QoE-driven Secure Video Transmission in Cloud-edge Collaborative Networks
aa r X i v : . [ c s . MM ] J a n QoE-driven Secure Video Transmission inCloud-edge Collaborative Networks
Tantan Zhao, Lijun He, Xinyu Huang, Fan Li ∗ Abstract —Video transmission over the backhaul link in cloud-edge collaborative networks usually suffers security risks. Onlya few existing studies focus on ensuring secure backhaul linktransmission. However, video content characteristics, which havesignificant effects on quality of experience (QoE), are ignoredin the study. In this paper, we investigate the QoE-driven cross-layer optimization of secure video transmission over the backhaullink in cloud-edge collaborative networks. First, we establishthe secure transmission model for backhaul link by consideringvideo encoding and MEC-caching in a distributed cache scenario.Then, based on the established model, a joint optimizationproblem is formulated with the objective of improving userQoE and reducing transmission latency under the constraintsof MEC capacity. To solve the optimization problem, we proposetwo algorithms: a near optimal iterative algorithm based onrelaxation and branch and bound method (MC-VEB), and agreedy algorithm with low computational complexity (GreedyMC-VEB). Simulation results show that our proposed MC-VEBcan greatly improve the user QoE and reduce transmissionlatency within security constraints, and the proposed GreedyMC-VEB can obtain the tradeoff between the user QoE and thecomputational complexity.
Index Terms —QoE, cross-layer optimization, backhaul linksecurity, MEC-caching, video encoding.
I. I
NTRODUCTION
With the rapid development of video processing technol-ogy and mobile communication technology, large numbersof ultra-high-definition (UHD) video-on-demand (VoD) fac-ing massive links have emerged. The number of user videorequests is growing dramatically, leading to the heavy trafficload of networks and high latency of users. These factorscould bring poor QoE for video-requesting users. Luckily,mobile edge computing (MEC) technology, as one of thekey technologies of the cloud-edge collaboration networks inthe fifth generation(5G) system, provides a promising methodto handle these challenges [1], [2]. Since MEC servers arecloser to the users at the network edge and own powerfulintelligent storage capabilities to precache hot videos, massivevideo contents can be delivered directly to users from MECservers to reduce backhaul traffic burden [3] and transmissionlatency. Therefore, how to utilize MEC to meet the high QoErequirements of video users is worth studying.
Manuscript received January 6, 2021. This work was supported in part bythe National Science Foundation of China under Grant 62071369 and in partby the Key Research and Development Program of Shaanxi Province underGrant 2020KW-009..T. Zhao, L. He, X. Huang and F. Li are with the School of Infor-mation and Communications Engineering, Xi’an Jiaotong University, Xi’an710049, China (e-mail: { zhao10111446, xinyu huang } @stu.xjtu.edu.cn; { lijunhe, lifan } @mail.xjtu.edu.cn). (Corresponding author: Fan Li, email:[email protected]) MEC ServersCloud ServersUsers
Control Flow Data Flow
Backhaul Link
Fig. 1. Transmission Architecture in Cloud-edge Collaborative Networks.
In recent years, the copyright protection of video is becom-ing more and more important. Moreover, the emerging paidVIPs and confidential data services that only specific users canreceive make the secure transmission of video contents into anissue that cannot be ignored in the cloud-edge collaborativenetworks.To be specific, for the video transmission in the cloud-edgecollaborative networks, when the video data is transmittedfrom the cloud server to the user in unicast mode, theeavesdropping user and the legitimate user receive informationon the same frequency channel at the same time. Once thechannel condition of the eavesdropper is better than that of thelegitimate user, the eavesdropper could successfully interceptthe video packets, which causes data leakage and infringes onthe video copyright and the benefits of the users. Therefore,the secure data transmission is important. For the transmissionsecurity of the link from the MEC server to the users, asdepicted in Fig. 1, the existing physical layer secure (PLS)mechanism, which has been studied intensively and exten-sively, is sufficient. [4]–[7]. However, the PLS mechanism iscomplicated and high-cost because it could ensure the securityof each video packet. If it is utilized to ensure the transmissionsecurity of the backhaul link from the cloud server to the MECserver, as depicted in Fig. 1, the traffic load of the backhaullink is so heavy that the cost and system overhead could beunbearable in the distributed cache scenario, where an MECserver may be connected to multiple base stations. Therefore, it is an urgent issue to develop a secure mechanism with lowcomplexity and cost to ensure the secure transmission of thebackhaul link from the cloud to the MEC server, rather thanusing the strict and complicated traditional PLS mechanism.In recent years, the issue of the secure backhaul link inthe cloud-edge collaborative networks is rarely considered.Only the authors in [33] considered the security risks of thebackhaul link when studying the optimal cache placement inedge heterogeneous networks. Nevertheless, the issue aimed atgeneral data transmission, ignoring the characteristics of thevideo applications, which resulted in the poor performancefor video transmission applications. Therefore, secure videotransmission through the backhaul links in the cloud-edgecollaborative networks is still an open question.To address the abovementioned problems in secure videotransmission through backhaul links in cloud-edge collabora-tive networks, we propose a QoE-driven cross-layer optimiza-tion algorithm to improve the user QoE, reduce transmissionlatency and guarantee the security of the backhaul links. Themain contributions of this paper can be summarized as follows.1)
Establishing a Video Encoding and MEC Caching-basedSecure Transmission Model:
Video encoding and MECcaching act together in ensuring secure transmissionof backhaul links. However, the existing secure trans-mission model for backhaul links completely ignoresthis important characteristic of video encoding. Thelack of flexible adjustable features of video encodingparameters leads to the secure transmission for backhaullinks not being able to be guaranteed when the cachingcapacity of MEC servers is limited. Based on this issue,we comprehensively consider the interaction of videoencoding parameters and MEC caching strategy andestablish video encoding and a secure MEC caching-based transmission model for backhaul links.2)
Formulating Joint Optimization Problem of Video En-coding and MEC Caching:
Different from general dataservices, the fundamental goal of video services is to im-prove user QoE. Based on the established secure trans-mission model for backhaul links, we incorporate videoencoding and MEC caching into the same mathematicalmodel and formulate a joint optimization problem ofvideo encoding parameters and MEC caching strategyto improve user QoE, reduce transmission latency andprevent video information leakage.3)
Proposing Near Optimal and Suboptimal Solutions:
Wepropose a near-optimal algorithm based on relaxationand branch and bound to solve the formulated optimiza-tion problem, which is a nonlinear mixed 0-1 integerprogramming problem. To be specific, we first relax theoriginal optimization problem into a nonlinear program-ming problem without integer constraints, then use the0-1 branch and bound method to obtain the integer solu-tion of the original optimization problem. Furthermore,considering that the near-optimal algorithm is time-consuming, we also propose a suboptimal algorithmbased on the greedy method with low computationalcomplexity to get the tradeoff between the user QoEand the computational complexity. The rest of this paper is organized as follows. SectionII reviews the related works. In Section III, we introducethe system model, which includes the framework of QoE-driven cross-layer system and describe the secure transmissionmodel. In Section IV, we formulate the QoE maximization andlatency minimization problem under the secure constraints. InSection V we propose a near optimal solution based on jointoptimization of video encoding and MEC caching. In SectionVI, we propose a suboptimal solution based on greedy method.Section VII gives the experimental results, and discusses theperformance gains of the proposed algorithms compared to theexisting algorithm. Finally, Section VIII concludes this paper.II. R
ELATED W ORK
In this section, we will review and analyze the progress ofexisting related work from the following two aspects.
