Energy-Efficient Joint Caching and Transcoding for HTTP Adaptive Streaming in 5G Networks with Mobile Edge Computing

Renchao Xie＊,Zishu Li,Jun Wu,Qingmin Jia,Tao Huang,2

1 State Key Laboratory of Network and Switching Technology,Beijing University of Posts and Telecommunications,Beijing 100876,China

2 Purple Mountain Laboratories,Nanjing 211111,China

3 Dhurakij Pundit University,110/1-4 Prachachuen Rd.,Laksi,Bangkok 10210 Thailand

4 Institute of Sensing Technology and Business,BUPT,214315,China

Abstract: With the new promising technique of mobile edge computing (MEC) emerging,by utilizing the edge computing and cloud computing capabilities to realize the HTTP adaptive video streaming transmission in MEC-based 5G networks has been widely studied.Although many works have been done,most of the existing works focus on the issues of network resource utilization or the quality of experience (QoE) promotion,while the energy efficiency is largely ignored.In this paper,different from previous works,in order to realize the energy efficiency for video transmission in MEC-enhanced 5G networks,we propose a joint caching and transcoding schedule strategy for HTTP adaptive video streaming transmission by taking the caching and transcoding into consideration.We formulate the problem of energy-efficient joint caching and transcoding as an integer programming problem to minimize the system energy consumption.Due to solving the optimization problem brings huge computation complexity,therefore,to make the optimization problem tractable,a heuristic algorithm based on simulated annealing algorithm is proposed to iteratively reach the global optimum solution with a lower complexity and higher accuracy.Finally,numerical simulation results are illustrated to demonstrated that our proposed scheme brings an excellent performance.

Keywords: mobile edge computing; HTTP adaptive streaming; caching; transcoding; energy efficiency

I.INTRODUCTION

With the emerging application of 4K/8K video,virtual reality (VR)/augmented reality (AR),and Internet of Things (IoT),the mobile data traffic is growing dramatically.According to a recent report from Cisco [1],mobile data traffic will increase 7-fold between 2017 and 2022,up to 77.5EB per month by 2022,and nearly 82% of the all traffic is expected to be video traffic.An explosive growth of video traffic brings huge challenges for mobile network during video transmission,which requires that the network has the ability to provide higher data rate and lower latency for video transmission in a time varying wireless environment in order to satisfy the users’ quality of experience (QoE).In order to cope with these challenges,the HTTP adaptive streaming (HAS) technique has been designed to realize video transmission over mobile networks [2]-[4].The core idea of the HTTP adaptive video streaming over mobile networks is that a video file is divided into consecutive segments and each segment is encoded to multiple discrete bitrates,then the suitable bitrate of video is selected based on the achievable data rate in the time varying wireless environment [5].

Since the technique of HTTP adaptive video streaming over mobile networks is proposed,the adaptive video transmission strategies in mobile networks to optimize the users’ QoE have been studied [6]-[8].In [6],the issue of joint user association and rate allocation for HTTP adaptive streaming in heterogeneous cellular networks is studied,then the authors model the optimization problem as a mixed integer programming problem,and joint user association and rate allocation based on the distributed greedy matching algorithm is proposed.The authors in [7] consider a stochastic QoS-aware Robust Predictive-DASH (RPDASH) scheme over future wireless networks,and then the imperfect rate prediction is taken into account to achieve long-term quality fairness among the DASH users while capping the probability of service degradation.The problem of maximizing the experienced video quality at all the users is studied in [8] by jointly optimizing the time-domain resource partitioning (TDRP) for the HCN,the rate allocated to each specific user,and the selected video quality transmitted to a use.Then a primal-dual approximation algorithm is designed to solve the optimization problem.

On the other hand,with a new promising technique named multi-access edge computing (MEC) proposed by European Telecommunications Standards Institute (ETSI),by using the MEC enhanced 5G networks to realize the video transmission has also been attracted a lot of attention [9]-[11].This is because that the MEC can utilize the edge IT and cloud computing capabilities not only to perform video content placement during off-peak hours but also to realize the video transcoding,thereby smoothing out the temporal traffic variability,reducing congestion and response latency,and improving the users’ QoE.

