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556 IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING, VOL. 2, NO. 2, JUNE 2018

Utilization of Stochastic Modeling for GreenPredictive Video Delivery Under

Network UncertaintiesRamy Atawia , Member, IEEE, Hossam S. Hassanein, Fellow, IEEE, Najah Abu Ali, Member, IEEE

and Aboelmagd Noureldin, Senior Member, IEEE

Abstract—Predictive resource allocation (PRA) has gainedmomentum in the network research community as a way tocope with the exponential increase in video traffic. ExistingPRA schemes have demonstrated profound energy savings andubiquitous quality of service (QoS) satisfaction under idealis-tic prediction of future network states. In this paper, we relaxthe main assumption of existing PRA work and tackle uncer-tainties in predicted information which resulted from space andtime variation of the network load and users demands. A robustgreen PRA (R-GPRA) is proposed to: model the uncertainties asrandom variables, ensure a probabilistic satisfaction of QoS con-straints, and follow a risk-aware preallocation of future demand.A recourse programming model is used to represent the trade-off between the energy-savings and the risk of wasting resourceswhile considering the probability of a user terminating the videosession at each time slot. Thus, the scheme prevents the networkfrom prebuffering the future video content that might be skippedby the user. Similarly, a chance constrained programming modelis proposed to provide a probabilistic QoS representation toguarantee that the sum of resources, predetermined to videostreaming users, do not surpass the total time-varying networkcapacity. We prove that a near-optimal solution is attainable byproposing a guided heuristic search with small optimality gap tonumerical methods. Simulation results demonstrate the abilityof R-GPRA to deliver energy-efficient video streaming with lessresources than existing PRA while promising QoS satisfaction.These results provide the incentive to implement the R-GPRA infuture wireless networks.

Index Terms—Channel state prediction, energy efficiency, par-ticle filter, radio access networks, resource allocation, robustness,video streaming.

I. INTRODUCTION

THE GLOBAL Internet traffic is expected to grow tremen-dously reaching 2.3 zettabyte by 2020 [1]. At that time,

Manuscript received June 15, 2017; revised September 23, 2017 andDecember 5, 2017; accepted January 25, 2018. Date of publicationFebruary 1, 2018; date of current version May 17, 2018. The associate editorcoordinating the review of this paper and approving it for publication wasE. Ayanoglu. (Corresponding author: Ramy Atawia.)

R. Atawia is with the Electrical and Computer EngineeringDepartment, Queen’s University, Kingston, ON K7L 3N6, Canada (e-mail:[email protected]).

H. S. Hassanein is with the School of Computing, Queen’s University,Kingston, ON K7L 3N6, Canada (e-mail: [email protected]).

N. Abu Ali is with the College of Information Technology, United ArabEmirates University, Al Ain, UAE (e-mail: [email protected]).

A. Noureldin is with the Electrical and Computer Engineering Department,Royal Military College of Canada, Kingston, ON K1R 7Y6, Canada (e-mail:[email protected]).

Digital Object Identifier 10.1109/TGCN.2018.2800708

mobile devices will be contributing to more than two-thirdsof the total Internet traffic, where more than three-quartersof such traffic is expected to be video content. Maximizingstreaming quality while minimizing the number and durationsof stops remains the ultimate goal for mobile video streamingusers. This, however, will put network operators under hugepressure as they strive to meet users’ QoS expectations giventhe available network resources and infrastructure to maximizetheir profit. Nevertheless, the unprecedented increase in carbonfootprint and energy costs raised the need for energy-efficientvideo delivery over wireless networks [2], [3]. Such challengesprompt optimal design for QoS-aware resource allocationschemes that can target energy minimization during servicedelivery [4]. Such design augments the gains of research workdone on regulating spectrum access and maximizing radioresources [5], [6].

Supported by mobility and channel predictions [7]–[9],predictive resource allocation (PRA) was recognized as a newparadigm showing great potential of remarkable energy sav-ings and pervasive QoS satisfaction [4], [10], [11]. Today’snetworks adopt opportunistic schemes that perform resourceallocation decisions based on current and previous measure-ments. On the contrary, the PRA leverages future networkconditions to recognize users moving towards regions withlow channel rates (typically needing more resources) andprebuffers their video content upfront. Whereas prebuffering ispostponed for other users heading to regions with high channelrates. Despite the reported energy and QoS gains in the liter-ature, the following practical challenges related to predictionuncertainty must be addressed:

• Channel Rate Variations: The first parameter used inPRA is the future channel rate of mobile users basedon their trajectory. Both mobility traces and channelstate prediction accommodate errors due to the noiseof their raw data, adopted low-cost filters, and tempo-ral variations of the wireless signal [12], [13]. Existingapproaches in [14] and [15] considered robust heuristicdecisions that exploit states of the rate predictor or adaptthe allocation window size to minimize the impact ofuncertainty.

• Demand uncertainty: The user demand is represented byboth the streaming bitrate (i.e., video quality) and thewatching duration. Users can frequently change the qual-ity of video, skip some frames or terminate the session

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ATAWIA et al.: UTILIZATION OF STOCHASTIC MODELING FOR GREEN PREDICTIVE VIDEO DELIVERY UNDER NETWORK UNCERTAINTIES 557

completely before the end [16]. The Non-PRA approachin [17] and [18] controlled the buffer size during the shortterm decisions based on the stability level of the ses-sion. The impact of demand uncertainty is more severein the case of PRA. Fig. 1(a) depicts an example ofenergy wastage as a result of terminating the session att = 5. The risk of wasting resources increases as PRAmaximizes prebuffering for users experiencing peak rates.Existing robust non-PRA techniques [17], [18] aim todecide when to prebuffer the video at the current slot, tosave the tail energy, or postpone the delivery. The PRA,however, requires further efforts to consider the trade-offover the time horizon since postponing full video deliveryrequires more resources to transmit the remaining contentduring future poor channel conditions.

• Network resources: The stochastic arrival of users withstringent service delay requirements, such as voice calls,will decrease the total available resources for stream-ing users. In turn, this will increase the risk of violatingQoS requirements for cell-edge video users who are allo-cated a small portion of the available resources. Fig. 1(b)depicts this scenario where the network follows a stingyallocation for a cell-edge user to minimize the energyconsumption. The risk of violating the demand, when theuser do not receive the minimum amount of data, has tobe modelled by the PRA. Thus, the minimal allocation isfollowed during resources stability while an opportunisticstrategy is adopted in uncertain conditions.

