Sequence optimization for media objects with due date constraints in multimedia presentations from digital libraries

(1)

Sequence optimization for media objects with due date constraints

in multimedia presentations from digital libraries

Feng-Cheng Lin

a

, Jen-Shin Hong

b,n

, Bertrand M.T. Lin

c a

Geographic Information Systems Research Center, Feng Chia University, Taichung, Taiwan, ROC

b

Department of Computer Science and Information Engineering, National Chi Nan University, Nantou, Taiwan, ROC

c

Institute of Information Management, National Chiao Tung University, Hsinchu, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 18 May 2009 Received in revised form 20 October 2010 Accepted 6 May 2012 Recommended by: G. Vossen Available online 28 May 2012 Keywords:

Multimedia presentation scheduling Presentation lag

Digital library Due date constraint Buffer constraint

a b s t r a c t

This study investigates sequence optimization of media objects in a multimedia presentation that is dynamically composed from digital libraries. Each media object can be associated with a due date. The aim is to schedule the media objects in a delay-prone network environment such that the overall presentation lag and the due date penalties of the media objects of presentations can be minimized. We formulate the sequencing problem with buffer constraints in the media player into a flowshop scheduling problem and present a reduction strategy with a branch and bound algorithm to derive optimal sequences. The algorithm can be applied in applications with up to a dozen objects to be scheduled. In addition, we propose a modified NEH-based heuristic algorithm which can provide approximate solutions with an average error rate of less than 4%. The computation-efficient heuristic, when deployed in applications with heavily loaded servers, can obtain near-optimal sequences for problems with more than a dozen objects. The proposed algorithms are embedded into a prototype system for providing digital library services.

1. Introduction

In a multimedia digital library system, a query to the database typically retrieves a number of relevant media objects. In general, while most existing systems provide interfaces for users to view the objects by repetitively ‘‘clicking, downloading, and playing’’ the objects one by one, there is a desire of users for a ‘‘TV-like’’ presentation style where the objects are continuously played. A pre-sentation of this kind sequentially combines and continu-ously presents the media objects such that the user does not have to repetitively click to retrieve and play the media objects. Applications preferring a TV-like presenta-tion would arise from any system that can combine

multiple separate media objects into a continuous pre-sentation. Examples include assembling a TV-like docu-mentary based on queries to a multimedia database, continuously showing media items in an online multi-media album, etc. A continuously played TV-like presen-tation particularly suits hand-held portable devices such as pocket PCs, organizers, and cell phones. The input interfaces of these portable devices usually are more difﬁcult to operate than a mouse. In particular, traditional repetitive ‘‘click-and-play’’ operations are less effective when users are in motion. In practice, to suit more users with different navigation preferences, the design of the navigation interface should provide both click-and-play and TV-like presentations.

In a typical online multimedia presentation applica-tion, the media objects are retrieved from a server through the Internet. The total latency of a presentation is thus an important factor in the overall quality of the

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Corresponding author.

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service. To cope with the congestion and delay problems, a commonly used strategy is to ‘‘prefetch’’ the media objects before their presentation due time. In an on-the-fly assembled presentation delivered from digital libraries, there is no pre-defined order for presenting the media objects. Hence, the ordering of the objects is determined dynamically on-the-fly. In a typical multi-media presentation, the modalities of the multi-media objects might include text, images, audio, video, vector graphics, etc. Each media type has its unique data compression capabilities. For the same amount of data transmitted, the expected presentation durations for different media types differ drastically. To reduce the total presentation lag, the delivery and presentation order of the media objects should be properly planned.

Media streaming technology is an example application of prefetch technology that aims to reduce the presenta-tion lag. A streaming-based media player prefetches and buffers small chunks of a media object so that the data can be processed before it is rendered. As soon as the buffer is full, the media object starts to play. While the media object is playing, more data is being downloaded.

Typically, for a multimedia presentation delivered

through a network environment with a reasonable band-width, the only playback idle time is the initial download duration for the ﬁrst chunk, which in general is rather short. Therefore, a practical approach is to present the streamed objects before other non-streamed objects to keep the overall presentation latency low. The main theme of this study is to explore and exploit optimization techniques for ordering the non-streamed media objects of a prefetch-enabled presentation through a slow net-work such that the presentation lag is minimized.

In general, the end-to-end delay of a presentation depends on: access delay in the server side, communica-tion delay due to network transmission, packetizacommunica-tion, buffering, depacketization, and rendering overhead at the player site. In an environment where the bandwidth of the communication channel is rather restricted, the com-munication delay dominates the end-to-end delay. In this study, we assume that the download time of an object is deterministic. This assumption is reasonable for applica-tions where the end-to-end transmission delay is mainly attributed to a last-mile bottleneck or a server-assigned bandwidth quota limit. In these cases, the end-to-end transmission usually does not exhibit signiﬁcant band-width variations. As compared to commonly-adopted approaches that use random sequences, simulation

experiments to be presented in Section 7 nevertheless

show that optimized sequences based on the determinis-tic download transmission time signiﬁcantly reduce the presentation lags in real life network environments with stochastic variations in the transmission rate.

In Lin et al. [22,23], we provided the essential

back-ground and an overview of the prefetch-enabled media

object scheduling problems [4] with different real-life

constraints. A number of different problem settings have been thoroughly discussed. We identified several problem settings that had never before been explored. In this study, we propose a solution for a specific one of these un-solved problems. Specifically, this study considers the

media object scheduling problems with a player-side ‘‘buffer constraint’’ and ‘‘due-date’’ constraints on the media objects. The player-side buffer constraint is com-mon in applications where the multimedia objects are to be presented in small-scale devices, such as pocket PCs and organizers, with restricted memory capacity. The due-date constraints arise from commercial online ser-vices in which the media servers are implemented to automatically insert various intermittent media objects for advertisements while the users are viewing a presen-tation that dynamically combines media objects retrieved from the servers. These advertisement media objects are presented between two neighboring objects in the pre-sentation. Often, an advertisement object is required to be completed within a predetermined time slot in the ﬁnal presentation, mostly depending on the agreements between service providers and funding supporters. The problems addressed in this paper will be mathematically formulated and computationally solved. Numerical simu-lations will be described to assess the performance of the proposed algorithms under real-life wireless network conditions.

2. Notations and problem statements

To better illustrate the operations scenarios of the

problem setting under study,Fig. 1shows a Gantt chart

illustrating the download and playback of a sequence of media objects. The objective is to ﬁnd an optimal sequence of media objects with the minimum sum of total presentation time and due date penalties, which are calculated from the overdue times of the media objects. This object sequencing problem could be formulated as a two-machine ﬂowshop scheduling problem subject to a player-side buffer constraint and presentation due date

constraints. The correspondence is shown inTable 1.