Taking these advantages into account,many works have been done for the HTTP adaptive video streaming transmission in MEC-based 5G networks recently [12]-[17].The authors in [12] study the problem QoE-traffic optimization through collaborative edge caching in adaptive mobile video streaming,then a self-tuned bitrate selection algorithm with low complexity is designed to solve the optimization problem.A real-time,context-aware collaboration framework based on the MEC is studied in [13]-[14],then the authors propose a cooperative caching and processing strategy called CoPro-CoCache for multi bit video streaming to enhance network resource utilization.An MEC enhanced adaptive bitrate (ABR) video delivery scheme is designed in [15] by combining content caching and ABR streaming technology together to make the cooperation between cache and radio resource allocation.The authors of [16] study a QoE-driven mobile edge caching placement optimization problem for dynamic adaptive video streaming,then the different rate distortion (R-D) characteristics of videos and the coordination among distributed edge servers are studied.In [17],the authors design an adaptive wireless video transcoding framework based on edge computing by deploying edge transcoding servers close to BSs,then an adaptive transcoding strategy is formulated as a network utility maximization (NUM) problem and a low-complexity algorithm is proposed.

Although many works have been done for the dynamic adaptive video streaming in the MEC based 5G networks,most of them focus on the problem of caching or bitrate adaptation algorithm to optimize the network resource utilization or promote the users’ QoE,and the issue of the energy efficiency is largely ignored.However,the problem of energy-efficient video transmission is a key performance indicator in future 5G networks [18] due to the rapidly rising energy costs and increasingly rigid environmental standards.This is because that mobile video traffic enjoys the highest rate of growth and will account for seventy-eight percent of the total mobile data traffic by 2021,which will lead to an alarming rising in energy costs [19].Therefore,to realize the energy efficient video delivery in MEC-based 5G networks is very important to meet the challenges raised by the high demands of traffic and energy consumption.Therefore,to fill this gap,based on our previous works [20],we give more detail consideration about the issue of energy-efficient joint caching and transcoding schedule strategy for HTTP adaptive video streaming in MEC based 5G networks in this paper.The main contributions of this paper can be summarized as follows:

·By utilizing the caching and computing capabilities of MEC at the edge of radio access network (RAN),we focus on the HTTP adaptive video streaming transmission in MEC based 5G networks and consider the joint caching and transcoding by taking the distribution of the requested video segments into account.The issue studied in this paper can greatly alleviate the burden on backhaul link,whittle down the responding delay and improve the users’ QoE.

·Then,taking the energy efficiency as a key performance indicator,we study the problem of joint optimization of caching,transcoding and transporting to achieve the minimum energy consumption of the network.Then three different modes for the process of video requesting and responding are considered,that is:direct hit,transcoding hitandmiss.Especially,we go deep into thetranscoding hitmode and arrange a transcoding schedule to determine whether to respond users by transcoding or not,thus gains a good performance improvement than the strategies without transcoding schedule.

·Due to finding the optimal solution is NPhard for an integer programming problem,which brings huge computation complexity.Therefore,to make the optimization problem tractable and reduce the computation complexity,a heuristic scheme based on simulated annealing (SA) algorithm is proposed to iter- atively reach the global optimization of our formulation.

Finally,extensive simulation results are illustrated to demonstrate the performance of the proposed scheme based on SA algorithm.And numerical simulation results are shown that our proposed scheme has a lower complexity and higher accuracy than other classical algorithms,such as the genetic algorithm and greedy algorithm.

The rest of the paper is organized as follows.We first give the system model and problem formulation in Section II.Then,the joint caching and transcoding scheme based on a simulated annealing algorithm is designed In Section III.In Section IV,numerical simulation results are illustrated and discussed.Finally,we conclude our paper in Section V.

II.SYSTEM MODEL AND PROBLEM FORMULATION

In this section,we first describe our system model and then the problem of joint caching and transcoding for HTTP adaptive streaming to realize the energy efficiency is formulated.

2.1 System model

As shown in Figure 1,we consider a 5G mobile network integrating the mobile edge computing (MEC) at the Radio Access Network (RAN).That is,the IT and cloud computing capabilities are introduced at RAN and the mobile computing,network control and storage are pushed to network edges.In this case,the services (i.e.video delivery etc.) can be quickly provided to the users,the quality of experience can be improved,and the network traffic through the backhaul link can be largely reduced.