A. QoE-driven MEC Video Caching
The MEC servers are closer to users and have powerfulstorage capabilities. By caching multimedia contents duringoff-peak hours, delay and congestion can be reduced, therebyimproving mobile user QoE [8], [9].To exploit the storage capacity of MEC servers, the authorsin [10] proposed a distributed cache optimization algorithmthrough belief propagation of MEC heterogeneous networks,which greatly reduced the download delay of users. Fromthe perspective of the basic information theoretical limit ofMEC-caching, the authors in [11] gave the best trade-offbetween latency and caching. Considering the particularityof video transmission, the researchers in [12] proposed a co-caching strategy for small-cell base stations (SBSs) and mobiledevices, which greatly reduced the delay in video contentdelivery.In addition to latency, the popularity of video contents alsodetermines whether the cached videos meet the needs of users.The authors in [13], [14] proposed a context-aware cachingscheme to predict the popularity and learn the video popularityof a specific context online, which is used to determinethe cache replacement strategy. However, with the increasingheterogeneity of user groups demanding specific video content,the issue of caching mobile video streaming has become amore complicated task. Therefore, there are also many papersthat use machine learning to predict preferences of users [15]–[20].The studies mentioned above are for traditional videostreaming, to improve the QoE of dynamic adaptive stream-ing users. The authors in [21] studied the QoE-driven op-timization of MEC-caching placement for dynamic adaptivevideo streaming, which considers the different rate-distortioncharacteristics of videos and the coordination among dis-tributed MEC servers. The authors in [22] proposed a refinedcaching update strategy based on video popularity, contentimportance, and user playback status, which ensured thatthe video segments to be played by users could be cachedin time. To further improve user QoE, multiple modules inaddition to MEC -aching are considered to be optimizedcomprehensively. The authors in [23] proposed to enhance the QoE-aware wireless edge caching with bandwidth provi-sioning in software-defined wireless networks. Specifically, ajoint optimization mechanism of caching strategy, bandwidthconfiguration, and adaptive video streaming was designed toreduce delay and improve QoE. In addition, the researchersin [24] proposed a joint scheme of caching strategy, powerallocation, user association, and adaptive video streaming toimprove the system spectrum efficiency and user QoE, butthis scheme will cause a greater burden on backhaul traffic.Therefore, in [25], the authors studied the joint optimizationscheme of mobile terminal QoE and backhaul traffic, whichreduced power consumption and backhaul traffic, meanwhileimproving QoE. Although the above studies aim to improvethe QoE of mobile users, security issues in the cloud-edgecollaborative networks were not considered.
B. Caching-based Secure Transmission
With the increasing complexity of the network environment,legal transmission in the networks is inevitably attacked byexternal malicious nodes, or the SBS originally used forcaching becomes a malicious node and implements eavesdrop-ping. Therefore, the cache-based secure transmission schemearoused the interest of researchers.For the secure transmission of general wireless cachingnetworks, the authors in [26] studied the security of cachingnetworks from the perspective of information theory by usingthe network coding, while the authors in [27] consideredthe security of device-to-device caching networks. Based onthe previous studies, in [28] , the authors studied the securedevice-to-device coding and caching scheme in the senseof information theory, and the authors in [29] proposed adecentralized secure coding caching method in wireless adhoc networks. However, all above studies focus on wirelessphysical layer security, which is ensured by the complicatedPLS mechanism with high cost.For the secure transmission of the mobile edge hetero-geneous cache network, the researchers in [30] studied theattack models in MEC systems and proposed a securitysolution based on reinforcement learning techniques for themobile edge caching. The authors in [31] proposed a securecaching solution for disaster backup in mobile social networksusing fog computing, and the authors in [32] proposed asecure caching solution in heterogeneous multihoming edgecomputing networks. However, all the above studies are aboutthe secure transmission problem of the attacked cache serveritself and ignore the security risks of backhaul links.Apart from the above studies, for the security risks ofbackhaul links, the authors in [33] studied the optimal cacheplacement problem under secrecy constraints of backhaullinks in edge heterogeneous networks. Specifically, the authorsproposed an MEC-caching strategy to minimize the averagebackhaul link rate and ensure the security of backhaul links.However, what has been studied in this study is a secure trans-mission scheme for general data, which ignored the uniquecharacteristics of videos, i.e., different encoding parameterscorrespond to different encoding rates which bring differentQoEs. Therefore, the proposed secure scheme is not specificto video transmission services.
SBS MBS
SBS K SBS SBS
K-1
Cloud Servers
MEC Network
Various Video Applications
MECServer Video Encoding
Backhaul Link Security
Video Encoding
MECServer MECServer
K-1
MECServer K Core Network
Fig. 2. VoD Downlink Transmission in Cloud-edge Collaborative Networks.
Joint Optimization of Video Encoding and MEC Caching
Joint Optimization FormulationNear Optimal Solution
MEC Servers
Caching TaskMEC Caching CapacityConstraints
Video Encoding
Encoding Rate - QoE Model
Secure Backhaul Link Model Based on Distributed CacheDistribution of Video Popularity Requesting Information
MBSCloud Servers Users
Encoding Strategy Caching StrategyMEC InformationVideo Information
SBSs
Forwarding Information Forwarding Video
Wireless Link (Control Flow)
Wireless Link (Data Flow)
MEC Caching Strategy E n c od i ng P a r a m e t e r s VideoData Video DataVideo Data
Video Data
Requesting Information
Wired Link (Data Flow)Wired Link (Control Flow)
Fig. 3. QoE-driven Joint Optimization Scheme of Video Encoding and MECCaching Based on Secure Backhaul Link Model.
III. SYSTEM MODEL
A. Framework
In this paper, we consider a VoD downlink scenario inthe cloud-edge collaborative networks, where multiple usersrequest video files from the cloud servers via a macro-cell basestation (MBS), which has access to the cloud servers throughwired core network. SBSs are deployed in the coverage areaof the MBS to serve user video requests, as depicted in Fig.2. The number of MEC servers is K , and let K denote theset of K MEC servers and the caching capacity of each MECis Φ k , ∀ k ∈ K . Each MEC is connected to an SBS. A userrequesting video files is initially served by SBSs. For videoservices without packet loss, n encoding packets are requiredto successfully decode video information. If the number ofvideo packets sent by all MEC servers within the connectionrange is m and less than n , the decoding conditions are notmet. Then, the MBS is contacted to send the remaining n − m video packets to the user via backhaul link. Based on the above scenario, we propose a QoE-driven jointoptimization scheme of video encoding and MEC-cachingbased on the secure transmission model for the backhaul link,as illustrated in Fig. 3.Specifically, the whole block diagram of the joint optimiza-tion scheme contains the modules of MBS, cloud servers,SBSs, MEC servers and users. First, the video encodinginformation, i.e., encoding rate, QoE model and the distri-bution of popularity, from the cloud servers, and the MECinformation, i.e., the caching capacity and the number ofMEC servers from the SBSs are sent to the system analysismodule MBS. Then, the optimal encoding and caching strategybased on the collected information and the secure transmissionmodel of backhaul link are designed by the MBS and sentto the cloud servers and the SBSs, respectively. The securetransmission model of the backhaul link is video encoding andMEC-caching-based, which means that the encoding packetsize, the number of encoding packets cached in the MECservers and the capacity of MEC servers together determinewhether the secure transmission can be achieved. Finally, thevideo streamings are encoded by the cloud servers accordingto the designed encoding strategy and cached in the MECservers according to the designed caching strategy after be-ing transmitted from the cloud servers. Different from theeavesdropping which comes from the wireless physical layer,here we consider utilizing the adjustable encoding parametersand the distributed MEC cache to avoid data leakage in thebackhaul links from the MBS to the SBSs and construct thesecure transmission model of backhaul links. Based on thesecure transmission model, the QoE-driven joint optimizationmodel of video encoding and MEC caching is established.