Existing PRA assumed idealistic scenarios [4], [10], [11],[19] where the average values of all three parameters areadopted. In order to maintain the prediction gains, mobilebuffering capabilities have to be fully exploited while apply-ing long-term decisions at the beginning of the time horizon.Our recent work on robust PRA [20]–[25] tackled the firstparameter (i.e., rate uncertainty) and showed that predictiongains are still attainable when probabilistic risk-aware PRA isapplied.

We focus on the second and third sources of uncertainties byconsidering the possibility of video termination and variationsin network resources while deriving long-term energy-efficientallocations. The proposed R-GPRA should measure the risk ofwasting resources and compare it to the possibility of energysavings to determine when and which content to prebuffer.This is in addition to considering the scenarios in which thetotal available network resources are shared with real-timeusers. A probabilistic metric is defined to guarantee a min-imal level of QoS satisfaction and controls the impact of suchscenarios.

This paper introduces, for the first time in literature, a robuststochastic green PRA framework that achieves energy sav-ings and QoS satisfaction over a time horizon under bothdemand and network resources uncertainties. The frameworkis referred to as R-GPRA and incorporates the followingcontributions:

1) We capture the uncertainties in both the demandand network resources by proposing a stochasticoptimization model. The main objective is to minimizethe total allocated resources, i.e., less energy, while

satisfying the time slot demand constraint. The modelrelies on Recourse Programming (RP) and ChanceConstrained Programming (CCP) to represent the uncer-tainties in the objectives and constraints as randomvariables. This is unlike existing PRA work [11], [26]that assumed perfect prediction and used determinis-tic formulation based on the average value of predictedinformation. In essence, our RP considers the risk ofwasting resources due to video streaming users termi-nating the session before watching the entire video [16],[27]. Similarly, the CCP controls the QoS degradationsunder resources fluctuations due to the random arrivalof users with real-time services. The CCP allows thenetwork operator to adjust both the maximum alloweddegradation level and the energy-saving gains over thetime horizon.

2) We leverage the temporal statistical data of video con-tent and users arrival to obtain a robust allocation ofnetwork resources over the time horizon. Such datais used to develop a deterministic equivalent form forthe stochastic RP and CCP models. In essence, theprobability distribution of video watching durations isused to quantify both the possibility of energy-savingand the risk of wasting resources. Thus, the networkprebuffers future demands that has high likelihood ofwatching, and delays the delivery of future uncertaincontent. Similarly, the probability distribution of users’arrival and their traffic load are used to calculate thefluctuations in the time-varying network resources. Theresultant allocation ensures that the QoS degradations donot surpass predefined level in the CCP model when theremaining network resources for video users are scarce.As such, a deterministic resource allocation model isobtained and takes into account both energy-savingsand the risk of QoS violation during resources uncer-tainty. As opposed to traditional non-predictive robustapproaches [28], [29], our model considers allocationwith RP and CCP over a time horizon that capturesdependency between the constraints.

3) For the network to obtain an on-line solution, a guidedheuristic search algorithm with polynomial complexity isdeveloped. The algorithm exploits the trade-off betweenthe network constraints, i.e., resources and slot demand,and prediction gains. The heuristic considers the impactof decisions at one slot on the energy savings and QoSsatisfaction in future slots. This strategy generates solu-tions that satisfy the probabilistic QoS level definedin the CCP model without compromising the energysavings of the RP. Whilst commercial solvers do notprovide solutions in real-time, they can be only used asbenchmarks.

This paper is organized as follows. In Section II weprovide a background on PRA and robust stochastic-basedoptimization. Section III presents the system model and theproblem definition. Section IV introduces the robust prob-abilistic formulation, and recourse and chance-constrainedprogramming based deterministic formulations. The low com-plexity guided heuristic is presented in Section V, simulation



results are discussed in Section VI, and finally, we concludethe paper in Section VII.

II. BACKGROUND AND RELATED WORK

A. Existing PRA for Video Streaming

Extensive network measurements demonstrated thepredictability of users’ behaviour up to 93% [30], includinghuman mobility and activity [9]. Meanwhile, the radio signalstrength and available bandwidth are found to follow repet-itive spatio-temporal patterns [12], [13]. The availability ofnavigation systems at current user devices (e.g., smartphones)has enabled mobile operators to correlate the radio mea-surements (e.g., channel rates) with geographical locations,and construct the Radio Environment Map (REM) [31]. TheREM is further used to retrieve the future radio conditions(e.g., channel rate) for the predicted mobility traces enablingthe PRA to derive long-term proactive decisions over theanticipated time horizon.

The video delivery approaches in [4], [10], [11], [19],and [26] have applied the concept of PRA to achieve optimalradio resource utilization. Hence, the PRA minimizes theenergy consumption and maximizes the delivered video qual-ity, in low load scenario, while maximizes the QoS satisfactionby avoiding video stops, in high load scenarios. The PRA ingeneral tries to avoid allocating resources to users during poorradio conditions, that consume more airtime per byte, whilemaximizing the allocation during peak conditions by leverag-ing the content availability and prebuffering capabilities at theBase Station (BS) and user devices. To calculate the resourceshare for each user, the PRA typically follows one of twostrategies: greedy prebuffering or minimal allocation. The firstis applied to users experiencing their peak channel rates wherethe network transmits as much video content as possible toavoid transmission with future poor channel rates. This is doneunder the assumption that the user will be watching the wholevideo. Prior to reaching such peak rates, the network servesthe users with the minimal amount of resources to barely sat-isfy the time slot demand. The base station after prebufferingthe video or sending the minimal amount, can then go into thesleeping mode to save energy or serve other real-time users.

To derive performance gains over opportunistic RA, thePRA in [4], [10], [11], [19], and [26] all assumed stableuser behaviour with perfect knowledge of users’ demands andnetwork resources. Thus, in low load scenarios, the BS wouldbe able to prebuffer a long video segment for users experienc-ing peak channel rates. However, the user might terminate thesession before watching the prebuffered content which resultsin suboptimal resource utilization diminishing the predictiongain compared to the opportunistic non-predictive RA. Aswell, the random arrival of real-time users will impact theresource availability for video streaming users. This impactincreases the risk of resource scarcity for the PRA target usersespecially during the minimal allocation strategy, resulting inincreased video stops and QoS degradations.

