A Quantitative Framework for Guaranteeing QoE ofVideo Delivery over Wireless

Hemant Kowshik∗, Partha Dutta∗, Malolan Chetlur∗ and Shivkumar Kalyanaraman∗∗IBM India Research Lab, Bangalore

Email: {hkowshik, parthdut, mchetlur, shivkumar-k}@in.ibm.com

Abstract—In this paper, we study the problem of efficientvideo delivery over the cellular downlink. The key objective isto maximize the Quality of Experience (QoE) of the user, asmeasured by application level metrics such as the buffering ratioand low bit rate ratio. We present a two-tiered solution witha standard basestation scheduler that works on a per-packetbasis and a Video Management System (VMS) that works at thegranularity of thousands of video frames.

The video management system uses knowledge of the videoplayout curves and future channel states to develop a schedulingpolicy that is feasibility optimal. The algorithms are simpleand leverage recent results on real-time scheduling in wirelessnetworks. We evaluate the performance of our algorithms usingreal video traces and a standard channel model. The VMSensures that the per-user QoE guarantees are maintained, ascompared with a standard PF scheduler that is oblivious toapplication level QoE requirements.

I. INTRODUCTION

With the increasing adoption of smartphones, mobile trafficis expected to increase 18 fold in the period from 2011 to 2016[1]. The increased data rates in 4G cellular networks enablea host of video-based applications like streaming video, videocalling and mobile gaming. Video traffic is a major componentof the mobile traffic mix, currently accounting for 52% ofmobile traffic, and expected to rise to 70% by the year 2016.

There are two plausible ways of coping with the grow-ing demand. First, operators could invest in new networkinfrastructure which incurs enormous costs and yields limitedrevenue. Second, operators could optimize use of the wirelessspectrum, easing the load on the network and ensuring gracefuldegradation in overload scenarios. We focus on the latterand address the problem of optimizing video delivery tomultiple mobile users while maximizing network utilisationand providing guarantees on the Quality of Experience (QoE).

We fix attention on streaming video flows generated byservices like Youtube and Netflix. The main contribution ofthis paper is a framework that directly considers metricsof experience, and algorithms that provide long-term QoEguarantees to each user. The framework is rich enough to cap-ture different performance metrics, and provide differentiatedservice guarantees for different classes of users. The key obser-vation we make is that while schedulers work at a per-packetgranularity, the experience of video watching is only affectedat the granularity of a few seconds. Hence, we propose a two-tiered solution consisting of a standard basestation schedulerthat works at a MAC frame-level granularity (timescale of 2-5 ms) and a Video Management System(VMS) that works at

the granularity of superframes (of the order of a few thousandframes = a few seconds). Given the average bitrates over thenext superframe by the basestation scheduler, the VMS mustchoose the subset of videos to serve, and their bitrates.

We use a Lyapunov function based approach to derivescheduling policies that maintain per-user QoE guarantees inthe face of arbitrary channel variation. The proposed policiesare feasibility optimal, i.e., the admissible region of thesepolicy dominates the admissible region of any other policy.We consider two key QoE metrics, namely the Buffering Ratiodefined to be the fraction of time the user spends in a stalledstate, and the Low Bitrate Ratio which is the fraction of timethe user is served a lower resolution video.

Finally, we conduct a simulation study to evaluate theperformance of our algorithms against a standard basestationscheduler. The simulations show that in the presence of our al-gorithms, each user adheres to its QoE guarantee, irrespectiveof the bitrate of the video. This is in contrast with the weightedProportional Fair (PF) scheduler which shows widely varyingQoE depending on the video bitrate and channel conditions.

II. RELATED WORK

The variable bit rate of compressed videos makes it difficultto provide performance guarantees on their delivery. Multiplesmoothing schemes have been proposed to address this prob-lem [2], [3], [4], [5]. In this work, we require that the bit rateof a video is maintained to be a constant over the duration ofa superframe, which can be ensured using one of the existingsmoothing schemes.

Several MAC layer scheduling algorithms have been pro-posed for multiplexing data streams in wireless networks [6],[7], and in particular cellular networks [8]. These algorithmsseek to optimize QoS parameters like delay, jitter, throughputand packet-loss rate [9], [10]. In this paper, we focus on guar-anteeing QoE rather than optimizing QoS. We use a Lyapunovfunction based approach introduced in [11]. More recently, thisapproach has been used to analyze delay behaviour [12], andto devise scheduling policies for real-time traffic [13].

