Admission Control and Scheduling for
QoS Guarantees for Variable-Bit-Rate
Applications on Wireless Channels
I-H. Hou and P.R. Kumar
Department of Computer Science University of Illinois
Proc. of ACM MobiHoc, pages 175–184, 2009
報告人：李宗穎
Outline
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Introduction
A model for QoS with Probabilistic Arrival
Example for Application
Necessary Condition for Feasibility
Scheduling Policies
Implementation and Simulation
2
Introduction
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Two major issues concerning QoS over wireless
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admission control
scheduling
describe the QoS requirements by four criteria
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traffic pattern
channel reliability
delay bound
throughput bound
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A model for QoS with Probabilistic
Arrival (1/7)
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QoS requirements that generalizes a model
that has been proposed in [5]
[5] I-H. Hou, V. Borkar, and P. R. Kumar. A
theory of QoS for wireless. To appear in Proc.
of INFOCOM 2009.
4
A model for QoS with Probabilistic
Arrival (2/7)
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Clients generate jobs for the server to
accomplish, and during each time slot, the
server can attempt exactly one job
The time slots are grouped into intervals,
with each interval containing τ time slots
Unfinished jobs are discarded at the end of
an interval, so a delay bound of τ time slots
is imposed on all jobs
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A model for QoS with Probabilistic
Arrival (3/7)
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Don’t restrict attention only to clients that
generate one job during each interval
Clients generate jobs according to a
probability mass function and exactly every
client in S generates a job in an interval is
R(S)
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A model for QoS with Probabilistic
Arrival (4/7)
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Because wireless channels are unreliable,
the job gets delivered with probability pn,
which is called the reliability for client n
Each client n requires a long-term average
throughput of qn delivered jobs per interval
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A model for QoS with Probabilistic
Arrival (5/7)
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Definition 1.
Let Ht be the set of all possible histories of
the system up to time slot t. A scheduling
policy is a function η: Ht{1, 2,…, N, ψ}
with the interpretation
at time slot t + 1, the server attempts to
transmit the job from client n if η(ht) = n or
idles if η(ht) = ψ
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A model for QoS with Probabilistic
Arrival (6/7)
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Definition 2.
A set of clients is said to be fulfilled by a
scheduling policy η if the long-term average
throughput of each client n is at least qn jobs
per interval with probability 1
qn the timely throughput bound of client n
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A model for QoS with Probabilistic
Arrival (7/7)
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Definition 3.
A set of clients is said to be feasible if there
exists a scheduling policy η that fulfills it
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Definition 4.
An optimal scheduling policy is a policy
that fulfills every feasible set of clients
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Video Stream
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MPEG alternates between three coding
modes (I,P,B) that require different numbers
of bits per frame
a higher bit rate implies a higher arrival
probability, and can be converted into a
timely throughput bound, and captured by
the parameter qn
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VoIP Stream
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VoIP traffic involves both uplink traffic and
downlink traffic
This paper consider audio codecs that
generate CBR traffic, such as ITU-T G.711
The job generation time for clients may be
offset
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a set of three clients {1, 2, 3}
client {1 (1,3,5…) 2 (2,4,6…) 3 (1,4,7…)}
R(1, 3) = R(2, 3) = 1/2
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Real Time Surveillance
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there may be sensor nodes for monitoring
heart activity, blood pressure, and body
temperature
Paper assume each client generates jobs
periodically, with the differing frequencies
of job generation reflecting the importance
of the corresponding data
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Necessary Condition for
Feasibility (1/6)
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Paper extend some Lemma to a necessary
condition in [5] for a set of clients to be
feasible to the more general model with
variable traffic arrival patterns
[5] I-H. Hou, V. Borkar, and P. R. Kumar. A
theory of QoS for wireless. To appear in Proc.
of INFOCOM 2009.
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Necessary Condition for
Feasibility (2/6)
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LEMMA 1.
The long-term average timely throughput of
a client n is at least qn jobs per interval if
and only if the server, on average, attempts
jobs from that client wn = qn/pn times per
interval
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Necessary Condition for
Feasibility (3/6)
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LEMMA 2.
A set of N clients is feasible only if
ΣN
wn≦τ
Since the length of an interval is τ time slots
and the server can attempt jobs at most once
in each time slot
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Necessary Condition for
Feasibility (4/6)
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LEMMA 3.
γn be the random variable denoting the number
of attempts the server needs to make for a job
from client n
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Prob{γn = t} = pn(1 - pn)t-1 (Geometric dist.)
LS ,
  nS  n , if nS  n   ,

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0, otherwise,
Delay Bound Guarantee ?
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Necessary Condition for
Feasibility (5/6)
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LEMMA 4.
E[LS]: expected number of idle time slots in interval
R(S): an interval occurs with probability
N
w
n 1
n
    R( S ) E[ Ls ]
S
I S '  R( S ) E[ LS S ' ]
S
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Necessary Condition for
Feasibility (6/6)
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LEMMA 5.
A set of clients is feasible only if nS wn    I S
holds for every subset S
It may seem that the condition for a strict subset
S of {1,2,…,N} is redundant, and that we only
need to evaluate the condition for all clients
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Example
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interval length τ = 3, and two clients
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Client 1  p1=0.5 q1=0.876 R{1}=1
Client 2  p2=0.5 q2=0.45 R{2}=1
So We can calculate following value
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w1 = 1.76 ; w2 = 0.9
I{1} = I{2} = 1.25 ; I{1,2} = 0.25
w1 + w2 = 2.66 > 2.75 = τ – I{1,2} (feasible)
w1 = 1.76 > 1.75 = τ – I{1} (unfeasible!!)
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largest time-based debt first
policy
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DEFINITION 6.
Let un(t) denote the number of attempts that
the server has made for jobs from client n
up to time slot t. The time-based debt for
client n is defined to be wnt - un(t)
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largest weighted-delivery debt
first policy
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DEFINITION 7.
Let cn(t) denote the number of jobs for
client n accomplished by the server up to
time slot t. The weighted delivery debt for
client n is defined to be [qnt - cn(t)]/pn
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Largest Debt First Policy
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VoIP traffic
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Group A : 60ms, 21.3kbits/s, 99% delivery ratio
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Group B : 40ms, 32kbits/s, 80% delivery ratio
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Subgroup {A1, A2, A3}, Ai begin i, i+3, i+6…
Subgroup {B1, B2}, Bj begin j, j+2…
Feasible set  6 clients in each subgroup Ai,
5 clients in each subgroup Bj (infeasible Bj=6)
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The channel reliability of the nth client in each subgroup
is (60 + n)%
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Timely throughput insufficiency
for VoIP traffic
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MPEG Video Streaming
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Group A:0.765 packet/interval, 90% delivery ratio
Group B:0.34 packet/interval, 80% delivery ratio
Feasible set  4 clients in each subgroup Ai,
4 clients in each subgroup Bj (infeasible Aj=5)
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The channel reliability of the nth client in each subgroup
is (60 + n)%
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Timely throughput insufficiency
for video streaming
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Conclusion
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Paper have analytically addressed the
problem of providing QoS support for
heterogeneous VBR traffic flows over
unreliable wireless channels
Paper have also addressed implementation
issues under IEEE 802.11, and implemented
the two scheduling policies in ns-2
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