Fig.1.The architecture of the 5G mobile networks with MEC.

Under this framework,we mainly take the HTTP adaptive video streaming delivery into account by using the computing and caching capabilities of MEC in this paper.We assume that there are totalVvideos with a corresponding video set R= {1,2,… ,v,…,V} that can be requested by users.Each videovis divided intoNvconsecutive video segments with the corresponding set of segments as Zv= {Sv1,Sv2,…,Svn,…,SvNv},where theSvndenotes thenth segment of videov.Then,we unify sets from Z1to ZVand define the set of all video segments as Z={S11,S12,… ,S1N1,… ,SV1,SV2,… ,SVNV}.And to make the description simple,we redefine the set Z as {1,2,… ,s,… ,S} to denote the segments of all the videos,andis the total number of video segments of all videos where thesdenotes thesth segment in the whole segment set.In particular,the probability distribution vector of the segments can be denoted by F= {p1,p2,… ,ps,… ,pS},referred to as the segment popularity,where segmentsis requested with probabilitypsand=1.We also assume that each segment containsLseconds in playtime,and each segment can be encoded toKdifferent bitrates and we define the set Ξ= {1,2,… ,k,… ,K} to denote the possible bitrate versions.The bitrate versions in set Ξ are arranged in ascending order,which meansk=1 represents the lowest bitrate version andkK= represents the highest bitrate level.LetRskbe the bitrate of thesth segmentwith thekth bitrate version,and a higher bitrate than versionkof the same segment is defined asRsk+.For simplicity,in the remainderof this article,we also useRskandRsk+to present the actual content of segmentswith bitrate versionkand the exact content of segmentswith a bitrate version higher thank,respectively.We assume that for each segment,the bitrate is constant,thus,the size of segmentswith bitrate levelkcan be described asL*Rsk.

Relying on the caching and computing capabilities,the MEC server can not only cache different video segments with different bitrate versions but also can realize transcoding between different bitrate versions of the same video segment.Hence,every time when video requests forRskis arrived at MEC server,there would be three possible modes as inspired by [21]:

·Direct hitmode:whenRskexactly exists in the MEC server,then MEC server will respond to users directly by deliveringRsk.

·Transcoding hitmode:ifRskdose not exist in the MEC server,however there is a higher bitrate version of the segments,denoted asRsk+.In this case,the transcoding schedule may be triggered.That is,MEC server can choose to transcodeRsk+toRsk,or to requestRskfrom the origin content server through backhaul links,which depends on the scheme of transcoding schedule decision.Here,we notice that a higher bitrate version can be transcoded to a lower bitrate version,conversely,it is not able to upgrade a lower bit rate version to a higher bit rate one as proposed in [13].

·Missmode:NeitherRskexists,nor a higher bitrate versionRsk+exists in the MEC server.Undermissmode,the MEC server will respond to user requests by gettingRskfrom the origin server.

The above three possible cache response mode are described in Figure 2.As there are two optional ways to serve requests of users under thetranscoding hitmode,here we bring some more discussion on the necessity to do this choice,which we call “transcoding schedule”.Consider a scenario in which there is a request forRsk=500kbpsand the MEC server only holds a higher bitrate versionRsk+=5Mbps.If the MEC server chooses to transcodeRsk+toRsk,the difference of segment size between the higher bit rate version and the requested bit rate version can be presented as (Rsk+-Rsk)*L,which is much greater than the data size of retrievingRskfrom origin server.And transcoding cost is determined by three factors:input bit-rate,target bit-rate,and video length,therefore,here we use (Rsk+-Rsk)*Lto present the data size involved to be dealt with by the MEC server.Thus,there is a tradeoff between transcoding cost and retrieving cost and it is wise to arrange a transcoding schedule to enhance the network performance.

Under this setup,taking the caching and transcoding mechanism into consideration,two main problems should be carefully solved to optimize the network performance:content placement and transcoding schedule,under the constraints of the caching capacity and computing capability of MEC server.Due to the energy efficiency is one of the most important key performance index in 5G networks,we mainly take the energy efficiency into account,and consider the joint caching and transcoding to improve the energy efficiency in this paper.

