Cross-layer optimization for streaming scalable video over fading wireless networks

Abstract

We present a cross-layer design of transmitting scalable video streams from a base station to multiple clients over a shared fading wireless network by jointly considering the application layer information and the wireless channel conditions. We first design a long-term resource allocation algorithm that determines the optimal wireless scheduling policy in order to maximize the weighted sum of average video quality of all streams. We prove that our algorithm achieves the global optimum even though the problem is not concave in the parameter space. We then devise two on-line scheduling algorithms that utilize the results obtained by the long-term resource allocation algorithm for user and packet scheduling as well as video frame dropping strategy. We compare our schemes with existing video scheduling and buffer management schemes in the literature and simulation results show our proposed schemes significantly outperform existing ones.

Full text

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1
Cross-layer Optimization for Streaming Scalable
Video over Fading Wireless Networks
Honghai Zhang, Member, IEEE, Yanyan Zheng, Mohammad A. (Amir) Khojastepour, Member, IEEE,
and Sampath Rangarajan, Senior Member, IEEE
Abstract—We present a cross-layer design of transmitting
scalable video streams from a base station to multiple clients
over a shared fading wireless network by jointly considering the
application layer information and the wireless channel conditions.
We first design a long-term resource allocation algorithm that
determines the optimal wireless scheduling policy in order to
maximize the weighted sum of average video quality of all
streams. We prove that our algorithm achieves the global op-
timum even though the problem is not concave in the parameter
space. We then devise two on-line scheduling algorithms that
utilize the results obtained by the long-term resource allocation
algorithm for user and packet scheduling as well as video frame
dropping strategy. We compare our schemes with existing video
scheduling and buffer management schemes in the literature
and simulation results show our proposed schemes significantly
outperform existing ones.
Index Terms—Scheduling, video streaming, scalable video,
fading, wireless networks
I. INTRODUCTION
Recent years have witnessed increasing popularity of
streaming video over wireless networks as both wireless data
communication and video compression techniques undergo
significant progress. On one hand, the data transmission rates
of wireless networks are steadily growing, e.g., 1Gbps target
rate for nomadic and 100Mbps for mobile users in 4G systems
[9]. On the other hand, H.264/MPEG4-AVC [1] achieves
more efficient video compression and the Scalable Video
Coding (SVC) extension [16] of H.264/MPEG4-AVC obtains
both high coding efficiency and high scalability. Nevertheless,
because the wireless medium is often shared by many users,
it is still important to adapt to the wireless channel conditions
in order to satisfy stringent bandwidth and delay requirement
of video traffic.
Streaming video over wireless networks has been studied
extensively by many researchers, but much of the previous
work ([7], [8], [25], [15], [22], [26] and the references
therein) has focused on the single-stream scenario where the
transmitter of a video streaming service adaptively adjusts its
transmission rate, re-transmission, video-truncation, Forward
Error Correction (FEC) and/or Hybrid ARQ (HARQ) policy
in order to optimize the received video quality. Multi-user
streaming where the wireless radio resources are shared by
multiple streaming users has also been considered in [24],
[10], [11], [13], [14], [12]. However, none of them considered
Manuscript received 19 March 2009; revised 20 October 2009.
Honghai Zhang, Mohammad A. Khojastepour, and Sampath Rangarajan
are with NEC Laboratories America (email:{honghai,amir,sampath}@nec-
labs.com.)
Yanyan Zheng is with the Electrical Engineering Department of Stanford
University(email:yyzheng@stanford.edu)
exploiting the fading wireless channel characteristics and the
scalable video encoding jointly.
Realtime radio resource scheduling algorithms have been
studied in [17], [3], [18] by considering the delay requirement
and channel conditions. An alternative formulation based on
optimizing a concave utility function and rate control over a
fading wireless networks has been considered [6], [19], [4].
However, these algorithms only warrant asymptotic conver-
gence without explicitly considering video applications (such
as the hard deadline constraint and bursty rate requirements).
In this work, we considerthe cross-layeroptimization of rate
adaptation and exploiting the multi-user diversity for video
streaming using scalable video coding over a shared fading
wireless channel. In a fading wireless channel, it is important
to exploit the multi-user diversity, i.e., by scheduling users
in relatively good channel conditions. With SVC [16], it is
possible to adapt the video transmission rate to the wireless
channel capacity.
We first develop an empirical model to relate the aver-
age video quality (measured by PSNR (Peak Signal-to-Noise
Ratio)) and the average throughput based on SVC [16]. We
then formulate the following cross-layer problem: maximizing
the weighted sum of video quality of all users subject to
the achievable long-term (ergodic) rate constraint under a
fading wireless channel model. To solve the problem, we
develop a long-term radio resource allocation algorithm which
determines the wireless scheduling policy and the parameters
used by the scheduling policy. We prove the convergence
and the optimality of the proposed algorithm under mild
conditions.
Aiming to exploit multi-user diversity, we propose two
online scheduling algorithms that meet the realtime video
traffic QoS (Quality of Service) requirement. The Static
scheduling algorithm only uses the results obtained from
the aforementioned long-term resource allocation algorithm.
And, the Dynamic scheduling algorithm further adapts the
scheduling parameters to meet the instantaneous rate, deadline
requirement of video traffic and wireless channel conditions.
The underlying objective function for the optimal scheduling
problem is non-convex/concave and non-differentiable. We
transform the problem to an equivalent, but differentiable
one. We then develop a gradient-based approach to solve the
problem and prove that it converges to the optimal solution
even though the objective function is non-convex/concave. We
also design frame dropping strategies that determine when and
which frames will be dropped.
We carry out extensive simulations to validate our proposed
schemes using SVC-encoded real video sequences. Simulation
results show that our proposed scheduling schemes achieve
significant improvement over existing real-time video schedul-