This study assumes that a media object can be down-loaded only if the free space of the buffer is sufficient to accommodate the object. Once the playback of an object is finished, the buffer space occupied by this object is immediately released. In the literature, there are several papers investigating flowshop scheduling with an upper limit on the number of objects that can be allocated in the intermediate storage buffer. For the case without a buffer constraint (denoted as N-buffer in Papadimitriou and

Kanellakis[29]), an optimal solution can be obtained by

Johnson’s algorithm[16]. For the case in which no job is

allowed to be kept in the intermediate storage buffer

1 1 b1 2 2 b2 c1 c2

loading idle time

... ... loading playback idle1 idle2 3 3 b3 idle3

playback idle time

a2

a1

loading time playback time

a3

(3)

(denoted as zero-buffer or no-wait in Papadimitriou and

Kanellakis [29]), we can use the polynomial algorithm

proposed by Gilmore and Gomory [11] for a speciﬁc

variant of the traveling salesman problem. Beyond these two cases, buffer-constrained ﬂowshop scheduling has been shown to be strongly NP-hard by Papadimitriou and

Kanellakis [29,10]. To obtain exact solutions to such a

problem with a ﬁnite intermediate job-number-based buffer, a number of solution methods have been proposed,

for example Leisten [20], Smutnicki [32], Dutta and

Cunningham[9], Brucker et al.[5], Tang and Xuan [33],

and Wang et al. [35]. In these studies on ﬂowshop

scheduling, the number of jobs allowed to keep in the buffer is ﬁxed throughout the process. In the online multimedia applications addressed in this study, we consider the memory size of the player-side buffer instead of the number of objects allowed in the buffer. Therefore, for a given buffer size, the number of objects allowed in the buffer depends on the ﬁle sizes of the current playing objects and other unscheduled objects. In an environment with a constant transmission bit rate, the download time of an object (i.e., the processing time on M1) is

propor-tional to its ﬁle size. Jobs of larger sizes require longer processing (or transmission) times. The number of jobs allowed in the buffer thus depends on job processing times. The problem under study is different from conven-tional buffer-constrained ﬂowshop scheduling. Our buffer model exhibits another unique feature that the buffer

resides on machine M2 rather than acting as an

inter-mediate buffer in between two machines. Therefore, a job

currently being processed on machine M2 resides in the

buffer and occupies the buffer space until its completion. In conventional scheduling problems, a job released from the buffer for processing on the next machine immedi-ately frees the space it had acquired. To the best of our knowledge, the scheduling model formulated from the studied object sequencing problem is new to the schedul-ing community. In the followschedul-ing, we introduce the nota-tion that will be used throughout the paper.

2.1. Notation

N ¼{J1, J2,y, Jn} a set of n media objects;

Ji a speciﬁc object in N;

ai download time of media object Ji;

bi playback time of media object Ji;

M1 the ﬁrst machine (server);

M2 The second machine (client);

Ci completion time of the playback of media

object Ji;

idlei idle time immediately before Jion machine M2;

di due date of Ji;

Ti tardiness of Ji, i.e. max{Cidi, 0}

NExc a subset of N in which the objects are

‘‘exclu-sive’’ (i.e., large media objects that cannot reside in the buffer with any others);

ND a subset of N in which each object is associated

with a due date;

NExc D NExc\NDa subset of NExcin which each object is

associated with a due date;

NA NExc\{N\ND} a subset of NExc in which no due

date is assumed;

NBB N\NAthe object set considered in the branch and

bound solution after the problem reduction strategy;

NSD subset of objects of NBB which are already

scheduled;

NBUF subset of NBBwhich are in the buffer;

SN a particular sequence of jobs of set NBB;

SNSD a particular sequence of jobs of set NSD;

CSD maximum completion time of the objects in

sequence SNSD;

Cmax maximum completion time of the objects in

sequence SN;

Tmax maximum tardiness in sequence SN;

S

Ti sum of tardiness in sequence SN.

2.2. Problem statements

In the problem addressed in this paper, the optimiza-tion goal is to minimize the weighted sum of the make-span (Cmax) and a due-date related criterion (Tmaxor

S

Ti).

Tardiness reﬂects service quality and makespan indicates system throughput as well as service quality. In practice, the optimization metrics could be either one of the following two formulations of a weighted bi-criteria optimization problem:

Case 1.

a

Cmaxþ(1

a

)Tmax

Case 2.

a

Cmaxþ(1

a

)

S

Ti

With the processing-time-dependent buffer constraint, the above two bi-criteria combinations have never before been explored. In both settings, the number of objects Table 1

Correspondence between object ordering and two-machine ﬂowshop scheduling.

Media object scheduling ordering Two-machine ﬂowshop scheduling Notation

A set of media objects A set of jobs N

A media object A job Ji

Server (sends data to the client) First machine M1

Client (receives/playbacks data from the server) Second machine M2

Download time of a media object Processing time on ﬁrst machine ai

Playback time of a media object Processing time on second machine bi

Completion time of the playback of a media object Completion time of job Ji Ci

(4)

allowed to be kept in the buffer depends on the proces-sing times (ai) of the jobs on machine M1. Based on the

standard three-ﬁeld notation introduced in Graham et al.

[12], we denote the above two problems by F29ai

-buf-fer9

a

Cmaxþ(1

a

)Tmax and F29ai-buffer9

a

Cmaxþ(1

a

)

S

Ti,

respectively. For two-machine ﬂowshop scheduling

with-out any buffer constraint, Lenstra et al.[21]proved that

F299Lmax and F299

S

Ti are strongly NP-hard. With the

processing-time-dependent buffer constraints enforced in both cases, it is clear that F29ai-buffer9

a

Cmaxþ(1

a

)

Tmaxand F29ai-buffer9

a

Cmaxþ(1

a

)

S

Tiinherit complicated

structures that are computationally challenging as well. In the literature, Daniel and Chambers[8], Chakravarthy and Rajendran[6], and Allahverdi[2]have proposed branch-and-bound algorithms and heuristic approaches for solving

F299

a

Cmaxþ(1

a

)Tmax. To our knowledge, no solution

algorithm has been proposed for F299

a

Cmaxþ(1

a

)

S

Ti. In

this paper, we develop a branch-and-bound algorithm for

both problems. Section 3 presents a problem reduction

algorithm that decomposes the original problem into a set of independent sub-problems that are relatively easy to solve. Several lower and upper bounds for the two problems are then established.

3. A problem reduction algorithm (PRA)

This section presents a problem reduction strategy that is applied to decompose the original problems into several sub-problems. The problem reduction algorithm (PRA) arrives at a solution with less search efforts than required to solve the original problem. First, we introduce the notion of exclusive object. Given a buffer with a limited capacity, when a relatively large object is being played and thereby occupying the lion’s share of the buffer space, the transmission of the next incoming object is prohibited due to the space limit. We term such a media object as an exclusive object. That is, whenever an

exclu-sive job is under processing on machine M2, the

proces-sing of other objects on machine M1is not allowed.