2.2 Problem formulation

Based on the above assumption,we will formulate the optimization problem for the energy-efficient joint caching and transcoding in this subsection.Before given the optimization problem,we first give some assumptions for the variables and constants used in the problem formulation which are summarized in Table I,then the detailed explanation of variables and constants are as follows.Letxskbe the caching variable that indicates the decision of whether to cache the video segmentswith versionk.Andxsk=1 denotes that the video segmentswith versionkis cached at MEC server,otherwise,xsk=0.

We also assume that the MEC server has the maximum caching capacityCm(GB).In this case,the total caching size of MEC server could not exceed the maximum caching capacity,which can be expressed as follows.

As the MEC server can provide the computing capability to realize transcoding between different bitrate versions of the same video segment,we can letzsk+be the variable to indicate whether there exists a higher bitrate version than versionkof segmentscached in MEC server.We setzsk+=1 when MEC server caches a higher version of segmentk,zsk+=0 otherwise.Therefore,we can easily draw a conclusion that the transcoding procedure possibly be executed only when there is a segment with higher bitrate version cached in the MEC server,sozsk+andxskshould follow the following constraint.

Fig.2.Three possible cache hit modes.

Table I.Main parameters used in the formulation.

In the above assumption,xskandzsk+are the binary variables to indicate the content placement decision.As for the transcoding schedule decision,here we use binary variableyskto describe.Andysktakes 1 if MEC server chooses to transcodeRsk+toRskand 0 ifRskis retrieved from the origin server.Consider that the transcoding schedule is valid only when a content request corresponds to thetranscode hitmode,ysksubjects to the following constraint:

Then from an energy efficiency perspective,our objective of proposing the joint caching and transcoding schedule policy is to minimize the energy consumption of the 5G networks.And there are the following three kinds of energy consumption should be considered in our problem formulation.

·Caching EnergyEc:This component is the energy required to store the contents to the MEC server,which is directly proportional to the data size stored in MEC server.Here we adopt an energy proportional model [22]-[23].Assume that the caching energy required for storing each bit of content in an MEC server during per unit time iswcm(J/bit),then the energy consumed by cachingRskis given by:

·Transport EnergyEt:Notice the fact that it is an inevitable process to transport content from MEC server to users through wireless links under the fore-mentioned three cache hit mode,which means that this part contributes the same amount of energy consumption to the total energy consumption of the three requesting-responding modes.For simplicity,we ignore this wireless transporting part and focus on the transporting energy consumption caused by retrieving content from the origin server to the MEC server through backhaul links.Assuming that the transporting energy efficiency and the bandwidth of the backhaul link between the MEC server and the origin server areeom(Watt/bit) andWom(Mbps)[22],respectively,then we can get the transporting delay through the following formula [23]:

then,considering the contribution as proportional with respect to the amount of data transported by the network [24],we give the transporting energy consumption as follows:

·Transcoding energyEd:Assuming that the number of CPU cycles required to process one bit input iscm(cycles/bit),thus,the time consumed by transcoding can be given by [24][25]:

wheref0(GHZ) and the numerator in the above formula are the dominant frequency of CPU and the total CPU cycles required to transcodeRsk+toRsk,respectively.Then,inspired by [26],the transcoding energy consumption can be given:

whereδ(Watt/GHz) is the energy efficiency for MEC server to execute one CPU cycle.

According to the above analysis and taking the request probability distribution into consideration,the average total energy consumption of serving the video requests can be given by the following formula:

To achieve an energy-efficient network system,we now formulate the optimization problem as the following integer linear programming (ILP) problem:

Subject to:`

The objective function expects to minimize the total energy consumption of the system under the constraints.And the first constraintthat the total content size cached in the MEC server should below the constraint of caching capacity,the second constraintdenotes that the computation using the transcoding should not exceed the finite capacity of the CPU.The third constraintindicates the availability of a higher bitrateversion for transcoding,in whichzsk+is highly coupled withxsk.The fourth constraintysk≤zsk+provides a precondition for the availability of transcoding schedule.The last three formulas expose binary constraint to the indications of the content placement and transcoding schedule respectively.