To tackle the uncertainty problem, we adopt robust stochas-tic optimization to measure the uncertainty in user demands

and network resources. In addition to the predicted informa-tion, the stochastic optimization employs the probability ofterminating the video, represented by watching time distri-bution, and the probability of scarce resources, representedby the user arrival distribution and load. The schematic dia-grams presented in Fig. 2(a) and Fig. 2(b) illustrate the maindifference between existing PRA and the proposed R-GPRAwhere the latter takes into consideration the uncertainties inboth demand and network resources. As such, the robustPRA will only prebuffer the content which in all likelihoodwill be viewed by the user before terminating the videosession and during time slots with a high probability ofresource availability. We consider energy minimization wherethe proposed scheme will be referred to as robust greenpredictive resource allocation (R-GPRA) which is based onstochastic optimization techniques reviewed in the followingsubsection.

B. Robust Stochastic Optimization

Robust stochastic optimization refers to incorporating uncer-tain values in the mathematical programming model. In partic-ular, these values are represented as random variables, and thusthe set of constraints becomes probabilistic while the objec-tive function appears in a non-closed scenario-based form [32].As such, stochastic optimization provides the network designerwith the flexibility of modeling the trade-off between maxi-mizing prediction gains and minimizing the risk of violatingthe QoS.

The CCP is adopted to handle the probabilistic constraintsby transforming them into a deterministic equivalent which istypically done using either the Probability Density Function(PDF) or Moment Generating Function (MGF) of the randomvariable as in Scenario Approximation (SA) and BernsteinApproximation (BA), respectively. The SA exploits the PDFof a random variable to construct all the possible realizationsover the time horizon and their probabilities (i.e., probabil-ity mass function). The constraint will be represented in aform that guarantees a solution satisfying N scenarios, wherethe total probabilities of such N scenarios is above a minimallevel denoted by β. Satisfying more scenarios will generate aconservative solution that has a lower value of the objectivefunction and hence lower prediction gains. On the contrary,satisfying scenarios with less total probability will result in anon-robust solution that violates the QoS level.

Similar to CCP, the Recourse Programming (RP) is usedfor handling problem uncertainties that impact the value ofobjective function. The RP model essentially consists of twoterms in the objective function. The first term models thenetwork gain by using the average of random variables whilethe second term adopts their PDF to prevent risky deci-sions that preserve the total gains in the network duringuncertain conditions resulting in a deterministic closed formRA formulation which can be further solved by mathemat-ical optimization techniques. As opposed to existing robustnon-predictive RA [29], [33], our problem considers a timehorizon that takes into account the interdependency betweenthe resources of a single time slot and the future demandsrepresented in a cumulative form.



Fig. 1. Illustration of wasting resources and QoS degradations.

Fig. 2. Schematic diagrams of existing and proposed frameworks.

Both CCP and RP have been discussed in the literature fornon-predictive RA (without a time horizon) to handle uncer-tainties in the demand and channel rates [29], [33]. While thePRA typically involves decisions over a time horizon, the CCPhas to account for the interdependency between the constraints.

The violation of a time slot’s constraint can propagate andimpact the satisfaction of the next slot demand. For the RP,preventative decisions should be taken at the beginning of thetime horizon to avoid suboptimal future decisions; unlike theconventional RP that reactively takes counter actions (e.g.,



releasing extra allocated resources) after the exact values ofuncertain parameters are unveiled.

Motivated by the uncertainty modelling in [12] and [13], ourearlier work in [20]–[22], and [34] focused on energy-efficientrobust PRA where the uncertainty was only in future channelrates. In this paper, the proposed stochastic based R-GPRAachieves long-term energy savings and QoS satisfaction underdemand and network uncertainty, which are demonstrated bythe probability of video termination and resource unavailabil-ity at each time slot. A discrete linear formulation is obtainedby RP and CCP, which can be solved by commercial solversfor benchmark solutions. Moreover, a low complexity guidedheuristic for real-time allocations is introduced. This heuris-tic exploits the problem structure to achieve near optimalenergy savings, and satisfy all the QoS and resource limitationconstraints.

III. SYSTEM MODEL AND PROBLEM OVERVIEW

A. System Model

Each BS is serving a set of video streaming users denotedby M, where each user index is i ∈ M. To achieve energysavings, a constant streaming rate is assumed which can beeither manually selected by the user or decided by the network.Both the users’ locations and channel rates are known for thenext T time slots, where each slot index is denoted by t ∈ T .The total video is available at the serving BS, at t = 0, andthe bottleneck is assumed to be the radio link. The predictionof channel rates is performed by mapping the user’s currentlocation to the REM at the mobile operator. The REM containsboth the user’s locations and their corresponding channel ratesri,t for user i at time slot t [31].

1) Resource Allocation: The users of the same BS share theavailable radio resources every time slot t, where each user i isallocated a fraction of the slot’s airtime denoted by xi,t ∈ [0, 1].Other real-time users are sharing the same resources, but theirallocation is not handled by the R-GPRA.

2) Predicted User Demand: The average demand of useri at time slot t is denoted by vi,t which corresponds to thedata content played back with fixed quality. We assume thatthe user can either terminate the session completely at anytime slot t or skip part of the video and watch the subsequentframes. Unlike existing models in [35] that handle the firstcase only, our model allows the network to prebuffer the futurecontent which might be watched by the user after skippingsome frames of the video. Accordingly, the per slot demandis modeled as a random variable vi,t that is equal to 0 (userterminated the video) or vi,t (user streaming the video). Thecumulative demand is denoted as a random variable Di,t =∑t

t′=0 vi,t′ .3) Predicted Network Resources: At each time slot, the

resources are shared among both the streaming users (con-sidered by the R-GPRA) and other real-time users. The trafficof the latter is modeled using their arrival rate and demandedresources. The arrival of real-time traffic users is modeled asa Poisson distribution with mean λ, and the demand per useris denoted by C. The total airtime share allocated to real-timetraffic users at time slot t is denoted by the random variable

Ct. It has to be noted that we model the arrival of users’ real-time traffic demand which is typically modelled as Poissonprocess [36], and not the mobile users admission or arrival atthe BS.

