Scheduling Heterogeneous RealTime Traffic over Fading Wireless
Channels
I-Hong Hou
P.R. Kumar
University of Illinois,
Urbana-Champaign
1/24
Background: Wireless Networks

There will be increasing use of wireless networks for
serving traffic with QoS constraints:


Example: VoIP, Video Streaming, Real-time Monitoring,
Networked Control, etc.
Client requirements include


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Specified traffic patterns
Delay bounds
Timely throughput bounds
2 /24
Previous Work and Challenges

Prior work [Hou et al] [Hou and Kumar]:





Q: How to deal with more complicated scenarios?

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
Clients have hard throughput requirements
Static but unreliable wireless channels
All clients require the same delay bounds
Optimal packet scheduling policies are proposed
Rate adaptation may be applied
Channel qualities can be time-varying
Clients may require different delay bounds
This work extends the model in prior work and
proposes a guideline for these scenarios
3 /24
Client-Server Model



A system with N wireless clients and one AP
Time is slotted
AP schedules all transmissions
2
1
AP
3
4 /24
More General Traffic Model


{1,.,3}
Group time slots into periods with T time slots
Clients may generate packets at the beginning of
each period
{.,2,.}
{1,2,3}
{1,.,3}
{.,2,.}
{1,2,3}
T
2
1
AP
{1,.,3}
3
{.,2,.}
{1,2,3}
5 /24
Different Delay Bounds

arrival
Deadline for client n = τn
τ1=4
2
1
deadline
AP
3
τ3=3
arrival
deadline
τ2=5
arrival
deadline
6 /24
Channel Model
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Channel changes from period to period
Channels are static within a period
System may or may not support rate adaptation
With Rate Adaptation


Transmission takes sc,n
time slots under
channel c
Transmissions are
error-free
Without Rate Adaptation


Transmission takes 1
time slot
Transmissions succeeds
with probability pc,n
7 /24
Timely Throughput Requirements

Timely throughput
# of delivered packets
=
# of periods

Client n requires timely throughput qn

Q: How to design a scheduling policy to fulfill
requirements of all feasible sets of clients?

Feasibility optimal scheduling policy
8 /24
Pseudo-debt

Delivery debt: deficiency of timely throughput
(t / T )qn  # of packets delivered for client n

Time debt: deficiency of time spent on a client
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Pseudo-debt

rn(t) quantifies the behavior of client n up to time t
rn (t ) 
] converges
 The set of clients is fulfilled  [
t
to 0 in probability
9 /24
Sufficient Condition for Optimality
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Let μn be the reduction on debt for client n

Theorem:


A policy that maximizes E{ rn (t ) n } for each period
n
is feasibility optimal.

Analogous to Max-Weight scheduling in wireline
networks
10 /24
Rate Adaptation with Different Delay
Bounds

Scenario:

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Rate adaptation used
Clients may have different per packet delay bounds, τn
Modified Knapsack Policy:

Find an ordered set S={m1,m2,…} to maximize total debt
τ1=4
τ2=7
τ3=10
S1 = 3
S2 = 5
S1 = 3

S3 = 4
S3 = 4
A variation of knapsack problem and can be solved by DP
11 /24
Rate Adaptation with Different Delay
Bounds

Scenario:



Rate adaptation used
Clients may have different per packet delay bounds, τn
Modified Knapsack Policy:

Find an ordered set S={m1,m2,…} to maximize total debt
τ1=4
τ2=7
τ3=10
S1 = 3
S2 = 5
S2 = 5

S3 = 4
S3 = 4
A variation of knapsack problem and can be solved by DP
12 /24
Rate Adaptation with Different Delay
Bounds

Scenario:



Rate adaptation used
Clients may have different per packet delay bounds, τn
Modified Knapsack Policy:

Find an ordered set S={m1,m2,…} to maximize total debt
τ1=4
τ2=7
τ3=10
S1 = 3
S2 = 5
S1 = 3