III.THE SOLUTION TO THE JOINT CACHING AND TRANSCODING FOR ENERGY EFFICIENCY

In this section,we will solve the joint caching and transcoding problem for energy efficiency formulated in (10).From the optimization problem in (10),we can observe that the problem of joint caching and transcoding is an integer linear programming problem (ILP) and finding the optimal solution is an NP-hard problem,which may bring huge computation complexity.Therefore,in order to reduce the computation complexity,an approximate method based on simulated annealing (SA) algorithm is proposed to obtain the best solutions for our problem in this section.We first give a brief introduction for the basic principle of the simulated annealing in Subsection III-A.Then the joint caching and transcoding scheme for energy efficiency based on the simulated annealing algorithm is proposed in Subsection III-B.

3.1 The basic principle of the simulated annealing

Simulated annealing is a classical optimization technique to solve combinatorial optimization problems,which is derived from annealing in metallurgy,a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce its defects [27].

Using the physical annealing process as an analogy,the working process of simulated annealing applied to combinatorial optimization problems can be described as follows:It starts by setting a random initial feasible solution as the initial state and computes its corresponding profit by applying the objective function,which is energy in physical annealing.The control parameterTis also set at a relative high value,which will gradually decrease to zero in the search process under the control of a given annealingfactorthat is advised to take a value between 0.8 and 0.99 [28].At each state,a neighboring solution will be calculated by using a well defined function namedgenerate.Then if the profit difference of the two states leads to profit decrement,the new neighboring solution is accepted.Otherwise,it is accepted by a probability which is defined as Boltzman’s distribution PDF,which can ef-fectively avoid falling into the local minimum [29] and will be justified in the Section IV.At last,the algorithm will achieve the optimum solution of the combinatorial optimization problem,which is called the frozen state in physical annealing.

Table II.Relationship between physical annealing and simulated annealing used in combinatorial optimization.

Algorithm 1.The joint caching and transcoding for energy efficiency based on the simulated annealing algorithm.

3.2 The joint caching and transcoding for energy efficiency based on the simulated annealing algorithm

According to the above description and based on the optimization problem in (10),we can first design the relationship among our proposed scheme based on simulated annealing and physical annealing,as well as the general simulated annealing used in common combinatorial optimization problems,which is summarized in Table II.In our proposed scheme based on SA algorithm,the binary variablesx,yandzdenote a set of feasible solutions in general simulated annealing and a system state in physical annealing,while the set ofx*,y*andz* denotes a set of neighboring solutions and indicates a change of state in physical annealing.Meanwhile,Etotin the formula (9) corresponds to the objective function profit in general simulated annealing,which is an analogy concept of energy in physical annealing.In our proposed scheme based on SA algorithm,we still adopt the temperatureTas the control parameter and the optimum solution in our scheme and the traditional SA corresponds to the frozen state in physical annealing.

Then combining our proposed formulation with the above physical annealing process and simulated annealing process,the structure of our proposed scheme based on SA algorithm is described as Algorithm 1.

Algorithm 1 starts by setting a set of initial solution onx,yandz,wherex,yandzdenote a possible combination ofxsk,yskandzsk+,respectively.The control parameter,temperatureT,is also initialised to a reasonable high value,max_temper,which will eventually decrease tomin_temperin the search process under the control of a given annealingfactor.Every time there generates a new set of neighboring solutions,x*,y*andz*,the algorithm computes the energy consumption difference,denoted as ΔE＜0,between the new solution and the current solution.If the difference value is negative,then accept the new solution as the current solution,otherwise,accept the new solution ife-ΔE/T＞rand(1),which avoids getting stuck in a local minimum.

As the Algorithm 1 describes the basic framework of our iteration process,we can see that an important premise to push the iteration process is generating a new neighboring solution subjecting to the constraints from formula (11) to (17) at each state,which also prevents the occurring of useless solutions that do not obey our formulation assumptions.Therefore,how to generate the new neighboring solution is a key step in the Algorithm 1.Based on this,we design the procedure of SA generate to randomly generate the new neighboring solution,x*,y*andz*,from the feasible data set near the current feasiblesolutionx,yandzunder the constraints from formula (11) to (17).The structure of the procedure of SA generate is described in Algorithm 2.