4) Energy Minimization: With the current BS ON/OFFswitching capabilities, the energy consumption E in the down-link is calculated using the consumed power P and the timeX during which the base station was switched ON. ThusE = P × X = (PW + PD) × X, where P is the summationof both the power radiated over the wireless link, denoted byPW , and the power for operating devices denoted by PD. Thevalue of PW is constant since power control is not appliedin LTE [37]. Similarly, the dominant part of PD is consumedby the RF devices which is either fixed or negligibly vary-ing and thus the power values is also constant, [38]. Thus, theenergy consumption can be expressed in terms of the airtime Xwhich corresponds to the time in which the above-mentioneddevices are switched ON and the signal is radiated over thewireless link. In addition, measuring the energy consumptionusing the airtime will provide a common ground for energy-efficient PRA as the power term differs across BSs based onthe efficiency of devices [39]. In conclusion, and similar to theexisting PRA in [4] and [40], our framework will express theenergy consumption as the total time fractions

∑xi, t allocated

to the users.

B. Problem Description

The robust Green Predictive Resource Allocation (GPRA)scheme aims to calculate the airtime fractions xi,t for eachuser at time slot t such that the total allocated resources areminimized to achieve energy-saving or efficient bandwidth uti-lization. The possibility of terminating the video by the userat a certain time slot is taken into account. By doing so, thisprevents the PRA from prebuffering future content to userswho might terminate the video at any time slot with a certainprobability. Typically, this results in more energy savings andoptimal bandwidth utilization compared to existing non-robustPRA that assumed perfect demand prediction.

As illustrated in Fig. 3 (a), the values of predicted rates forthree time slots would typically lead the PRA to prebuffer thewhole content during the first slot to save energy as depictedin Fig. 3 (c). However, as shown in Fig. 3 (b), the high prob-ability of terminating the video at the third time slot preventsthe robust PRA from prebuffering the future content due tothe high risk of wasting energy. As such, only the content ofthe second slot, with a low probability of video termination,is prebuffered whereas the delivery of the third slot’s contentwill be postponed as illustrated in Fig. 3 (d). To summarizethe example, delivering the rest of the video content in thethird time slot costs more energy, in case of non-termination,while prebuffering all the contents causes a waste of resourcesin case of termination of viewing. The proposed robust PRAcalculates this trade-off based on both the predicted rates andthe probability of termination to perform the energy-efficientand QoS-aware allocation.

The uncertainty of future network resources, due to ran-dom user arrival, will interfere with the strategy mentioned



Fig. 3. Illustration of R-GPRA under Uncertain Video Streaming Demand.

earlier. Delaying the transmission in the case of high termina-tion probability might be considered suboptimal if the futurenetwork resources are scarce. The network, in that case, willmiss the chance of exploiting the current channel peaks andvacant resources, and without being able to satisfy the userdemand given the future anticipated limited resources. As aresult, fewer energy-savings are attained in the case of futurepeaks with low resources, while video stops are observed iffuture low channel rates are further reduced by real-time trafficuser’s arrival.

IV. R-GPRA FORMULATION UNDER UNCERTAIN

DEMAND AND RESOURCES

In this section, we mathematically formulate the problem ofrobust GPRA (R-GPRA) using stochastic optimization, andthen adopt recourse and chance constraint programming toobtain deterministic equivalent forms.

A. Stochastic Formulation

The introduced energy-efficient robust PRA is formulatedusing stochastic optimization. In particular, the uncertaindemand and future network resources are represented byrandom variables as follows:

minimizex

{∑

∀i∈M

∑

∀t∈Txi,t

}

subject to:

C1:t∑

t′=0

ri,t′xi,t′ ≥ Di,t, ∀ i ∈ M,∀t ∈ T ,

C2:M∑

i=1

xi,t ≤ 1 − Ct, ∀t ∈ T ,

C3: xi,t ≥ 0, ∀ i ∈ M, t ∈ T . (1)

The objective function aims to minimize the total consumedenergy represented as a function of the total BS airtime [39].The QoS constraint in C1 guarantees that the total deliveredcontent to the user satisfies the anticipated cumulative randomdemand. C2 models the limited resources at each BS by ensur-ing that the sum of allocated airtime is less than the total avail-able network resources (allocation slot duration) while con-sidering the random resources allocated to the real-time trafficusers. The last constraint C3 ensures the non-negativity of thedecision variables. The main difference between the proposedrobust formulation and the existing PRA work is the first andsecond constraints that now incorporate random demand andnetwork resources. Such randomness has an impact on bothobjective function value and QoS satisfaction. In particular,when the random demand equals to vi,t, the objective functionis minimized by prebuffering the future content in peak rates.On the other hand, when the random demand becomes 0 (dueto session termination) the objective function is minimized byavoiding prebuffering of future content. Similarly, the networkshould avoid prebuffering when available resources are low(due to the periodic arrival of real-time traffic users) as thepre-calculated resources will not be attainable.

B. Recourse and Chance Constrained Model

To represent the relation mentioned above between con-straints C1, C2 and the objective function in a deterministicform, Recourse Programming (RP) and Chance ConstrainedProgramming (CCP) models are used as depicted below:

minimizex,y

{∑

∀i∈M

∑

∀t∈Txi,t + E

[H(y, D)

]}

subject to:

C1:t∑

t′=0

ri,t′xi,t′ ≥t∑

t′=0

vi,t′ , ∀ i ∈ M,∀t ∈ T ,



C2: Pr(

M∑

i=1

xi,t ≤ 1 − Ct) ≥ β, ∀t ∈ T ,

C3: xi,t ≥ 0, ∀ i ∈ M, t ∈ T .

