Near-Optimal Packet Allocation Algorithm forContent Uploading to Media Cloud via

Collaborative Wireless NetworkGe Zhang

School of Computer EngineeringNanyang Technological University

SingaporeEmail: zh0001ge@ntu.edu.sg

Yonggang WenSchool of Computer Engineering

Nanyang Technological UniversitySingapore

Email: ygwen@ntu.edu.sg

Yew-Soon OngSchool of Computer Engineering

Nanyang Technological UniversitySingapore

Email: asysong@ntu.edu.sg

Abstract—This paper investigates the problem of uploadinguser-generated content files (e.g., video captured on mobiledevices) to a media cloud via a cooperative wireless network.The multi-path uploading capability of the cooperative networkprovides new opportunities by optimally allocating the packetsinto multiple paths to reduce end-to-end file uploading delay, thusimprove the end user experience. In this paper, we formulatethe delay minimization problem as an optimization task whichis then studied using evolutionary algorithm (EA). Particularly,we perform a comprehensive investigation on two EA methods,namely, a simple mutation-based method and then the covariancematrix adaptation evolution strategy (CMA-ES) for minimizingthe uploading delay. Extensive numerical simulations demon-strate their near-optimal performance, where the CMA-ES isshown to generate more efficient and robust results. The insightsfrom this paper serves to provide some guidelines in futureplatform and application development.

Index Terms—File delay minimization, collaborative wirelessnetwork, evolutionary algorithm, mutation-based, CMA-ES, con-tent uploading.

I. INTRODUCTION

As the popularity of smart phones continues to grow,an exponential increase of mobile media is generated withtheir ubiquitous wireless Internet access. Nowadays, mobiledevices are normally capable to capture high-quality videosand images with their embedded cameras. Hence, users couldupload these user-generated contents to their Facebook pagesand Youtube accounts in the media cloud. And such emergingusage pattern has contributed significant amount of mobilemedia traffic. According to a recent study by Cisco [1], mobiledata traffic is increasing by a factor of 40 between 2009 and2014; by 2015, video will take up two-thirds of world’s mobiledata.

However, content uploading is faced with many constraints.First it is constrained by the limitation of resource on mobiledevices, such as transmission power, and battery life, etc [2].In addition, the user file uploading experience is hamperedby the signal fading effect in wireless channels. Meanwhile,mobile applications usually need to squeeze the duration ofuploading session in order to accommodate the time frame and

fit in the wireless connections or just to avoid user impatience,therefore, uploading has to complete within some deadline. Asa consequence, it is critical to minimize the end-to-end fileuploading delay to meet application requirements and users’needs, under the physical constraint of wireless links.

The emergence of cooperative wireless networks [3] pro-vides a novel paradigm for the resource-constrained mo-bile device. With the advancements of technology, multiplewireless network interfaces (e.g., 3G, WiFi, Bluetooth, etc)enable mobile devices to overcome many limitations of asingle wireless link (e.g., relaying data transfer via machine-to-machine (M2M) communications). This has introduced anew concept called cooperative wireless network, which opensup a new research area to improve the performance of wire-less communication. As such, cooperative wireless networksprovided provably a lot of advantages, such as, increasingthe network throughput [4], extending the network coverage[5], decreasing the energy cost [6], [7], and reducing the filedownloading and uploading delay in [8], [9], to name a few.Nevertheless, exploiting multi-path opportunity also comeswith several challenges, such as, the complexity of manag-ing multiple simultaneous connections and the heterogeneityamong different paths.

In this paper, we aim to minimize the file delay for contentuploading to the media cloud via multiple connections overcooperative wireless networks. Our previous work in [9] isable to find a near-optimal allocation by proposing an iterativeallocation algorithm. However, there is still room to improvethe optimality of the uploading delay. In this work, weformulate the uploading delay minimization problem as a non-linear programming problem and attempt to solve it usingevolutionary algorithm (EA).