In a fixed state,the time complexity to generate a new neighboring solution of our proposed scheme based on SA algorithm can be described asOSK(* ),and the total number of states has close relationship with the control parameterTand the annealingfactor.The higher the initial value ofTand the annealingfactor,the higher the global search capacity of our proposed scheme and the more time it needs to find the optimum solution,conversely,the time complexity will decrease but the global search capacity will be degraded if the initial value ofTand the annealingfactordecrease.That is,taking appropriate parameter combination,the algorithm will be characterized by a relatively low time complexity while achieving an ideal convergence.The innovative feature of our scheme based on SA to accept the ”bad solution” by a probability can effectively avoid falling into the local minimum and eventually achieve the global optimum approximate solution [29],which outperforms the traditional algorithm such as greedy algorithm.On the other hand,compared to the genetic algorithm which depends on population integrity search and needs to encode and decode for the population,the proposed scheme based on simulated annealing algorithm searches the optimum solution by a single individual and omits the encoding and decoding process,thus is very simple and can be used for the optimization of complex nonlinear problems.

Algorithm 2.Procedure of SA generate.Input:x,y and z Output:x＊,y＊ and z＊1.begin 2.overfilled ← false ,overComputed ← false ,flag ← false 3.if(∑∑S K **＞) then 4.overfilled ← true 5.end if 6.While(not overfilled) do 7.Select a xsk randomly from x which equals 0,and let xsk← 1 8.if(∑∑x LR Csk sk ms k = =1 1S K **＞) then 9.overfilled ← true 10.end if 11.end 12.While(overfilled) do 13.Select a xsk randomly from x which equals 1,and let xsk← 0 14.if(∑∑x LR Csk sk ms k = =1 1S K **≤) then 15.overfilled ← false 16.end if 17.end 18.y ← 0,z ← 0 19.for(s in 1:S) do 20.for(k in 1:K) do 21.zsk+← min{1,∑ikx LR Csk sk ms k = =1 1K=+1xsi}22.if (y z sk＞ sk+) then 23.flag ← true 24.end if 25.if (flag) then 26.ysk ← 0 27.end if 28.end 29.end 30.if (∑∑S K (sk+- ＞) 0) then 31.overComputed ← true 32.end if 33.While(overComputed)do 34.select a ysk randomly from y which equals 1,and let ysk ← 0 35.if (∑∑y L R R c f * * *sk sk ms k = =1 1S K (sk+- ≤) 0) then 36.overComputed ← false 37.end if 38.end 39.End y L R R c f ** *sk sk ms k = =1 1

IV.SIMULATION RESULTS AND DISCUSSIONS

In this section,we use the computation simulation method to demonstrate the performance of the proposed scheme.On the one hand,we reveal the key system parameters that affect the performance of our proposed video delivery strategy,on the other hand,we provide the performance comparison between our proposed joint caching and transcoding strategy and another two strategies.Furthermore,we provide illustrations of the performance advantages of our proposed scheme based on simulated annealing algorithm by comparing to the traditional greedy algorithm and random algorithm as proposed in [24].

Fig.3.Temperature impact on the convergence rate of the proposed scheme based on simulated annealing algorithm.

In our simulation,the simulation parameters are set as follows.We investigate an MEC server withf0=3.4GHz,cm=300cycles/bit[30] andδ=1Watt/GHz[26].The caching capacity of MEC server isCm=5GBand the caching energy efficiency iswcm=8*10-8J/bit[22].Bandwidth and the transporting energy efficiency of the backhaul link are given byWom=30Mbpsandeom=8*10-6Watt/bit[22],respectively.As for the video segment,we setS=300,Ls=10 andK=4,unless otherwise specified.We also assume that the popularity of the segments is arranged in a descending order according to the Zipf’s law,the request probability of segmentscan be writtenaswhereα∈[0.5,1.5] is the skewness reflecting the concentration of the popularity distribution.In addition,we provide five available sets of bitrate versions with different intervals,listed as [1,1,1,1]Mbps,[1,6,11,16]Mbps,[1,11,21,31]Mbps,[1,16,31,46]Mbps,[1,21,41,61]Mbps.