Consider subset ND, the subset of N containing the

objects constrained by due dates and NExc, the subset of N

containing the exclusive objects. Given the buffer size, we ﬁrst partition the original media set into two disjoint subsets: exclusive objects without due date constraints (denote by NA¼NExc\{N\ND}), and the others (denoted by

NBB¼N\NA). Whenever an object of NAis under processing

on machine M2, the processing of other objects on

machine M1 is prohibited. Therefore, by intuition all the

objects of NA should follow all the objects of NBB. An

optimal sequence of NBB(denoted by SBB) can be obtained

using a branch-and-bound algorithm. The main idea of

the PRA is to ignore the objects of NA in the search

process. In this case, the original problem can be down-sized to a sub-problem that considers only the ordering of the objects of NBB, and the objects of NAcan be positioned

after the derived sequence SBBthat minimizes the

speci-ﬁed objective function. Such a problem reduction approach is particularly useful when most of the media objects are of sizes comparable to that of the buffer in a given setting.

In the following section, we present a

branch-and-bound algorithm for the sub-problem on NBB obtained

after applying the reduction step to the original media set.

The sub-problem considers only the media set NBB. We

propose several lower bounds and upper bounds for this sub-problem. Computational experiments will be con-ducted to examine the effectiveness and efﬁciency of the bounds.

4. Lower bounds

This section prosents three lower bounds for problems F29ai-buffer9

a

Cmaxþ(1

a

)Tmaxand F29ai-buffer9

a

Cmaxþ(1

a

)

S

Ti. Development of some lower bounds is adapted from

previous results of the single-criterion makespan mini-mization problem studied in Lin et al.[22].

4.1. Lower bound on Cmax(LB1)

Referring to Fig. 2, we consider a node that

corre-sponds to a partial schedule of the search tree. Let NSDbe

the set of jobs already scheduled, SNSD a sequence of the

jobs of set NSD, and CSDthe makespan of sequenceSNSD. Let

Jp, Jq, Jrbe the last three objects in sequence SNSD. Consider

the instance when an object Jris being processed on M2.

A reasonable estimate of the minimum remaining

proces-sing time at this node is the total procesproces-sing time ai

required for all unscheduled objects minus the total

allowable processing time on M1before all the buffered

objects ﬁnish their playback.

In the case where the last object Jris exclusive, the only

object residing in the buffer is Jr. Therefore, on M1the total

allowable processing time before all the buffered objects ﬁnish their playback is zero (Fig. 2(a)). In the case where

the last object Jr is not exclusive, there could be other

buffered objects waiting for processing on machine M2

(e.g., Jpand JqinFig. 2(b)). The total allowable processing

time on M1 before all the buffered objects ﬁnish their

ap aq bp bq ar br . . . . . . ap aq ar br

Tduring_p Tduring_q Tduring_r

bp bq

. . . . . .

tinit

(5)

playback is calculated based on the duration that is allowed for further downloading objects during the play-back of all buffered objects, denoted by Tduring_buffer and

computed by summing the durations allowed for further download of objects during the processing time of each buffered object Ji(denoted by Tduring_i). We use the

follow-ing two values to help compute this value: (1) duration required to fully ﬁll up an empty buffer (denoted by Tbuffer), and (2) duration allowed to fully ﬁll up the residual

free buffer space at the instant the ﬁrst object in buffer, Jp,

starts its playback (denoted by Tﬁll). In the following, we

elaborate the derivation of a lower bound using the above terms.

Assume the data transmission bit rate BR on machine

M1is constant. Then, the time required to completely ﬁll

up the empty buffer is Tbuffer¼BUF/BR.

For a given partial schedule, the current residual free buffer space BUFfreeis the buffer size minus the size of the

processing object on machine M2and other standby jobs

in the buffer. Hence, the duration allowed to fill up the residual free buffer space at the instant the first object in buffer starts its playback is Tfill¼BUFfree/BR.

There are two different scenarios for calculating the duration allowed for further download of objects during

the processing time of an object Ji on M2 (denoted by

Tduring_i). In the ﬁrst case (Fig. 3(a)), bpis larger than Tﬁll.

During the processing time of Jp on M2, the processing

on M1 will be suspended once the buffer is fully ﬁlled.

The maximum allowable download time is equal to Tﬁll.

Hence, Tduring_p¼Tﬁll.

In the second case (Fig. 3(b)), the buffer is not fully occupied before Jqcompletes on M2. The buffer has a free

space for downloading the next object, say Jr. In such a

case, Tduring_qcan be given as bq.

By combining the above two scenarios, we compute

the allowable download time Tduring_iduring the playback

of a buffered object Jias

Tduring_i¼min ðTf ill,biÞ ð1Þ

The total allowable download time for all buffered objects at that node can then be given as

Tduring_buf f er¼

X

Ji2NBUFTduring_i ð2Þ

For the case inFig. 2(a) where the last object belongs to set NExc D, it is not possible to download an

unsched-uled object before the completion of the buffered object. Therefore, Tduring_buffer¼0.

In summary, for a node in the search tree with the last item Jrand sequence SNSD, we have the following decision

rule to compute the value of Tduring_buffer:

If Jr2NExcD Tduring_buf f er¼0, Else Tduring_buf f er¼ X Ji2NBUFTduring_i ð3Þ

We now propose a lower bound based on Tduring_buffer.

Given CSDas the current makespan of the scheduled jobs,

the minimum remaining time required to download other unscheduled jobs after the playback of all the currently buffered objects is TR¼max X Ji2N\NSDaiTduring_buf f er,0 n o ð4Þ In the following paragraphs, we present methods that maximize Tduring_pfor each buffered object.Fig. 4depicts

an example where Jp, Jq, and Jrare scheduled and Ji, Jj, and

Jk are unscheduled. Given a partial schedule where Jp

starts playing, there are two cases to consider for

calcu-lating Tduring_p (duration allowed for further download

during the processing time of Jp).