Two EA methods, namely., a simple mutation-based methodand the covariance matrix adaptation evolution strategy (CMA-ES) method are chosen to find the optimal allocation. Ex-tensive numerical simulations are then carried out to validatethe performance of two EA methods. Our obtained numericalresults suggest that CMA-ES is capable of locating a nearoptimal solution. The insights obtained from our research,

Fig. 1. Collaborative wireless network for uploading user-generated contentfiles to media cloud: mobile device communicates with the media cloud viamultiple paths including direct connection to base station or access point andindirect connections via machine-to-machine cooperation.

when properly applied, can provide practical guidelines forapplication development and software design.

The rest of the paper is organized as follows. Section IIpresents a system model and a problem formulation for thepurpose of analysis. Section III first introduces the basics ofEA and then studies two EA methods for minimizing the fileuploading delay in wireless media cloud. In section IV, wevalidate the efficiencies of the EA algorithms, i.e., how longthey take to find a solution and effectiveness i.e., how optimaltheir solutions are. Finally, Section V concludes this paper.

II. SYSTEM MODEL AND PROBLEM FORMULATION

In this section, both network model and analytical modelon file-based content uploading via cooperative wireless net-works are presented; and based on these models, the researchproblem is formulated into non-linear programming problem.

A. Network Model

In this paper, we consider a collaborative wireless networkfor file uploading to the media cloud, as illustrated in Figure1. We assume that a mobile device has multiple networkinterfaces, supporting different wireless protocols (e.g., 3G,WiFi and Bluetooth, etc). In addition, mobile devices arecapable to communicate with media cloud through multiplerouting paths. It can not only directly connect to a basestations and / or access points, but also indirectly reaches themedia cloud via peer-relay, i.e., machine to machine (M2M)communication

In our research, the design objective is to minimize theend-to-end content uploading delay, defined as the durationof time between the moment when the mobile device startsthe transmission of the content packets and the moment whenall the packets are received at the media cloud.

Fig. 2. Multi-path transmission model for content uploading: a content fileof k packets is dispersed into p parallel paths, each of which is modeled asa FIFO queue with service rate of µi.

B. Mathematical Model

The mathematical model for multi-path uploading is mod-eled in Figure 2. It consists of three components: the source,the destination, and a set of network links.

On the source side, a content file of k packets, is dispersedinto p disjoint paths through the network. Path i is assumedto carry ki packets, and we assume that

∑pi=1 ≥ k for load

conservation.On the network side, path i is modeled as an independent

FIFO queue. Following the widely adopted exponential delaymodel [10], the delay of packet j along routing path i, denotedas νij , is modeled as an exponential random variable withrate of µi. In addition, the problem is then formulated underthe assumption where the delays experienced by individualpackets on the same network link are IID (identically andindependently distributed ); and delays experienced by indi-vidual packets on different paths are independent of each other.Hence, the delay of transferring ki packets, denoted as τi , canbe expressed as,

τi =

ki∑j=1

νij , (1)

which is an Erlang random variable with order ki .Upon receiving all the k packets, the file can be regenerated

in the destination side. The end-to-end file delay, τ , is definedas the maximum of all the path delays, i.e.,

τ = max{τi, i = 1, 2, · · · , p}. (2)

C. Problem Formulation

Under this system model, the research problem can be statedas follows: given a content file of k packets, how to transfer itthrough p parallel connections to its destination so that the filedelay is minimized. Specifically, we are seeking an efficientalgorithm to strategically allocate file packets over differentpaths. Mathematically, it can be modeled as the following non-linear programming problem,

mink

E{τ}, (3)

s.t. k1 + k2 + · · ·+ kp = K.

where k = (k1, k2, · · · , kp) denotes a packet applicationvector.

Fig. 3. Work flow of a general evolutionary algorithm.

