TIME UTILITY FUNCTION BASED PACKET SCHEDULING ALGORITHM FORSTREAMING SCALABLE MEDIA

Rongshan Yu, Haiyan Shu, Susanto Rahardja

Institute for Infocomm Research, A*STAR, SingaporeEmail: [ryu, hshu, rsusanto]@i2r.a-star.edu.sg

ABSTRACT

In this paper, a packet scheduling algorithm that is based ona Time-Utility Function (TUF) is proposed. In the proposedsystem, the scalable media is partitioned into data units ofdifferent quality layers, which are then prioritized and trans-mitted according to their TUF’s that capture both their qual-ity contributions to the decoded media and urgencies with re-spect to their playback schedule. For optimal streaming qual-ity and meanwhile maintaining a reasonable computationalcomplexity, the scheduling of packet transmission is obtainedfrom a low-complexity packet scheduling algorithm based onutility accrual maximization. Experimental results show thatthe proposed scheduling algorithm achieves near optimal per-formance when compared to the operational rate distortionbound of the stream source at the capacity of the network.

Index Terms— Time Utility Function, scalable media,media streaming, packet scheduling, utility maximization.

1. INTRODUCTION

The vigorous development of network and multimediastreaming technologies have made the internet based mediaapplication ubiquitous in human life. Compared to traditionalfile download based service, media streaming is more appeal-ing to end users because it constantly delivers the media con-tent from a server to the end users and renders it almost “in-stantaneously”. However, this appealing feature makes me-dia streaming technology in general more sensitive to fluctu-ations in transmission network conditions such as bandwidth,delay, and error rates. To overcome this problem, adaptivestreaming technologies [1, 2] have been proposed, which canadapt the streaming strategy according to the network condi-tions and media contents in order to achieve maximum end-to-end streaming quality under stringent time and networkconstraints.

To provide adaptive streaming service for different endusers with various quality and bandwidth requirements, sev-eral solutions have been proposed. The most straightforwardscheme is to store several copies of the same media contentwith different bit rates. The output stream can be switchedbetween different sources to adapt to the network bandwidth.

While this works generally well in most situations, the sys-tem is unable to adapt to channel error and delay, which isessentially due to the fact that the source is pre-coded withoutin the first place considering the network condition. In addi-tion, it requires huge space to store these same content copies.To address the channel condition, transcoding scheme is pre-sented. With this scheme, the coded media bit-stream can betranscoded and transmitted on-the-fly. The channel conditioncan be considered in the transcoding process, and the out-put bit-stream can be received and decoded with high quality.The drawback of transcoding solution is the obvious compu-tational complexity in real time process. Another drawbackis that one transcoder can only be dedicated for one output,which makes it hard for broadcasting services. Scalable codedmedia with combined packet scheduling can well solve theabove mentioned problem without introducing high codingcomputation. In this solution, the source coding only com-presses the media content into spatial and/or temporal scal-able format. In the server, these scalable layers are packetizedand transmitted based on a scheduling policy with the consid-eration of channel conditions and user requirements. The basequality can be guaranteed by transmitting the base layer unitsonly when the bandwidth is very low. In addition, this schemecan provide broadcast service for different users at the sametime.

In [2], a general framework for rate-distortion optimized(RaDiO) scheduling of media data units is introduced. TheRaDiO framework abstracts transmission of groups of inter-dependent media data units in terms of policies for transmit-ting single data unit, which are determined in a rate-distortion(RD) optimization manner in order to minimize Lagrange costfunction obtained from rate and distortion information associ-ated with different transmission policies. The RaDiO frame-work has laid down necessary groundwork for many researchworks in this direction, and has proven to be flexible enoughto accommodate many different application scenarios [2, 3].

The optimal solutions of the RaDiO scheduling problemexhibit high computational complexities [4] and hence are notsuitable for many practical solutions. Low-complexity alter-natives to RaDiO have been previously proposed in [5, 6].Most of these works propose greedy scheduling algorithmsthat perform step-wise optimization for the current transmis-

sion opportunity without considering future transmissions op-portunities. Those greedy algorithms have difficulty in iden-tifying the real quality contribution of data units without re-ferring to future transmission due to interdependency existingamong data units. As a result, they in general produce no-ideal packet scheduling with suboptimal RD performance [7].In addition, the RaDiO framework doesn’t include urgency ofpackets with respect to their playback deadline into optimiza-tion process.