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ing algorithms in the literature. Our proposed schemes obtain
up to 8-10 dB gain of average video quality compared to
several well-known existing schemes. Moreover, our proposed
schemes are much more robust under weak wireless channel
conditions. At low SINR, some videos are not decodable with
existing video scheduling schemes because of heavy packet
drop, while nearly all videos are decodable even at very weak
channel conditions by using the dynamic scheme. Finally, our
proposed algorithms are robust to channel estimation errors.
Our main contributions are threefold. First, we design a
long-term radio resource allocation algorithm and prove that it
achieves the global optimum of the objective function. Second,
we design two online scheduling algorithms and also prove the
optimality of the obtained scheduling parameters used by the
dynamic scheduling algorithm. Third, we develop intelligent
frame/layer dropping strategies based on both the long-term
resource allocation algorithm and the dynamic scheduling
algorithm.
The rest of the paper is organized as follows. In Section
II, we discuss SVC and the rate-quality model. The proposed
long-term radio resource allocation scheme is given in Section
III. We present two algorithms for on-line scheduling of video
streaming traffic in Section IV. Simulation results based on
SVC-encoded real video sequences are reported in Section V
and the paper is concluded in Section VI.
II. SCALABLE VIDEO CODING AND RATE-QUALITY
MODEL
SVC can be referred to as both the general concept of
scalable video coding and the special extension [16] of
H.264/MPEG4-AVC [1]. As a general concept, an SVC stream
has a base layer and several enhancement layers. As long as
the base layer is received, the receiver can decode the video
stream. As more enhancement layers are received, the decoded
video quality is improved. For a detailed overview of SVC,
please refer to [16].
As in [27], we use PSNR (Peak Signal to Noise Ratio) as a
measure of video quality and develop a model to characterize
the relationship between the rate and PSNR. It turns out
that the relationship between the PSNR Si of video stream
i and the video rate r can be described as a piece-wise linear
function:



where r0
quality layers are included, and the last line specifies the
maximum encoding rate of a video sequence. In figure 1,
we plot both the sample points of rate and PSNR and the
model we have obtained for eight video sequences: News,
Hall, Silent, City, Foreman, Crew, Harbour, and Mobile, all
of which can be downloaded from [21] (more video sequence
models are obtained but are omitted for the clarity of the
figure). The points in the figure show the sample points of
the rate and PSNR and the lines show the regression models
we obtained based on Eq. (1). It can be seen that our model
is quite accurate. Note that Li> Ki> 0 based on the models
of the real video sequences, so the function Si(r) is concave,
continuous, and non-decreasing with respect to r.
Si(r) =


S0
S0
S0
i+ Li(r − r0
i+ Ki(r − r0
i+ Ki(rmax
i)
i)
− r0
if r ≤ r0
if r0
else
i
i< r ≤ rmax
i
ii)
(1)
i,S0
iare the rate and PSNR when only the base
0 20040060080010001200140016001800
15
20
25
30
35
40
45
rate (Kbps)
PSNR (dB)


