Mahdi Lotfinezhad,Ben Liang, and Elvino S' Sousa

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Mahdi Lotfinezhad,Ben Liang, and Elvino S' Sousa

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Title: Mahdi Lotfinezhad,Ben Liang, and Elvino S' Sousa

1
On the Stability Region of Linear-MemorySchedu
ling for Time Varying Channels

Mahdi Lotfinezhad,Ben Liang, and Elvino S. Sousa
ECE Department
University of Toronto
Summer 2007

2
Throughput Optimal Policies

Ensure network stability for any input rate that
is within the network layer capacity region.
One example At each timeslot find a rate vector
that maximizes backlog-rate product Tassiulas
Ephremides, INFOCOM92, Neely et al., JSAC05.
X(t) Backlog vector, s(t) Channel state
vector, D(s(t),I) Rate vector, the set of
schedules.
These policies, however, are complex.

3
Related Research

Tassiulas INFOCOM98 proved that
linear-complexity algorithms are sufficient for
non-time varying channels.
We can still use linear-complexity policies for
time-varying channels Eryilmaz et al ToN05,
Chaporkar et al INFOCOM06.
Problem Ensuring network stability, for all
input rates within the network layer capacity
region, requires a memory that exponentially
increases with the number of users.
Question How much sub-optimality in the
network throughput is introduced by the reduced
memory requirement?

4
Linear-Memory Policy
The policy generates a candidate schedule
that satisfies the following w.p.
Different values of and allow us to model
algorithms with different complexity levels.
5
Linear-Memory Policy (contd.)
where
6
Rate Region Characterization

7
A Simple Example
A network with two channel states, and three
schedules. We assume that the candidate schedule
is selected from the schedules with equal
probability.
8
Capacity Region Scaling Factor
9
Conclusions

We have modeled a class of scheduling policies
with different complexity levels, and with
linear-memory requirement.
Our analysis has characterized the capacity
region of these policies, and quantified the
scaling factor of the stability region based on
the limiting behavior of rate changes due to
channel variations and the inefficiencies
inherent in the scheduling policies
Our results indicate how channel memory helps
reduce the uncertainty of the scheduling policy
in selecting a suitable candidate schedule