referredto as ”Cross-Edge” [20]. The strategy mentioned in our workis referred to as ”Cloud-Edge”.
Average task delay (s)
D a t a a r r i v a l r a t e ( M b i t / s ) M a r k o v G a m e C r o s s - E d g e C l o u d - E d g e
Fig. 2. Average task delay under different data arrival rate.
The experiment first got the effect of the data arrival rate onthe average task delay, as shown in Fig.2. In most cases, themethod proposed in this paper performs best, ensuring that thesystem selects priority resources to minimize the system task delay and ensure that the system is non-blocking. When thetask arrival rate increases, it reduces the system blockage asmuch as possible by reasonably cooperating with cloud serverand edge server resources to minimize the system task delayunder blockage conditions.Fig.3 shows the effect of different data reaching rates on thesystem processing speed. In the case of low data arrival rate,the advantage of task processing speed compared to the othertwo algorithms is not obvious due to idle resources, while inthe case of high data arrival rate, the other two algorithms enterthe blocked state due to the resource bottleneck of a singlenode, and the task processing reaches the upper limit. Evenwith the blessing of cloud services, Cross-Edge has graduallyreached the processing limit due to the cost of mission failure.
System processing speed (Mbit/s)
D a t a a r r i v a l r a t e ( M b i t / s )
Fig. 3. System blocking queues under different data arrival rates.
System blocking queue
D a t a a r r i v a l r a t e ( M b i t / s )
Fig. 4. System blocking queue under different data arrival rates.
Fig.4 shows the impact of the data arrival rate on the systemblocking queue, which is obtained by adding the waiting datapackets of all nodes. In the Matlab simulation experiment,it represents the block queue’s size when the system isblocking the worst case after performing specific processingtasks. Compared with the other three algorithms, the methodproposed in this paper reduces a load of bottleneck nodesin the system by balancing the communication resources andomputing resource consumption of cloud computing and edgecomputing. Because it can improve the computing throughputand reduces the accumulation of the blocking data packet inthe system, the blocking situation of this data packet is thelightest. VI. C
ONCLUSION
In this paper, we have proposed a computation offloadingstrategy based on optimal transport theory in a collaborativecloud-edge environment. By setting the Monge–Kantorovichtransportation problem, the paper transforms the offloadingover the collaborative cloud-edge networks into an optimiza-tion problem that only involves resource of the current timeslot on the server. To solve the convex optimization problem,we propose an algorithm based on semidefinite programming,which is designed to decide to offload the task to an edgeserver near the base station, an adjacent edge server, or acloud data center. Experimental results show that computingtasks are offloaded to the edge and central cloud throughedge computing, which provides a practical way for resourceallocation and application scheduling.A
CKNOWLEDGMENT