News
Hall
Silent
City
Foreman
Crew
Harbour
Mobile
Fig. 1.Sample points and linear regression models of the rate and PSNR.
Along with the model, we also obtain the priority of
different video layers. Note that a layer can be specified with
a temporal level t and quality level q (when the video is
encoded with temporal and quality scalability). We use q = 0
to represent a base (quality) layer. We then determine the
priority of each layer based on the average ratio of the PSNR
drop to the rate decrease for each truncated layer; the details
are omitted due to space limit. Once the priority is determined,
we can drop video layers in ascending order of their priority
to obtain any desired transmission rate and the corresponding
PSNR can be obtained based on the model (1).
Stuhlmuller [20] et al. also proposed a rate-distortion model.
The major difference between our model and their model is
that the different rates in the model in [20] are obtained by
encoding with different source coding rates and INTRA rates
while those in our model are obtained via dropping layers in
the increasing order of layer priority. As a result, our model
is more appropriate in wireless networks where video packets
may be dynamically dropped depending on wireless channel
conditions.
III. LONG-TERM RADIO RESOURCE ALLOCATION FOR
STREAMING VIDEO
When a wireless base station receives multiple requests
for streaming service of different video sequences, it has to
decide i) how much radio resources should be allocated to
each user in order to maximize the overall video quality, ii)
how to achieve the desired radio resource allocation. In a non-
fading wireless network, these problems can be simply solved
by Time Division Multiple Access (TDMA) (e.g. [11], [12]).
But mobile networks often experience fast fading. In a fading
wireless network, channel state dependent scheduling is often
used to exploit multi-user diversity.
We describe the problem formulation under a fading channel
in subsection III-A. In subsection III-B, we develop an algo-
rithm to find the optimal scheduling policy and the associated
parameters. In subsection III-C, we rigorously prove that
the obtained scheduling policy and its parameters achieve
the global optimum of the overall video quality defined in
subsection III-A under mild conditions.
2