In this paper, we revisit the problem of packet schedul-ing under the framework of utility maximization. We notethat the priority of each media packet depends not only on itsquality contribution to the receiver, but also on its urgency intimeline due to the real-time constraint of media streaming.In addition, under a packet loss environment, the time con-straints for transmitting a media packet are in general “soft”in the sense that transmitting a media packet at any time willresult in some utility to the system, and that utility statisti-cally depends on the transmission time. The Time UtilityFunctions (TUFs) introduced in [8] quantify such a conceptby specifying the utility to the system resulting from an ac-tivity as a function of its completion time. It allows spec-ification of soft timeliness optimality criteria such that taskswith soft time constraints are scheduled as close as possible totheir optimal scheduling to yield maximal collective utility. Inthe proposed packet scheduling algorithm, the TUF for trans-mitting media packet is defined according to both their qual-ity sensitivities and urgencies with respect to their playbackschedule, and the transmission scheduling is then optimizedbased on the TUFs to maximize the aggregated utility accrualat the receiver side. The optimization problem can then beeffectively solved using a utility accrual packet scheduling al-gorithm. Since no rate distortion optimization is involved,the computational complexity is reduced significantly. It isshown in our simulation results that the proposed scheme canwell adapt to the channel condition and provide better qualityover traditional consideration.

The rest of this paper is organized as follows. In sec-tion 2, we briefly introduce the background knowledge ofscalable media and Time Utility Function. The proposed TUFbased scheduling scheme for scalable media is presented insection 3. Experimental results are given in section 4, andconclusion is drawn in section 5.

2. PRELIMINARIES

2.1. Scalable Media

In real time transmission and streaming system, it is generallyrequired that the streamed content should be able to adapt todifferent network conditions and/or different decoder capa-bilities from different users. Scalable coding was proposed toprovide a solution to this problem. Typically, the bit-streamproduced by a scalable media encoder has a layered structure

such that when resource is limited, optimal quality can be pro-vided with layers that can be made available given the band-width constraint. When more scalable layers are obtained, thereceiver can enjoy high quality media information. Examplesof scalable video and audio coding formats include MPEG-4FGS video, H.264/MPEG-4 SVC video, and MPEG-4 SLSaudio [9, 10, 11].

I I I I

E1 E1 E1 E1

En En En En

(a)

I P P P

(b)

I P P P I

E1 E1 E1 E1 E1

En En En En En

(c)

Fig. 1. Scalable media with directed acyclic dependency(a) quality dependency (b) temporal dependency (c) quality-temporal dependency.

In a scalable media bit-stream, decoding of enhancementquality layers may depend on the availability of base qualitylayers. Generally, the dependency of scalable media may bepresented as directed acyclic dependency graph. As shown inFig. 1(a), the first example is the quality dependency wherethe decoding of enhancement quality layers (𝐸𝑖’s) may de-pend on the core quality layer (𝐼) at the same time spot. Ex-ample of this type of dependency can be found in scalable au-dio coding format such as MPEG-4 SLS [10]. The second isthe temporal dependency, where decoding of a predictive unit(𝑃 ) rely on the 𝐼/𝑃 units that precedes it in timeline as shownin Fig. 1(b). This type of dependency is usually found in pre-dictive based video coding schemes [12, 13]. It is also possi-ble that a media file has mixed quality-temporal dependency,where quality and temporal dependencies are co-existing (seeFig. 1(c)). A typical example of this type of dependency canbe found in scalable extension of H.264/MPEG-4 AVC [13].

In a network environment with packet loss, scalable mediacan be utilized to increase the robustness of real-time mediaservice [14]. Essentially, a scalable media can be packetizedinto a set of units, which are then transmitted via network ac-cording to a scheduling algorithm such that important unitsare assigned with higher priorities. In this way, these impor-tant units may have better chance to be transmitted, thus min-imizing the impact of packet loss to the quality of the trans-mitted media.

2.2. Time Utility Function

Time Utility Function (TUF), which is also called time valuefunction, is a generalization of the concept of deadline to eval-uate the importance of a set of activities or tasks for real-timescheduling. It overcomes the issue of orthogonality of ur-gency and utility in traditional deadline-based scheduling op-timality criteria, and is particularly relevant during a “over-loading” situation when a subset of tasks have to be “shed”due to insufficient resources. In such a case, deadline-basedscheduling optimality criteria may no longer be appropriateas deadlines only represent urgency and not utility.

0

Umax

t

Util

ity

DTS

(a)

0

Umax

t

Util

ity

DTS

(b)

Fig. 2. Typical hard and soft deadlines related Time UtilityFunctions.

