Mahdi Lotfinezhad,Ben Liang, and Elvino S' Sousa

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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

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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.

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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?

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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.
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Linear-Memory Policy (contd.)
where
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Rate Region Characterization

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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.
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Capacity Region Scaling Factor
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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