(2)

The objective function herein comprises two terms whose sum-mation must be minimized. The first term represents the totalallocated resources (similar to the non-robust approach) whilethe second term corresponds to the expected value of wastedresources as a result of terminating the video before watchingthe prebuffered content. In C2, the probability of satisfying thenetwork resource constraint by the calculated airtime fractionsis set above the QoS level β. Where β ∈ [0, 1] represents theminimal probability of satisfying the QoS. Allocating moreresources than the available capacity, after accounting for thereal-time traffic users, will result in video stops since the userswill not be able to receive the minimal data amount calculatedby the R-GPRA. In the following, we show how to obtain aclosed form representation for both the recourse model in theobjective function, and the probabilistic constraint in C2.

1) Recourse Stage: The second term of the objective func-tion in Eq. 2, i.e., E

[H(y, D)

], is the optimal solution of the

recourse stage and formulated as follows1:

minimizey,x

{

ζ∑

∀i∈M

∑

∀t∈TpW

i,tyi,t

}

subject to:

C4: ri,t−1yi,t−1 + ri,txi,t − vi,t ≤ ri,tyi,t,

∀ i ∈ M,∀t ∈ T ,

C5: yi,t ≥ 0, ∀ i ∈ M, t ∈ T . (3)

The objective function of the recourse stage in Eq. 3 min-imizes the expected value of excess allocated resources (i.e.,prebuffered) and calculated as a function of both the secondstage decision variable yi,t and the probability of terminatingthe video denoted by pW

i,t. The variable ζ is used to model thetrade-off between the values of the two stages, and its value istypically less than one. The constraint in C4 is used to calcu-late the excess resources ri,tyi,t after every time slot t. The firsttwo terms on the left hand-side represent the total prebufferedand newly delivered content in this time slot, respectively.The third term represents the per slot demand in case of non-termination. The right hand-side shows the amount of excessresources after slot t which corresponds to the prebufferedfuture content.

2) Deterministic Equivalent: The probabilistic constraint inC2 is replaced by the following deterministic equivalent formwhich adopts the probability of user arrivals and their load.

C6:M∑

i=1

xi,t ≤ 1 − (Ct,ωδt,ω

) ∀t ∈ T , ∀ω ∈ �,

C7:∑

∀ω∈�

δt,ωpAt,ω ≥ β ∀ t ∈ T .

C8: δt,ω ∈ {0, 1} ∀ t ∈ T , ∀ω ∈ �, (4)

1This subsection was preliminary proposed in our prior work [41].

The binary decision variable δt,ω equals 1 if scenario ω attime slot t has to be satisfied by the airtime allocation, andequals 0 otherwise. The PDF of user arrival is used to con-struct the scenarios of network resources at each time slot asa result of real-time traffic user arrival. At each time slot t, thescenario ω represents the existence of ω real-time traffic users.The constraint in C6 demonstrates the scenarios in which thecalculated airtime fractions must satisfy the vacant networkresources 1−Ct,ω. In C7, the total probability of satisfied sce-narios must exceed the predefined QoS level β. pA

t,ω is theprobability of user arrival scenario ω at time slot t. When thescenario is ignored (i.e., δt,ω = 0), the right hand-side of C6will be the maximum slot duration (i.e., all network resourcesare available), and the QoS level β will avoid ignoring themost probable scenarios.

C. Deterministic R-GPRA Linear Formulation

The complete deterministic formulation of the proposedR-GPRA can be summarized in the following closed formrepresentation:

minimizex,y,δ

{∑

∀i∈M

∑

∀t∈Txi,t + ζ

∑

∀i∈M

∑

∀t∈TpW

i,tyi,t

}

subject to:

C1:t∑

t′=0

ri,t′xi,t′ ≥t∑

t′=0

vi,t, ∀ i ∈ M, ∀t ∈ T ,

C3: xi,t ≥ 0, ∀ i ∈ M, t ∈ T .

C4: ri,t−1yi,t−1 + ri,txi,t − vi,t ≤ ri,tyi,t,

∀ i ∈ M, ∀t ∈ T ,

C5: yi,t ≥ 0, ∀ i ∈ M, t ∈ T .

C6:M∑

i=1

xi,t ≤ 1 − (Ct,ωδt,ω

) ∀t ∈ T ,∀ω ∈ �,

C7:∑

∀ω∈�

δt,ωpAt,ω ≥ β ∀ t ∈ T .

C8: δt,ω ∈ {0, 1} ∀ t ∈ T , ∀ω ∈ �, (5)

The above formulation is obtained by combining Eq. 3 andEq. 4, resulting in a mixed integer linear programming model.In the next section, we explore the possibilities and challengesof solving this NP-complete model, and propose a guidedheuristic algorithm for real-time traffic allocation.

V. REAL-TIME OPTIMIZER

This section reviews the numerical optimization methodsthat can be used to solve the formulated problem, and intro-duces the details of heuristic search algorithm followed byanalysis of its computational complexity.

A. Optimal Solution

The robust formulation in Eq. 5 is a mixed integer lin-ear programming model. As such, an optimal solution, whichsatisfies all the constraints, can be obtained using branch-and-bound or branch-and-cut, among other. Although these



techniques are capable of reaching an optimal feasible solu-tion with a small duality gap, they suffer from low scalabilityand slow convergence. In particular, the complexity of suchnumerical optimization techniques grows exponentially withthe number of decision variables [42]. These limitations aredue to overlooking the problem structure and exploring a largearea of the search space to avoid local optimal solutions. Aguided heuristic algorithm is therefore proposed to provide areal-time feasible solution that is robust to prediction uncer-tainty. Commercial solvers (e.g., Gurobi [43]) that adopt theseoptimal techniques will be only used to evaluate the abilityof the heuristic technique to maintain the prediction gains andsatisfy the QoS constraints.

B. Guided Real-Time Heuristic

The proposed guided search heuristic algorithm uti-lizes knowledge about the problem’s structure such as theinterdependency and conflicts between the constraints, andtheir impact on the optimality of objective function. In essence,the algorithm starts by satisfying all the QoS constraints usingthe available radio resources while considering the distributionof user arrival and the predefined QoS level. To achieve energyminimization, resources are allocated to users that have notreached peak channel conditions. Then, the algorithm exploitsthe prebuffering capabilities of the mobile device for usersexperiencing peak channel conditions. This is done by push-ing the video content in advance to avoid allocation duringtime slots with low channel rates or high congestion. In thenext step, the value of the objective function is further mini-mized while examining the trade-off between possible energysavings during peak radio conditions, and the risk of wastingresources due to video termination in future time slots. Theheuristic is summarized in Algorithm 1 and Algorithm 2 anddetailed as follows.