B. Video Encoding and MEC Caching-based Secure Trans-mission Model
For the high-definition (HD)/UHD VoD services, we assumethat there are F original video streamings to be encoded andcached, and let F denote the set of F video streamings. p j , ∀ j ∈ F indicates the requesting probability of a user for the j -th video file, which is ranked in descending order of videopopularity. Without loss of generality, we can mark the mostpopular video file with index and the lowest popular videofile with index F . Specifically, the requesting probability of auser for a video file can be described as a Zipf distribution.Assuming that all video files are sorted according to theirpopularity, the probability of being requested for each videofile can be obtained by the following formula: p j = 1 (cid:14) j − θF P j =1 (cid:14) j − θ , < θ < , ∀ j ∈ F (1)where θ is the tilt factor of the distribution, which is usedto control the distribution of video popularity, and the largervalue means more concentrated probability of video requests.Specifically, the following assumptions are made whenencoding and caching video streamings:1) Each video file is encoded into n packets of differentsizes, and let N denote the set of n encoding packets. Let s i,j denote the size of the i -th video packet of the j -th video file. The n video encoding packets are cacheddistributedly in different MEC servers.2) ˜ m k,i,j denotes whether the i -th video packet of the j -thvideo file is cached in the k -th MEC server ( ˜ m k,i,j = 1) or not ( ˜ m k,i,j = 0) .Based on the above assumptions, the caching strategy ofMEC servers can be formulated as a matrix M K × F of size K × F , where the rows indicate the MEC servers, the columnsindicate the video files, and the element m k,j represents thenumber of video encoding packets of the j -th video file cachedin the k -th MEC server, obviously, m k,j = n P i =1 ˜ m k,i,j . Specif-ically, the matrix M K × F can be expressed as the followingform: M K × F = m · · · m F ... . . . ... m K · · · m KF (2)As a result, for each request, the number of video packetsof the j -th video file that need to be transmitted through thebackhaul links can be expressed as R j = n − min n, K X k =1 m kj ! (3)Meanwhile, assuming that the number of total requestsduring the whole delivery phase received by SBSs is Ψ , thenthe number of requests for the video file j received by SBSsis Ψ j = Ψ · p j , ∀ j ∈ F . Therefore, for Ψ j requests, the totalnumber of encoding packets for the j -th video file transmittedthrough the backhaul links can be obtained as follows P j = Ψ j · " n − min n, K X k =1 m kj ! (4)For clarity, considering that n ≥ K P k =1 m kj in our consideredscenario, Eq. (4) can be further formulated as P j = Ψ j · n − K X k =1 m kj ! (5)We know that for the video services without packet loss, securetransmission can be realized if and only if P j ≤ n − .Consequently, the secure transmission model of backhaul linkbased on the distributed MEC cache can be expressed by Ψ j · n − K X k =1 m kj ! ≤ n − (6)After further simplification, we can get K X k =1 m kj ≥ n · (cid:18) − j (cid:19) + 1Ψ j (7)Based on the above derivation, we know that the probabilityof secure transmission for the requested video is closely relatedto the encoding packets cached in each MEC server and thenumber of video requests. IV. P
ROBLEM F ORMULATION
Based on the secure transmission model achieved for back-haul links, the QoE-driven joint optimization problem of videoencoding parameters and MEC-caching strategy under theconstraints of MEC capacity and video encoding rate hasbeen formulated. We define the optimization variables as ˜M K × n × F = { ˜ m k,i,j , ∀ k ∈ K ; ∀ i ∈ N ; ∀ j ∈ F} and S n × F = { s i,j , ∀ i ∈ N ; ∀ j ∈ F} , where ˜ m k,i,j and s i,j denote thecaching strategy and the size of each video encoding packet,respectively. To improve user QoE, we construct the jointoptimization problem expressed by Eq. (8) as follows: max ˜M , S Q (cid:16) ˜M , S (cid:17) s.t. ( c
1) ˜ m k,i,j ∈ { , } , ∀ k ∈ K ; ∀ i ∈ N ; ∀ j ∈ F ( c F P j =1 n P i =1 ˜ m k,i,j s i,j ≤ Φ k , ∀ k ∈ K ( c K P k =1 n P i =1 ˜ m k,i,j ≤ n, ∀ j ∈ F ( c K P k =1 n P i =1 ˜ m k,i,j ≥ n · (cid:16) − j (cid:17) + j , ∀ j ∈ F ( c R min j ≤ n P i =1 s i,j T d ≤ R max j , ∀ j ∈ F (8)where Q ( · ) is the objective function for different applicationdemands, which can represent a single optimization objectiveor the combination of multiple optimization objectives, de-pending on the practical application demands. R min j , ∀ j ∈ F and R max j , ∀ j ∈ F denote the maximum and minimumencoding rates of the j -th video file, and the larger encodingrate means the higher QoE. T d denotes the duration of eachvideo file.Specifically, in our considered VoD downlink scenario, theoptimization objective is to maximize the QoE and minimizethe transmission latency at the same time. Then, the Q ( · ) canbe defined as Q (cid:16) ˜M , S (cid:17) = F X j =1 [ f ( s i,j ) − g ( ˜ m k,i,j , s i,j )] , (9)where f ( s i,j ) denotes the relationship between the size ofthe video encoding packets and QoE, which is determinedby the chosen QoE model, and g ( ˜ m k,i,j , s i,j ) denotes therelationship among the caching strategy, the size of videoencoding packets and the transmission latency. In particular,according to the MOS model in [34], for the j -th video file, f ( s i,j ) and g ( ˜ m k,i,j , s i,j ) can be expressed as f ( s i,j )= C j · n P i =1 s i,j T d + C j · n P i =1 s i,j T d + C j · n P i =1 s i,j T d + C j (10) where C j , C j , C j , C j , ∀ j ∈ F are QoE parameters whichcan be determined by the range of the video encoding rate ofthe j -th video file for a given MOS model. g ( ˜ m k,i,j , s i,j ) = V j · p j · n P i =1 s i,j − n P i =1 K P k =1 ˜ m k,i,j s i,j ! R bk (11) where V j , ∀ j ∈ F is the weighting coefficient of transmissionlatency for a given MOS model. R bk is the transmission rateof the backhaul link.Constraint ( c indicates whether the k -th MEC servercaches the i -th packet of the j -th video file or not. Constraint ( c indicates that the sum of video packet sizes cachedin each MEC server should not be greater than the MECcapacity Φ k , ∀ k ∈ K . Constraint ( c indicates the numberof video encoding packets cached in all MEC servers shouldnot be larger than the total number of video encoding packets n . Constraint ( c reveals the number of video encodingpackets that need to be cached in MEC servers to ensure thesecure transmission of backhaul links. Constraint ( c givesthe maximum and the minimum limits of encoding rate foreach video streaming.V. N EAR O PIMAL S OLUTION BASED ON J OINT O PTIMIZATION OF V IDEO E NCODING AND
MEC C
ACHING
The optimization problem formulated in section IV canbe observed to be a nonlinear mixed integer programmingproblem, which means that a part of the decision variablesmust be integers, called integer-variables, while others can benonintegers, called noninteger variables. To solve it, a near-optimal solution based on relaxation and branch and boundmethod is proposed in this subsection. Specifically, the wholesolving procedure can be divided into two steps, i.e., relaxationof the original nonlinear mixed 0-1 integer problem and thenear-optimal solution based on the 0-1 branch and boundmethod. In the following section of this paper, we will describethem in detail.