III. EVOLUTIONARY ALGORITHM METHODS IN FILEUPLOADING DELAY MINIMIZATION

In this section, we will present a brief background on the keyconcepts of Evolutionary Algorithms. Based on these concepts,we present a study on two EA methods for solving the non-linear programming problem formulated in section II.C.

A. Evolutionary Algorithm: The Basics

Evolutionary Algorithm (EA), which is inspired by Dar-win’s theory of evolution, is a well established population-based optimization approach that has received significantsuccess. EA makes use of mechanisms, which are similarto biological evolution process, i.e., reproduction, mutation,recombination and selection to resolve optimization problems.In a typical EA program, candidate solutions to the optimiza-tion problems play the roles as individuals in a population;and fitness function is used to evaluate the optimality ofcandidate solutions. Over generations of evolutions (itera-tions), only the individuals (candidate solutions) with mostappealing evaluation results will be chosen to produce thenext round of descendent; other candidates, however, do notcontribute to next generation because they do not fit in wellto the environment. The search continues until the terminationrequirements are satisfied. The main steps of basic EA aresummarized in Figure 3.

As is shown in the figure, how candidate solutions areevolved is not specified. In other words, given a group of

candidate solutions and their ranking of fitness, researchers canarrive at specialized schemes to produce the new generationcandidate solutions. As a result, various EA methods have beenproposed and comprehensively studied to date. Sometimes,multiple EA methods may be considered on a problem. Inthis case, we can benchmark an EA method by its solutionquality and method run time.

In our research, the candidate solution is a packet allo-cation weight vector k, whose element is wi, the weightsof packets allocated to each path. For example, ki = (0.33,0.67) represents a system with two uploading paths, where33% packets are allocated to path 1 and 67% packets areallocated to path 2. Fitness function f(∗) is a simulator whichtakes number of packets K and weight vector ki as input,simulate the uploading process and generate the uploadingdelay. τ = f(ki,K). The uploading process is modeled asa simple UDP scenario where packet service time follows anexponential distribution.

B. Mutation-Based EA Method

In this subsection, we study a simple mutation basedEA method for packet allocation. When reproducing nextgeneration, mutation occurs when the genetic informationof individuals (candidate solutions) changes. We model themutation process using a multivariate normal distribution asfollows.

km = kn + N(0, σ2), 0 ≤ n ≤ µ, µ+ 1 ≤ m ≤ λ (4)

Where ki denotes a candidate solution, and N(0, σ) denotesnormal distribution with standard deviation σ. If λ and µ areset such as µ = λ/2, then the mutation is further modified asfollows.

km+µ = km + N(0, σ2), 0 ≤ m ≤ µ (5)

Therefore, the original µ candidate solutions, together withthe newly generated λ− µ candidate solutions, they form thesubsequent candidate solutions. The basic steps of the simplemutation-based EA is summarized in Figure 4.

Next, we try to use the mutation-based approach to tacklethe optimization problem as shows in Algorithm 1.

C. Covariance Matrix Adaptation Evolution Strategy Method

In this sub-section, we proceed to study another EA method,namely, the covariance matrix evolutionary strategy (CMA-ES) method. This method is developed by Hansen [11]. CMA-ES makes use of covariance matrix in the evolution. It has beenwidely used in both research work and industrial activities.

In a CMA-ES strategy, new candidate solutions are gen-erated according to a multivariate normal distribution. InCovariance Matrix Adaptation (CMA), the covariance matrix,which is updated in each search, stores the dependenciesbetween the variables in the candidate solutions.

Each generation is composed of three main steps. First, thesampling of new candidate solutions using multivariate normal

Algorithm 1 The Mutation-Based Method to Find OptimalAllocation Policy k

Require: Initial population with λ candidate solutions, µ, amultivariate normal distribution N(0, σ2) and number ofpackets K.