In the ﬁrst case (Fig. 4(a)), bqis smaller than Tﬁll. The

buffer will not be fully occupied before the completion of

Jq. In such a case, Tduring_q¼bq. In the second case

(Fig. 4(b)), bp is larger than the Tﬁll. The maximum

allowable download time Tduring_p depends on possible

combinations of the unscheduled jobs. For example, in Fig. 4(b), aiand akoccupy more buffer space than aj. In

addition, ajand akcannot be allocated in the buffer at the

ap aq ar Tfill Tbuffer aq ar Tfill Tduring_p Tduring_p Tduring_q bp bq

(6)

same time since the sum of their download times is larger

than Tﬁll. In practice, the optimal combination of the

unscheduled jobs that maximizes Tduring_i (i.e., buffer

usage) can be obtained by solving the Subset-sum

pro-blem ([24,17]). In the Subset-sum problem, we wish to

ﬁnd a subset of w1, w2,y, wjwhose sum is as large as

possible but no greater than a given capacity U. Subset-sum is formulated as Maximize P j2NBB\NSD wjxj Subject to P j2NBB\NSD wjxjrU, where xj2 f0,1g ð5Þ

To maximize Tduring_p, we correspond aito weight wi,

and Tﬁllto capacity U in Subset-sum. The objective is then

to determine an optimal combination of ai’s among the

unscheduled jobs for which Tduring_iis maximized.

Subset-sum can be solved by dynamic programming algorithms (DP) in O(kTﬁll) time[17], where k is the number of objects

in NBB\NSD. We denote the solution obtained via

Subset-sum by Tduring_Subset_sum_pfor Jp.

By combining the above two cases, the allowable

download time during the playback of a buffer object Ji

is given by

If Tf ill4bi,Tduring_i¼bi else Tduring_i¼Tduring_Subset_sum_i

ð6Þ Given TR¼maxfPJi2N\NSDaiTduring_buf f er,0g, TR can be

maximized by using Tduring_i¼Tduring_Subset_sum_i for each

buffered object.

We now proceed to estimate the makespan using Tduring_buffer. In the case where the total processing time

on M1 of all unscheduled objects is not smaller than

Tduring_buffer(i.e.,PJi2NBB\NSDaiZTduring_buf f er), the makespan

should be the sum of the following values: (1) the current

makespan CSD, (2) the remaining time required to process

all unscheduled objects on M1 after the playback of all

buffered objects (TR), and (3) the total download idle time

(denoted by TDI, the time that cannot be allocated for

processing on M1 when the unscheduled objects are

under playback on M2). A basic lower bound for the

makespan can be given by CSDþTRþTDI. In the following,

we elaborate the process for deriving TDI.

During the playback of the buffered jobs on M2 (i.e.,

within CSD), there are Tduring_bufferunits of time for

down-loading other unscheduled objects on M1. The minimum

remaining time required to download the unscheduled jobs after the completion time of currently buffered jobs is thus given by TR¼PJi2NBB\NSDaiTduring_buf f er. Due to the

buffer constraint, the time span for downloading all unscheduled jobs could be larger than TR(Fig. 5(b)). When

an object Ji is processed on M2, the buffer is at least

occupied by Ji. Hence, the maximum allowable download

time on M1 during its playback is Tbufferai. When

Tduring_iobi(Fig. 6(a)), the minimum download idle time

Tdi_i¼bi(Tbufferai). Otherwise, Tdi_i¼0 (Fig. 6(b) and (c)).

Therefore, Tdi_ican then be given as

Tdi_i¼maxfbiðTbuf f eraiÞ,0g ð7Þ

Referring toFig. 7, when Tﬁll4bi(Fig. 7(a)), Tdi_i¼0. On

the other hand, when Tﬁll%bi (Fig. 7(b)), Tduring_i can be

computed by a dynamic program of the corresponding

Subset-sum problem. The download idle time for Ji can

then be given as

Tdi_i¼biTduring_Subset_sum_i ð8Þ

We conclude that Tdi_ican be given by the following

rule: If Jr2NExcD

Tdi_i¼bi,

Else

If Tf ill4bi,Tdi_i¼0, else Tdi_i¼biTduring_Subset_sum_i ð9Þ

The minimum download idle time for all unscheduled objects is the sum of the download idle time of all unscheduled objects

TDI¼

X

Ji2fNBB\NSD\NBB\NExcDgTdi_i

¼X

Ji2fNBB\NSD\NBB\NExcDgmaxfbiTduring_Sumset_sum_i,0g

ð10Þ Input Output aq ar Tfill Tduring_p T_{during_q} bq ap aq ar T_fill Tbuffer Tduring_Subset_sum_p ai ak bp Tfill ai a_j aj ak a_k ai aj a_i a_k

Possible solution for Subset_sum problem X X O O O O

(7)

In summary, denoting the set of (NBB\NSD) \

(NBB\NExc D) by Nset, we have the following rule for

deriv-ing a lower bound on makespan for different situations:

If ðTduring_buf f er¼0 or CSD¼0Þ, then LB1¼max CSDþamin Ji2Nset þ P Ji2Nset biþ P Ji2fNBB\NSDg\NExcD faiþbig, CSDþ P Ji2Nset aiþTDIþ P Ji2fNBB\NSDg\NExcD faiþbig 8 > > < > > : 9 > > = > > ; Else LB1¼ CSDþP Ji2Nset biþ P Ji2fNBB\NSDg\NExcD faiþbig if P Ji2NBB\NSD aioTduring_buf f er CSDþTRþTDIþ P Ji2fNBB\NSDg\NExcD faiþbig otherwise: 8 > > < > > : 9 > > = > > ; ð11Þ

4.2. LB2: Lower bound on Tmax

Let CSD denote the completion time of the scheduled

jobs, T0

max the maximum tardiness among the scheduled

jobs, and tinitthe download initialization time for the next

coming job Ji(Fig. 2). A lower bound on the maximum

tardiness can be given as

LB2a¼max

i2N\NSD

fmaxfmaxftinitþai,CSDg þbidi,0g,T0maxg ð12Þ

In principle, LB2acan be considered as a general lower

bound for problems with due date constraints. In the literature, several lower bounds for two-machine ﬂow-shop scheduling with due date related objectives have been proposed, for example, Sen et al.[31], Kim[18], Pan and Fan[26], and Pan et al.[27]. Pan et al.[27]showed that their lower bound outperforms those of Sen et al.

[31]and Kim[18]. Therefore, this study deploys a lower

bound on Tmaxwhich is generalized from Pan et al.[27]

LB2b¼max i2N\NSD

fmaxfmaxftinitþPi1þbkðS2Þ,CSDþPi2gSEDDi,0g,Tmax0g

ð13Þ where Pi1and Pi2are the sums of the i shortest processing

times among all the jobs on M1and M2, respectively, and

SEDDi is the job in the ith position of an earliest due date

(EDD) sequence of the unscheduled jobs, and bk(S2) is the

processing time of the job sequenced in the kth position of the SPT schedule on M2.

With LB2aand LB2b, we readily have a lower bound LB2

given as follows:

LB2¼maxfLB2a,LB2bg ð14Þ

4.3. LB3: Lower bound on

S

Ti

Similar to the principles described inSection 4.2for

obtaining the lower bounds on Tmax, given that the current

sum of due date penalties is known to be

S

T0_{, we}

can readily compute the lower bounds on

S

Ti as given

ai Tfill Tbuffer bi Tdi_i bi bi Tduring_i Tduring_i

Fig. 6. Calculation of minimum download idle time Tdi_iof Ji.