A. Relaxation of the Original Nonlinear Mixed 0-1 IntegerProblem
For the mixed integer programming problem, the classicalidea of solving the problem is to relax the original mixedinteger programming problem with integer constraints into therelaxing problem without integer constraints and obtain thesolution of the original mixed integer programming problembased on the solution of its relaxing problem. Therefore, wecan easily get the relaxing problem, which can be expressedby the following: max ˜M , S F P j =1 [ f ( s i,j ) − g ( ˜ m k,i,j , s i,j )] s.t. ( c F P j =1 n P i =1 ˜ m k,i,j s i,j ≤ Φ k , ∀ k ∈ K ( c K P k =1 n P i =1 ˜ m k,i,j ≤ n, ∀ j ∈ F ( c K P k =1 n P i =1 ˜ m k,i,j ≥ n · (cid:16) − j (cid:17) + j , ∀ j ∈ F ( c R min j ≤ n P i =1 s i,j T d ≤ R max j , ∀ j ∈ F (12) Particularly, the relaxing processing is based on the factthat the optimal solution of the mixed integer programming,denoted as ˜M opt and S opt , will not be superior to the optimalsolution of its relaxing problem, which is the upper bound ofthe original mixed integer programming. Here, the definition of the relaxing problem can be expressed as: the objectivefunction and remaining constraints of the original mixedinteger programming problem without considering the integerconstraints.The relaxing problem (12) above is a maximization prob-lem, which is obtained by removing the first integer constraint ( c in the original mixed 0-1 integer programming problem(8). For this maximization problem, as a typical reformulationmethod for optimization programming, we consider a mini-mization problem equivalent to the maximization problem (12)as follows min ˜M , S F P j =1 [ g ( ˜ m k,i,j , s i,j ) − f ( s i,j )] s.t. ( c F P j =1 n P i =1 ˜ m k,i,j s i,j ≤ Φ k , ∀ k ∈ K ( c K P k =1 n P i =1 ˜ m k,i,j ≤ n, ∀ j ∈ F ( c K P k =1 n P i =1 ˜ m k,i,j ≥ n · (cid:16) − j (cid:17) + j , ∀ j ∈ F ( c R min j ≤ n P i =1 s i,j T d ≤ R max j , ∀ j ∈ F (13) The minimization problem (13) is actually a nonlinearoptimization problem. Therefore, we consider utilizing theglobal optimal algorithm GlobalSearch provided by GlobalOptimization Toolbox of MATLAB to obtain its solution. Ac-tually, the near-optimal solution of the optimization problem(13) can be obtained by the use of the GlobalSearch algorithm,which is a kind of heuristic search algorithm. Here, we candenote the near optimal solution of the relaxing problem (13)as ˜M r and S r , and the corresponding objective function valueis Q r . B. Near Optimal Solution based on 0-1 Branch and Bound
To obtain the optimal solution of the original mixed integerprogramming, we employ the branch and bound method [35].Specifically, we can discuss the solution of the relaxingproblem (13) in two cases.In case one, the solution in ˜M r concerning integer-variables ˜M K × n × F = { ˜ m k,i,j , ∀ k ∈ K ; ∀ i ∈ N ; ∀ j ∈ F} are integers.Then, the optimal solution ˜M r and S r of the relaxing problemis also the optimal solution of the original nonlinear mixedoptimization problem and the optimal solution is obtained as ˜M opt = ˜M r , S opt = S r .In case two, an element of solution ˜M r concerning integer-variables ˜M K × n × F = { ˜ m k,i,j , ∀ k ∈ K ; ∀ i ∈ N ; ∀ j ∈ F} is notinteger. Then, the solution should be branched. The wholeprocedure of branching can be divided into the following threesteps. • Equality Constraints of 0 and 1 Branches Acquirement
The optimal solution ˜M opt can be initialized as ˜M opt = ˜M r . Without loss of generality, in our nonlinear mixed integeroptimization problem to be solved, we use ˜ m k ′ ,i ′ ,j ′ , ∀ k ′ ∈K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F to denote the integer-variable whichdoes not satisfy the integer constraint and b k ′ ,i ′ ,j ′ , ∀ k ′ ∈K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F to denote its corresponding nonin-teger solution. Specifically, branch means that the relaxing problem (13) obtained from the original nonlinear mixedinteger problem should be further relaxed into two newsub-relaxing-problems, which can be named sub-relaxing-problem one and sub-relaxing-problem two. Relaxing meansadding two inequality constraints concerning integer-variable ˜ m k ′ ,i ′ ,j ′ , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F to the relaxing problem(13) and keeping its original objective function and remainingconstraints. Specifically, for the sub-relaxing-problem one, theadded inequality constraint can be expressed as ˜ m k ′ ,i ′ ,j ′ ≤⌊ b k ′ ,i ′ ,j ′ ⌋ , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F , while for thesub-relaxing-problem two, the added inequality constraint is ˜ m k ′ ,i ′ ,j ′ ≥ ⌊ b k ′ ,i ′ ,j ′ ⌋ + 1 , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F , where ⌊·⌋ means rounding down.Particularly, in our original nonlinear mixed integer opti-mization problem (8), each indicative variable ˜ m k,i,j , ∀ k ∈K , ∀ i ∈ N , ∀ j ∈ F of the caching strategy has only twopossible values, namely, 0 or 1. As a result, the considerednonlinear mixed integer optimization problem (8) is actuallya nonlinear mixed 0-1 integer programming problem.Meanwhile, considering that 0-1 integer programming is thespecial case of the general integer programming problem, theidea of solving 0-1 integer programming is actually to add alower bound and an upper bound constraint to each integer-variable based on general integer programming. Therefore,from the characteristics of the branch and bound method and0-1 integer programming problem, the inequality constraintshere in the two sub-relaxing-problems can be simplified intothe equality constraints. Specifically, the inequality constraint ˜ m k ′ ,i ′ ,j ′ ≤ ⌊ b k ′ ,i ′ ,j ′ ⌋ , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F in thesub-relaxing-problem one can be equivalently transformed intoequality constraint ˜ m k ′ ,i ′ ,j ′ = 0 , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F and the inequality constraint ˜ m k ′ ,i ′ ,j ′ ≥ ⌊ b k ′ ,i ′ ,j ′ ⌋ + 1 , ∀ k ′ ∈K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F in the sub-relaxing-problem, the twocan be equivalently transformed into the equality constraint ˜ m k ′ ,i ′ ,j ′ = 1 , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F . In this situation, wecan rename the general branch and bound method as the 0-1branch and bound method employed in our nonlinear mixed0-1 integer programming problem. • Two Sub-relaxing-problems Formulation
Based on the obtained minimization relaxing problem (13)and equality constraints of the 0-1 branch, we can easily getthe sub-relaxing-problem one and sub-relaxing-problem twoas follows:Sub-relaxing-problem one: min ˜M , S F P j =1 [ g ( ˜ m k,i,j , s i,j ) − f ( s i,j )] s.t. ( c F P j =1 n P i =1 ˜ m k,i,j s i,j ≤ Φ k , ∀ k ∈ K ( c K P k =1 n P i =1 ˜ m k,i,j ≤ n, ∀ j ∈ F ( c K P k =1 n P i =1 ˜ m k,i,j ≥ n · (cid:16) − j (cid:17) + j , ∀ j ∈ F ( c R min j ≤ n P i =1 s i,j T d ≤ R max j , ∀ j ∈ F ( c
