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Data Broadcast Scheduling in Broadcast/UMTS
Integrated Systems Using Mathematical Modeling
and Computing Techniques
WANG Hui, WANG Ying, ZHANG Ping, TAO Xiaofeng
Wireless Technology Innovation (WTI) Institute
Key Lab. of Universal Wireless Communications, Ministry of Education
School of Telecommunications Engineering
Beijing University of Posts and Telecommunications (BUPT)
10 Xitucheng Road, Beijing, P.R.China 100876
wanghui.wti@gmail.com, {wangying,pzhang,taoxf}@bupt.edu.cn
Abstract—Wireless broadcast systems provide the users with
high bandwidth while 3G cellular systems provide complemen
tary service to support personality and interactivity. In this
paper, we develop a novel scheduling algorithm for the integrated
Wireless Broadcast/3G system. The proposed algorithm combines
Analytic hierarchy process (AHP) and Grey relational analysis
(GRA). Simulation results are presented to demonstrate that the
proposed algorithm could effectively support data dissemination
with low response time, request drop rate, and the unfairness of
request drop.
I. INTRODUCTION
In recent years, handheld terminals are packed with new
technologies that broaden their functions to game console,
music player, portable radio, agenda, camera, etc. Now, they
are beginning to add their latest and perhaps boldest new
capability: TV. However, if many people at the same time
and place wish to enjoy multimedia services with high data
rate requirements, even 3G pointtopoint networks like UMTS
encounter their limitations. This is where terrestrial digital
broadcast transmission for handheld retrieval, which is able
to transmit high volume data to a large number of mobile
devices simultaneously, comes to play. Mobile telecommu
nication networks enable onetoone interactive individual
services while broadcast networks are well suitable for data
intensive services. The ondemand broadcast mode combines
the advantages of the two types of networks, where a large
and dynamic client population requests data items from an
information server and the server broadcasts data items in an
ordered way to the clients based on the requests [1].
A number of ondemand data broadcast scheduling algo
rithms have been proposed in the literatures. Most of them
[2, 3] consider one decision factor. Such single factor, for
example waiting time, pending request numbers or deadline,
is not able to present the whole request urgency. Some others
consider multiple decision factors [4, 5]. Whereas the over
restricted assumptions, such as equal item length, reduce the
feasibility of the system models to a large extent. In order to
increase the feasibility of the system model, some unnecessary
constraints on the assumptions should be removed and more
factors should be considered. And furthermore, multimetric
evaluation criteria should be taken into account to measure the
performance of the scheduling algorithm, rather than only one
metric is used in the above algorithms.
In this paper, we design a novel data dissemination algo
rithm through integrating two matehmetical techniques, Ana
lytic hierarchy process (AHP) [6] and Grey relational analysis
(GRA) [7] and we call our algorithm DAG algorithm (on
Demand data scheduling utilizing AHP [6] and GRA [7]). We
will consider waiting time, pending requests, and deadline as
selection criteria. AHP is responsible for evaluating the users
preferences and service requirements on their contributions to
the final goal. Then GRA combines the priority settings of
these parameters with the performances of the sequence of
data item alternatives to make decision. The data scheduling
process is modeled as a multiple factors decisionmaking and
best optionselecting process. Our goal is to devise the broad
cast scheduling algorithm that provides good performance in
responding to user request as quickly as possible, satisfying
as many requests as possible and treating request to different
data items as equally as possible regardless of their popularity.
The rest of this paper is organized as follows. The system
model and some terminology is proposed in Section II. We
introduce AHP and GRA theory respectively in section III
and IV, and then apply AHP and GRA to the ondemand data
broadcast scheduling algorithm in Section V. We exhibit and
analyze the simulation results of the algorithm performance on
response time, request drop rate, and unfairness of request drop
in Section VI. Finally, conclusions of this paper are detailed
in Section VII.
II. PRELIMINARIES
This section introduces much of the assumptions and ter
minology to be used in the rest of the paper.
All information requested is assumed to be available on the
server. Database in the broadcast server is divided into many
information items. The items are not necessarily of the same
15253511/08/$25.00 ©2008 IEEE
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size. The time required to broadcast an item of unit length is
referred to as one time unit. Hence time required to broadcast
an item of length l is l time units. M denotes the total number
of information items in the server’s database. The items are
numbered 1 through M. lirepresents the length of item i.
A large group of clients retrieve data items from a broad
cast server. The clients send requests to the server through
radio channel. Each request is characterized by a 3tuple:
< id,t,d >, where id is the identifier of the request item,
t is the time of request, and d is a relative deadline.
The client monitors a downlink broadcast channel for the
requested item until the item is broadcasted or the lifetime
of the request expires. The uplink and downlink channels are
independent.