Managing the delivery of video streams over wireless chan-nel has been studied in multiple papers. The authors in [14]study the probability distribution of the number of bufferingevents (or stalls). Scheduling schemes for delivery of multiplevideos over wireless has been studied in [15] to reduce andfairly distribute the number of buffering events, and in [16]

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to reduce energy consumption. However, unlike our work, themethods proposed earlier do not provide any QoE guarantees.

Multiple techniques have been designed to adapt tof dete-riorating network conditions on the QoE of video delivery.Prioritizing video packets based on their importance [17] andscalable video coding [18] are two such approaches. Ourframework differs from earlier work on prioritizing videopackets in two ways: first, prioritization is done at the level ofvideo streams rather than individual packets, and second, thetime-granularity of serving packets is at the superframe levelrather than single video frames.

III. DESCRIPTION OF VIDEO DELIVERY FRAMEWORK

We consider a single basestation serving multiple video-on-demand requests seeking immediate playout. The videorequests arrive and depart in arbitrary fashion. Each video isvariable bit rate (VBR) and the wireless channel has variablethroughput due to fading and shadowing effects. Given thechannel quality and the state of playout for each user, theobjective of the basestation is to decide which video requeststo serve, and at what bitrates.

The classical approach to ensure quality of service(QoS) among competing flows is to enqueue video requestsand devise a priority-based service discipline. The assignedpriority typically depends on channel quality and queuelength.These algorithms guarantee throughput optimality while stillmaintaining QoS guarantees. However, basestation schedulingpolicies cannot effectively monitor QoE of video requests.(i) Basestation schedulers are unaware of the particularapplication, current video bitrate or the state of playout of thevideo. Thus, there is very little opportunity to intelligentlyprioritize flows and provision bandwidth.(ii) Basestation schedulers work at a per-packet level Clearly,there is a discrepancy between the timescale at which thescheduler works (a few milliseconds) and the timescale atwhich user experience is evaluated (a few seconds).(iii) Video requests demand a certain minimum throughputfor acceptable performance. Any bitrate below this results indegraded QoE. This sharp threshold behavior distinguishesvideo traffic from file transfers.

Fig. 1. Two-tiered Architecture

To address these issues, we propose a two-tiered schedulingframework (see Figure 1). We suppose that each incomingvideo request is pre-smoothed and that the bitrate of thesmoothed video stays constant over the course of a few

thousand frames, which we define to be a superframe. At thelower tier, we have a standard basestation scheduler, whichpromises certain bitrates to each user, given the current channelconditions. At the higher tier, there is a video managementsystem (VMS) which works at the timescale of a superframe.At the beginning of each superframe, the VMS chooses asubset of video requests to serve actively and their respectiverates. These video requests will be played out during thecurrent superframe while the other requests are either bufferingat a lower rate, or completely throttled.

A. QoE metric

Buffering Ratio (BR): The buffering ratio is defined tobe the fraction of the video session when the user is stalled.A recent study [19] indicates that the buffering ratio is theparameter that is most highly correlated with dissatisfied usersterminating their video session. We suppose that the stalllength is at least one superframe (typically 2 to 5 seconds),and we seek to guarantee that the long term fraction of stalledsuperframes for user i is less than αi.Low Bitrate Ratio (LBR): Another measure of QoE derivesfrom the fact that videos are not always served at a fixedbitrate. Depending on the available bandwidth, the server cantranscode the video frames to a lower or higher bitrate. Weconsider a metric, called the low bit rate ratio, that keeps trackof the long-term fraction of superframes served at the lowerbit rate. Thus, we seek to guarantee that the low bit rate ratiois less than βi.

B. Debt-based Feasibility Optimal Policy

Consider a set of N users in the system each of who caninitiate and terminate a video at the edge of a superframe. LetSk be the set of users with active video requests in superframek. Let us denote the bitrate of video i during superframe k tobe bi(k). Since the video has been smoothed beforehand, wesuppose that the bitrate of the video stays constant during asuperframe. We suppose that the set of active video requestsSk, and their bitrates bi(k) evolve according to a stationaryirreducible Markov chain with finite state. We also supposethat the set of active video requests at time t and their availablebitrates are independent of the channel states at time t.