In general, TUF can take arbitrary shapes depending onthe task or applications. Typically, the TUF of a task mayvary over time, and becomes negative as a penalty or goes tozero if it passes the deadline. For scalable media, the uni-modal TUF with non-increasing utilities may be consideredfor modeling the time utility of a media unit for transmissionscheduling considering both its sensitivity to the quality andplayback timeline. Two typical Time Utility Functions formedia streaming are presented in Fig. 2. In Fig. 2(a), the timeutility goes from 𝑈max to zero immediately when deadlinereaches, which shows a “hard” deadline. Fig. 2(b) shows an-other type of TUF. The utility gradually decreases from 𝑈max

to zero after a certain time, where a “soft” deadline is pre-sented.

3. PROPOSED TUF BASED SCALABLE MEDIASCHEDULING

3.1. Network Model

In this paper, we consider a scalable media streaming systemgoing through an independent time-invariant packet erasurechannel with random delay. Under this assumption, a dataunit transmitted at time 𝑡 is either lost with probability 𝜖𝐹 ,independent of time, or received by the receiver at time 𝑡′ forwhich the forward trip time 𝐹𝑇𝑇 = 𝑡′−𝑡 is a random variablewith probability density function 𝑝𝐹 (𝑡). Similarly, feedbackfrom the receiver is either lost with probability 𝜖𝐵 , or receivedafter a backward trip time 𝐵𝑇𝑇 , which is a random variablewith probability density function 𝑝𝐵(𝑡). Finally, the roundtrip time is defined by 𝑅𝑇𝑇 = 𝐹𝑇𝑇 + 𝐵𝑇𝑇 . As in [2], bysetting 𝐹𝑇𝑇 = +∞ when a data unit is lost, the random vari-able 𝐹𝑇𝑇 can be extended to include packet loss, yielding anextended random variable 𝐹𝐹𝑇 of which the cumulative dis-tribution function is given by:

𝑃{𝐹𝐹𝑇 ≤ 𝜏} =

∫ 𝜏

0

(1− 𝜖𝐹 )𝑝𝐹 (𝑡)𝑑𝑡. (1)

The same extension can be done for 𝐵𝑇𝑇 , yielding an ex-tended random variable𝐵𝐵𝑇 . Finally,𝑅𝑇𝑇 denotes the sum𝐹𝑇𝑇 +𝐵𝑇𝑇 .

As introduced in [15], long-range dependent internet traf-fic is modeled as shifted Gamma distribution. In such a case,𝑝𝐹 (𝑡) is given by:

𝑝𝐹 (𝑡) =𝛼𝑛𝐹

𝐹

Γ(𝑛𝐹 )(𝑡− 𝑘𝐹 )𝑛𝐹−1𝑒−𝛼(𝑡−𝑘𝐹 ), (2)

where 𝛼𝐹 , 𝑛𝐹 , and 𝑘𝐹 are the parameters defining the proba-bility density function. The distribution 𝑝𝐵(𝑡) and its parame-ters 𝛼𝑏, 𝑛𝐵 , and 𝑘𝐵 can be defined similarly for the feedbackchannel.

3.2. Unit Time Utility Function

In this part, the proposed unit TUF for scalable media is in-troduced. We first consider a simple case where a streamingnetwork is characterized with bandwidth of 𝑅, and no packetloss is presented. In this case, all transmitted data units willbe successfully received, and the quality of streamed mediais determined by the data units being transmitted under thebandwidth limitation. Optimal solution for this problem canbe specified by the operational RD bound, which can be ob-tained efficiently from, e.g., the optimal pruning algorithmof [16]. The resulting bound 𝑄target is the maximum achiev-able quality of the streaming media under bandwidth limit 𝑅.

In an error-prone network, there is no guarantee that thedata units being sent will be received by the receiver on time.In addition, due to the dependencies existing among data unitsthere is also no guarantee that the data units arrived on time

can be correctly decoded. For this reason, the impact a dataunit to the final quality of the streamed media can only beevaluated statistically. Assuming a data unit 𝑙 ∈ Φ, where Φis the set of data units from a streamed scalable media, beingtransmitted according to a certain transmission policy 𝜋𝑙, theexpected value of its quality contribution, or utility, is givenby