In the first stage, minimal radio resources are calculated(line 2-18) in order to satisfy the QoS constraint C1 in Eq. 2for each slot while considering the network resources uncer-tainties. The available network resources at each time slot arecalculated as follows (lines 2-12):

1) The amount of resources in each scenario are initiallysorted in ascending order and update the correspondingprobability mass function

2) The scenarios are considered iteratively until the totalprobability reaches the QoS level β. Including morescenarios will result in a conservative solution thatover-satisfies the QoS and deteriorates the value of theobjective function.

3) The resources of the last considered scenario (i.e.,the scenario that needs the maximum resources) areselected.

4) The total vacant capacity C′t remaining for video stream-

ing users is calculated and used in the next stage.After satisfying constraints C7 − C8, the algorithm proceedsto fulfill the per slot demand constraint C1. This is accom-plished by setting C1 to an equality and calculate the resourcesharing xi,t that guarantee the satisfaction of demand. Suchminimal allocation continues until the user reaches peak radio

conditions (line 14). In high load scenarios, due to the largenumber of users or high streaming rates, the total allocatedresources in a certain time slot might violate the airtime con-straint C6 in Eq. 5. Accordingly, the preceding time slotswith vacant resources will be used to prebuffer the contentof the highly loaded time slots as depicted in lines 19-36 ofAlgorithm 1. While efficient exploitation of the radio resourcesis mandatory for these scenarios, the algorithm prebuffers thecontent of the user with the highest achievable rate. Thus, lessairtime is consumed which increases the chance of satisfyingthe radio resource constraint C2. In the case of non-vacantresources, to accommodate the excess demand, the problem issaid to be infeasible (lines 34-36).

To further minimize energy consumption, a calculated riskprebuffering strategy is applied by Algorithm 2. In essence,the possibility of prebuffering is checked. For each timeslot following this peak, the amount of resources in thecase of prebuffering and non-prebuffering is checked whileconsidering the probability of video termination (lines 3-5)which approximates the objective function in Eq. 3. Inthe case of more resource saving (line 7), prebuffering isdone (line 8-10). Otherwise, the risk of wasting resourcesis found to be high and minimal allocation is done for thedemand of this slot without prebuffering in the previous slots(lines 13-16).

C. Algorithm Complexity

The first stage of the heuristic consists of sorting the sce-narios (line 3) and calculating the total probability (line 6-11),each has a complexity of O(N2) in the worst case scenario.This stage is repeated for a maximum of T time slots, thus,the total complexity (lines 2-12) is O(2T × N2). The min-imal allocation in lines 13-18 has complexity of O(MT),while the repairing of resources in lines 19-37 has a com-plexity of O(MT2) due to revisiting the preceding time slotsto check the possibility of prebuffering. Similarly, the secondpart of the heuristic has a complexity of O(MT2) in whichprevious slots are also revisited for prebuffering any of thefuture slots with lower rates. Thus, the complexity of thewhole proposed heuristic is O(MT2) which is a polynomialand significantly lower than the mathematical optimizationmethods whose complexity is non-polynomial and depends onthe number of decision variables and constraints.

VI. PERFORMANCE EVALUATION

A. Simulation Environment

The proposed R-GPRA is developed in Network Simulator3 (ns-3) Long Term Evolution (LTE) module where Gurobi(a commercial solver) is integrated to obtain benchmark solu-tions [44]. The probability of terminating the video at anytime slot t is calculated using the model in [16]. Users followrandom mobility traces within the cell coverage region at aconstant velocity typical for suburban areas. The simulationparameters and numerical values are shown in Table I. Thesimulation is performed 25 times, and the average results ofall runs are reported in the next subsections.



Algorithm 1: QoS Satisfaction Under NetworkResource Uncertainty

Input : Users: M, Time Horizon: T , PredictedRates: R, Demand Distribution: P,Streaming Rate: V ;

Output : X;Initialization: X = ∅, B = ∅, Y = ∅, Z = ∅ Nt = 0

∀t ∈ T;1 Define: t′i = argmax

{ri,t,∀t ∈ T

};

2 for t ∈ T do3 C′

t = Sort(PAt ∀ω ∈ �);

4 Initialize St = 0;5 Set minimum capacity C′

t = 1 ;6 while St ≤ β do7 for omega ∈ � do8 Update probability sum: St = St + PA

t,ω;9 Update minimum capacity: C′

t = 1 − Ct,ω;10 end11 end12 end13 for i ∈ M do14 for t ∈ T |t ≤ t′i do15 Calculate minimal airtime xi,t = vi,t/ri,t;16 Update used slot fraction Nt = Nt + xi,t;17 end18 end19 for t ∈ T do20 if Nt > 1 then21 Set k = t − 1;22 while k > 0&Nt > C′

t do23 if xi,t > 0|i = argmax

{ri,k,∀i ∈ M

}then

24 Calculate the violated airtime�xi,t = Nt − 1;

25 Calculate the demanded airtime�xi,k = �xi,t × ri,t

ri,k;

26 if Nk + �xi,k ≤ 1 then27 Update xi,k, xi,t, Nt and Nk ;28 break;29 end30 end31 k = k − 1;32 end33 end34 if Nt > C′

t then35 Return Infeasible Problem;36 end37 end

The main metric to assess the energy consumption is thetotal BS airtime [4], while the QoS of video streaming isquantified by the number and duration of video stops [45].In addition, the corresponding Quality of Experience (QoE)of both number and duration of the stops is quantified by theMean Opinion Score (MOS) [46], [47]. In essence, the QoEis a subjective metric that represents the service end-to-end

Algorithm 2: Calculated Risk Prebuffering forEnergy Minimization

Input : Users: M, Time Horizon: T , PredictedRates: R, Demand Distribution: P,Streaming Rate: V ;

Output : X;Initialization: X = ∅, B = ∅, Y = ∅, Z = ∅ Nt = 0

∀t ∈ T;1 Define: t′i = argmax

{ri,t,∀t ∈ T

};