5) ˜ m k ′ ,i ′ ,j ′ = 0 , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F (14) where constraint ( c represents the 0 branch of the integer-variable ˜ m k ′ ,i ′ ,j ′ , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F . Sub-relaxing-problem two: min ˜M , S F P j =1 [ g ( ˜ m k,i,j , s i,j ) − f ( s i,j )] s.t. ( c F P j =1 n P i =1 ˜ m k,i,j s i,j ≤ Φ k , ∀ k ∈ K ( c K P k =1 n P i =1 ˜ m k,i,j ≤ n, ∀ j ∈ F ( c K P k =1 n P i =1 ˜ m k,i,j ≥ n · (cid:16) − j (cid:17) + j , ∀ j ∈ F ( c R min j ≤ n P i =1 s i,j T d ≤ R max j , ∀ j ∈ F ( c
5) ˜ m k ′ ,i ′ ,j ′ = 1 , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F (15)where constraint ( c represents the 1-branch of the integer-variable ˜ m k ′ ,i ′ ,j ′ , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F .The remaining constraints ( c to ( c in sub-relaxing-problem one (14) and sub-relaxing-problem two (15) are theconstraints in the minimization relaxing problem (13), and theobjective function is the objective function in the minimizationrelaxing problem (13). • Near Optimal Solution Obtainment
The sub-relaxing-problem one formulated in Eq. (14) andthe sub-relaxing-problem two formulated in Eq. (15) can alsobe solved by the GlobalSearch algorithm due to their formssimilar to the minimization relaxing problem (13).There are only two possible solution for the two sub-relaxing-problems expressed by Eq. (14) and Eq. (15), i.e.,infeasible solution or integer solution, due to the equivalenttransformation of inequality constraints into equality con-straints when considering the 0-1 branch and bound method.For the convenience of solving the problem, if the infeasiblesolution appears for the sub-relaxing-problem, we can directlyset it as positive infinity or negative infinity, which dependson whether the relaxing problem is a maximization problemor a minimization problem. Then, the optimal solution forone iteration of 0-1 branch and bound can be obtained bycomparing the objective function values of the two sub-relaxing-problems to find the minimization branch and itscorresponding solution, denoted as ˜M min and S min , whichare used to update the optimal solution ˜M opt and S opt foreach iteration by letting ˜M opt = ˜M min and S opt = S min .A new noninteger solution may appear in the updatedsolution ˜M opt due to the 0-1 branch and bound. Therefore,if there is still one noninteger solution in the obtained ˜M opt ,the 0-1 branch and bound should be executed continuallybased on the sub-relaxing-problems formulated in Eq. (14)and Eq. (15). Specifically, 0 and 1 constraints concerning thenew noninteger solution should be added to the sub-relaxing-problems (14) and (15). Then, the optimal solution ˜M opt and S opt can be obtained by updating them as the optimal solutionof the minimization branch of the current iteration of 0-1branch and bound. Finally, the optimal solution of the originalnonlinear mixed integer optimization problem can be obtaineduntil there is no noninteger solution in the updated optimalsolution ˜M opt . The corresponding objective function value Q min can be obtained by substituting the near optimal solution ˜M opt and S opt into the objective function of the optimizationproblem (13).Generally speaking, to obtain the near-optimal integer so-lution of the considered optimization problem formulated inEq. (13), the maximum iteration to execute 0-1 branch andbound is K · n · F , which is actually the number of ele-ments in the three-dimensional integer variable ˜M K × n × F = { ˜ m k,i,j , ∀ k ∈ K ; ∀ i ∈ N ; ∀ j ∈ F} . Particularly, for each iter-ation of the 0-1 branch and bound, if there is more than onenoninteger element, denoted as N n , N n ≥ , in the updatedsolution ˜M opt , 0-1 branch and bound should be executed foreach noninteger solution. Then, · N n branches are generated,which are compared to find the minimization branch and itscorresponding solution ˜M min and S min to update the optimalsolution as ˜M opt = ˜M min , S opt = S min .The solving procedure of our proposed near-optimal algo-rithm is summarized in Algorithm 1 named Near Optimal Al-gorithm Based on Relaxation and Branch and Bound Method.VI. S UBOPTIMAL S OLUTION BASED ON G REEDY M ETHOD
Considering that the near-optimal algorithm proposed aboveis time-consuming, we propose a greedy algorithm with lowcomputational complexity to obtain the sub-optimal solutionof the original nonlinear mixed 0-1 integer programmingproblem.The main idea of the greedy algorithm is to optimizevariables ˜M = { ˜ m k,i,j , ∀ k ∈ K ; ∀ i ∈ N ; ∀ j ∈ F} and S = { ˜ s i,j , ∀ i ∈ N ; ∀ j ∈ F} separately. The whole procedure ispresented in the following two subsections. A. Caching Strategy Optimization with Encoding ParametersFixed
First, we optimize variable ˜M K × n × F = { ˜ m k,i,j , ∀ k ∈ K ; ∀ i ∈ N ; ∀ j ∈ F} with the encodingparameters fixed. The solution of variable ˜M K × n × F = { ˜ m k,i,j , ∀ k ∈ K ; ∀ i ∈ N ; ∀ j ∈ F} can be obtained bysolving the optimization problem (8) in the condition ofgiving the variable S = { ˜ s i,j , ∀ i ∈ N ; ∀ j ∈ F} a fixed valueaccording to a given encoding rate. Actually, the solvingprocess is the special case of Algorithm 1 with a fixedknown S , which greatly reduces the complexity of solvingthe optimization problem compared with a variable S sincethe dimension of the optimization variable reduces.According to Algorithm 1, with a fixed known S , theoptimization problem (13), (14) and (15) should be changedaccordingly. Specifically, the minimization relaxing problem(13) can be reformulated as min ˜M F P j =1 g ( ˜ m k,i,j ) s.t. ( c F P j =1 n P i =1 ˜ m k,i,j s i,j ≤ Φ k , ∀ k ∈ K ( c K P k =1 n P i =1 ˜ m k,i,j ≤ n, ∀ j ∈ F ( c K P k =1 n P i =1 ˜ m k,i,j ≥ n · (cid:16) − j (cid:17) + j , ∀ j ∈ F (16) Algorithm 1
Near Optimal Algorithm Based on Relaxationand Branch and Bound Method
Input: myf un : the objective function of optimzaton prob-lem (13); myf un : nonlinear constraints of optimiza-tion problem (13); linear constraints of optimizationproblem (13); ˜M , S : initial solution of ˜M and S . Output: ˜M opt , S opt and Q min . Initialize:
Obtain ˜M r , S r and the objective function value Q r by solving relaxing problem (13) utilizing the global optimalalgorithm GlobalSearch. Calculate the initial total number ofnon-integer solution in ˜M r , denoted as N n , and obtain thecorresponding position index vector N in . Initialize the leftcoefficient matrix of equality constraints ( c of 0 branchin Eq. (14) and 1 branch in Eq. (15) as A eq = , and thecorresponding right coefficient vector of equality constraintsas b eq = . if N n = 0 then ˜M opt = ˜M r ; S opt = S r ; Q min = Q r ; else Initialzie ˜M opt = ˜M r . Set the number of non-integersolution in ˜M opt for each iteration of 0-1 branch andbound as N b = N n and the corresponding position indexvector N i = N in . for p = 1 to N n dofor q = 1 to N b do Update A eq ( p, N i (: , q )) = 1 ;Obtain the left coefficient matrix of equalityconstraints for 0 and 1 branch A eq zero = A eq (1 : p, :) , A eq one = A eq (1 : p, :) ;Update b eq ( p, :) = 0 ;Obtain the right coefficient vector of equality con-straints for 0 branch b eq zero = b eq (1 : p, :) ;Update b eq ( p, :) = 1 ;Obtain the right coefficient vector of equality con-straints b eq one = b eq (1 : p, :) ;Solving the sub-relaxing-problem one (14) and thesub-relaxing-problem two (15) by utilizing theglobal optimal algorithm GlobalSearch. end Compare the objective function values of all 0-1branches of N b non-integer variables, and find theminimization branch and obtain its correspondingsolution , denoted as ˜M min and S min ;Update ˜M opt by setting ˜M opt = ˜M min , S opt = S min ;Update N b and N i based on ˜M opt . end Obtain ˜M opt , S opt and the objective function value Q min by substituting ˜M opt and S opt into the objective function myf un of optimization problem (13). end Based on the reformulated minimization relaxing problem(16), the sub-relaxing-problem one (14) and sub-relaxing-problem two (15) can be reformulated as Sub-relaxing-problem one: min ˜M F P j =1 g ( ˜ m k,i,j ) s.t. ( c F P j =1 n P i =1 ˜ m k,i,j s i,j ≤ Φ k , ∀ k ∈ K ( c K P k =1 n P i =1 ˜ m k,i,j ≤ n, ∀ j ∈ F ( c K P k =1 n P i =1 ˜ m k,i,j ≥ n · (cid:16) − j (cid:17) + j , ∀ j ∈ F ( c
4) ˜ m k ′ ,i ′ ,j ′ = 0 , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F (17)where constraint ( c represents the 0 branch of the integer-variable ˜ m k ′ ,i ′ ,j ′ , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F .Sub-relaxing-problem two: min ˜M F P j =1 g ( ˜ m k,i,j ) s.t. ( c F P j =1 n P i =1 ˜ m k,i,j s i,j ≤ Φ k , ∀ k ∈ K ( c K P k =1 n P i =1 ˜ m k,i,j ≤ n, ∀ j ∈ F ( c K P k =1 n P i =1 ˜ m k,i,j ≥ n · (cid:16) − j (cid:17) + j , ∀ j ∈ F ( c
4) ˜ m k ′ ,i ′ ,j ′ = 1 , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F (18)where constraint ( c represents the 1 branch of the integer-variable ˜ m k ′ ,i ′ ,j ′ , ∀ k ′ ∈ K ; ∀ i ′ ∈ N ; ∀ j ′ ∈ F . B. Encoding Parameters Optimization Based on the GreedyMethod
Then, based on the caching strategy ˜M g obtained, the solu-tion of variable S = { ˜ s i,j , ∀ i ∈ N ; ∀ j ∈ F} can be obtainedas S g by gradually increasing the encoding rate for each videofile one by one in a certain reasonable step. In this way, wecan find the one which brings the maximum MOS value ofthe current iteration until not meeting the constraints ( c and ( c of the optimization problem (13).Finally, the suboptimal solution of the original nonlinearmixed noninteger solution can be obtained as ˜M g and S g .The corresponding objective function value Q min can beobtained by substituting the suboptimal solution ˜M g and S g into the objective function of the optimization problem (13).The solving procedure for the greedy algorithm is summarizedin Algorithm 2 named Greedy Algorithm based on Relaxationand Branch and Bound Method.VII. S IMULATION R ESULTS
In this section, we provide simulation results to highlight theperformance of our algorithms. We consider a VoD downlinkscenario in the cloud-edge network where the total number ofvideo files is F , the total encoding packet of each video fileis n , and the number of the MEC servers is K . The tilt factorof the Zipf distribution is assumed as θ = 0 . . The durationof each video file is assumed as T d = 2400 s . The weightingcoefficient of transmission latency is V j = 0 . , ∀ j ∈ F . The Algorithm 2
Greedy Algorithm Based on Relaxation andBranch and Bound Method
Input:
Caching strategy ˜M g , which is obtained by utilizingAlgorithm 1 with the known S based on the givenencoding rate which satisfies constraint ( c in opti-mization problem (13). Output: ˜M g , S g and Q min . Initialize: initialize S g according to the minimum encodingrates of all video files; initialize Q min as Q min = Q g whichis calculated based on the obtained ˜M g and S g ; initialize in-creasing step of encoding rate as T d · n ; initialize the searchingtimes N and N as N = ( R max − R min ) · T d · N , N = F ,where N is the number of video files whose encoding rate liesbetween the minimum encoding rate R min and the maximumencoding rate R max . for p = 1 to N dofor q = 1 to N do Obtain all possible S g which satisfy constraints ( c and ( c in optimization problem (13) according tothe increasing step T d · n .Obtain all possible Q g by substituting all possible S g , ˜M g into the objective function of optimizationproblem (13). end Compare all possible Q g and find the one which bringsthe most increments to Q min , denoted as Q gmin and itscorresponding encoding parameters, denoted as S g min .Update S g by setting S g = S g min ;Update Q min by setting Q min = Q gmin . end transmission rate of the backhaul link is R bk = 10Gbps /F .The total number of video requests received by SBSs duringthe whole delivery phase is ψ . In particular, we considerthree types of video files, the encoding rates of which satisfydifferent encoding rate ranges:Type 1: The encoding rates of the 1st to the ( /F )-th videofiles vary from 0.3 Mbps to 0.7 Mbps;Type 2: The encoding rates of the ( /F +1 )-th to the ( /F +4 /F )-th video files vary from 1Mbps to 4 Mbps;Type 3: The encoding rates of the ( /F + 4 /F + 1 )-th tothe F -th video files vary from 4 Mbps to 8 Mbps.The detailed parameter settings are presented in Table I. Thesecure issue of backhaul links in the cloud-edge collaborativenetworks is rarely considered, and only the authors in [33]studied the optimal cache placement in the condition ofsecure transmission of backhaul links. Therefore, our proposedschemes and the secure method in [33] are presented andanalyzed: • MC-VEB : Our proposed near-optimal MEC caching andvideo encoding-based (MC-VEB) algorithm includesvideo encoding parameters and an MEC-caching strategythat are jointly optimized. • Greedy MC-VEB : Our proposed greedy MEC cachingand video encoding-based (Greedy MC-VEB) algorithmwith lower complexity compared with the near optimal
TABLE IVIDEO FILE PARAMETERSTypes Encoding rate range QoE parametersType 1 0.3Mbps-0.7Mbps C = 0 . , C = − . , C = 3 . , C = 2 . Type 2 1Mbps-4Mbps C = 0 . , C = − . , C = 1 . , C = 1 . Type 3 4Mbps-8Mbps C = 0 . , C = − . , C = 0 . , C = 2 . Index of Video File M O S MC-VEB Greedy MC-VEB MCBST
Fig. 4. MOS of each video file. algorithm, includes video encoding parameters and anMEC caching strategy optimized step by step. • MCBST in [33]: The MEC-caching-based secure trans-mission (MCBST) scheme, which aims to minimize thebackhaul link rate under secrecy constraints by utilizingMEC caching strategy for general data transmission, doesnot consider adjusting encoding parameters for the videostreaming.We validate the algorithm performance in terms of MOSand average MOS with different simulation configurations.