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A. Problem formulation
We assume that the instantaneous transmission rate for each
user i at each time slot t is
C(hi(t)) = B log(1 + ρ|hi(t)|2/Γ)
(2)
where B is the channel bandwidth,ρ is the transmission power,
hi(t) is the channel gain of user i, normalized with respect
to the standard deviation of noise (and interference), Γ ≥ 1
represents the gap between the actual coding scheme and
the Shannon capacity. We assume discrete time system and
a TDMA transmission strategy: at each time slot, the server
picks only one user (which may depend on the channel states
of all the users) and sends information with the supportable
rate of the channel of this scheduled user.
Our objective is to maximize the weighted sum of average
PSNR of all users:
max
n
?
i=1
r ∈ R
wiSi(ri)
s.t.(3)
where wiis the weight of user i, Siis the PSNR of user i as
modeled in Eq. (1), r = (r1,··· ,rn) and R is the achievable
ergodic (long-term average) rate region.
The major challenge in solving problem (3) is that the
achievable rate region cannot be explicitly specified in a
fading environment. We next develop an algorithm to solve
the problem.
B. Algorithm to solve problem (3)
We first consider a randomized channel-state-dependent
TDMA scheduling strategy (which is also called static service
split (SSS) in [2]): given the channel states h of all users at
a time slot, the scheduler picks user i with probability πi(h)
and?n
randomized TDMA strategy is decided by the randomized
scheduling function π(h):
i=1πi(h) ≤ 1. The achievable rate region under this
R = {r : ri≤ Eh[πi(h)C(hi)],1 ≤ i ≤ n}
(4)
It was shown in [19] that the achievable rate region under this
randomized TDMA strategy is convex, bounded, and closed.
Because the PSNR function Si(r) is a non-decreasing
function of the rate r, there must exist an optimal solution
to problem (3) on the boundary of the achievable rate region
(i.e., which is Pareto-optimal). It was proved in [2] that for
any achievable rate vector r on the boundary of the achievable
rate region, there exists a vector µ = (µi> 0,i = 1,··· ,n)
such that the rate vector r can be achieved by the following
scheduling function:
πi(h) > 0 ⇒ h ∈ {h : µiC(hi) ≥ µkC(hk),∀k ?= i}.
(5)
The solution in (5) is essentially a deterministic scheduling
function: at each time slot, the user with the largest µiCi
is chosen for scheduling, if we ignore the set of channel
states h for which µiC(hi) = µkC(hk) which in fact has
zero probability if the distribution of h is continuous. We
call the scheduling policy defined by s(h) in (5) as maximal
scheduling policy, due to the fact that this scheduler only
obtains the set of rates in the boundary which are Pareto-
optimal.
We can now view a boundary point r = (r1,··· ,rn) as
a function of the parameter set µ = (µ1,··· ,µn), where the
average rate riof user i can be written as
ri= E[C(hi)I(µiC(hi) > µjC(hj) for all j ?= i)].
(6)
where I is an indicator function.
Let γi = ρ|hi|2denote the SINR (Signal-to-Noise-Ratio)
of the user i with PDF (Probability Density Function) func-
tion fγi(γ) and CDF (Cumulative Density Function) function
Fγi(γ). Let R(γ) = B log(1+γ/Γ). Thus, the rate rican be
computed as
ri(µ) =
?∞
0
R(γ)Πj?=iFγj(R−1(µiR(γ)/µj))fγi(γ)dγ
(7)
Now our objective is simply to
maximize
Y =
n
?
i=1
wiSi(ri(µ))
(8)
Note that Si(ri) is a non-decreasing concave continuous
function of ri.
A general approach to solve an optimization problem is the
gradient-based method. But the challenge with problem (8)
is i) the function Y is not differentiable at the points when
some ri = r0
i
, ii) the function Y is generally
not concave (or convex) with respect to µ. When a function is
not concave or convex, the solution generated by the gradient-
based approach is often only a local maximum (or minimum)
but not a global maximum. In the following we develop an
algorithm and prove that the limit point of the algorithm is
the global maximum of problem (8) under mild conditions.
To resolve the first issue, we note that although Si is
not differentiable at ri = r0
sided derivatives. For functions with one-sided derivatives, the
following lemma is a simple generalization of the first-order
necessary optimality conditions.
ior ri = rmax
ior ri = rmax
i
, it has one-
Lemma 1 If µ∗is a local maximum of Y , then
Y′
i+(µ∗) ≤ 0 and Y′
i−(µ∗) ≥ 0
(9)
for all 1 ≤ i ≤ n, where Y′
sided partial derivative and Y′
partial derivative.
i+(µ∗) =
i−=
∂Y
∂µi+(µ∗) is the right-
∂Y
∂µi−(µ∗) is the left-sided
Now with the one-sided partial derivative, we can obtain an
iterative modified gradient-based solution as follows. First we
compute the modified gradient g(k)= (g(k)
each iteration k:
1,g(k)
2,...,g(k)
n ) in
g(k)
i
=
8
<
:
0,
Y′
Y′
if Y′
if Y′
otherwise
i+(µ(k)) ≤ 0 and Y′
i+(µ(k)) > 0 and Y′
i−(µ(k)) ≥ 0
i+(µ(k)) ≥ −Y′
i+(µ(k)),
i−(µ(k)),
i−(µ(k))
Let i0 = argmax(|g(k)
be d(k)= (0,··· ,g(k)
direction d(k)is all zero except the i0th element, which takes
the value g(k)
direction but d(k)is unless d(k)is zero.
i
|). The ascent direction is chosen to
i0,··· ,0). In other words, the ascent
i0. Note that g(k)is not necessarily an ascent
3