Experimental results show that the setting of the control parameterTand the annealingfactorinfluence the global search performance of our proposed scheme significantly [29],thus the parameters must be carefully taken and the convergence of our proposed scheme must be verified before we actually begin our simulation,which is the basis of our whole simulation.Figure 3 shows the relationship that energy consumption with the decreasing of control parameter,temperature.To reach the convergence,we set the start temperature at 100,and the annealingfactorat 0.99,while the end temperature is set at 0.05 [28].In Figure 3,we can observe that the tendency of convergence rate is shown clearly by the results of the energy consumption.In the beginning,energy consumption decreases fast,and with the temperature decreasing at a relatively lower level,it displays a premature convergence and then maintains at a nearly constant value.Our next simulations are carried out at the basis of the setting of above two parameters.It is worth noting that Figure 3 also validates the capability of our proposed scheme based on SA algorithm to jump out of a local minimum and approximate the global optimal result.

By verifying the convergence of the proposed scheme in Figure 3,now in our next simulation,we will first focus on the three strategies which are described as follows:

·Our proposed scheme,which takes the transcoding schedule into consideration under thetranscode hitmode.In the other words,when there occurs atranscode hit,MEC server can respond to users by bitrate transcoding or requesting corresponding segment from the origin server,which depends on the result of energy consumption optimization.

·Caching and transcoding,which means there is no trans-porting undertranscode hitmode.Every time when atranscode hitoccurs,MEC server transcodes a higher bitrate version to the requested one,no matter how much the data size it need to process [14].

·Caching and transporting,which means there is no transcoding undertranscode hitmode.Every time when atranscode hitoccurs,MEC server responds the request by retrieving corresponding segment from the origin server,which indicates that the MEC server does not hold the transcoding capability anymore.This strategy actually corresponds to the video delivery in traditional cellular network without MEC [31].

In Figure 4,we investigate the impact of the playtime length of video segments on the energy consumption and [1,10,30,60]Mbpsis given as the set of segment bitrate ver-sions.As formulas of (4),(7) and (8) show,Ec,Et,Edare linear inL,as a result,their product,Etot,is quadratic inL,which is responsible for the shape of the curves in Figure 4.The red curve presents the energy consumption under our proposed formulation,while the blue curve describes the energy consumption without transporting under transcode hit mode and the green curve depicts the energy consumption without transcoding undertranscode hitmode.All of the three curves show an upward trend with the increase of segment playtime length,due to the increasing of data size of each video segment essentially.When the playtime length is relatively short,the data size of the video segment,L*Rsk,is small.Correspondingly,the difference between different bitrate versions of the same video chunkL*(Rsk+-Rsk),is relatively small as well.As a result,transcoding process can be done by high-performance MEC server in a very short time period with lower energy consumption than retrieving content segment through the time-consuming and energy-consuming backhaul link.Thus,the red curve and the blue curve tend to overlap with each other when the playtime length is short,as both of the two strategies would choose to respond to users by transcoding when there occurs atranscode hit.In addition,the third strategy that without transcoding undertranscode hitmode yields more energy consumption than the other two strategies,which is not obviously presented due to the limit of data size when the playtime length is relatively short.With the increasing of playtime lengthL*(Rsk+-Rsk) would be much greater thanL*Rsk,which would cause higher energy consumption if we insist on transcoding a higher bitrate version to a lower one.Thus,it is wise to introduce a transcoding schedule to minimize the energy consumption.Our simulation results also confirm this analysis,and the experimental data also indicates that our transcoding schedule strategy outperforms the other two strategies and brings an approximate six percent performance improvement.

Fig.4.Playtime length of video segments impact on energy consumption.

Fig.5.Interval between bitrate versions impact on energy consumption.

Fig.6.Number of video segment impact on energy consumption.