𝑈(𝑙) = 𝑈max(𝑙)𝑃𝑠(𝜋𝑙), ∀𝑙 ∈ Φ, (3)

where 𝑃𝑠(𝜋𝑙) is the probability that data unit 𝑙will be receivedby the receiver on time, 𝑈max(𝑙) ≜ 𝑄target − 𝑄max(𝑙), and𝑄max(𝑙) is the maximum achievable quality under bandwidthconstraint 𝑅 if data unit 𝑙 is lost. Note that in the above cal-culation it is assumed that all the interdependent data units ofdata unit 𝑙 will be decoded correctly up to 𝑄target, which isclearly an overoptimistic assumption. However, it effectivelydecouples the quality contributions of data units to the trans-mission history of their interdependent data units, and thussimplifies the optimization problem. In addition, the “positivebias” of this calculation is applied equally to all data units.Therefore, the ranking of data units in terms of their impactsto the quality of the streamed media, which is important tothe scheduling problem, is essentially preserved. Note thatby proper definition of 𝑄max(𝑙) that quantifies quality degra-dations due to loss of data units with different types depen-dencies, the proposed system can support different scalabilitysuch as temporal, spatial and quality scalability.

To further simplify the problem, we assume a TCP likebrute-force re-transmission policy such that a data unit is re-transmitted if and only if its previous transmission attempthas not been acknowledged after a predetermined timeout du-ration 𝑇𝑜. Under the brute-force retransmission scheme, it canbe seen that probability of successfully receiving data unit 𝑙 isnow a function of its initial transmission time 𝑡 as follows:

𝜌(𝑙, 𝑡) = 1−∏

𝑘:𝑡+𝑘𝑇0<𝐷𝑇𝑆(𝑙)

𝜀𝑘(𝑙, 𝑡), (4)

where 𝐷𝑇𝑆(𝑙) is the deadline of unit 𝑙, and

𝜀𝑘(𝑙, 𝑡) = 𝑃{𝐹𝑇𝑇 > 𝐷𝑇𝑆(𝑙)− (𝑡+ 𝑘𝑇𝑜)}. (5)

Then the expected utility becomes a TUF which is given asfollows:

𝑈(𝑙, 𝑡) = 𝑈max(𝑙)𝜌(𝑙, 𝑡), ∀𝑙 ∈ Φ. (6)

An example of 𝑈(𝑙, 𝑡) is given in Fig. 3. As can be seenfrom this figure, the TUF reflects both the quality contribu-tion of a data unit as well as its urgency with respect to itstransmission deadline. In particular, in a packet error free en-vironment, i.e., 𝜖𝐹 = 0, the TUF of initiating a packet trans-mission attains its maximum value before it reaches the trans-mission deadline. After that, it decreases to zero immediately.In that case, the TUF closely resembles those tasks with hard

deadlines from traditional scheduling problems. The cases ofsoft deadline can be found when 𝜖𝐹 > 0. In these cases,the value of TUF will be gradually reduced when the initialtransmission is approaching the transmission deadline, whichis reasonable since in such a case, the packet under consid-eration will have less retransmission opportunities before thedeadline.

0

Umax

tU

tility

εF = 0

εF = 0.2

εF = 0.4

DTS

T0

Fig. 3. Examples of TUF in the proposed scheme.

3.3. Scheduling Scheme

With the TUF introduced in previous subsection, the packetscheduling problem can be now formulated as a maximizingsum utility problem as follows:

max𝜋

∑{𝑙∈Φ∣𝑡𝑙∈𝜋} 𝑈(𝑙, 𝑡𝑙)

𝑠.𝑡. 𝑟(𝜋) <= 𝑅, (7)

where 𝜋 ≜ {𝑡𝑙} represents the set of transmission policy thatcontains the initial transmission time of all the data units be-ing scheduled for transmission, 𝑟(𝜋) is the data rate requiredto implement transmission policy 𝜋, and 𝑅 is the availablebandwidth for streaming. By using different implementationof 𝑟(𝜋), the bit-rate constraint can be implemented as averageor constant bit-rate constraint depending on applications.

It can be shown that the scheduling problem (7) is equiva-lent to the non-preemptive task scheduling problem addressedin [17]. The optimal solution of this scheduling problem is,nevertheless, NP-hard. To overcome this issue, approxima-tion algorithms such as the Utility Accrual Packet SchedulingAlgorithm (UPA) proposed in [18] can be used, which hasshown to perform close to that of the optimal algorithm fora wide range of TUFs such as quadratic, linear, and expo-nential, and has a more tractable complexity. Furthermore,it can be shown that for 𝑛 packets under scheduling, UPA’scost is 𝑂(𝑛2). In practical applications, a look ahead window

can be used to exclude data units that are still far away fromtheir playback deadline to further reduce the complexity ofthe scheduling algorithm for large 𝑛.