{ai, aj, ak}

{Tdi_i, Tdi_j}

time span for downloading with buffer constraint Minimum time required for downloading the unscheduled jobs

{ai, aj, ak}

(8)

in Eqs. (15) and (16) LB3a¼

X

i2N\NSDmaxfmaxftinitþai,CSDg þbidi,0g þ

X T0

ð15Þ LB3b¼

X

i2N\NSDmaxfmaxftinitþPi1þbkðS2Þ,CSDþPi2

g SEDDi,0g þ

X T0

ð16Þ The two lower bounds together imply the following one

LB3¼maxfLB3a,LB3bg ð17Þ

4.4. Aggregate lower bounds for the bi-criteria problems Based on the lower bounds on the different objectives described above, we can readily obtain two lower bounds for the bi-criteria problems using a weighted sum of lower bounds on Tmaxand

S

Ti

LB4¼

a

LB1þ ð1

a

ÞLB2 ð18Þ

LB5¼

a

LB1þ ð1

a

ÞLB3 ð19Þ

5. Upper bounds

This section is devoted to the development of three

heuristics that are modiﬁed from the NEH algorithm[25]

to provide approximate solutions or upper bounds. The NEH method has been applied in various makespan minimization problems with impressive performances (for example,[1,30]). Two general dispatching rules, Ear-liest Due Date First (EDD) and Shortest Processing Time First (SPT), are incorporated into our NEH-based heuristic algorithms. The EDD rule sequences the jobs in

non-decreasing order of their due dates[15]and is commonly

used to minimize the maximum lateness among jobs for numerous scheduling problems. The SPT rule schedules jobs in ascending order of their processing times and is

commonly in the minimization of the average waiting time of jobs.

The basic idea in the NEH approach is to ﬁrst optimally schedule the ﬁrst two objects; then place the remaining jobs by decreasing order of aiþbi, one by one, in one of the

positions between the scheduled jobs such that the make-span is minimum at the step. In the following, we present three heuristics, where UB1is the NEH heuristic, and UB2

and UB3are modiﬁed from the NEH heuristic by deploying

the EDD and SPT rules. We outline the main steps of the modiﬁed NEH-based upper bounds (termed as MNEH). Algorithm UB1.

Step 1: Sort the objects in non-increasing order of aiþbi.

Step 2: Take the ﬁrst two objects in the sorted list, and sequence the two objects to minimize the bi-criteria objective function.

Step 3: Insert the 3rd object into the partial schedule. There are three positions for inserting the 3rd object. Among the three positions, select the position that achieves the smallest bi-criteria objective function value.

Step 4: For k¼4 to n do

Insert the kth object into the current partial schedule. There are k possible positions for this insertion. Select the position that achieves the smallest the bi-criteria objective function value.

Step 5: Output the ﬁnal sequence given at the comple-tion of Step 4.

Algorithm UB2.

Step 1: Apply the EDD rule to ND (the set of objects with due dates). Apply the SPT rule to the objects of

N\ND on machine M1.

Step 2: Take the ﬁrst two objects in ND, and sequence the two objects to minimize the bi-criteria objective function (k¼2). ai Tfill T_buffer Tdi_i bi Tduring_i Tduring_Subset_sum_i aj aj bi Input Output Tfill aj ak ak O O X

Possible solution for Subset_sum problem

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Step 3: Insert the 3rd object in N\ND into the partial schedule if 9ND942. From among the three positions, select the one which achieves the smallest bi-criteria objective function values (k¼3).

Step 4: For k¼4 to 9ND9 do (9ND94 3)

Insert the kth object into the previous partial schedule. Select the position that achieves the smallest bi-criteria objective function values.

Step 5: For p ¼1 to n 9ND9 do

Insert the pth object into the schedule of N\ND obtained in the previous step. There are kþp possible positions for this insertion. Select the position that achieves the smallest bi-criteria objective function values.

Step 6: Output the ﬁnal sequence given at the comple-tion of Step 5.

Algorithm UB3.

Step 1: Apply the EDD rule to ND (the set of objects

with due dates). Apply the SPT rule to the objects of

N\NDon machine one.

Step 2: Take the elements of NDas the initial sequence.

Step 3: Insert the ﬁrst object from N\NDinto the partial

schedule. There are 9ND9 þ1 possible positions for

inserting the (9ND9 þ1)th object. Select the position

that achieves the smallest bi-criteria objective function values.

Step 4: For k¼2 to n 9ND9 do

Insert the kth object into the previous partial schedule. There are 9ND9 þk possible positions for this insertion.

Select the position that achieves the smallest bi-criteria objective function values.

Step 5: Output the ﬁnal sequence reported at the completion of step 4.

Finally, we select the smallest value among UB1, UB2,

and UB3as the upper bound (UB).

UB ¼ minfUB1,UB2,UB3g ð20Þ

6. Computational results

This section presents the computational experiments designed and conducted to evaluate the effectiveness and efﬁciency of the proposed lower bounds and upper bounds. The simulation programs were written in Cþþ language, and the experiments were performed on IBM Series 206 m computers with 3.4 GHz Dual-CPU and 2 GB RAM, running Microsoft Windows Server 2003. All run times reported are in CPU-seconds. Computational experiments were conducted with different problem sizes. Two buffer sizes, 16,000 KB and 30,720 KB, were adopted. We assumed that 20% of the media objects in the original media set are associated with due date con-straints. It was given that Y ¼Pni ¼ 1bi as the sum of

playback times of all media items, and due dates diwere

randomly drawn from the uniform interval [0, 0.75Y]. For each experiment, 50 independent randomly

gen-erated object sets were tested. The processing times ai

and biwere randomly generated from uniform interval

[1,100]. Computational results are summarized inTables

2–5, where the average number of nodes (Avg_nodes), the

maximum number of nodes (Max_node), and the average computation time (Avg_t) for obtaining the optimal solu-tion are presented. The branch-and-bound algorithm was aborted when 600 CPU seconds expired before reporting the optimal solution. Among each 50 data sets, the number of problems that could not be optimally solved was recorded (denoted by ‘‘NF’’ in the tables). We list the

results for problems with different weights,

a

, ranging

from 0.1 to 0.9, in the objective functions. Note that for

a

¼1, the bi-criteria problem becomes the makespan

minimization problem; similarly,

a

¼0 dictates the

max-imum tardiness or total tardiness minimization problem. The experiments were conducted for four problems sizes with n¼10, 12, 14, and 16. The computation results for instances of F29ai-buffer9

a

Cmaxþ(1

a

)Tmax are given in

Tables 2 and 3for different buffer sizes. FromTable 2, it is clear that the proposed branch-and-bound algorithm solved all the problems with n¼10, 12, or 14 objects, but could fail for n¼16.Table 3reveals that as the buffer size decreases, the number of visited nodes and the computation time increase when compared with the results for the large buffer size problems listed inTable 2. In this case, as the

value of

a

increases, the average number of visited nodes

and the average computation time increase as well. The computational results for the problems with the objective of

a

Cmaxþ(1

a

)Tmaxare given inTables 4 and 5. The results

reveal similar information as those shown inTables 2 and 3.