2 for t ∈ T |t > t′i do3 Calculate airtime without Prebuffering x′

i,t = vi,t/ri,t;4 for τ ∈ T |τ < t, ri,τ > ri,t, Bi,t = 1 do5 Calculate airtime with prebuffering zi,τ = vi,t/ri,τ ;6 Calculate excess resources yi,τ = γ × pW

i,t × zi,t;7 if x′

i,t > zi,τ + yi,τ then8 Update xi,τ = xi,τ + zi,τ ;9 Update used slot fraction Nt = Nt + zi,τ ;

10 Update prebuffering statusBi,t = 1;11 end12 end13 if Bi,t = 1 then14 Update airtime without prebuffering xi,t = vi,t/ri,t;15 Update used slot fraction Nt = Nt + xi,t;16 end17 end18 return X

performance level from the user’s perspective, and can becalculated using the MOS formula in [46] and [47] depictedbelow:

MOSVS = 1

|M||M|∑

i=1

(2.99 × e−0.96ηi + 2.01). (6)

MOSVD = 1

|M||M|∑

i=1

4.59 × e−3.44ζi . (7)

where MOSVS and MOSVD are the MOS values due to numberand duration of video stops, respectively. The average numberand duration of video stops are denoted by η and ζ , respec-tively. The value of MOS varies from 1 to 5 which representsvery poor to excellent service, respectively.

We adopt these metrics to evaluate the proposed R-GPRA,the existing non-robust PRA and the opportunistic RA (i.e.,non-predictive). The following abbreviations are used in thenext subsection:

• PF (Non-PRA): the traditional opportunistic proportionalfair scheduler is used to represent the class of non-predictive schemes. It allocates the resources to theusers based on their current channel measurements andcumulative served traffic in previous slots [48].

• NR-GPRA: is the existing energy-efficient predictiveresource allocation that assumes perfect prediction andadopts deterministic formulations [4]. This scheme is sim-ulated by setting the values of ζ and Ci,t to zero in theobjective function of Eq. 5, and the resultant formulationis solved using Gurobi optimizer [43].



TABLE ISUMMARY OF MODEL PARAMETERS

• PK-GPRA: this refers to a hypothetical PRA with perfectknowledge of uncertain demand and network resources.As such it is aware of exact watching duration and amountof available resources. This is achieved by replacing therandom variables in Eq. 1 by the exact values from thesimulation.

• OR-GPRA: this represents the proposed robust greenpredictive resource allocation as formulated in Eq. 5.The probability of video termination follows the distri-bution in [16]. The optimal solution is obtained by thebranch-and-cut methods in Gurobi optimizer [43].

• HR-GPRA: this refers to the heuristic version of OR-GPRA in which the solution is obtained by the proposedguided search in Algorithm 1 and Algorithm 2.

B. Simulation Results

1) Evaluating Demand Uncertainties: We initially evaluatethe impact of uncertain demand solely on the prediction gains(i.e., energy savings). The system load, in terms of numberof users and streaming rates, was configured and set belowthe available radio resources. Hence, no video stops wereobserved, and thus the QoS was satisfied by all the schemes,while the main focus remains on energy consumption. Themaximum energy saving gap, referred to as prediction gain,is observed between the opportunistic non-predictive RA andhypothetical perfect knowledge PRA. As reported in the PRAliterature [19], and shown in Fig. 4(a), the gain can reach up to400 % due to the minimal allocation strategy adopted for celledge users moving to peak radio conditions. This is in additionto maximizing the allocation for users exiting the cell.

The existing non-robust PRA (NR-GPRA), however, hasdiminished the gain to 150% as a result of the greedy pre-buffering for cell center users exiting the cell, as yet notwatching the full buffered video. On the contrary, the proposedrobust GPRA has strategically prebuffered the video content tothe users with poor future conditions, rather than transmittingtheir full content. Such risk-aware prebuffering strategy avoids

greedy prebuffering of the future content whose delivery canbe postponed until the corresponding time slots are reached,or the user arrives at time slots which have a low probabilityof terminating the video. This is in addition to following theminimal allocation to users experiencing poor conditions untilthey reach peak rate values. As such, the robust scheme wasable to maintain the prediction gain at 320 %.

The same impact of uncertainty on the prediction gain wasobserved while increasing the streaming rate for fewer usersFig. 4(b). In this scenario, the maximum prediction gap canreach up to 150%, however, the uncertainties resulted in a25% prediction gap as depicted by the non-robust scheme. Thegain was retained to 100% by adopting the stochastic basedrobustness.

2) Evaluating Joint Demand and Resources Uncertainties:The simulations are extended to incorporate the resourcesuncertainties, where the QoS and QoE performance aredepicted in Fig. 5(a)-Fig. 5(b) and Fig. 5(c)-Fig. 5(d),respectively.

The resources uncertainties violated the QoS level underthe existing non-robust predictive scheme for a different num-ber of users. Due to the arrival of real-time users, the networkwas unable to deliver the video content with the pre-calculatedamount of resources. As such, the demand of cell edge usersis not met by the minimal allocated resources that might beshared by the real-time users. The cell center video streamingusers were not impacted due to the prebuffered content thatsurpasses the demand. Nevertheless, the substantial increasein the normalized number and durations of stops is attributedto the short video segments watched by the streaming users(i.e., demand uncertainty). The corresponding QoS demon-strates the exponential decay of users’ experience as a resultof experiencing a large number and durations of stops.

Unlike the non-robust scheme, the proposed optimal robusttechnique has satisfied the predefined QoS level (β) for allnumber of users. The robust scheme balances the amountof allocated resource to the cell edge and cell center users.Prebuffering is minimized for the cell center users and moreresources can be reserved for the real-time users. As a result,the amount of allocated resources to cell edge users will besecured during the arrival of real-time users.

The performance of non-robust and robust predictiveschemes is compared at different streaming rates and real-timeuser traffic as shown in Fig. 6(a) and Fig. 6(b). As the trafficload (streaming or real-time) increases, so does the numberof unsatisfied users. With regards to energy savings and theprediction gain, the ability of robust scheme to maintain a highvalue was observed. Thus, the cost of robustness is said to bevery low as the robust scheme avoided generating conservativesolutions.