4. SIMULATION RESULTS

Experimental results based on the proposed scheme are re-ported in this section. In the simulation, channel with constantbit-rate 𝑅 is considered. The channel parameters are set asfollows: 𝜂𝐹 = 4𝑛𝑜𝑑𝑒𝑠, 𝑘𝐹 = 25𝑚𝑠, and 1/𝛼𝐹 = 12.5𝑚𝑠.The corresponding forward error rate and backward error rateare given by 𝜖𝐹 = 0.2 and 𝜖𝐵 = 0.1, respectively. We furtherassume that during transmission, each data unit has the trans-mission opportunity every 𝑇 = 75𝑚𝑠. The re-transmissiontimeout is set to 𝑇𝑜 = 225𝑚𝑠.

The video bit-stream encoded from foreman is used inour experiment. Video content is coded with H.264/MPEG-4SVC hierarchical B prediction structure [13], where the pro-duced bit-stream has both time and quality dependencies asshown in Fig. 1(c). It can be observed that the decoding orderof the bit-stream is different from that of the playback order.This makes the scheduling problem more complicated whenconsidering the time urgency. The GOP size of the bit-streamis 16, and each frame is packetized into 4 quality enhance-ment units with the same size.

500 1000 1500 2000 250030

32

34

36

38

40

42

44

Bit rate (kbps)

PS

NR

(dB

)

foreman

ProposedGreedy AlgorithmNo error controlOperational bound

Fig. 4. Comparison of three streaming schemes for quality-temporal dependency media bit-stream foreman.

In this simulation, we include the scheme consideringno error control and the scheme based on a low-complexitygreedy algorithm proposed in [19] for comparison. The re-sults are shown in Fig. 4, where the average qualities ofthe decoded video from different stream schemes at differentchannel rates are shown. The operational RD bounds gener-ated by using the optimal pruning algorithm [16], which in-

dicates the theoretical operation limits of any streaming sys-tem, are also included in this figure for reference. For faircomparison, effective channel rates (1 − 𝜖𝐹 )𝑅 are used asthe capacities of the channel when calculating the operationalRD bound. For the scheme with no error control system, dataunits are transmitted according to their deadline only with-out any consideration on transmission error/delay and qual-ity sensitivity of different data units. The qualities of thestreamed video are, as expected, rather poor in particular atlow channel rates when the qualities of the decoded videoare significantly affected by loss of important data units frombase layers. The greedy algorithm achieves a better stream-ing quality when compared to no error control scheme sinceboth time urgencies and quality sensitivities of data units areconsidered in its scheduling algorithm based on step-wiseoptimization [19]. However, there is still a significant per-formance gap when compared to the optimal rate-distortionbound due to its myopia step-wise optimization.

From Fig. 4, it can be observed that the proposed schemeachieves much better performances compared to those of theother two schemes. Essentially, the good performance of theproposed algorithm can be attributed to the applications of theTUF, which essentially captures both the timeliness and qual-ity aspects of data units, and the UPA algorithm, which effec-tively identifies the most important data units for transmittingconsidering both current and future transmission opportunityin the scheduling algorithm. In fact, it achieves near to op-timal performance when compared to the optimal RD upperbound, which is significant.

Another set of simulation is done with the video sequencefootball. Same coding parameters and test environment areconsidered as the previous simulation. The results are shownin Fig. 5. The proposed scheme presents output quality muchclose to that of the operational RD bound. In addition, theproposed scheme outperforms the other two schemes in termsof output quality. This result is similar to the previous simu-lation.

In practical implementation, 𝑈max(𝑙) in (3) can be calcu-lated off-line. When channel parameters are available, 𝑃𝑠(𝑡)in (4) can be solved with look-up-table. These make the com-putation on TUF very low. In addition, the solution of UPAproposed in [18] reduces the high computation on optimiza-tion significantly.

5. CONCLUSION

In this paper, a Time Utility Function based scheduling algo-rithm is introduced for packet priority based media streamingsystem. The time utility function effectively captures both thequality sensitivity of multimedia data units and their timeli-ness, thus enabling optimal packet transmission schedulingusing task scheduling algorithm based on maximization ofutility accrual. The performance of the proposed scheme isverified using experimental results from streaming of scal-

200 600 1000 140020

24

28

32

Bit rate (kbps)

PS

NR

(dB

)football

ProposedGreedy AlgorithmNo error controlOperational bound

Fig. 5. Comparison of three streaming schemes for quality-temporal dependency media bit-stream football.

able video encoding using H.264/MPEG-4 SVC, which showthat the proposed scheme significantly outperforms the otherschemes. In addition, it achieves near to optimal performancewhen compared to the operational RD bound of the source atthe capacity of the channel.

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