On receiving a request, the server inserts it into the request
queue. At each broadcast instance, the scheduler selects a new
item from request queue. The selected item is sent to clients
and the associated request(s) are removed from the request
queue.
The primary goal of a scheduling algorithm is to try best
to meet requests more quickly, satisfy more requests and
treat items fairer. These can be measured by the following
evaluation criteria.
Average response time, denoted as W [8], is defined as
the mean value of the amount of time a client waits for an
information item it needs, given by:
W =
N
?
i=1
Wi/N
(1)
where N denotes the total number of user requests and Wi
denotes the waiting time of the ith user request.
Request drop rate, denoted as D [4], is defined as the ratio
of the number of requests missing their deadlines to the total
number of requests and can be expressed as:
D = Nd/N
(2)
where Nddenotes the total number of requests dropped.
Unfairness of request drop, denoted as U [9], is defined as
the statistical variance of the request drop rate, which can be
referred as:
?
i=1
U =
?
?
?
N
?
(di− D)2/(M − 1)
(3)
where M denotes the total number of items in the server
database and didenotes the request drop rate of the ith item.
Three factors influence these metrics directly and they are
waiting time, request number and deadline.
Waiting Time, denoted as α, is defined as the amount of
time a client waits for an information item it needs.
Request Number, denoted as β, is defined as the number of
active requests. A request is active if and only if its lifetime
does not expire and they are not handled.
Deadline, denoted as γ, is defined as the deadline is absolute
(service) deadline of a request, given by t+d , beyond which
the receipt of the requested item is considered invalid to the
client.
Thus the optimized selection process can be expressed as:
ITEM = m∗
i= argmin{W,D,U}[mi(α,β,γ)]
(4)
where midenotes the ith alternative item.
III. AHP IMPLEMENTATION
AHP is defined as a procedure to divide a complex problem
into a number of deciding factors and integrate the relative
dominances of the factors with the solution alternatives to find
the optimal one. AHP is carried out in five steps [6]:
Step 1 Structuring a problem as a decision hierarchy of
independent decision elements
Step 2 Collecting information about the decision elements
Step 3 Comparing the decision elements pairwise on each
level in the matter of their importance to the elements in the
level above
Step 4 Calculating the relative priorities of decision ele
ments in each level
Step 5 Synthesizing the above results to achieve the overall
weight of each decision alternative
In a typical hierarchy, the problem to be resolved is in the
topmost level. For example, one telecommunication operator
is trying to make a selection among public bidding from
companies A, B, C, D and E respectively. The topmost
level would be ”choosing a bidding”.The subsequent levels
comprise the deciding factors, possibly price, quality, time
limit for a project, and credit. The solution alternatives (i.e.,
the companies) are in the bottom level.
The relative magnitudes of factors and subfactors with
respect to their parents are estimated through pairwise com
parison based on knowledge and experience. The smaller one
of a pair is chosen as a unit, and the larger one is estimated
as a multiple of that unit based on the perceived intensity of
importance. The judgments are ranked on a 9point scale in
AHP. Numbers 1 to 9 are used to present equally, weakly mod
erately, moderately, moderately plus, strongly, strongly plus,
very strongly, very very strongly, and extremely important to
the objective, respectively. When one element is less important
than another, the comparison result equals the reciprocal of one
of the numbers.
The comparison results within each parent are presented in
a square matrix to which we refer as the AHP matrix. The
decision factors under a parent are arranged in the same order
in row and column headings. When the ith element in the
column heading is compared to the jth element in the row
heading, the judgment is presented at the ith row and jth
column. An example of an AHP matrix on choosing a bidding
is shown in Table 1. It is observed that the diagonal elements
of the matrix are 1, showing the elements’ selfcomparisons.
The other entries in the matrix are symmetric with respect to
the diagonal, as a result of the inverted comparisons.
The relative weights of the factors are achieved through
calculating the eigenvector of the matrix with the eigenvalue
xmax that is closest to the number (n) of factors [6]. Since
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TABLE I
AN EXAMPLE OF AN AHP MATRIX
Price
1
0.5
0.33
0.25
Quality
2
1
0.5
0.33
Time
3
2
1
0.5
Credit
4
3
2
1
Price
Quality
Time
Credit
comparisons performed in AHP are subjective, judgment er
rors are inevitable and have to be detected through calculating
a consistency index (CI) of the AHP matrix, given by (xmax−
n)/(n−1), and then comparing it with a random index (RI),
which is the average CI of a randomly generated reciprocal
matrix. All RI values for different matrix dimensions are
provided by [6]. If CI is equal to zero, the matrix is perfectly
consistent; otherwise, CI should be positive. The ratio of CI
to RI for the same dimension matrix is called the consistency
ratio (CR). Adjustment of the comparisons is needed when
CR > 10 percent. This process is repeated downward level
by level to the bottom of the hierarchy.