3) Performance of Heuristic: The above-mentioned obser-vations over different system and streaming loads are alsoreported for the proposed heuristic. In essence, the heuris-tic was capable of satisfying the QoS level and maintain theprediction gap under demand and network uncertainties. Thecomplexity of both the optimal and heuristic techniques ismeasured in terms of the computation time of a Quad Core i7-Processor, 3.2 GHz machine. The heuristic algorithm requires



Fig. 4. Airtime-based energy consumption with uncertain demand only.

Fig. 5. QoS and QoE for number and duration of stops with uncertain demand and network resources.

less than 0.1ms. to solve the robust PRA formulation for allthe network configurations (i.e., number of users and stream-ing rate values). On the other hand, the performance of Gurobi

is sensitive to network load and capacity. The execution timevaries from 1s to 15s depending on the number of unsat-isfied users in the previous time slots, their streaming rate,



Fig. 6. Distribution of QoS values for robust and non-robust GPRA.

and available channel capacity. Requests from users for highstreaming rates while experiencing low channel capacity willresult in a narrow feasibility region. Such situations are verychallenging for the solver that overlooks the problem structureand generates a large number of branches and nodes to solvethe integer programming model.

VII. CONCLUSION

We introduced a robust green predictive resource allocation(R-GPRA) scheme for video streaming that handles uncertain-ties in both the users’ demands and network resources overa time horizon. Hence, R-GPRA avoids wasting resourcesand QoS violation. A stochastic formulation is proposedand a deterministic equivalent closed form representationwas achieved using Recourse Programming (RP) and ChanceConstrained Programming (CCP) models that adopt the prob-ability of random video termination and arrival of real-timeusers. The resultant RP and CCP based formulations can besolved either by commercial solvers for benchmark solutions,or by the introduced guided heuristic search for real-time deci-sions. The performance evaluation, using a standard compliantsimulator, demonstrated the ability of the introduced R-GPRAto maintain the energy-saving gains of PRA while satisfy-ing the QoS levels. An increase in system load underlinesthe importance of having a robust scheme to avoid unneces-sary excessive prebuffering for users leaving the cell centernegating the high probability of terminating the video beforeviewing the full content. This is unlike existing PRA schemesthat greedily exploit the peak radio conditions by prebuffer-ing the whole future content without taking into considerationthe users unstable demands. The proposed robust model can beextended to Dynamic Adaptive Streaming over HTTP (DASH)where the objective function can represent other QoS or QoEmetrics such as average quality or quality switches. The videostops in that case will be handled by the probabilistic QoSconstraints. Our future work thus considers the extension to

DASH which jointly optimizes the resources and video quali-ties. This is in addition to considering other robust predictiveforms such as long-term fairness and risk allocation for highload scenarios.

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Ramy Atawia (S’12–M’17) received the B.Sc.and M.Sc. degrees in communication engineeringfrom the German University, Cairo, Egypt, in 2012and 2013, respectively, and the Ph.D. degree inelectrical and computer engineering from Queen’sUniversity in 2017. He is currently an IndoorRadio Solutions Developer with Ericsson Researchand Development, Canada. He was a Member ofTechnical Staff and a Researcher with Bell Labs,Nokia. He was with Vodafone on autonomousoptimization of radio networks, and was with Nokia

on customer experience management and analytics. He was a teaching assis-tant and a guest lecturer where he delivered tutorials on optimization, wirelessnetworks, and programming. His research work has appeared in top-tier IEEEjournals and conferences, and it has led to 15 patents. His research includesstochastic optimization, predictive video streaming, machine learning, and AIin communication networks. He was a recipient of the Best Paper Award atIEEE GLOBECOM 2017. He also serves as a TPC member and a reviewerin IEEE flagship conferences and journals.

Hossam S. Hassanein (S’86–M’90–SM’05–F’17) isa leading authority in the areas of broadband, wire-less, and mobile networks architecture, protocols,control, and performance evaluation. He is also theFounder and the Director of the TelecommunicationsResearch Laboratory, Queen’s University School ofComputing, with extensive international academicand industrial collaborations. His record spans over500 publications in journals, conferences, and bookchapters, in addition to numerous keynotes and ple-nary talks in flagship venues. He was a recipient

of several recognitions and best papers awards at top international confer-ences. He is a Former Chair of the IEEE Communication Society TechnicalCommittee on Ad hoc and Sensor Networks. He is an IEEE CommunicationsSociety Distinguished Speaker (Distinguished Lecturer from 2008 to 2010).



Najah Abu Ali (M’07) received the B.Sc. andM.Sc. degrees in electrical engineering from theUniversity of Jordan, and the Ph.D. degree from theDepartment of Electrical and Computer Engineering,Queen’s University, Kingston, Canada, specializingin resource management in computer networks. Sheis currently an Associate Professor with the Facultyof Information Technology, United Arab EmiratesUniversity (UAEU). She has further co-authored aWiley book on 4G and beyond cellular communica-tion networks. Her general research interests include

modeling wireless communications, resource management in wired and wire-less networks, and reducing the energy requirements in wireless sensornetworks. She has strengthened her focus on the Internet of Things, particu-larly at the nano-scale communications level, in addition to vehicle-to-vehiclenetworking. Her work has been consistently published in key publicationsvenues for journals and conference. She has also delivered various seminarand tutorials at both esteemed institutions and flagship gatherings. She has alsobeen awarded several research fund grants, particularly from the EmiratesFoundation, ADEC, NRF/UAEU funds, and the Qatar National ResearchFoundation.

Aboelmagd Noureldin (S’98–M’02–SM’08)received the B.Sc. degree in electrical engineeringand the M.Sc. degree in engineering physicsfrom Cairo University, Egypt, in 1993 and 1997,respectively, and the Ph.D. degree in electricaland computer engineering from the University ofCalgary, Alberta, Canada, in 2002. He is a Professorwith the Departments of Electrical and ComputerEngineering, Royal Military College of Canada(RMCC) with a cross-appointment with the Schoolof Computing and the Department of Electrical and

Computer Engineering, Queen’s University. He is also the Founder and theDirector of the Navigation and Instrumentation Research Group, RMCC.His research is related to GPS, wireless location and navigation, indoorpositioning, and multisensor fusion. He has published over 230 papers injournals and conference proceedings. His research work led to ten patents inthe area of position, location, and navigation systems.


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