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TABLE I
ALGORITHM A1
A1: Pseudo-code to find the solution to problem(8)
/* ǫ,σ,α0 are positive constant values. ǫ is close to 0, and 0 < σ <
1.*/
1: Select a starting point µ(0)
i
= 1 for all 1 ≤ i ≤ n.
2: Compute d(0)from µ(0)
3: k = 0;
4: while |d(k)|2≥ ǫ do
5:/* Choose the step size */
6:
α = α0
7:
while Y (µ(k)+ αd(k)) − Y (µ(k)) < σα · |d(k)|2do
8:
α = α · β
9:
end while
10:
µ(k)= µ(k)+ α · d(k)
11:k = k+1
12:Recompute d(k)from µ(k)
13: end while
Stepsize selection using modified Armijo Rule: In any
gradient-based approach, we also need to choose the step size
α(k)appropriately in order for the algorithm to converge to a
local maximum. For this purpose, we apply a modified Armijo
rule [5] where the gradient ∇Y (µ(k)) is replaced with d(k)
because the gradient ∇Y (µ(k)) may not exist. The pseudo-
code of our algorithm A1 is listed in Table I.
We can now show the convergence of the algorithm, which
is summarized next. The proof follows similar ideas in the
standard proof of the limit points of the stationary points for
gradient-based methods (see e.g., [5]) and is omitted.
Lemma 2 Algorithm A1 converges to a point µ∗satisfying the
necessary conditions of a local maximum in Eq. (9), assuming
that the finite stopping condition (in line 4 of Algorithm A1)
is removed.
C. Optimality of the algorithm A1
For all practical purpose, we can assume that the PSNR
function Y is continuously differentiable, non-decreasing and
concave with respect to r (we can always connect the two line
segments using a smooth curve to make the function continu-
ously differentiable). Under this assumption, we can prove that
the limit point of algorithm A1 is a global maximum. This is
quite significant as the function Y is generally not concave
with respect to the controlling variable µ. We first prove the
following lemma.
Lemma 3 For any rate vector r(µ) achieved using the max-
imal scheduling policy (5) with parameter µ, all achievable
rate region is below the hyper-plane defined by
{r(µ) +∂r
∂µ|µu : u ∈ Rn}
(10)
where
column is
rate vector r′, we can find a vector u ∈ Rnsuch that r′≤
r +∂r
∂r
∂µ|µ is a matrix whose element at i’th row and j’th
∂ri
∂µj|µ). More precisely, for any other achievable
∂µ|µu element wise.
Proof. The intuition is quite clear. At any point r that is
achieved by the maximal scheduling scheme with parameter
vector µ, there is a tangent hyperplane. All the achievable
rate region is below the tangent hyperplane. Next we give a
rigorous proof.
Since r is on the boundary of the achievable rate region,
which is convex, from Proposition B.12 in [5], there is a vector
b ?= 0 such that
bT(r′− r) ≤ 0
(11)
for any r′in the achievable rate region. We now show two
properties of the vector b. First, bT ∂r
be the rate achieved using parameter set µ′= (µ′
where µ′
of Eq. (11) by µ′
µ′
we let µ′
r is continuously differentiable with respect to µ, we obtain
bT ∂r
The second important property is b ≥ 0 element wise.
Suppose b = (b1,··· ,bn). We choose r′
for all j ?= k. Clearly, r′is a achievable rate vector. So from
Eq. (11), we get 0 ≥ bT(r′−r) = bk(r′
we have bk≥ 0.
We now look at the intersection point of the line {r′+bt :
t ∈ R} and the hyper plane (10). At the intersection point, we
have
r′+ bt = r +∂r
∂µk= 0 for all k. Let r′
1,··· ,µ′
n)
j= µj for all j ?= k and µ′
k− µk we obtain that bT (r′−r)
k> µk and µ′
k< µk and µ′
k> µk. Divide both sides
k−µk≤ 0. Let
∂µk≤ 0. Similarly, if
k→ µk−, we get bT ∂r
µ′
k→ µk+, we have bT ∂r
∂µk≥ 0. Since
∂µk= 0 for all 1 ≤ k ≤ n.
k< rk and r′
j= rj
k−rk). Since r′
k< rk,
∂µ|µu
(12)
Multiplying both sides by bTfrom the left and doing a little
re-arrangement, we get
bTbt = bT(r − r′) + bT∂r
∂µ|µu = bT(r − r′) ≥ 0
where the second equality is because of the first property of
vector b and the last inequality is from Eq. (11). Since bTb >
0, we obtain t ≥ 0. Therefore, the intersection point r′+ bt
is on the hyper plane (10) and is larger than or equal to r′
element wise (because t ≥ 0 is a scalar and bj≥ 0 for all j).
?
Next we prove the main theorem. Note that we can always
connect the two line segments of the function Si(ri) with a
smooth curve such that the function Si(ri) is continuously
differentiable.
(13)
Theorem 1 The limit point of the algorithm A1 is a global
maximum of function Y assuming that the PSNR function
Si(ri) is non-decreasing, concave, and continuously differen-
tiable with respect to ri.
Proof. Let µ and r(µ) be the limit point of the algorithm
A1. Clearly r(µ) is a boundary point of the achievable rate
region. Applying Lemma 3, for any achievable rate vector r′,
there exists a vector u such that r′≤ r +∂r
wise. Because of the non-decreasing property of the function
Y over each ri, we have
Y (r′) ≤ Y (r +∂r
∂µ|µ u element
∂µ|µu)
(14)
We next show that, for any point r +
hyperplane (10),
Y (r(µ) +∂r
∂r
∂µ|µu on the
∂µ|µu) ≤ Y (r(µ)),
(15)
4