At the beginning of superframe k, we suppose that we knowthe maximum feasible bitrate Bi(k) for user i in superframek. Thus, if video i must be served, the base-station needs toallocate bi(k)

Bi(k)fraction of slots in superframe k to user i. Let

xi(k) be an indicator variable that is 1 if video i is served insuperframe k, and 0 otherwise.

QoE requirement: Define Ti(k) :=∑k

l=1 1{i ∈ Sl}where 1 is the indicator function. For simplicity, we willsuppose that Ti(k) → ∞ as k → ∞, for all i. Our objectiveis to guarantee that

limk→∞

1

Ti(k)

k∑l=1

(xi(l)1{i ∈ Sl}) ≥ (1− αi) for each i

In order to monitor the QoE requirement, we define theperformance deficit for user i at the end of superframe k to

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be the number of superframes where user i should have beenserved minus the number of superframes where user i wasactually served. We have

δi(k) = (1− αi)Ti(k)−

k∑l=1

(xi(l)1{i ∈ Sl}) ,

δi(k + 1) =

{δi(k) + (1− αi)− xi(k) if i ∈ Sk,δi(k) otherwise.

For simplicity, let us define zi := 1−αi. We say that a vector[zi] is feasible if there exists a scheduling policy that ensuresthat the QoE requirement for each user is met. Since the wholesystem can be modeled as a controlled Markov chain, anyfeasible vector [zi] can be fulfilled by a stationary randomizedpolicy that is allowed to depend on the channel states and thehistory of stalls. A feasible vector [zi] is said to be strictlyfeasible if [zi/θ] is also feasible for some θ < 1.

Definition 1 (Feasibility Optimality [13]): A schedulingpolicy is said to be feasibility optimal, if it can fulfil any QoEvector [zi] that is strictly feasible.

In this paper, we present a feasibility optimal schedulingpolicy using a Lyapunov function based approach, along thelines of Theorem 3 in [13]. We begin by recalling the followingstandard result from Lyapunov stability theory.

Theorem 1: Let L(k) be a non-negative Lyapunov function.Suppose there exists B > 0, and a non-negative function f(k)adapted to the past history of the system such that:

E[L(k + 1)− L(k)| history up to time k] ≤ B − εf(k),

for all k, then lim supk→∞

∑k

l=1 E{f(l)} ≤ B/ε.�Theorem 2: Consider a scheduling policy that solves the

following optimization problem at the beginning of the kth

superframe.

Max.∑i∈Sk

E[δ+i(k − 1)xi(k)|[bi(k)], [Bi(k)], Sk, [δi(k − 1)]

](1)

The above policy is feasibility optimal.Proof: Let us begin by defining a Lyapunov function L(k) =12

∑N

i=1 δ2i(k − 1). The drift of the Lyapunov function ΔL(k)

is defined to be

E [L(k + 1)− L(k)|Sk, [δi(k − 1)]]

=∑i∈Sk

1

2

(E

[(δi(k − 1) + 1− αi − xi(k))

2

−δ2i (k − 1))|Sk, [δi(k − 1)]

]=

∑i∈Sk

1

2(1− αi − xi(k))

2

+∑i∈Sk

E [δi(k − 1) (1− αi − xi(k)) |Sk, [δi(k − 1)]]

≤N

2+

∑i∈Sk

E [δi(k − 1) (1− αi − xi(k)) |Sk, [δi(k − 1)]]

For a feasible vector [zi], let ε be small enough so that[z′

i] ≡ (z1 + ε, . . . , zN + ε) is also inside the feasible region.

Thus there exists a stationary randomized policy, say P ′, thatsatisfies users with QoE requirements specified by [z′

i]. Let

x′

i(k) be the decrease in performance deficit for user i under

P ′. Thus, we have, for any i ∈ Sk,

E [x′

i(k)|Sk, [δi(k − 1)]]

= E [E [x′

i(k)|[bi(k)], [Bi(k)]] |Sk, [δi(k − 1)]]

≥ zi + ε, (2)

Further, if policy P achieves the maximum in (1), we have∑i∈Sk

E(δ+i(k − 1)xi(k)|[bi(k)], [Bi(k)], Sk, [δi(k − 1)])

≥∑i∈Sk

E(δ+i(k − 1)x′

i(k)|[bi(k)], [Bi(k)], Sk, [δi(k − 1)])

We can restrict attention to policies that only work on clientswith δi(k − 1) > 0, and show that one can still establishfeasibility optimality, despite doing less work. Thus we have

N

2+

∑i∈Sk

E[δ+i(k − 1)(1− αi − xi(k))|Sk, [δi(k − 1)]

]

≤N

2+

∑i∈Sk

E[δ+i(k − 1)(1− αi − x′

i(k))|Sk, [δi(k − 1)]]

≤N

2− ε

(∑i∈Sk

δ+i(k − 1)

)from (2)

Thus, from Theorem 1, we have

lim supk→∞

1

k

k∑l=1

E

⎡⎣ ∑i∈Sl+1

δ+i(l)

⎤⎦ ≤ N

2ε.