A. MOS of Each Video File
Fig. 4 shows the MOS value of each video file with n = 20 , F = 8 , K = 1 and Φ k = 26880 Mb , ∀ k ∈ K . Fig. 4 showsthat, for each video file, the MOS performance of MC-VEBalgorithm is not always superior to the MOS performanceof the Greedy MC-VEB algorithm and MCBST scheme inspite of the obvious advantage in the average sense. Theaverage MOS values of the MC-VEB algorithm, Greedy MC-VEB algorithm and MCBST scheme are 3.7935, 3.4021 and3.4021, respectively, because our optimization goal is thewhole performance advantage of all video files rather thanthe performance advantage for a single video file. Thus, thereis no absolute superiority of MOS value for each video filein our proposed algorithm. Specifically, to obtain the wholeperformance advantage of the MOS value, the 1-st to 6-thvideo files, as depicted in Fig. 4, which can get higher QoEwith lower encoding rate, are more likely to be distributed withcaching capacity to improve QoE on the condition of limited Caching Capacity of MEC Server A v e r age M O S MC-VEBGreedy MC-VEBMCBST
Fig. 5. Average MOS vs. different caching capacity of MEC server caching capacity, while the 7-th and 8-th video files, whichrequest higher encoding rate, are distributed with less cachingcapacity.Each video file has a different caching strategy and encodingparameter. Therefore, the number and the size of encodingpackets cached in the MEC server vary for different video files.Therefore, the QoE and transmission latency of each video fileare different for the three schemes, which results in differentMOS values in the case of the same caching capacity of theMEC server. Furthermore, the MOS values of the GreedyMC-VEB algorithm and MCBST scheme are the same foreach video file, because each video file of both schemes isencoded into the minimum encoding rate, and the cachingstrategy for them is the same when the caching capacity is Φ k = 26880 Mb , ∀ k ∈ K , which allows all encoding packetsof each video file to be cached in the MEC server at theminimum encoding rate. B. Average MOS with Different Caching Capacity of MECserver
In Fig. 5, the average MOS value versus different cachingcapacity of MEC server with n = 20 , F = 8 , K = 1 ispresented. As shown in Fig. 5, the average MOS values ofthe MC-VEB algorithm and the Greedy MC-VEB algorithmincrease with the increasing caching capacity of the MECserver, which eventually tends to the same maximum valuedetermined by the maximum encoding rate of each video fileand the optimal caching strategy when the caching capacityof MEC server is sufficient to cache all encoding packets.The MC-VEB algorithm also achieves a considerable perfor-mance gain compared with the Greedy MC-VEB algorithm.The minimum average MOS value of the proposed MC-VEB algorithm is obtained when the caching capacity of theMEC server is just enough to cache the minimum number ofencoding packets to satisfy the security constraints, while theGreedy MC-VEB algorithm cannot find the feasible solutionthat satisfies the security constraints at this point, marked bythe purple circle in Fig. 5. As the caching capacity of the TABLE IIMOS OF EACH VIDEO FILE UNDER DIFFERENT CACHINGCAPACITY
MOS of Each Video File under the Smallest Caching Capacity
Index ofVideo File 1 2 3 4 5 6 7 8Encoding Rate(Mbps) 0.3 0.3 0.3 0.3 1 1 4 4Number ofCached Packets 15 19 17 14 18 18 16 15MOS 3.302 3.303 3.303 3.300 2.984 2.966 2.708 2.695
MOS of Each Video File under the Largest Caching Capacity
Index ofVideo File 1 2 3 4 5 6 7 8Encoding Rate(Mbps) 0.7 0.7 0.7 0.7 4 4 8 8Number ofCached Packets 20 20 20 20 20 20 20 20MOS 4.116 4.116 4.116 4.116 3.932 3.932 4.261 4.261
MEC server increases, the gap of the average MOS values firstincreases, then gradually narrows because that large cachingcapacity can provide more choices of caching strategy andencoding rate, which could bring better performance on QoEand transmission latency.Furthermore, the average MOS value of the MCBSTscheme, which is always worse than the average MOS valueof the proposed MC-VEB algorithm and Greedy MC-VEBalgorithm, remains unchanged with the increasing cachingcapacity. This scenario is reasonable since the minimumencoding rate is adopted in the MCBST scheme, and thecaching strategy is the same regardless of the caching capacitybecause its aim is to minimize the backhaul link rate. As aresult, the video encoding packets cached in the MEC serverwill be as many as possible if the caching capacity is largeenough and all encoding packets are cached in the MEC serverwhen each video file is encoded into its minimum encodingrate.The Greedy MC-VEB algorithm and the MCBST schemecannot achieve secure transmission when the caching capacityvalue is very small, i.e., the first point marked by the purplecircle in Fig. 5 with caching capacity Φ k = 21540 Mb , ∀ k ∈ K ,while the proposed MC-VEB algorithm can ensure securetransmission and obtain a feasible average MOS value byadjusting caching strategy and encoding parameters at thesame time. The observations above demonstrate the benefitsof the proposed algorithms, which comprehensively considerthe interaction of caching strategy and encoding parameters.To show the changes of encoding parameters and cachingstrategy under different caching capacity, encoding rates andthe number of cached packets for two selected points in Fig.5 are given in Table II. From Fig. 5, at the first point markedby the purple circle, the minimum average MOS value of theproposed MC-VEB algorithm is obtained and at the last pointmarked by the black circle, the same maximum average MOSvalues of the proposed MC-VEB algorithm and Greedy MC-VEB algorithm are obtained. Table II gives the MOS valueof each video file at the first point when the MEC serverhas the smallest caching capacity Φ k = 21540 Mb , ∀ k ∈ K and at the last point when the MEC server has the largestcaching capacity Φ k = 69660 Mb , ∀ k ∈ K . The minimumMOS of each video file is obtained at the first point. In this Number of Video File A v e r age M O S MC-VEBGreedy MC-VEBMCBST
Fig. 6. Average MOS vs. different number of video files situation, all video files in the MC-VEB algorithm are encodedinto the minimum encoding rates, and the minimum numberof encoding packets are cached in the MEC server to satisfythe security constraints due to the limited caching capacity.Meanwhile, the minimum number of cached packets variesfor different video files, because different video files have adifferent number of requests. At the last point, the maximumMOS of each video file is obtained, all video files of bothalgorithms are encoded into the maximum encoding rates, andin both algorithms, all encoding packets are cached in theMEC server due to the sufficient caching capacity.