It is important to remember that the weights achieved by
calculating the eigenvector of the comparison matrix only
reflect appropriate distributions to the elements’parent, not the
final goal. These weights must be transformed into the final
weights through being multiplied by the weight of their parent
with respect to the goal.
IV. GRA IMPLEMENTATION
GRA is a method that decides the best option through
defining the similarity between each option and the ideal
option. The more is the similarity, the more preferable is the
option. Grey relational coefficient (GRC) is used to describe
the similarity.
Step1 Bound Definition and Data Normalization
The subsequent level comprises the decision factors. The
solution alternative data items are in the bottom level. The
performance of different data items is evaluated by GRA. We
assume that n (the number of data items actively requested)
series (E1,E2,...,En) are compared, and each series has k
(k = 3 here) entities corresponding to the decision factors.
Then each series is presented as Ei= {ei(1),ei(2),...,ei(k)},
where i = 1,2,...,n . For waiting time and request number,
which are largerthebetter, the normalizations are performed
as
e∗
Uj− Lj
For deadline, which is smallerthebetter, the normalizations
are performed as
i=Uj− ei(j)
Uj− Lj
where j = 1,2,...,k,
Uj= max{ei(j),e2(j),...,en(j)},
Lj= min{ei(j),e2(j),...,en(j)}.
Step2 Grey Relational Coefficient Calculation
i=ei(j) − Lj
(5)
e∗
(6)
The upper bound in largerthebetter and the lower bound
in smallerthebetter are chosen to compose the ideal option
E0= {e0(1),e0(2),...,e0(k)}. The grey relational coefficients
are calculated as:
Γ0,i=∆min+ ∆max
∆?
?k
min(i,j)(e0(j) − e∗
function of computing the maximum/minimum value of a set
of numbers varying with i and j, ,which are independent. The
decision maker compares the GRCs of different data items,
and chooses the item with the largest GRCs as the next one
to be broadcasted.
i+ ∆max
(7)
where ∆?
weight. ∆max = max(i,j)(e0(j) − e∗
i(j)), where max(i,j)()/min(i,j)() is the
i=
j=1e0(j) − e∗
i(j),wj is the jth entity’s
i(j)) and ∆min =
V. ONDEMAND BROADCAST SCHEDULING APPROACH
DAG USING AHP AND GRA
We design the scheduling approach through integrating two
mathematical techniques, analytic hierarchy process (AHP)
and grey relational analysis (GRA). The function of AHP [10,
11] is to find the best solution to the complex problem by
synthesizing all problemdecision factors. GRA is a method
of selecting the best option among the comparative choices
through building grey relationships with an ideal option [12,
13].
Fig. 1.The AHP and GRA based scheduling approach
The whole algorithm is demonstrated in Fig. 1 and described
as follows.
VI. SIMULATION RESULTS AND ANALYSIS
To evaluate the performance of our algorithm, it has been
simulated and compared its performance with FCFS (First
Come First Served) [2] and MRF (Most Requests First)
[3]. For evaluating a broadcast scheduling algorithm for a
particular set of parameters, the broadcast schedule is produced
for 2,000,000 time units. For a given broadcast schedule, to
produce such a large schedule would have been to determine
the broadcast cycle produced by the algorithm and determine
the waiting time for the broadcast cycle. However, the time
required to determine the broadcast cycle would be very
large in many cases. The default and range value of the
parameters are set as Table 2. The distributions assumed have
been described in simulation environment subsection. Similar
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Algorithm 1 DAG Algorithm
Target = set of all factor values for items which need to be
scheduled
WT = waiting time column in Target
D = deadline column in Target
t = earliest time slot at which scheduling can occur
M = the total number of items in the server database Define
the AHP matrix A
W = AHP (A)
1: procedure DAG(t)
2:
Target += value for new requests to data items /* new
requests are the ones which come after the time when an
item was most recently transmitted or the time zero when
no item was broadcasted before */
3:
if Target = ø
4:
return
5:
else
6:
Target?=Normalize (Target)
7:
GRC = GRA (W, Target?)
8:
i= the data item with the largest GRC /* If this
holds for more than one item, choose any one of them
arbitrarily.*/
9:
li= the length of i
10:
delete all the requests for the ith item from the Target
11:
reserve interval (t, t + li) to broadcast i
12:
t+ = li
13:
WT+ = li
14:
For j ← 1 to M
15:
if(D(j) < t)
16:
delete all the requests for the jth item from the
Target
17: end procedure
settings and assumptions are made by other researchers as well
[4,5,8].