Finally, since |∑N

i=1 δ+i(k) −

∑N

i=1 δ+i(k − 1)| is bounded

for all k, we have 1kE

[∑N

i=1 δ+i(k)

]→ 0 as k → ∞. Thus,

δ+

i(k)

kconverges to zero in probability. �

Note 1: The problem in (1) reduces to a deterministicknapsack problem to be solved for each superframe k

[KNAPSACK] Maximize∑

i∈Skδ+i(k − 1)xi(k)

s.t.∑

i∈Sk

bi(k)xi(k)Bi(k)

≤ 1

That is, given a set of items where the ith item has cost bi(k)Bi(k)

and profit δ+i(k − 1), one needs to pick a subset of items to

maximize profit for a given total cost.The knapsack problem is known to be NP-complete, and

has been widely studied in the algorithms literature. In thispaper, we suppose that we simply use one of the polynomialtime approximation schemes for the knapsack problem.

Note 2: Since we have considered an on-off frameworkwhere videos are either served or stalled, the wireless resourcesmay not be efficiently utilized. This can be addressed byallowing the variables {xi(k)} to take values from the interval[0, 1]. That is to say, in superframe k, video i can be partiallyserved by provisioning a bitrate of xi(k)bi(k). As before, wecan derive a feasibility optimal scheduling policy. Further, theknapsack problem can be solved using a greedy algorithm.

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Theorem 3: The scheduling policy which solves the follow-ing fractional knapsack problem at the beginning of the kthsuperframe is feasibility optimal.

Maximize∑i∈Sk

δ+i(k − 1)xi(k)

s.t.∑i∈Sk

xi(k)bi(k)

Bi(k)≤ 1; 0 ≤ xi(k) ≤ Xi(k)

C. Low Bitrate Ratio as a QoE metric

In this section, we suppose that the base-station can serveparts of the video at a lower bitrate, and we consider the LBRmetric described in Section III-A. Thus, one can simultane-ously monitor two parameters namely the fraction of stalledframes and the fraction of frames served at low bit rate.

We suppose that superframes can be served partially, andfurther, that the bitrate at which a video is served can bechanged at a frame-level, thus resulting in a fraction of asuperframe being served at the lower bitrate. Let bi(k) andb̃i(k) be the high and low bitrates of the two available versionsof video i in superframe k. As before, we know the maximumfeasible bitrate Bi(k) for user i in superframe k. Let vi(k) bean indicator variable that is 1 if video i is served at low bitratein superframe k, and 0 otherwise. Similarly, let yi(k) be anindicator variable that is 1 if video i is served at high bitratein superframe k, and 0 otherwise.QoE requirement: The revised QoE objective is to ensurethat the fraction of stalled superframes is less than αi, and thatthe fraction of low bitrate superframes is less than βi, i.e.,

limk→∞

1

Ti(k)

k∑l=1

xi(l)1{i ∈ Sl} ≥ (1− αi),

limk→∞

1

Ti(k)

k∑l=1

yi(l)1{i ∈ Sl} ≥ (1− αi − βi)

for each i. In order to monitor the QoE requirement, we definetwo forms of debt for user i at the end of superframe k.

δi(k) = (1− αi − βi)Ti(k)−

k∑l=1

yi(l)1{i ∈ Sl}

δ̃i(k) = (1− αi)Ti(k)−

k∑l=1

xi(l)1{i ∈ Sl}

Theorem 4: Consider the scheduling policy that solves thefollowing optimization at the start of the kth superframe.