As a general observation, when

a

increases (that is, the

makespan is more emphasized in the objective function than due date penalties) or buffer size decreases, more computation time is required for ﬁnding optimal solutions. To investigate the performance of the proposed

heur-istic algorithms, we present inTable 6the average error

ratios between the optimal solutions (OPT) and the heuristic solutions (UB) for each media set. Error ratio is deﬁned by (UB OPT)100%/OPT. In all the tested cases, the error ratios between the heuristic solutions and the optimal solutions are less than 4% for problems with smaller buffers and less than 3% for those with larger buffers. The probability that a heuristic produced optimal solutions increases as the buffer size increases. In either case, the results indicate that for most of the test cases the heuristic algorithm constructed approximate solutions that are close to the optimal ones.

7. Prototype system implementation

To demonstrate the practical signiﬁcance of an optimal schedule in reducing the presentation lag for a presentation delivered through a real world network environment, we have implemented a prototype system and conducted experi-ments under various settings. Our implementation followed

the system architecture depicted in Fig. 8. The following

paragraphs discuss the system components in detail: 1) Multimedia Database. The database manages the

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Table 2

Results for F29ai-buffer9aCmaxþ(1 a)Tmaxwith a 30,720 KB buffer.

N 10 12 14 16

a Avg_nodes Max_node Avg_t Avg_nodes Max_node Avg_t Avg_nodes Max_node Avg_t B&B NF

0.1 4.18E þ03 2.39Eþ 04 0.009 1.17E þ 05 2.41Eþ 06 0.183 1.60Eþ 06 2.10E þ07 3.643 NA 6

0.2 3.46E þ03 3.63Eþ 04 0.007 7.64E þ 04 2.41Eþ 06 0.112 6.27Eþ 05 1.07E þ07 1.184 NA 6

0.3 7.31E þ03 9.52Eþ 04 0.013 1.60Eþ 04 1.87Eþ 05 0.028 3.94Eþ 06 7.89E þ07 6.857 NA 4

0.4 3.29E þ03 4.21Eþ 04 0.007 7.85E þ 04 2.41Eþ 06 0.112 1.44Eþ 06 4.25E þ07 3.392 NA 4

0.5 1.92E þ03 2.31Eþ 04 0.002 1.08Eþ 04 1.72Eþ 05 0.016 1.47Eþ 05 3.18E þ06 0.364 NA 2

0.6 5.58E þ03 9.19Eþ 04 0.010 1.87E þ 04 1.95Eþ 05 0.028 2.65Eþ 06 7.89E þ07 3.703 NA 4

0.7 3.18E þ03 2.45Eþ 04 0.006 4.21E þ 04 4.79Eþ 05 0.062 6.57Eþ 05 1.34E þ07 1.523 NA 8

0.8 4.64E þ03 3.87Eþ 04 0.007 8.83E þ 04 2.41Eþ 06 0.123 6.15Eþ 05 6.80E þ06 1.237 NA 5

0.9 1.36E þ04 3.80Eþ 05 0.020 1.39E þ 05 9.34Eþ 05 0.230 2.00E þ 06 3.20E þ07 4.433 NA 3

Table 3

Results for F29ai-buffer9aCmaxþ(1a)Tmaxwith a 16,000 KB buffer.

n 10 12 14

a Avg_nodes Max_node Avg_t Avg_nodes Max_node Avg_t Avg_nodes Max_node Avg_t NF

0.1 1.02Eþ 04 7.51Eþ 04 0.026 1.19Eþ 05 1.30Eþ 06 0.299 2.05E þ06 2.68E þ 07 5.554 0

0.2 9.58Eþ 03 7.65Eþ 04 0.023 1.27Eþ 05 1.40Eþ 06 0.322 2.76E þ 06 6.01E þ07 7.312 0

0.3 9.86Eþ 03 7.76Eþ 04 0.025 1.28Eþ 05 1.48Eþ 06 0.340 3.09E þ06 7.21E þ 07 8.015 0

0.4 1.14Eþ 04 9.09Eþ 04 0.027 1.40Eþ 05 1.62Eþ 06 0.379 3.51E þ 06 8.61E þ 07 9.129 0

0.5 1.11Eþ 04 1.05Eþ 05 0.026 1.50Eþ 05 1.81Eþ 06 0.429 3.92E þ 06 9.93E þ 07 10.448 0

0.6 1.26Eþ 04 1.18Eþ 05 0.033 1.82Eþ 05 2.18Eþ 06 0.559 5.28E þ 06 1.44E þ 08 14.276 0

0.7 1.55Eþ 04 1.37Eþ 05 0.040 2.61Eþ 05 2.88Eþ 06 0.842 7.35E þ 06 2.04E þ08 21.274 0

0.8 2.15Eþ 04 1.92Eþ 05 0.058 4.73Eþ 05 4.60Eþ 06 1.555 1.13E þ 07 2.75E þ 08 36.278 0

0.9 3.56Eþ 04 2.96Eþ 05 0.094 1.56Eþ 06 2.30Eþ 07 4.367 NA 4

Table 4

Results for F29ai-buffer9aCmaxþ(1a)STiwith a 30,720 KB buffer.

n 10 12 14 16

a Avg_nodes Max_node Avg_t Avg_nodes Max_node Avg_t Avg_nodes Max_node Avg_t B&B NF

0.1 3.55E þ 03 2.27Eþ 04 0.008 1.10Eþ 05 2.41E þ06 0.165 2.67Eþ 06 7.21E þ07 9.435 NA 6

0.2 3.09Eþ 03 3.39Eþ 04 0.004 7.39Eþ 04 2.41E þ06 0.101 7.21Eþ 05 1.13E þ07 1.607 NA 5

0.3 6.59E þ 03 9.19Eþ 04 0.011 1.48Eþ 04 1.56E þ05 0.020 2.89Eþ 06 7.89E þ07 4.314 NA 5

0.4 3.13E þ 03 3.94Eþ 04 0.005 7.13Eþ 04 2.41E þ06 0.092 7.72Eþ 05 1.14E þ07 1.605 NA 4

0.5 1.73E þ 03 2.31Eþ 04 0.002 8.11Eþ 03 1.70E þ05 0.010 1.46Eþ 05 3.18E þ06 0.332 NA 2