A. Simulation Environment
We design and set up our simulation environment according
to the user activity model and system model adopted by most
researchers [15].
• Arrival of Request: It is assumed to follow Poisson
Process, and λ represents the average request intensity.
• Demand Probability Distribution: It is assumed to follow
Zipf distribution. The Zipf distribution may be expressed
as follows:
pi=
(1/i)θ
?M
i=1(1/i)θ,1 ≤ i ≤ M
(8)
where θ is a parameter named access skew coefficient.
Different values of the access skew coefficient θ yield
different Zipf distributions. We just set θ = 1 for the
famous ”8020” law, that is most people only access 20%
of the information while the remaining 80% is accessed
only a few.
TABLE II
PARAMETERS AND SETTINGS
SymbolDefault
1000
100
100
1
1
10
Range


[0,1000]



Run Time (time unit)
M
λ (requests/ time unit)
θ
L0
L1
• Length Distribution: It is assumed to follow increasing
distribution.
li= round((L1− L0
M − 1(i − 1) + L0),1 ≤ i ≤ M
where L0 and L1 are parameters that characterize the
distribution. L0 and L1 are both positive integers. The
round() function above returns a rounded integer value
of its argument [8].
• Relative Deadlines: It is assumed to follow normal dis
tribution. represents the mean, and standard derivation is
set to be µ/3.
(9)
B. Results & Discussion
Fig. 2 plots the average response time for different user
request intensity. In average, 17% and 39% improvements
are accomplished using DAG compared with FCFS and MRF
algorithm respectively. The differentiated performance lies in
the fact that both FCFS and MRF ignore factors which also
influence the response time. In such case, the item with earliest
request but requested by very few clients, or the item with
most requests but a little waiting time will be broadcasted
first. While in DAG, both waiting time and request number
are considered and the item is only broadcasted because it is
popular (request by many clients) and/or clients requesting for
it have been waiting for a certain amount of time.
10
0
10
1
10
2
10
3
0
10
20
30
40
50
60
70
lambda(req/time unit)
mean response time(time unit)
DAG
FCFS
MRF
Fig. 2.
user request intensity
Comparison of overall mean response time for different values of
The request drop rate is shown in Fig.3. It can be seen that
according to different user request intensity, 74% and 80%
improvements are accomplished using DAG compared with
FCFS and MRF algorithm respectively. The reason for that
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is FCFS ignores the popularity of item while MRF algorithm
only tries to satisfy the need of hot data item so that requests
for infrequently accessed items must wait until sufficient
requests have arrived. The success of DAG is due to the fact
that it takes into account the time constraints for satisfying
more urgent requests earlier and provides more bandwidth to
hot data items while avoiding starvation of cold data items.
10
0
10
lambda (req/time unit)
1
10
2
10
3
0
0.02
0.04
0.06
0.08
0.1
0.12
request drop rate
DAG
FCFS
MRF
Fig. 3.
intensity
Comparison of request drop rate for different values of user request
The unfairness of request drop is shown in Fig.4 and it
can be seen that according to different user request intensity,
89% improvements are accomplished using DAG compared
with MRF algorithm while a little worse than FCFS. This is
because FCFS allocates the same bandwidth to all requested
items regardless of their popularity, and therefore performs a
little better than DAG. In contrast, MRF is not a starvation
free algorithm; it is quite possible that a request for a very
cold data item is never satisfied.
10
0
10
1
10
2
10
3
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
lambda (req/time unit)
unfairness of request drop
DAG
FCFS
MRF
Fig. 4. Comparison of unfairness of request drop for different values of user
request intensity
From the above simulation results, we can see that DAG
approach performs much better than FCFS and MRF for all
three metrics in most situations.
VII. CONCLUSIONS
In this article we present a novel ondemand data broadcast
scheduling approach DAG, by using a combination of AHP
and GRA to evaluate user requests quantitatively and rank
the data item alternatives efficiently. AHP takes advantage
of hierarchy and pairwise comparison, and GRA focuses on
finding the difference between the comparative and ideal
options. Unlike other approaches, we consider multiple de
cision factors, and weight them based on their importance
to user experience. Assumption of equal data item length is
discarded in our algorithm, and multi evaluation metrics are
used for measuring its performance. The simulation results
reveal that the proposed scheduling approach can always
guarantee quicker response, satisfy more requests and treat
the data items fairer.
ACKNOWLEDGMENT
This study is supported by EU Project 045461 – MING
T (Multistandard Integrated Network Convergence for Global
Mobile and Broadcast Technologies) under the Information
Society Technologies (IST) Programme.
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