Maximize∑i∈Sk

(δ+i(k − 1) + δ̃+

i(k − 1)

)yi(k)

+∑i∈Sk

δ̃+i(k − 1)vi(k)

s.t.∑i∈Sk

b̃i(k)yi(k)

Bi(k)+

∑i∈Sk

bi(k)vi(k)

Bi(k)≤ 1

where 0 ≤ yi(k) ≤ Xi(k), 0 ≤ vi(k) ≤ Xi(k),

yi(k) + vi(k) ≤ Xi(k),

where Xi(k) is the remaining fraction of the current super-frame for user i. The above policy is feasibility optimal.Further, we have a modified greedy algorithm that solves theabove optimization problem. (Refer [20] for details.)

IV. SIMULATION STUDY

A. Simulation Framework

Video Traces: In our simulation study, we use video tracesfrom the Arizona State University video trace library [21].The average bitrate of the videos varies from 175Kbps to3.85Mbps. The frame rate of the videos is 30 frames persecond. The videos are smoothed with a window size of 100video frames, making the length of a superframe 3.3 seconds.Mobility model: Users are positioned in a cell with a nominalcell side of 577m. At the beginning of each superframe, thedistance of each user from the basestation is chosen to beindependent and uniformly distributed.Channel Model: The channel is modeled using the COSTHata 231 path loss model. The path loss is given by

Path loss(in dB) = (44.9− 6.55 log10 hbs) ∗ log10(ssdist1000

)

+ 45.5 + (35.46− 1.1hss) ∗ log10 fc

− 13.82 ∗ log10 hbs+ 0.7hss + C

where hbs = 32m is the height of the basestation, ssdist isthe distance of the subscriber from the base-station, hss =1.5m is the height of the subscriber, fc = 2.5GHz is thecarrier frequency and C is a parameter that is set to be 0dBfor suburban and 3dB for urban environments [22].

We also model the effect of shadowing on a frame-by-framebasis. The shadowing loss (in dB) is modeled as a Gaussianrandom variable with a standard deviation of 8.9dB [22].Scheduler The baseline scheduler is the standardweighted Proportional Fair (PF) scheduler. In each slot,the scheduler picks the flow with the highest value of(weight ∗ instantaneous rate

average rate

). Here the average rate is calculated

as a moving average over the past 100 Wimax frames. Theweight is chosen to be proportional to the required bitrate.

B. Experimental Results

1) Buffering ratio metric: Throughout this section, we con-sider 8 concurrent video flows at a basestation, and comparethe performance of the VMS scheduler with the weightedPF scheduler. We begin by evaluating the performance ofthe VMS for videos of homogeneous bitrates and a uniformbuffering ratio requirement of 0.2. Figures 2(a) and 2(b) showthe time evolution of the buffering ratio for two candidatevideos. The VMS scheduler maintains tight control over thebuffering ratio, while the PF scheduler shows large fluctuationsin the buffering ratio. Figure 2(c) shows a phase plot of thebuffering ratio versus number of stalls for all the eight videos.The VMS scheduler performs significantly better in terms ofproviding QoE guarantees for each user.

Next, we consider videos with heterogeneous bitrates and auniform target buffering ratio of 0.2. The phase plot in Figure

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0 100 200 300 400 500 6000

0.05

0.1

0.15

0.2

0.25

Time(in superframes)

Buf

ferin

g R

atio

VMSPF

(a) Video 1

0 100 200 300 400 500 6000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Time(in superframes)B

uffe

ring

Rat

io

VMSPF

(b) Video 2

0 50 100 1500

0.05

0.1

0.15

0.2

0.25

Buf

ferin

g R

atio

Number of Stalls

VMSPF

(c) Phase Plot

Fig. 2. BR metric, Homogeneous Bitrates

3 shows that the VMS scheduler maintains all users close tothe target QoE while the PF scheduler shows large variationsacross videos.

0 20 40 60 80 1000.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Number of Stalls

Buf

ferin

g R

atio

VFSPF

Fig. 3. BR metric, Heterogeneous Bitrates

2) Buffering ratio and Low bitrate ratio metrics: We nowconsider a combination of the buffering ratio and low bitrateratio metrics. We consider videos with homogeneous bitratesand a uniform requirement given by αi = 0.1, βi = 0.1. InFigure 4, the phase plot of buffering ratio versus the low bitrateratio shows that the VMS scheduler perfectly maintains theQoE guarantee uniformly, while the PF scheduler shows lowerbuffering ratios but highly varying low bitrate ratios.

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0.12

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0.2

Low Bitrate Ratio

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ferin

g R

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