0.6 5.23E þ 03 9.19Eþ 04 0.009 3.46Eþ 04 9.07E þ05 0.070 2.32Eþ 06 7.89E þ07 2.884 NA 5

0.7 2.95E þ 03 2.45Eþ 04 0.005 3.35Eþ 04 4.79E þ05 0.054 5.54Eþ 05 9.07Eþ06 1.186 NA 7

0.8 3.82E þ 03 2.61Eþ 04 0.006 8.06Eþ 04 2.41E þ06 0.109 7.29Eþ 05 1.28E þ07 1.649 NA 4

0.9 9.34E þ 03 1.99Eþ 05 0.015 7.03Eþ 04 7.11E þ05 0.113 1.64Eþ 06 2.89E þ07 3.454 NA 4

Table 5

Results for F29ai-buffer9aCmaxþ(1a)STiwith a 16,000 KB buffer.

n 10 12 14

a Avg_nodes Max_node Avg_t Avg_nodes Max_node Avg_t Avg_nodes Max_node Avg_t

0.1 9.54Eþ 03 7.51E þ 04 0.024 1.09E þ05 1.30E þ06 0.267 2.53Eþ 06 5.79E þ 07 5.879

0.2 8.97Eþ 03 7.65E þ 04 0.022 1.14E þ05 1.40E þ06 0.279 2.78Eþ 06 6.85E þ 07 6.435

0.3 9.34Eþ 03 7.68E þ 04 0.022 1.19E þ05 1.48E þ06 0.298 3.00E þ 06 7.58E þ 07 6.998

0.4 1.06Eþ 04 7.85E þ 04 0.025 1.30E þ05 1.60E þ06 0.333 3.81Eþ 06 1.12E þ 08 8.751

0.5 1.03Eþ 04 8.60Eþ 04 0.025 1.36E þ05 1.76E þ06 0.366 4.12Eþ 06 1.21E þ 08 9.682

0.6 1.16Eþ 04 9.84E þ 04 0.030 1.63E þ05 2.08E þ06 0.447 4.84Eþ 06 1.40Eþ 08 11.699

0.7 1.44Eþ 04 1.21E þ 05 0.036 2.21E þ05 2.61E þ06 0.634 6.42Eþ 06 1.80Eþ 08 16.392

0.8 1.97Eþ 04 1.73E þ 05 0.053 3.39E þ05 3.80E þ06 1.008 7.75Eþ 06 1.67E þ 08 22.698

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objects based on a user’s query. Each object has certain metadata describing its contents, ﬁle size, playback duration, and due date constraints.

2) Bandwidth Estimation Module. The main function of this module is to estimate the average available end-to-end bandwidth in a presentation session. The bandwidth is used to estimate the transmission durations of the requested media objects. In the past, researchers have worked to obtain accurate end-to-end measurement algorithms for available bandwidth. A variety of techni-ques (refer to[28]for a survey of different approaches) can be applied to estimate the average bandwidth for which the transmission duration can be approximated based on the ﬁle size of an object. In principle, an accurate estimation of bandwidth is crucial to providing the optimal schedule of the media objects. Nevertheless, an optimal schedule computation based on a rough estimation of the bandwidth could still signiﬁcantly

reduce the overall presentation lag as compared to random sequences. In the evaluation experiments, we will provide results showing such a situation.

3) Scheduling Engine. The Scheduling Engine computes the optimal sequence based on the estimated band-width, the given constraints, the ﬁle sizes, and

play-back durations of the selected media objects.

Depending on the required response times of the online applications, the ﬁnal sequence could be the optimal solution for problems with a small number of objects, or a near-optimal solution when the server needs to serve a large number of clients in real time. The ﬁnal sequence is a ‘‘playlist’’ that will be sent to the client.

4) Object Prefetcher. Based on the playlist, Object Pre-fetcher requests and transmits the media objects under a typical HTTP protocol. For applications with a client-side buffer constraint, the presentation status Table 6

Average (Avg.) and maximum (Max.) error ratio.

n¼10, buffer¼ 16,000 KB n¼ 10, buffer ¼30,720 KB

aCmaxþ(1 a)Tmax aCmaxþ(1a)STi aCmaxþ(1 a)Tmax aCmaxþ(1 a)STi

a Avg. Max. UB ¼OPT Avg. Max. UB ¼ OPT Avg. Max. UB ¼ OPT Avg. Max. UB ¼OPT

0.1 1.697 7.333 12 1.819 8.175 12 1.127 4.940 21 1.146 6.995 22 0.2 1.631 7.333 15 1.710 7.333 16 1.089 6.543 23 1.066 6.000 25 0.3 1.923 8.833 16 2.065 8.833 17 1.185 7.536 21 1.199 6.000 20 0.4 2.136 8.872 18 2.195 9.474 17 1.277 8.154 21 1.233 6.000 21 0.5 2.122 8.500 18 2.140 8.500 17 1.240 5.419 24 1.530 8.576 23 0.6 2.425 15.722 14 2.561 15.722 14 1.424 8.436 21 1.441 8.883 21 0.7 2.495 13.571 15 2.559 15.048 15 1.352 6.486 20 1.629 9.115 21 0.8 2.344 8.958 14 2.407 10.708 13 1.519 10.508 16 2.047 8.008 15 0.9 1.844 5.745 13 1.950 6.148 11 1.158 4.593 15 1.965 8.284 14 n¼12, buffer¼ 16,000 KB n¼ 12, buffer ¼30,720 KB

0.1 1.914 11.936 11 1.770 11.936 10 0.968 7.912 22 1.256 8.793 17 0.2 1.974 10.345 11 2.027 10.758 12 0.992 7.407 23 1.203 7.510 21 0.3 2.257 14.147 12 2.181 14.147 11 1.039 7.298 24 1.235 7.298 19 0.4 2.143 10.942 11 2.283 10.942 12 1.093 6.856 23 1.280 5.823 18 0.5 2.495 19.401 12 2.395 10.128 11 1.137 7.005 22 1.362 5.901 18 0.6 2.417 14.123 10 2.561 15.739 10 1.235 9.035 18 1.460 7.912 14 0.7 2.496 13.634 10 2.871 11.392 9 1.304 6.988 19 1.710 6.988 15 0.8 2.515 11.174 10 2.733 12.019 7 1.499 6.760 14 1.814 8.022 11 0.9 2.195 7.486 10 2.336 9.254 6 1.168 6.988 7 1.634 6.988 7 n¼14, buffer¼ 16,000 KB n¼ 14, buffer ¼30,720 KB

0.1 2.151 7.443 3 2.513 9.238 5 1.473 8.477 18 1.615 8.477 17 0.2 2.349 7.861 5 2.790 9.663 7 1.148 10.596 18 1.708 11.71 20 0.3 2.633 8.645 5 3.150 10.581 7 1.236 9.272 18 1.778 9.272 15 0.4 2.729 8.445 5 3.116 10.061 6 1.315 8.344 17 2.129 10.462 13 0.5 2.730 8.485 3 3.245 12.539 3 1.437 8.212 17 2.223 9.504 13 0.6 2.882 8.035 2 3.394 12.990 2 1.486 10.331 15 2.076 10.331 11 0.7 2.671 6.288 3 3.179 10.312 4 1.492 9.499 14 1.872 9.745 10 0.8 2.625 6.917 1 3.125 8.380 1 1.396 8.015 15 1.708 8.015 10 0.9 2.084 6.547 2 2.786 12.078 2 1.187 7.682 12 1.627 9.978 7

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and buffer status detected from Media Presenter are used to decide the exact time to prefetch an object. 5) Media Presenter. The major function of Media Presenter

is to integrate and continuously play the retrieved media objects. Furthermore, during a presentation, it reports the playback and buffer status to Object Prefetcher.