Ensure: µ = λ/2for each candidate solution ki, where1 ≤ i ≤ λ do

Fitness yi = f(ki,K)end forSort candidate solutions based on fitness values ywhile not terminate do

for 0 ≤ i ≤ µ doki+µ = ki + N(0, σ2)

end forfor each candidate solution ki, where1 ≤ i ≤ λ do

Fitness yi = f(ki,K)end forSort candidate solutions based on fitness values y

end while

Fig. 4. The logic flow of mutation-based method.

distribution is performed. Second, ranking of the candidatesolutions is carried out based on their evaluated fitness. Andlastly, the covariance matrix, mean and standard deviationof the multivariate normal distribution are adapted as thesearch progresses.In what follows, we describe CMA-ES ingreater details. There are five key state variables in a CMA-ES algorithm. They are mean of the distribution, m, standarddeviation of the distribution, σ, covariance matrix C and twoevolution path vectors, pσ and pC .

Under our problem formulation, m is a vector of p numbersrepresenting the weights of packets allocated to p availablepaths. m is used as the mean to generate a population of all λ

candidates solutions. The sampling step can be expressed inthe following.

ki = m+ N(0, σ2C), 0 ≤ i ≤ λ (6)

Where N denotes the multivariate normal distribution. Thealgorithm can be summarized in Algorithm 2.

Algorithm 2 The CMA-ES Method to Find Optimal Alloca-tion Policy k

Set λInitialize m, σ, C = I, pσ = 0, p(C) = 0while not terminate do

for each candidate solution ki, where1 ≤ i ≤ λ doki = N(m, σ2)Fitness yi = f(ki,K), where K is total number ofpackets

end fork1...λ = ks(1)...s(λ) with s(i) = argsort(y1...λ, i)

m′ = mUpdate m← k1...λUpdate pσ ← pσ, σ, C, m and m′

Update pC ← pC , pσ, σ, m and m′

Update C ← C, pC , k1, kλ, m′ and σUpdate σ ← σ and pC

end whileReturn m or k1

CMA-ES is a handy and well established tool to solvenon-linear programming problem. To use it, one only needsto provide with the initial state variables, fitness functionand terminating condition as inputs, and final solution willbe generated when it terminates. For complete knowledge,please refer to [11]. The logic flow of CMA-ES are brieflysummarized in Figure 5.

IV. NUMERICAL PERFORMANCE ANALYSIS

In this section, we analyze the performances of the twoEA methods for file uploading delay minimization in thefollowing two aspects, i.e., first, method run-time and second,solution optimality. Based on the simulation results, CMA-ES is observed to be more efficient and effective. Hence,further simulations are conducted to evaluate CMA-ES methodagainst exhaustive search. In this section, 50 independent runsof simulations are made for for each candidate solution.

A. The Run-time results of EA Methods

First, we plot the number of fitness function calls (FFC)versus number of packets received in Figure 6 and Figure 7.Since the run time performance of the evolutionary algorithmsis dominated by the number of calls made on the fitnessfunction (simulator).

In this subsection, we make use of the results obtainedin [9] as a baseline for comparing two EA methods. Thenumbers of FFCs are recorded when the first time the bestcandidate solution from EA outperforms or reach that of

Fig. 5. The logic flow of CMA-ES method.

Fig. 6. A comparison between the simple mutation-based method and CMA-ES method on (512 128 32 8 2) Mbps links.

Fig. 7. A comparison between mutation-based method and CMA-ES methodon (500 400 300 200 100) Mbps links.

Fig. 8. The delay percentage difference between the CMA-ES method andmutation-based method

the heuristic algorithm proposed in [9]. For example, theiterative allocation algorithm can achieve 0.1 sec delay, andafter several generations, the best sampled candidate solutionfrom EA is observed to achieve 0.1 sec (before that moment,delays of candidate solutions are higher than 0.1 sec). In thiscase, a FFCs of 310 shall be plotted in the figure.

From the plots obtained, two key observations can be madeas follows.