S2 = 5
S3 = 4
A variation of knapsack problem and can be solved by DP
13 /24
Time-Varying Channels
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Scenario:
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Joint Debt-Channel Policy:
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Same delay bounds for all clients, τ≡τn
Time-varying channels, pn(t)
Applicable to Gilbert-Elliot fading Model
Let rn(t) be delivery debt
Clients with larger rn(t) pn(t) get higher priorities
Theorem: The Joint Debt-Channel policy is
feasibility optimal
14 /24
Heterogeneous Delay Bounds
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Scenario:
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Static channels, pn≡pn(t)
Different delay bounds for all clients, τn
Adaptive-Allocation Policy:
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Let rn(t) be time debt
Estimate the # of slots needed by client n for a successful
transmission, ηn

Dynamically allocate slots to maximize  rn (t ) n
n
15 /24
Evaluation Methodology

Evaluate four policies:
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Proposed policies for each scenario
PCF with randomly assigned priorities (random)
Two policies proposed by [Hou, Borkar, and Kumar]
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Time debt first policy
Weighted-delivery debt first policy
Metric: Total delivery debt
16 /24
Rate Adaptation: VoIP Setup
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Period length = 20 ms
Two groups of clients:
Group A
One packet every 60 ms
Group B
One packet every 40 ms
21.3 kb/s traffic
require 19.2 kb/s timely
throughput
Starting times evenly spaced
32 kb/s traffic
require 22.4 kb/s timely
throughput
Data rates alternate between 11 Mb/s and 5.5 Mb/s

66 Group A clients and 44 Group B clients
17 /24
Rate Adaptation: VoIP Results
18 /24
Time-Varying Channels: VoIP Setup
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Period length = 20 ms
Two groups of clients:
Group A
One packet every 60 ms
Group B
One packet every 40 ms
21.3 kb/s traffic
require 19.2 kb/s timely
throughput
Starting times evenly spaced
32 kb/s traffic
require 22.4 kb/s timely
throughput
Channel evolves based on Gilbert-Elliot model

57 Group A clients and 38 Group B clients
19 /24
Time-Varying Channels: VoIP Result
20 /24
Heterogeneous Delay Bounds:
VoIP Setup

Two groups of clients:
Group A
One packet every 60 ms
21.3 kb/s traffic
Group B
One packet every 40 ms
32 kb/s traffic
require 19.2 kb/s timely
throughput
Delay bound = 20 ms
Starting times evenly spaced
require 22.4 kb/s timely
throughput
Delay bound = 13 ms
Average channel reliabilities between 80% and 96%

57 Group A clients and 38 Group B clients
21 /24
Heterogeneous Delay Bounds:
VoIP Result
22 /24
Conclusion

Extend previous model for more complicated
scenarios
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With or without rate adaptation
Time-varying channels
Heterogeneous delay bounds
Identify a sufficient condition for optimal scheduling
policies
Design policies for several cases

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Time-varying channels, heterogeneous delay bounds with
rate adaptation
Time-varying channels without rate adaptation
Heterogeneous delay bounds without rate adaptation
23 /24
24/24
Rate Adaptation: MPEG Setup

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Period length = 6 ms
Two groups of clients:
Group A
Group B
1700 kb/s traffic
1360 kb/s traffic
require 1530 kb/s timely
require 816 kb/s timely
throughput
throughput
Data rates alternate between 54 Mb/s and 24 Mb/s

6 Group A clients and 6 Group B clients
25
Rate Adaptation: MPEG Results
26
Time-Varying Channels: MPEG Setup


Period length = 6 ms
Two groups of clients:
Group A
Group B
1700 kb/s traffic
1360 kb/s traffic
require 1530 kb/s timely
require 816 kb/s timely
throughput
throughput
Average channel reliabilities between 80% and 89%

4 Group A clients and 4 Group B clients
27
Time-Varying Channels: MPEG Setup
28