We provided a prototype system implementation

using Macromedia Flash technology.Fig. 9shows a

snap-shot of a Flash-based prefetch-enabled media player supporting TV-like presentations for desktop platforms. Fig. 10 shows two snapshots of the Flash-based media players for the PDA platforms. The bandwidth estimation algorithm applied was based on a naive approach where the server sends a small file to the client, and the client sends an acknowledgment signal once the file is comple-tely downloaded. The bandwidth is given as the ratio of file size to the corresponding transmission time.

Using the prototype system implementation, this sec-tion presents experiments for evaluating the proposed MNEH heuristic algorithm in real-world network envir-onments with certain network ﬂuctuations. We compared the objective function values (i.e., the weighted sum of the presentation lag and due date penalties) of job sequences yielded by the proposed MNEH heuristic algo-rithm and the EDD dispatching rule. The experiments investigated cases with 20% due date-constrained objects in the presentation. The media objects in the server were delivered to a PDA client through a public 3 G wireless

network using WCDMA technology[13]with a maximum

bandwidth of 384 k bytes/s.

In the ﬁrst experiment, we randomly selected 10 sets of media objects from an educational media archive on our campus. Each data set contains 10 different media objects with different ﬁle sizes and playback durations. In the second experiment, each dataset contains 20 objects.

The buffer size of the media players in the PDA was set to 8 Mbytes.

For each data set, we conducted 3 runs with random sequences and another 3 runs with sequences computed by the proposed MNEH heuristic algorithm based on the band-width estimated immediately before each presentation ses-sion. For each run, the transmission time and playback time of the objects through the WCDMA network were recorded. The values of the objective function

a

Cmaxþ(1

a

)Tmaxwith

a

¼0.5 were calculated accordingly.

Figs. 11 and 12 show the average objective function values of the EDD-based sequences and the proposed MNEH sequences for the ﬁrst experiment (10 objects) and the second experiment (20 objects), respectively. The results for both experiments signify a clear reduction of up to 20% in the average objective function values if the proposed MNEH heuristic algorithm was applied. 8. Conclusions and future work

In this study, we formulated the problem of sequencing media objects in a dynamically composed multimedia presentation from digital libraries so as to reduce the overall presentation lag and due date penalties. The addressed problem was mapped to two-machine ﬂowshop scheduling with buffer and due date constraints. Two different bi-criteria objective functions, namely

a

Cmaxþ(1

a

)Tmaxand

a

Cmaxþ(1

a

)

S

Ti, are considered. Exact and approximation

algorithms were proposed and implemented in our system for providing digital library services. Experimental results show that the proposed methods can obtain optimal solu-tions for problems with up to 14 objects with a small buffer, and 16 objects with a large buffer. Furthermore, the proposed NEH-based heuristic solutions appeared to pro-vide quality approximate solutions with an average error rate of under 4%. The heuristic algorithm can be applied to heavily-loaded servers that require a quick response on the

Internet

Server Client Query Interface Bandwidth Estimation Receiver Bandwidth Estimation Module Schedule Engine Multimedia Database WWW server Query Objects metadata Transmission

rate _Playlist _{Object Requestor}

Packets Acknowledgement Object requests Media objects Presentation status Media objects Media Presenter

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near-optimal sequence of a media set with more than a dozen objects. Experiments with WCDMA wireless net-works indicate that the proposed MNEH heuristic algo-rithm can produce solutions whose objective function values are in general smaller than the solutions yielded by the EDD dispatching rule.

Following this study, there are some potential research directions. The studied settings assumed that the end-to-end transmission rate is deterministic. This assumption

can be regarded an acceptable approximation for applica-tions in which the end-to-end transmission delay is mainly subject to the last mile bottleneck without sig-nificant bandwidth variations. However, many Internet applications provide only best-effort data delivery and cannot guarantee a very consistent transmission rate during a presentation session. In such cases, stochastic variations of the network transmission rate (or the down-load time of a media object) should be considered in the sequence optimization process. In the literature, stochas-tic flowshop scheduling problems deal with cases for which the processing times of jobs on each machine are governed by a random variable. In general, the stochastic flowshop scheduling problems are not all that easy to solve. Most of the existing studies focus on problems where the job processing time is a random variable following an ‘‘exponential distribution’’. The objective is to find the schedule that minimizes the expected

make-span E(Cmax). Such a case with exponentially distributed

process times has been shown to be, in general, tractable

([34]; Bagga[3]; Cunningham and Dutta[7]; and Ku and

Niu[19]). Unfortunately, for Internet multimedia delivery applications, the probability density function of an

end-to-end bandwidth is, typically, inverse bell-shaped[14].

The probability density function of the download time of a media object should resemble a truncated normal distribution or an Erlang distribution with high shape parameters. Two-machine ﬂowshop scheduling problems with these two distributions have never been solved and Fig. 9. Snapshot of a Flash-based prefetch-enabled media player for Desktop platforms, (a) retrieved objects, (b) buffer status, (c) the presentation of the object currently under playback, (d) transmission status of each object, (e) Gantt chart.

Fig. 10. Snapshot of a Flash-based prefetch-enabled media player supporting TV-like presentations for (a) 3 G PDA phone, (b) PDA platform.

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thus are worthy of research attention. In addition, in many applications the media objects in a digital library are subject to different categories of temporal constraints (e.g., sequence, parallel, precedence). Development of exact or approximate algorithms for these problems requires further investigation.

Acknowledgments

Feng-Cheng Lin was supported by the National Science Council of Taiwan, under grant NSC 100-2625-M-035-003 and NSC 100-2119-M-035-001. Jen-Shin Hong was sup-ported by the National Science Council of Taiwan, under grant NSC 96-2221-E-260-020-MY3. Bertrand M.T. Lin was supported in part by the National Science Council of Taiwan, under grant NSC 96-2416-H-009-012-MY2. References

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