C. Average MOS with Different Parameters of Video Files
Fig. 6 shows the average MOS value versus differentnumber of video files with n = 10 , K = 1 and Φ k =39000 Mb , ∀ k ∈ K . From Fig. 6, the average MOS valuedecreases with the increasing number of video files for theproposed MC-VEB algorithm and the Greedy MC-VEB al-gorithm. The gap between them increases with the increasingvideo files when the number of video files is less than or equalto F = 12 . However, the Greedy MC-VEB algorithm has nosolution as the number of video files continues to increase to F = 16 and F = 20 , marked by the black and cyan circlesin Fig. 6, while the MC-VEB algorithm still has the feasibleand effective solution, and the minimum average MOS valueis obtained at the last point marked by the cyan circle whenall video files are encoded into the minimum encoding rates,and the minimum number of encoding packets are cached inthe MEC server.The reasons contributing to these observations are that whenthere are four video files, all of them in the two algorithm areencoded into the maximum encoding rates, and all encodingpackets are cached in the MEC server due to the sufficientcaching capacity, which brings the best MOS values as shownby the first point. As the number of video files increases, onlypart of the encoding packets can be cached in the MEC serverdue to the limited caching capacity, which also cannot allowall video files to be encoded into the maximum encoding
12 13 14 15 16 17 18 19 20
Number of Video Encoding Packets A v e r age M O S MC-VEBGreedy MC-VEBMCBST
Fig. 7. Average MOS vs. different number of video encoding packets rates. In this situation, the caching strategy and encodingparameters of the proposed two algorithms are different. Forthe MC-VEB algorithm, the near optimal average MOS valuecan be obtained by jointly optimizing the caching strategyand encoding parameters flexibly, while the Greedy MC-VEBalgorithm achieves worse MOS values or even an infeasible so-lution because it optimizes the caching strategy and encodingparameters step by step and thus, cannot satisfy the complexand strict security constraints when there are many videofiles. This phenomenon further demonstrates the performanceadvantage of the near optimal MC-VEB algorithm.Furthermore, it is interesting to find that there is onlyone feasible point marked by the purple circle in Fig. 6 forthe MCBST scheme when there are four video files in theconsidered scenario, and the performance of its average MOSvalue is much worse than the proposed algorithms, becausewhen the encoding parameters are fixed, the MCBST schemecannot satisfy the security constraints by adjusting its cachingstrategy when there are many video files, and the cachingcapacity is limited. Meanwhile, the simple caching strategyof the MCBST scheme demands that the number of encodingpackets cached in different MEC servers must be the same forthe same video file.In Fig. 7, the average MOS value versus the differentnumber of video encoding packets with F = 8 , K = 1 and Φ k = 28000 Mb , ∀ k ∈ K is presented. From Fig. 7, the averageMOS values of the proposed MC-VEB algorithm, GreedyMC-VEB algorithm and the comparable MCBST schemeare almost stable with the increasing number of encodingpackets. The MOS performance of the proposed near-optimalMC-VEB algorithm fluctuates slightly when the number ofencoding packets changes, which is significantly superior tothe Greedy MC-VEB algorithm and the comparable MCBSTscheme. Specifically, the MOS performance increases slowlyat first, then decreases when the encoding packets increase to n = 18 , and finally increases to the maximum value whenthe number of encoding packets is n = 20 . The fluctuationsresult from the caching strategy and the encoding parameters
50 60 70 80 90 100 110 120 130
Number of Total Requests M i n i m u m C a c h i ng C apa c i t y o f M E C S e r v e r MC-VEBGreedy MC-VEBMCBST
Fig. 8. Minimum caching capacity vs. different number of total requests varying slightly with the changing total number of encodingpackets when the caching capacity and the number of videofiles remain unchanged. As the number of encoding packetsincreases, there are more choices of caching strategy to satisfythe security constraints and obtain the better performance ofQoE and transmission latency. However, with the increasingnumber of encoding packets, the size of each encoding packetbecomes smaller at the same encoding rate, which could causethe increase in transmission latency. Therefore, the wholeperformance of the average MOS value cannot change much.A tradeoff exists between the total number of encoding packetsand the size of each encoding packet, which results in thefalling fluctuation when the number of encoding packets is n = 18 . In this situation, the proposed near-optimal MC-VEBalgorithm will wisely consider this balance and achieve thenear-optimal results by joint adjustment of caching strategyand encoding parameters, which also brings the reasonablefluctuations.As for the Greedy MC-VEB algorithm, its performanceof the average MOS value is still better than that of thecomparable MCBST scheme, while the average MOS valuesof both schemes almost remain unchanged when the numberof encoding packets changes. This is because that both ofthem optimize the caching strategy with the fixed encodingparameters, which results in the same caching strategy whenthe caching capacity of the MEC server and the number ofvideo files keep unchanged in spite of the changing number oftotal encoding packets. Furthermore, we can find that the gapsof the average MOS values between the proposed MC-VEBalgorithm, Greedy MC-VEB algorithm and the comparableMCBST scheme in Fig. 7 are strictly consistent with thoseof Fig. 5 when the caching capacity of MEC server is Φ k =28000 Mb , ∀ k ∈ K , which further validates the rationality ofour simulation results. D. Average MOS with Different Number of Requests of Users
Fig. 8 shows the minimum caching capacity of the MECserver versus different number of total requests with n = 10 , F = 8 , K = 1 . The minimum caching capacity of the threeschemes increases with the increasing number of total requestsand eventually tends to the same value when the number oftotal requests reaches ψ = 130 because, as the number of totalrequests increases, more caching capacity is needed to cachemore video encoding packets to ensure the requirements ofQoE, transmission latency and security constraints.Furthermore, Fig. 8 shows that the the minimum cachingcapacity of the proposed MC-VEB algorithm is much smallerthan the minimum caching capacity of the Greedy MC-VEB algorithm and the comparable MCBST scheme. Thisphenomenon shows that the proposed MC-VEB algorithm stillhas relatively good performance even with limited cachingresources and can spare more caching resources to achievebetter QoE and low latency under the condition of ensuringthe security constraints. The minimum caching capacity of thethree schemes finally reaches the same value as the numberof total requests increases to ψ = 130 , resulting from morerequests indicating that more video encoding packets shouldbe cached in the MEC server for any scheme. As a result,almost all video encoding packets are cached in the MECserver at the minimum encoding rates to satisfy the securityconstraints and guarantee the QoE and latency requirementswhen the number of total requests reaches ψ = 130 . E. Complexity Analysis
In this subsection, the computational complexity of ourproposed MC-VEB algorithm, Greedy MC-VEB algorithmand the MCBST scheme in [33] is analyzed.(1) MC-VEB: For our proposed near-optimal MC-VEBalgorithm, the computational complexity is determined by theGlobalSearch algorithm and 0-1 branch and bound methodas shown in Algorithm 1. For the GlobalSearch algorithm,the dimension of the optimization variable is ( K + 1) · n · F .Then, the computational complexity of the GlobalSearchalgorithm can be given by O ( h g (( K + 1) · n · F )) , where h g ( · ) is the number of operations positively related tothe dimension of the optimization variable. Finally, thecomputational complexity of the MC-VEB algorithm is O ( h g (( K + 1) · n · F ) + N n · N b · h g (( K + 1) · n · F )) .(2) Greedy MC-VEB: As shown in Algorithm 2, thecomputational complexity of our proposed Greedy MC-VEBalgorithm is determined by the Algorithm 1 with a fixedknown S and the optimization algorithm of encoding pa-rameters based on the optimized caching strategy ˜M g . ForAlgorithm 1 with a fixed known S , since the dimensionof optimization variable is K · n · F , then the computationalcomplexity can be given by O ( h g ( K · n · F )) . Finally, thecomputational complexity of the Greedy MC-VEB algorithmis O ( h g ( K · n · F ) + N n · N b · h g ( K · n · F ) + N · N ) .(3) MCBST in [33]: For the MCBST scheme, since itonly aims to optimize caching strategy without consider-ing video encoding, then the computational complexity is O ( h g ( K · n · F ) + N n · N b · h g ( K · n · F )) .Based on the analysis above, compared with the GreedyMC-VEB algorithm, the increase in the dimension of theoptimization variable in our proposed near-optimal MC-VEB algorithm brings higher computational complexity, which hasa much greater impact on the running time than the increasein the number of iterations caused by optimizing the encod-ing parameters alone based on the greedy method. In oursimulation, the running time of the near-optimal MC-VEBalgorithm is approximately times the running time of theGreedy MC-VEB algorithm. For the MCBST scheme in [33],the computational complexity is lower than our Greedy MC-VEB algorithm because the video encoding is not considered.However, as mentioned above, the increase in the numberof iterations for optimizing the encoding parameters has atrivial effect on the running time. Therefore, the differencebetween the computational complexity of the Greedy MC-VEB algorithm and the MCBST scheme in [33] is very small,which can be considered almost the same to some extent.VIII. C ONCLUSIONS
In this paper, we proposed a QoE-driven cross-layer op-timization scheme for secure video transmission over thebackhaul link in cloud-edge networks. First, we established avideo encoding and MEC-caching-based secure transmissionmodel for the backhaul link. Based on the established model,we formulated a joint optimization problem of video encod-ing parameters and MEC caching strategy to improve userQoE and reduce transmission latency. Then, a near-optimalalgorithm based on the relaxation and branch and bound wasdesigned to solve the joint optimization problem. Furthermore,we proposed a greedy algorithm with low complexity to obtainthe sub-optimal solution. Simulation results were presentedto show that our proposed algorithms can greatly improveQoE and reduce transmission latency under the condition ofensuring secure transmission of the backhaul link comparedwith the existing algorithm. In addition, our proposed algo-rithms are proven to be more robust for caching capacity andcan ensure secure transmission for more videos with limitedcaching capacity of MEC servers.R
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