First, CMA-ES is observed to be more stable than thesimple mutation-based method, since the latter varies greatlyversus the number of packets. The reason is likely due to themechanisms of CMA-ES, which makes it less vulnerable tothe randomness in the simulator.

Second, CMA-ES, in general takes fewer numbers of FFCsthan the simple mutation-based algorithm to arrive at lower orcompetitive file uploading delay to that reported in [9].

B. Solution Quality of the EA Methods

In this subsection, we will analyze the minimum file up-loading delays of both EA methods. For the sake of faircomparison, the solution qualities of file uploading delays arereported when a maximum FFCs of 3,000 is reached.

The delay between the Mutation-based method and MA-ESis plotted against the number of packets of the content file inFigure 8.Once again, the plots for two sets of link rates areconsidered. They are (500 400 300 200 100) and (512 128 328 2) Mbps.

From the plots, the following observations have been made.There is insignificant differenceon the delay minimized byboth approaches. The worst case percentage difference remainsto be bounded within 10%. CMA-ES outperforms the simplemutation-based method most of the time.

Thus, CMA-ES is more robust and efficient for file upload-ing delay minimization.

Fig. 9. The delay percentage difference between CMA-ES method andexhaustive search.

C. Compare CMA-ES versus Exhaustive SearchIn this subsection, we investigate the performance of CMA-

ES against the exhaustive search. To be specific, we conductthe CMA-ES method and exhaustive search method separately,and present their minimum delays.

We explore several sets of degrading links, on which simu-lations are made separately. These link set-ups can be broadlyclassified into two categories, i.e., exponentially degradinglinks and linearly degrading links. For each category, we tryto simulate two cases as follows. First, fast degrading linkswhose rates vary greatly, e.g., 512, 84, 8; and second, slowlydegrading links whose rate degrading factor is small, e.g., 512,256, 128.

In all the test cases, the size of the packet is set to 128bytes. And the link rates are in Mbps. Now, we explore thefollowing test cases. They are 500 300 100, 500 400 300 and500 450 400 for the linear category; and 512 64 8, 512 12832 and 512 256 128 for the exponential category.

From Figure 9, we observe the following features. First, thepercentage difference in the worst case is less than 1.5%, andthe worst case occurs when k is small. Second, a convergingfashion can be observed from the plot where the percentagedifference decreases when the number of packets increases.Third, when the number of packets is greater than 2000, CMA-ES can generate a delay quality with a percentage differencelower than 1%.

Although the heuristic algorithm proposed in [9] can alreadygenerate good solution, we manage to improve the near-optimal quality of the file uploading delay minimization prob-lem in this present work. Note that this is crucial for enhancinguser experience and minimizing the file uploading delay, usingEA is shown to be viable and rewarding. However, due tothe stochastic nature of EAs, the drawback is longer timeto generate a good quality solution over other fast heuristicmethods.Nevertheless, appropriate balance between stochastic(quality) and deterministic search (speed) can be attained viathe design of effective memetic algorithms [12] [13], thus ourwork is appealing to both users and applications’ needs.

V. CONCLUSION

In this research, the optimization problem of minimizingthe file uploading delay have been extensively investigated.The objective is to improve the end user experience for fileuploading in mobile applications to the media cloud throughmultiple transmission paths in cooperative wireless networks.Specifically, we have attempted to address the optimizationproblem using evolutionary algorithms (EA). Two EA meth-ods, namely, a simple mutation based method and the CMA-ES method have been investigated comprehensively. Numeri-cal simulations indicated that the CMA-ES was more efficientand robust. Validation of CMA-ES against the exhaustivesearch indicated that CMA-ES can achieve a higher levelsolution quality under limited computational budgets.

As future work, we will investigate the strategy of applyingthe technique of inter-path packet coding in order to furtherimprove the quality of the allocation algorithm. To interfaceour research to the industrial standards, we are also lookinginto the interaction with TCP/IP protocols.

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