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012345
µ2
6789 10
45
50
55
60
65
70
75
80
Sum PSNR (dB)
Fig. 2.Sum PSNR vs. µ2 while µ1= 1
given that µ is the limit point of algorithm A1. With the
assumption that Y is continuously differentiable with respect
to both r and µ, from Lemma 2, the limit point µ of algorithm
A1 satisfies, for any 1 ≤ k ≤ n,
0 =∂Y
∂µk
=
n
?
i=1
∂Y
∂ri
∂ri
∂µk,
(16)
where the second equality is from the chain rule of partial
derivative.
Because of the concavity of Y over r,
Y (r +∂r
∂µ|µu)≤Y (r) + ∇Y (r)T∂r
∂µ|µu
n
?
k=1
∂Y
∂rj
=Y (r) +
n
?
j=1
n
?
k=1
∂Y
∂rj
n
?
j=1
?
∂rj
∂µkuk
=Y (r) +
∂rj
∂µk
???
=0
uk
=Y (r)
(17)
where the last equality is from Eq. (16).
Combining Eq. (14) and (17), we obtain that Y (r′) ≤
Y (r(µ)) for any achievable rate vector r′provided that µ is
the limit point of the algorithm A1.
In general, for a non-convex (or non-concave) problem,
a stationary point is only a local maximum (or minimum).
It appears surprising that although the objective function Y
is not a concave function with respect to µ, the stationary
point is the global maximum of Y . To further understand the
problem, we consider a two-user scenario and fix µ1 = 1.
The objective function Y is then the function of µ2. Using
parameters derived from two real video sequences, we plot
the sum PSNR of the two users vs µ2 in Fig 2. We can
observe from the figure that the function Y is neither convex
or concave, and that the stationary points of the function are
not even unique. However, all the stationary points are indeed
the global maximum of Y .
?
IV. ONLINE SCHEDULING FOR SVC VIDEO STREAMING
An online scheduling algorithm for real-time video appli-
cations needs to address three issues:
1. User scheduling: at each time slot, which user should be
scheduled?
2. Frame scheduling: after a user is selected, which pack-
ets/frames of the selected user should be transmitted?
3. Dropping strategy: when does it need to drop frames and
which frames should be dropped?
The resource allocation algorithm presented in the section
produces two results: 1) the vector µ used for user-scheduling,
2) the achievable average rate rifor each user i. We next de-
scribe two online scheduling schemes exploiting these results.
In the first scheme, we simply apply the results obtained from
the resource allocation algorithm. In the second scheme, we
also consider the bursty and dynamic arrival and the deadline
of video frames.
A. Static scheduling scheme
In this first scheme, the vector µ is computed from the
previous section and is fixed during the process of streaming (µ
may be re-computed when new users join or some users leave).
At each time slot, the user with the largest µiCiis chosen for
scheduling, where Ci is the current channel capacity of user
i, and the vector µ = {µ1,µ2,··· ,µn} is computed from
the long-term resource allocation algorithm in the previous
section.
Frame scheduling for the selected user is based on both the
deadline and priority of the packets. We differentiate two types
of deadlines. Playout deadline is the time a frame need to be
displayed. Decoding deadline is the earliest time that a frame
is needed for decoding itself or other frames. The decoding
deadline of a frame can be computed as the minimum playout
deadline of all frames that depend on it. We then schedule
packets of a given user in the order of their decoding deadline.
Those packets with the same decoding deadline are scheduled
in the order of their priority, which is obtained in Section II.
As to the dropping strategy, there are two types of dropping.
The first is late dropping, which happens when the playout
deadline of a packet is passed. If the base layer of a frame
is dropped, all dependent frames are dropped too. Note that
when all packets of a frame are either successfully transmitted
or dropped, the decoding deadline of the frames that it depends
on need to be re-computed.
The second type of dropping is early dropping. With the
achievable rate computed from the previous subsection, we
can pre-determine which layers should be dropped based on
the rate requirement. We find the minimum priority such that
the average data rate of the packets with priority higher than or
equal to the minimum priority does not exceed the achievable
rate computed from the previous section. All packets with
priority lower than the minimum priority are dropped at the
beginning of the video streaming.
B. Dynamic scheduling scheme
The dynamic scheduling is built on top of the static
scheduling scheme with two additional enhancements. The
first enhancement is on the user scheduling. At each time slot,
still, the user with the largest µiCiis selected for scheduling.
However, the vector µ is periodically updated to reflect both
the bursty arrival and the deadline of video traffic.
5