As the interval between bitrate versions refers to the bitrate difference of the same video clip between a higher bitrate and a lower bitrate,which can be described asRsk+-Rsk,this value directly affects the data size needed to be proceed by MEC server when atranscode hitoccurs.In Figure 5,we use five sets of bitrate versions with different intervals 0Mbps,5Mbps,10Mbps,15Mbps,and 20Mbps,listed as [1,1,1,1]Mbps,[1,6,11,16]Mbps,[1,11,21,31]Mbps,[1,16,31,46]Mbpsand [1,21,41,61]Mbpsto investigate the relationship between energy consumption and the bitrate interval.Similar to the analysis of Figure 4,when the interval is small,its’ influence on data size is negligible,so the red curve and the blue curve tend to overlap with each other.As the interval increasing,it is unwise to always carry out a bitrate transcoding or a transporting form origin server without considering a transcoding schedule.Simulation results in Figure 5 show that our transcoding schedule strategy has obvious performance improvement when the bitrate version interval grows large than the other two strategies.Of course,the energy consumption of the three schemes increase as the bitrate interval increases.

In Figure 6,we study the impact of the number of video segment on the energy consumption under the three strategies.As Figure 6 shows,energy consumption increases as the number of video clips increases.When the number of video segments is small,the system tends to cache all the video segments due to the affluent storage space and the cheap caching energy efficiency.Therefore,direct hithappens with a very large probability whilemissandtranscode hitmay be absent.As a result,energy consumptions under the three strategies are approximately the same.As the number of video segments increases,the capacity-constrained MEC server would cache only a part of video segments,somissandtranscode hitoccur inevitably with a large probability.As analysis of Figure 4 and Figure 5,our proposed transcoding schedule will outperform the other two strategies without transcoding schedule,which has been proved by our experimental results in Figure 6.

Figure 7 shows the relationship between caching capacity of MEC server and the energy consumption under the three different strategies.When caching capacity is relative small,the MEC server can cache only a small part of segments,leading to a very low cache direct hit ratio.As a result,the majority of user requests ought to be responded to by transcoding or transporting from backhaul,thus producing a significant energy consumption.Meanwhile,leveraging the analysis in Figure 6,our proposed transcoding schedule will perform best when caching space is too small,which is proved by experimental results in Figure 7.As caching capacity increasing,the cache direct hit ratio raises,resulting in an energy consumption decline because more and more requests will be served directly by MEC server without transcoding or transporting from backhaul.When caching space is abundant,MEC server tends to cache all the video segments,leading to similar profits of the three strategies.

To prove the advantage of our proposed scheme based on simulated annealing algorithm,we draw a performance comparison of proposed scheme based on SA algorithm with two another classical algorithms:greedy algorithm and random algorithm.Figure 8 investigates the relationship between playtime length and energy consumption while Figure 9 and Figure 10 present the impact of bitrate interval and segment number on energy consumption under the three fore-mentioned algorithms.With the increasing of the three key factors:playtime length,the bitrate interval and the number of segments,the curves take an ascending trend and our proposed scheme based on SA algorithm performs best among the three algorithms while greedy algorithm ranks second.Figure 11 shows the relationship between caching capacity of MEC server and energy consumption.With the caching capacity increasing,the red and the blue curves in Figure 11 shows a downward trend while the green curve presents no evident trend.Furthermore,as the below four figures shows,our proposed scheme based on SA algorithm performs best thanks to the capacity of avoiding being stuck in a local optimization and random algorithm yields worst results due to its uncertainty.

V.CONCLUSIONS

Fig.7.Caching capacity of MEC server impact on energy consumption.

Fig.8.Playtime length of video segments impact on energy consumption.

Fig.9.Interval between bitrate versions impact on energy consumption.

Fig.10.Number of video segment impact on energy consumption.

Fig.11.Caching capacity of MEC server impact on energy consumption.

In this paper,we have proposed an energy efficient joint caching and transcoding schedule strategy to dynamically determine the placement of requested video segments and the way of responding users’ content requests.We have formulated the problem as an integer programming problem to minimize the system energy consumption,thus realize energy-efficient video delivery in MEC-enabled cellular networks.To solve this problem,we have introduced a joint caching and transcoding scheme based on simulated annealing algorithm,which can iteratively approximate the globe best solution.Simulation results have been illustrated to show that our strategy yields more significant gains,compared to another two strategies without transcoding schedule.Experimental outcomes have also proved that our proposed scheme based on SA algorithm takes advantage of the ability of global optimization,and hence has better performance than classical algorithms such as greedy algorithm and random algorithm.

ACKNOWLEDGEMENTS

This work was support by the Major National Science and Technology Projects (No.2018ZX03001014-003).